Enhanced oil recovery, Volume 13: Proceedings of the third European Symposium on Enhanced Oil Recovery, held in Bournemouth, U.K., September 21-23, 1981 (Developments in Petroleum Science)

Developments in Petroleum Science, 13

enhanced oil recovery

FURTHER TITLES IN THIS SERIES

1A, GENE COLLINS GEOCHEMISTRY O F OILFIELD WATERS 2 W.H. FERTL ABNORMAL FORMATION PRESSURES 3 A.P. SZILAS PRODUCTION AND TRANSPORT O F OIL AND GAS 4 C.E.B. CONYBEARE GEOMORPHOLOGY O F OIL AND GAS FIELDS IN SANDSTONE BODIES

5 T.F. YEN and G.V. CHILINGARIAN (Editors) OIL SHALE 6 D.W. PEACEMAN FUNDAMENTALS O F NUMERICAL RESERVOIR SIMULATION

7 G.V. CHILINGARIAN and T.F. YEN (Editors) BITUMENS, ASPHALTS AND TAR SANDS 8 L.P. DAKE FUNDAMENTALS OF RESERVOIR ENGINEERING

9 K. MAGARA COMPACTION AND FLUID MIGRATION 10 M.T. SILVIA and E.A. ROBINSON DECONVOLUTION O F GEOPHYSICAL TIME SERIES IN THE EXPLORATION FOR OIL AND NATURAL GAS 11G.V. CHILINGARIAN and P. VORABUTR DRILLING AND DRILLING FLUIDS 1 2 T. VAN GOLF-RACHT FRACTURED HYDROCARBON-RESERVOIR ENGINEERING

Developments in Petroleum Science, 1 3

Proceedings of the third European Symposium on Enhanced Oil Recovery, held in Bournemouth, U.K., September 21-23,1981

Edited by

EJOHN FAYERS Atomic Energy Establishment, Winfrith, Dorchester, England

ELSEVIER SCIENTIFIC PUBLISHING COMPANY AMSTERDAM -OXFORD -NEW YORK 1981

ELSEVIER SCIENTIFIC PUBLISHING COMPANY Molenwerf 1 P.O. Box 211, 1000 AE Amsterdam, The Netherlands

Distributors for the United States and Canada: ELSEVIER/NORTH-HOLLAND INC. 52, Vanderbilt Avenue New York, N.Y. 10017

ISBN 0-444-42033-9 (Vol. 13) ISBN 0-444-41625-0 (Series) 0 Elsevier Scientific Publishing Company, 1981

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Scientific Publishing Company, P.O. Box 330, 1000 AH Amsterdam, The Netherlands Printed in The Netherlands

V

TABLE OF CONTENTS

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

CHEMICAL FLOODING 1.

2.

Keynote Paper: “Fundamental Aspects of Surfactant-Polymer Flooding Process” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. 0. SHAH, University of Florida, USA Surfactants for EOR Processes in High-Salinity Systems; Product Selection and Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. H. AKSTINAT, Institute of Petroleum Engineering, Clausthal, West Germany

1

43

3. Preliminary Studies of the Behaviour or Some Commercially Available Surfactants in Hydrocarbon-Brine-Mineral Systems . . . . . . . . . . . . . . . . . 63 C. ANDREWS, N. COLLEY and R. THAVER, British Gas Corporation, London Research Station, UK 4. The Provision of Laboratory Data for EOR Simulation. . . . . . . . . . . . . . . . 81 C. E. BROWN and G. 0. LANGLEY, BP Research Centre, Sunbury, UK

5. Experimental Study and Interpretation of Surfactant Retention in Porous 101 Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. NOVOSAD, Petroleum Recovery Institute, Calgary, Canada 6. The EACN of a Crude Oil: Variations with Cosurfactant and Water Oil Ratio 123 MIN KWAN THAM and P. B. LORENZ, US Department of Energy, Bartlesville, OK, USA 7.

Dynamic Interfacial Phenomena Related to EOR. . . . . . . . . . . . . . . . . . . . 135 J. H. CLINT, E. L. NEUSTADTER and T. J. JONES, BP Research Centre, Sunbury, UK

8. Behaviour of Surfactants in EOR Applications at High Temperatures . . . . . . 149 L. L. HANDY, University of Southern California, Los Angeles, CA, USA 9. Surfactant Slug Displacement Efficiency in Reservoirs . . . . . . . . . . . . . . . . 161 R. J. WRIGHT and R. A. DAWE, Imperial College, University of London, UK 10. Some Aspects of the Injectivity of Non-Newtonian Fluids in Porous Media. . . 179 P. VOGEL and G. PUSCH, Institute. of Petroleum Engineering, Clausthal, West Germany

vi 11.

Basic Rheological Behaviour of Xanthan Polysaccharide Solutions in Porous Media: Effects of Pore Size and Polymer Concentration . . . . . . . . . . . . . . . 197 G. CHAUVETEAU and A. ZAITOUN, Institut Franqais du PCtrole, RueilMalmaison, France

12.

The Chateaurenard (France) Polymer Flood Field Test. . . . . . . . . . . . . . . . 213 A. LABASTIE, Elf Aquitaine, Boussens, Saint-Martory, France L. VIO, Elf Aquitaine, Centre de Recherche de Lacq, Artix, France

13.

Caustic Flooding in the Wilmington Field, California, Laboratory Modelling and Field Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 V. S. BREIT, Scientific Software Corp., Denver, TX, USA E. H. MAYER, THUMS Long Beach Co, CA, USA J. D. CARMICHAEL, City of Long Beach Department of Oil Properties

MISCIBLE GAS DISPLACEMENT 14.

Keynote Paper: “Miscible Displacement: Its Potential for Enhanced Oil 237 Recovery” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. J. BLACKWELL, Exxon Production Research, Houston, TX, USA

15.

Theoretical Aspects of Calculating the Performance of COz as an EOR 247 Process in North Sea Reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. S. HUGHES, J. D. MATTHEWS and R. E. MOTT, AEE Winfrith, DorChester, Dorset, UK

16.

A New Linear Displacement Model with Mass Transfer Between Phases, n.a. Adapted to C 0 2 Injection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. JAIN, Institut Franqais du PCtrole, Rued-Malmaison, France (This paper will be distributed at the Conference)

17.

Oil Recovery by Carbon Dioxide, the results of Scaled Physical Models and 267 Field Pilots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. M. DOSCHER, M. EL ARABI, S. GHARIB and R. OYEKAN, University of Southern California, Los Angeles, CA, USA

18.

Laboratory Testing Procedures for Miscible Floods . . . . . . . . . . . . . . . . . . 285 S. G. SAYEGH and F. G. MCCAFFERY, Petroleum Recovery Institute, Calgary, Canada

19.

299 Complex Study of C 0 2 Flooding in Hungary . . . . . . . . . . . . . . . . . . . . . . s. DOLESCHALL, G. ACS, v. BALINT, z. BIRO, E. FARKAS, T. PAAL, J. TOROK, Hungarian Hydrocarbon Inst., Szazhalombatta, Hungary

20.

An Iterative Method for Phase Equilibria Calculations with Particular Appli313 cation t o Multicomponent Miscible Systems . . . . . . . . . . . . . . . . . . . . . . . N. VAROTSIS, A. C. TODD and G. STEWART, Heriot-Watt University, Edinburgh, UK

vii 2 1.

Phase Equilibrium Calculations in the Near-Critical Region . . . . . . . . . . . . . 329 R. RISNES, Norsk Agip, Norway V. DALEN, J. I. JENSEN, Continental Shelf Institute, Trondheim, Norway

22.

The Effect of Simulated COz Flooding on the Permeability of Reservoir Rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 G. D. ROSS, A. C. TODD and J . A. TWEEDIE, Heriot-Watt University, Edinburgh, UK

NUMERICAL METHODS

.............

23.

Keynote Paper: “Computer Modelling of EOR Processes”. K. AZIZ, University of Calgary, Canada

24.

Three-Dimensional Numerical Simulation of Steam Injection. . . . . . . . . . . . 379 P. LEMONNIER, Institut Frangais du PCtrole, Rueil-Malmaison, France

25.

Special Techniques for Fully Implicit Simulators. . . . . . . . . . . . . . . . . . . . 395 J. R. APPLEYARD, I. M. CHESHIRE and R. K. POLLARD, Operatings Research Group, AERE Harwell, UK

26.

Some Considerations Concerning the Efficiency of Chemical Flood Simulators 409 R. W. S. FOULSER, AEE Winfrith, Dorchester, Dorset, UK

27.

Control of Numerical Dispersion in Compositional Simulation. . . . . . . . . . . 425 D. C. WILSON, T. C. TAN and P. C. CASINADER, Imperial College, University of London, UK

28.

Interphase Mass Transfer Effects in Implicit Black Oil Simulators. D. BANKS and D.K. PONTING, AERE Harwell, Oxfordshire, UK

........

367

441

EXPERIMENTAL TECHNIQUES 29.

45 1 A Novel Device for COz Flooding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. MEYN, Institute of Petroleum Engineering, Clausthal, West Germany

30.

The Use of Slim Tube Displacement Experiments in the Assessment of Miscible Gas Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 B. J. SKILLERNE DE BRISTOWE, BP Research Centre, Sunbury, UK

31.

Nuclear Measurements of Fluid Saturations in EOR Flood Experiments 483 N. A. BAILEY, P. R. ROWLAND and D. P. ROBINSON, AEE Winfrith, Dorchester, Dorset, UK

32.

Characterisation of EOR Polymers as to Size in Solution . . . . . . . . . . . . . . 499 R. DIETZ, National Physical Laboratory, Teddington, UK

viii 33.

Visualization of the Behaviour of EOR Reagents in Displacements in Porous Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 E. G. MAHERS, R. J. WRIGHT and R. A. DAWE, Imperial College, University of London, UK

THERMAL RECOVERY METHODS 34.

Keynote Paper: “The Interplay Between Research and Field Operations in the Development of Thermal Recovery Methods” . . . . . . . . . . . . . . . . . . . 527 J. OFFERINGA, R. BARTHEL and J. WEIJDEMA, Shell Exploration and Production Laboratories, Rijswijk, Holland

35.

U.S. Department of Energy R & D on Downhole Steam Generator for the Recovery of Heavy Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 R. L. FOX, Sandia Laboratories, NM, USA J. J. STOSUR, U.S. Department of Energy, Washington, DC, USA

36.

Steam Drive - The Successful Enhanced Oil Recovery Technology. . . . . . . . 549 T. M. DOSCHER and F. GHASSEMI, University of California, Los Angeles, CA, USA

37.

Down Hole Steam Generation using a Pulsed Burner . . . . . . . . . . . . . . . . . 563 D. A. CHESTERS, C. J. CLARK, F. A. RIDDIFORD, BP Research Centre, Sunbury, UK

38.

Hot Caustic Flooding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573 R. JANSSEN-VAN ROSMALEN and F. Th. HESSELINK, Shell Exploration and Production Laboratories, Rijswijk, Holland

UNITED STATES RESEARCH PROGRAMME 39.

Enhanced Oil Recovery Research and Development in the United States and in the U.S. Department of Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 J. J. G. STOSUR, U.S. Department of Energy, Washington, DC, USA

AUTHORINDEX

............................................

595

ix

FOREWORD

T h i s r e s i d e n t i a l symposium i s t h e t h i r d i n t h e series of symposia which have been h e l d on t h e s u b j e c t of enhanced o i l r e c o v e r y i r , t h e United Kingdom; t h e o t h e r two b e i n g h e l d a t B r i t a n n i c House of BP i n London i n May 1977, and a t Heriot-Watt U n i v e r s i t y i n Edinburgh i n J u l y 1978. S i n c e 1977, when t h e f i r s t symposium was h e l d i n London, t h e a n n u a l p r o d u c t i o n and t h e number o f f i e l d s i n o p e r a t i o n i n t h e UK s e c t o r o f t h e North Sea h a s roughly doubled and i t i s perhaps r i g h t t o r e - i t e r a t e t h e remarks of t h e Chairman of t h e o r g a n i s i n g committee of t h e f i r s t meeting. H e s a i d t h a t , "There i s an u r g e n t need t o d e c i d e which enhanced o i l r e c o v e r y t e c h n i q u e s a r e s u i t a b l e f o r u s e i n t h e North Sea. Once t h i s d e c i s i o n i s made, t h e s e l e c t e d R&D g o a l s s h o u l d b e v i g o r o u s l y p u r s u e d , l e a d i n g , h o p e f u l l y , t o t h e development of s p e c i f i c t a i l o r - m a d e t e c h n i q u e s e f f e c t i v e i n t h e i n d i v i d u a l f i e l d s i n t h e North Sea a r e a " . Although t h e s e remarks a r e s t i l l v a l i d t o d a y , i n t h e i n t e r vening p e r i o d t h r o u g h o u t Europe s i g n i f i c a n t p r o g r e s s has been made. W e have s e e n an i n c r e a s e i n t h e number o f p i l o t f i e l d experiments u n d e r t a k e n by t h e o i l i n d u s t r y , an i n c r e a s e i n t h e r e s e a r c h work c a r r i e d o u t a t u n i v e r s i t i e s , r e s e a r c h i n s t i t u t e s and o i l company laboratories. A number of Government programmes have been i n i t i a t e d o r expanded. A g a i n s t t h i s background of an i n c r e a s e d R&D a c t i v i t y , some s i g n i f i c a n t , a l b e i t t e n t a t i v e , s t e p s i n t h e a p p l i c a t i o n of enhanced o i l r e c o v e r y o f f s h o r e have been t a k e n . The c o n t i n u i n g i n c r e a s e i n t h e p r i c e of o i l o v e r t h e p a s t few y e a r s r e n d e r s t h e t i m i n g of t h e p r e s e n t symposium t o be p a r t i c u l a r l y r e l e v a n t t o t h e q u e s t i o n of improvement i n o i l recovery i n a l l t h e s e c t o r s of t h e North Sea and f o r t h e p r o v i s i o n of f u t u r e s u p p l i e s of e n e r g y t o Europe. The o c c a s i o n of t h e p r e s e n t c o n f e r e n c e p r o v i d e s an i n t e r n a t i o n a l forum f o r r e s e a r c h workers ins enhanced o i l r e c o v e r y t o exchange i n f o r m a t i o n and t o develop an i n c r e a s e d awareness of t h e r e s e a r c h s t u d i e s c u r r e n t l y b e i n g pursued e l s e w h e r e . I t i s hoped t h a t new d i r e c t i o n s f o r r e s e a r c h , a p p l i c a b l e t o t h e European C o n t i n e n t a l S h e l f , may become a p p a r e n t and t h e f u t u r e a d o p t i o n of enhanced o i l r e c o v e r y t e c h n i q u e s i n t h i s a r e a advanced. T h i s volume i s a c o l l e c t i o n of t h e p a p e r s t o b e p r e s e n t e d and d i s c u s s e d a t t h e Symposium.

F J FAYERS

Chairman, O r g a n i s i n g Committee September 1981

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CHEMICAL FLOODING

1

FUNDAMENTAL ASPECTS OF SURFACTANT-POLYMER FLOODING PROCESS

D.0.SHAH Department of Chemical Engineering and Anesthesiology, University of Florida, Gainesville, Florida 3261 I ABSTRACT Surfactant-polymer f l o o d i n g process o f f e r s a promising approach t o recover a d d i t i o n a l o i l from the water flooded r e s e r v o i r s which may conThe c a p i l l a r y number, t a i n as much as 70% o f o r i g i n a l o i l - i n - p l a c e . which determines the microscopic displacement e f f i c i e n c y o f o i l , can be increased b y 3 t o 4 orders o f magnitude by reducing the i n t e r f a c i a l tension (IFT) of o i l ganglia below 10-3 dynes/cm. Conceptual events involved i n the m o b i l i z a t i o n and displacement o f o i l ganglia are described i n c l u d i n g the r o l e o f u l t r a l o w i n t e r f a c i a l tension, t h e r o l e o f i n t e r f a c i a l v i s c o s i t y i n coalescence o f o i l ganglia and formation o f t h e o i l bank, the propagation o f the o i l bank, the surfactant-polymer incomp a t i b i l i t y , the formation and f l o w o f emulsions i n porous media, the r o l e o f w e t t a b i l i t y as well as the i n f l u e n c e o f surface charge d e n s i t y o f the r o c k / f l u i d i n t e r f a c e and o i l - b r i n e i n t e r f a c e i n o i l displacement e f f i ciency. It i s shown t h a t t h e r e are two regions o f u l t r a - l o w IFT; 1) i n the low surfactant concentration (0.1-0.2%) and the other i n t h e high s u r f a c t a n t concentration region (2.0%-10.0%). I n t h e low concentration systems, the u l t r a - l o w i n t e r f a c i a l tension occurs when t h e aqueous phase of the surfactant s o l u t i o n i s about the apparent c r i t i c a l m i c e l l e concent r a t i o n . And, the s a l i n i t y i s a t the c r i t i c a l e l e c t r o l y t e concentration for the coacervation process. The m i g r a t i o n o f surfactant from the aqueous phase t o the o i l phase v i a coacervation process appears t o be r e sponsible f o r the u l t r a l o w i n t e r f a c i a l tension. I n high surfactant concentration systems, a middle phase microemuls i o n i n e q u i l i b r i u m w i t h excess o i l and b r i n e forms i n a narrow s a l i n i t y range. T h e ' s a l i n i t y a t which equal volumes o f o i l and b r i n e are s o l u b i l i z e d i n the middle phase microemulsion i s r e f e r r e d t o as the optimal s a l i n i t y o f the system. A t t h e optimal s a l i n i t y , t h e i n t e r f a c i a l tension a t both i n t e r f a c e s i s equal. Evidence i s presented t h a t the middle phase microemulsion a t the optimal s a l i n i t y i s a water external microemulsion formed due t o coacervation and subsequent phase separation o f m i c e l l e s f r a n t h e aqueous phase. The optimal s a l i n i t y can be s h i f t e d t o a desired value by varying t h e s t r u c t u r e and 'concentration o f alcohol. The s h i f t i n optimal s a l i n i t y can be c o r r e l a t e d w i t h t h e b r i n e s o l u b i l i t y o f the alcohol used i n a given s u r f a c t a n t formulation. It was f u r t h e r observed t h a t the optimal s a l i n i t y increases w i t h the o i l chain length. I n order t o form middle phase microemulsions at very high s a l i n i t y , ethoxylated surfactants o r alcohols can be incorporated i n t o a s u r f a c t a n t formulation which can s h i f t the optimal s a l i n i t y t o as high as 32% NaCl concentration. Such high s a l i n i t y formulations c o n s i s t i n g o f petroleum sulfonates and ethoxylated sulfonates are r e l a t i v e l y i n s e n s i t i v e t o diva1ent c a t ions.

2

The coalescence r a t e o r the phase separation time was minimum at optimal s a l i n i t y . I t was also observed t h a t the apparent v i s c o s i t y was minimal a t the optimal s a l i n i t y f o r the f l o w o f microemulsions through porous media. The r a t e o f f l a t t e n i n g o f an o i l drop i n a surfactant f o r mulation increases s t r i k i n g l y i n the presence o f alcohol. I t appears t h a t the presence o f alcohol promotes the mass t r a n s f e r o f s u r f a c t a n t from the aqueous phase t o the i n t e r f a c e . The a d d i t i o n o f alcohol also promotes the coalescence o f o i l drops, presumably due t o a decrease i n the i n t e r f a c i a l v i s c o s i t y . The surfactant-polymer i n c o m p a t i b i l i t y can lead t o a phase separat i o n o f a surfactant and polymer even i n the absence o f o i l . I n the presence o f o i l , the formation o f middle phase microemulsion i s promoted by the presence o f polymer i n the aqueous phase. The surfactant-polymer i n c o m p a t i b i l i t y i s explained i n terms o f excluded volume e f f e c t s and the maximization o f solvent f o r polymer molecules. Some novel concepts f o r surfactant-polymer f l o o d i n g process have been discussed i n c l u d i n g the use o f tm, d i f f e r e n t s u r f a c t a n t slugs, two d i f f e r e n t polymer slugs, s a l i n i t y gradient design and the i n j e c t i o n o f an o i l bank t o promote o i l recovery.

PRODUCTION

BANK

PRODUCTION

WATER

WELLS

A

Fig. 1

B

C

D

Schematic diagram o f an o i l r e s e r v o i r and the displacement of o i l by water o r chemical flooding.

3 A.

INTRODUCTION

I t i s well recognized t h a t the energy consumption per c a p i t a and the standard of. l i v i n g o f a s o c i e t y are i n t e r r e l a t e d . Among various sources o f energy, f o s s i l f u e l s o r crude o i l s p l a y an important r o l e i n providing the energy supply o f t h e world. It also serves as a raw m a t e r i a l f o r feed stocks i n chemical industry. I n view o f the worldwide energy c r i sis, the importance o f enhanced o i l recovery t o increase t h e supply o f crude o i l i s obvious and various enhanced o i l recovery processes have been proposed and tested both on a l a b o r a t o r y scale and i n the f i e l d . For heavy o i l s , thermal processes have been used e x t e n s i v e l y whereas f o r l i g h t o i l s , chemical processes such as polymer flooding, caustic f l o o d ing , m i s c i b l e f 1ood ing and s u r f act ant-pol ymer f 1oodi ng have a t t r a c t e d great i n t e r e s t . The major research f i n d i n g s i n the enhanced o i l recovery area have been reported i n recent l i t e r a t u r e and the symposia proceedings of various conferences during the l a s t decade (1-11). The present paper focuses on the fundamental aspects o f the surfactant-polymer f l o o d i n g process and r e 1ated phenomena.

Figure 1 schematically shows a three-dimensional view o f a petroleum reservoir. A t the end o f water-flooding, t h e o i l t h a t remains i n the r e s e r v o i r i s believed t o be i n the form o f o i l ganglia trapped i n t h e pore s t r u c t u r e o f the rock as shown i n Figure 1A. These o i l ganglia are entrapped due t o c a p i l l a r y forces. However, i f a s u r f a c t a n t s o l u t i o n i s i n j e c t e d t o lower the i n t e r f a c i a l tension o f the o i l ganglia from i t s value o f 20-30 dynes/cm t o 10-3 dyneslcm, the o i l ganglia can be mobilized and can move through narrow necks o f t h e pores. Such mobilized o i l ganglia form an o i l bank as shown i n Figure 16. Figures 1C and 1D schematically show the o i l bank approaching the production well and the subsequent breakthrough o f t h e d r i v e water. Figure 2 schematically i l l u s t r a t e s a twodimensional view o f the surfactant-polymer f l o o d i n g process.

S URFACTANT SLUG

INJECTION

---- - - ---

PRODUCTION

-

THICKENED FRESH WATER

Fig. 2

Schematic diagram o f the surfactant-polymer f l o o d i n g process.

The s u r f a c t a n t slug i s followed by a polymer slug f o r a proper m o b i l i t y c o n t r o l o f the process.

4

B.

CAPILLARY NUMBER AND CONCEPTUAL ASPECTS OF THE PROCESS

Recently, i n an excellent review a r t i c l e , Taber (12) has summarized various emperical dimensionless numbers proposed by several i n v e s t i g a t o r s t o c o r r e l a t e t h e o i l displacement e f f i c i e n c y i n porous media. F i g u r e 3 shows such a c o r r e l a t i o n reported by Foster (13) between t h e c a p i l l a r y number and r e s i d u a l o i l i n porous media.

I10 ~ 1 0 2 0 3 00 4 0 5 0 6 0

l

RESIDUAL OIL, PERCENT PORE VOLUME Fig. 3

Dependence o f r e s i d u a l o i l s a t u r a t i o n on C a p i l l a r y Number (Foster, W.R., J. Pet. Tech., p. 206, Feb. 1973).

The c a p i l l a r y number represents the r a t i o o f viscous t o c a p i l l a r y forces uv/u+ where 11 and v are the v i s c o s i t y and v e l o c i t y of ! k e i i $ ? l i n g f l u i d , u i s the i n t e r f a c i a l tension and 4 i s t h e pore volume). A t the end o f water flooding, the c a p i l l a r y number i s around 10-6 and t h i s number has t o be increased by 3 t o 4 orders o f magnitude f o r t e r t i a r y o i l recovery processes (14). Under p r a c t i c a l r e s e r v o i r conditions, the reduc i o n i n ' n t e r f a c i a l tension from a high value of 20 o r 30 dyneslcm t o 1 0 - i o r 10-4 dynes/cm o f f e r s such a p o s s i b i l i ty. Therefore, the main f u n c t i o n o f t h e s u r f a c t a n t i s t o produce such an u l t r a - l o w i n t e r f a c i a l tension a t the o i l ganglia/surfactant formulation i n t e r f a c e . Figure 4 schematically shows the r o l e o f u l t r a l o w i n t e r f a c i a l tension i n promoting the m o b i l i z a t i o n o f o i l ganglia i n porous media. Subsequently, t h e displaced o i l ganglia must coalesce t o form an o i l bank. For t h i s a very low i n t e r f a c i a l v i s c o s i t y i s d e s i r a b l e (Figure 5). I t i s known t h a t h i g h i n t e r f a c i a l v i s c o s i t y r e s u l t s i n the formatin o f s t a b l e emulsion (15).

5 FOR THE MOVEMENT OF OIL THROUGH NARROW NECK OF PORES, A VERY LOW OIL / WATER INTERFACIAL TENSION IS DESIRABLE z .OOl DYNES/CM

Fig. 4

Schematic diagran of the role of low interfacial tension in the surf actant-pol ymer flooding process.

SURFACTANT SLUG

4

DISPLACED OIL GANGLIA MUST COALESCE TO FORM A CONTINUOUS OIL BANK : FOR THIS A VERY LOW INTERFACIAL VISCOSITY IS DESIRABLE

Fig. 5

Schematic diagran of the role of low interfacial viscosity in the surfactant-polymer flooding process.

Once an o i l bank is formed i n the porous medium, i t has to be propagated through the porous medium without increasing the entrapment of o i l at the t r a i l i n g edge of the oil bank. As shown in Figure 6 , the maintenance of ultralow interfacial tension at the o i l bank/surfactant/ slug interface i s essential for minimizing the entrapment of the oil i n the porous medium whereas the leading edge will coalesce with the o i l gang1 i a.

SURFACTANT " Yd SLUG

COALESCENCE OF OIL GANGLIA WITH OIL BANK CAUSES FURTHER DISPLACEMENT OF OIL Fig. 6

Schematic diagran of the role of coalescence of o i l ganglia i n the surf act ant-pol ymer flooding process.

6 Figure 7 schematically i l l u s t r a t e s the movement o f the o i l bank, surfactant s l u g and the m o b i l i t y c o n t r o l polymer slug i n the porous med ium

.

INTERFACES

t Since the f l o w i s through porous m e d i a , t h e e f f e c t o f dispersion for emulsification should b e minimized a t a l l 3 interfaces. A l s o a v o i d t h e formation of high v i s c o s i t y structures i n the o i l - water - surfactant dispersions i n

SURFACTANT SLUG

Fig. 7

OIL

Schematic i l l u s t r a t i o n o f t h e e f f e c t s o f dispersion and emulsif i c a t i o n between the various slugs during the surfactant-polymer f l o a d i n g process.

Since the f l o w through the porous mediun causes dispersion o f these f l u i d s , emulsions w i l l be formed a t the o i l bank/surfactant slug i n t e r face and a mixed surfactant-polymer zone w i l l occur a t t h e s u r f a c t a n t polymer s o l u t i o n i n t e r f a c e . High v i s c o s i t y - s t r u c t u r e s a t both these i n t e r f a c e s should be avoided i n order t o improve the e f f i c i e n c y o f t h e process. The mass t r a n s f e r o f s u r f a c t a n t t o t h e o i l bank can i n f l u e n c e the magnitude o f i n t e r f a c i a l tension (16). Trushenski (17) has shown t h a t surfactant-polymer i n c o m p a t i b i l i t y leading t o a phase separation o f surfactant and polymer s t r i k i n g l y reduces t h e e f f i c i e n c y o f t h e process.

PROPER CHOICE

Fig. 8

OF SURFACTANT CAN CHANGE@TO@

The r o l e o f w e t t a b i l i t y and contact angle on o i l displacement.

7 Figure 8 schematically i l l u s t r a t e s the r o l e o f w e t t a b i l i t y o f s o l i d surface on the o i l ganglia. The choice o f s u r f a c t a n t can i n f l u e n c e the w e t t a b i l i t y o f t h e rock surface t o o i l and b r i n e (12). Another parameter t h a t we have found (18, 19) t h a t influences the i n t e r f a c i a l tension and i n t e r f a c i a l v i s c o s i t y and o i l recovery i s t h e surface charge a t the o i l - b r i n e as well as rock-brine i n t e r f a c e s . We found t h a t a high surface charge d e n s i t y leads t o a lower i n t e r f a c i a l tension, lower i n t e r f a c i a l v i s c o s i t y and higher o i l recovery (Figure 9).

High Surface Charge Densky -Low Interfacial Tenslon Low Interfacial Vicorlty High Electrkal Repulsion Between Oil Droplets (i Sand

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Fig. 9

Schematic diagran o f the r o l e o f surface charge i n the o i l d i s placement process.

The conceptual processes described i n Figures 3 t o 9 are supported by t h e r e s u l t s o f our studies described i n the following sections.

C. LOW SURFACTANT CONCENTRATION SYSTEMS

Figure 10 shows the i n t e r f a c i a l tension as a f u n c t i o n o f s u r f a c t a n t concentration i n a dodecane/brine system. ' I t i s evident t h a t there are two regions o f u l t r a - l o w i n t e r f a c i a l tension (IFT). A t low surfactant concentrations, the system appears t o be a two-phase system, namely, o i l and b r i n e i n e q u i l i b r i u m w i t h each other, whereas a t high s u r f a c t a n t concentration systems (around 4 t o 8% s u r f a c t a n t concentration), a middle phase microemulsion e x i s t s i n e q u i l i b r i u n w i t h excess o i l and brine. The formation o f middle phase microemulsion and r e l a t e d phenomena w i l l be discussed i n section D.

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9 For low s u r f a c t a n t concentration systems, we have show t h a t t h e u l t r a l o w IFT occurs when s u r f a c t a n t molecules migrate from t h e aqueous phase t o the o i l phase (19-21). Figure 11 shows t h e i n t e r f a c i a l t e n s i o n and t h e p a r t i t i o n c o e f f i c i e n t o f a s u r f a c t a n t i n an octane/brine system. The u l t r a low IFT occurred around a p a r t i t i o n c o e f f i c i e n t o f u n i t y i n t h i s system (19,ZO). However, i t should be emphasized t h a t since t h e p a r t i t i o n c o e f f i c i e n t changes a b r u p t l y i n t h i s region the exact value o f p a r t i t i o n c o e f f i c i e n t can vary s i g n i f i c a n t l y around u l t r a l o w IFT. We bel i e v e t h a t a reasonable conclusion i s t h a t lowering o f i n t e r f a c i a l tension i s observed when m i c e l l e s leave the aqueous phase due t o coacervat i o n process (19-23). I(

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Fig. 11

E f f e c t o f added e l e c t r o l y t e on i n t e r f a c i a l tension and surfact a n t p a r t i t i o n c o e f f i c i e n t o f t h e system O.TXTRS 10-80 + b r i n e + octane.

Since c m e r c i a l petroleum sulfonates i n v o l v e a d i s t r i b u t i o n o f molecular weights and isomeric s t r u c t u r e s we also Investigated t h e i n t e r f a c i a l tension using i s o m e r i c a l l y pure sulfonates. Figure 12 shows the IFT behavior as a f u n c t i o n o f s a l i n i t y , o i l 'chain length and s u r f a c t a n t concentration using petroleum sulfonates (TRS 10-80 o r TRS 10-410 and an It i s evident t h a t both t h e s a l i n l t y i s o m e r i c a l l y pure s u r f a c t a n t UT-1). and o i l chain length e f f e c t s were s i m i l a r f o r both these classes o f sur-

10 PETROLEUM SULFONATES:

ISOMERICALLY PURE ALKYL BENZENE SULFONATES:

Fig. 12

Schematic diagram o f the e f f e c t o f s a l t concentration, o i l chain length and s u r f a c t a n t concentration on t h e i n t e r f a c i a l tension o f pure and impure a1 k y l benzene sulfonates.

factants, namely, t h e r e i s a s p e c i f i c s a l i n i t y and s p e c i f i c o i l chain length where we o b t a i n an u l t r a l o w IFT. However, the e f f e c t o f surfact a n t concentration on IFT was d i f f e r e n t f o r commercial and i s o m e r i c a l l y pure surfactants. For low surfactant concentration systems, we also observed t h a t the u l t r a low IFT appears when the aqueous phase i s a t t h e apparent anc f o r the surfactant remaining i n t h e aqueous phase. These conclusions were i n aggreement w i t h osmotic pressure, l i g h t s c a t t e r i n g and spectroscopic measurements on t h e e q u i l i b r a t e d aqueous phase (22). Figure 13 i s a generalized diagran showing t h e IFT, phase behavior and the two c r i t i c a l e l e c t r o l y t e concentrations f o r both pure and ctmwnerc i a 1 surfactants a t low as w e l l as high s u r f a c t a n t concentrations. By d i r e c t analysis o f surfactant concentrations i n each phase, we found (21) t h a t t h e s a l i n i t y a t which s u r f a c t a n t molecules leave t h e aqueous phase i s lower than the s a l i n i t y at which they enter t h e o i l phase. Thus, we d e f i n e two c r i t i c a l e l e c t r o l y t e concentrations, namely, CEC1, and CEC2, t o represent the e l e c t r o l y t e concentrations a t which t h e surf a c t a n t concentration begins t o decrease i n t h e aqueous phase and begin t o increase i n t h e o i l phase respectively. We f u r t h e r observed t h a t t h e minimun i n t e r f a c i a l tension occurs i n the v i c i n i t y o f t h e f i r s t c r i t i c a l I n between CECl and CEC2, t h e s u r f a c t a n t e l e c t r o l y t e concentration. m a y p r e c i p i t a t e o r may form a coacervate phase below t h e aqueous phase o r i n between the aqueous and the o i l phase depending upon i t s d e n s i t y (21).

11 I n low concentration systems, i t i s possible t h a t an extremely small volume o f middle phase may e x i s t between the o i l and b r i n e phases even though i t may not be v i s i b l e . This suggestion i s i n agreement w i t h observation t h a t the volume o f the middle phase microemulsion increases l i n e a r l y w i t h the surfactant concentration and the s t r a i g h t l i n e passes through the o r i g i n (24). It should be emphasized t h a t the general behavior and i n t e r - r e l a t i o n s h i p shown i n Figure 13 i s v a l i d f o r both commercial and i s o m e r i c a l l y pure surfactants (21).

NaCl Fig.

CONCENTRATION

Generalized d i a g r m o f the e f f e c t o f s a l t concentration on surf a c t a n t p a r t i t i o n i n g , phase behavior and i n t e r f a c i a l tension.

Figure 14 shows the e f f e c t o f o i l chain length on CEC and CEC2 i n Aerosol OT/brine/oil systems. I t i s evident t h a t the EEC! i n creases w i t h o i l chain length u n t i l i t reaches the c r i t i c a l o i l chain length (C11) above which the value o f CECl remains constant. On t h e other hand, CEC2 continues t o increase w i t h the o i l chain length. I n t e r e s t i n g l y , we observed t h a t the u l t r a l o w IFT o n l y occurs f o r o i l chain lengths below the c r i t i c a l o i l chain length (< C11), whereas the i n t e r f a c i a l tension remains high for o i l s above t h e c r i t i c a l o i l chain length (21). We propose t h a t a l l the o i l s below the c r i t i c a l o i l chain length are able t o s o l u b i l i z e i n the m i c e l l e s whereas the o i l s having chain length above the c r i t i c a l o i l chain length are unable t o s o l u b i l i z e i n the m i c e l l a r s o l u t i o n . Thus, i t appears t h a t s o l u b i l i z a t j o n o f o i l w i t h i n the m i c e l l e s i s an important requirement f o r producing u l t r a l o w IFT. From our extensive studies on i n t e r f a c i a l tension and p a r t i t i o n i n g o f surfactant i n r e l a t i o n t o many parameters, we have proposed the f o l l o w i n g 5 necessar y conditions t o achieve u l t r a l o w IFT's.

12

Fig. 14

E f f e c t of o i l chain length on the f i r s t and second c r i t i c a l e l e c t r o l y t e concentrations of Aerosol OT.

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E f f e c t of o i l chain length on the i n t e r f a c i a l tension o f t h e systems 1.0% AOT/brine/oil

.

13 The t o t a l surfactant concentration should be appreciably above the apparent anc i n the aqueous phase. The surfactant should be soluble i n both the aqueous and the hydrocarbon phase. Micelles i n the aqueous phase should be able t o s o l u b i l i z e o i l from the hydrocarbon phase. The aqueous phase s a l i n i t y should be near the f i r s t c r i t i c a l electrol y t e concentration (CECI). There should be a large slope i n the surfactant p a r t i t i o n c o e f f i c i e n t curve i n the region o f the ultralow IFT. (i.e. a steep p a r t i t i o n coe f f i c i e n t curve f o r surfactant).

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A correlation between i n t e r f a c i a l tension and electrophoretic m o b i l i t y f o r crude oil-NaOH solutions.

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Figure 16 shows the correlation of interfacial tension with electrophoretic mobility in crude oil/caustic systems (18,19,25,26). We have observed for several crude o i l s that the u l t r a low IFT occurs in the r e gion where the electrophoretic mobility is maximum. This suggests that the maximun in surface charge density coincides w i t h the m i n i m u m i n i n terfacial tension. T h i s correlation was also observed for the effect of s a l i n i t y and surfactant concentration (19). Figure 17 schematically i l l u s t r a t e s 3 components of the interfacial tension, namely, 1 ) surface concentration of the surfactant, 2) surface charge density, and 3) mutual solubilization of o i l and brine. W e propose that by a d j u s t i n g any of these variables one can influence the magnitude of interfacial tension. Using the conceptual approach shown i n Figure 17, we were able to broaden and lower the magnitude of interfacial tension as well as increase the s a l t tolerance limit of the surfactant formulation;

dyneskm

Fig. 17

A schematic i l l u s t r a t i o n of the factors affecting the magnitude of the interfacial tension.

Figure 18 shows the interfacial tension of a petroleum sulfonate TRS 10-410/n-octane/brine system when gradually the petroleum sulfonate i s replaced w i t h an ethoxylated phosphate e s t e r (Klearfac AA-270). The Klearfac AA-270 containing a phosphate group possesses two ionic oxygen atoms and hence can generate a high surface charge density a t the interface. This presumably i s responsible for lowering the magnitude of IFT and broadening the s a l i n i t y range over which the ultralow IFT occurs for the mixed surfactant systems (27).

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16 D.

HIGH SURFACTANT CONCENTRATION SYSTEMS AND THE OPTIMAL SALINITY

Many s u r f a c t a n t formulations e x h i b i t extreme flow o r s t a t i c b i r e f r i n g e n c e i n a given s a l i n i t y range o r i n a given temperature range. Often these o p t i c a l l y a n i s o t r o p i c formulations e x h i b i t u l t r a l o w IFT w i t h o i l . The m i c r o s t r u c t u r e o f such b i r e f r i n g e n t formulations should be o f i n t e r e s t i n understanding the changes i n molecular associations o c c u r r i n g i n these systems. Figures 19-21 i l l u s t r a t e the m i c r o s t r u c t u r e o f a b i r e f r i n g e n t surfactant formulation c o n s i s t i n g o f 5% TRS 10-410 + 3% isobutanol and 2% NaCl brine.

Fig. 19

Freeze-fracture e l e c t r o n micrograph o f t h e a n i s o t r o p i c system 5% TRS 10-410 + 3% Isobutanol + 2% NaCl ( 8 5 5 0 1x).

The freeze-fracture e l e c t r o n microscopic technique used t o o b t a i n these p i c t u r e s i s believed t o preserve the m i c r o s t r u c t u r e o f the sanples due t o the very r a p i d c o o l i n g r a t e (24). These e l e c t r o n micrographs c l e a r l y i n d i c a t e t h a t the b i r e f r i n g e n t formulations c o n s i s t o f bubbles f i l l e d w i t h ' b r i n e and separated f r a n each other by a t h i n s u r f a c t a n t membrane. Figure 21 c l e a r l y shows the s t r u c t u r e o f t h i s membrane c o n s i s t i n g o f several t h i n layers. The dimension o f each l a y e r i s close t o a surfact a n t b i l a y e r (approximately 70A). Therefore, I t appears t h a t when t h e s a l i n i t y i s increased i n the s u r f a c t a n t formulation, t h e s u r f a c t a n t molecules form the m u l t i l a y e r s t r u c t u r e w h i l e keeping t h e i r p o l a r groups i n contact with b r i n e and form such c e l l s o r f o m l i k e s t a b l e s t r u c t u r e . We have c a l l e d these s t r u c t u r e s b i r e f r i n g e n t c e l l u l a r f l u i d s (24).

17

Fig. 20

Fig. 21

Freeze-fracture electron micrograph o f the above system at 18,OOOX.

Freeze-fracture electron micrograph of the above system at 30, OOOX

.

18 Figure 22 shows the s i m i l a r i t y between coacervation o f a m i c e l l a r s o l u t i o n i n the absence o f o i l and the formation o f a middle phase microemulsion i n t h e presence o f o i l . The lower p a r t o f F i g u r e 22 shows t h e t r a n s i t i o n o f a b i r e f r i n g e n t s u r f a c t a n t formulation t o an i s o t r o p i c coacervate phase upon a d d i t i o n o f s a l t . (x, the other hand, t h e same formulation i n the presence o f an equal volume o f dodecane shows the formation o f lower phase, middle phase and upper phase microemulsions. We propose t h a t the middle phase microemulsion i s s i m i l a r t o t h e coacervated phase containing some s o l u b i l i z e d o i l . Additional studies i n support o f these models have been reported elsewhere (21, 23, 24).

Fig. 22

A comparison o f coacervation i n aqueous s o l u t i o n with middle phase format i o n i n s u r f act a n t / o i 1/ b r i ne/al coho1 systems.

19 Figure 23 schematically shows the mechanism o f formation o f middle phase microemulsions as s a l i n i t y i s increased.

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A schematic i l l u s t r a t i o n o f t h e l + m + u t r a n s i t i o n f o r t h e TRS 10-410/Isobutano1/0il /Brine System.

As one increases the s a l i n i t y , t h e anc decreases, the aggregation number o f the m i c e l l e s increases and the s o l u b i l i z a t i o n o f o i l w i t h i n m i c e l l e s increases. The compression o f the e l e c t r i c a l double l a y e r around m i c e l l e s w i l l occur, hence reducing the r e p u l s i v e forces between the m i c e l l e s . Thus t h e reduction i n the r e p u l s i v e forces and increase i n the a t t r a c t i v e forces between t h e m i c e l l e s w i l l b r i n g t h e m i c e l l e s c l o s e r and u l t i m a t e l y lead t o a separation o f a m i c e l l e r i c h phase forming the middle phase microemulsion. Upon f u r t h e r increase i n s a l i n i t y , the solub i l i z a t i o n o f o i l i n t h i s middle phase increases whereas t h a t o f b r i n e decreases. The magnitude o f i n t e r f a c i a l tension o f t h e middle phase w i t h o i l o r b r i n e depends upon the extent o f s o l u b i l i z a t i o n o f o i l and b r i n e i n the middle phase. I n general, t h e higher t h e s o l u b i l i z a t i o n o f oi.1 o r b r i n e i n the middle phase microemulsion, t h e lower i s t h e i n t e r f a c i a l tension w i t h respect t o these excess phases (28). The s a l i n i t y a t which equal volumes o f o i l and b r i n e are s o l u b i l i z e d i n the middle phase microemulsion i s r e f e r r e d t o as optimal s a l i n i t y f o r the s u r f a c t a n t - o i l - b r i n e systems under given physical chemical conditions (29, 30).

Figure 24 shows the f r e e z e - f r a c t u r e e l e c t r o n micrograph o f a middle phase microemulsion formed i n the system e x t e n s i v e l y studied by Reed and Healy (28-30). It c l e a r l y shows t h e d i s c r e t e spherical s t r u c t u r e s embedded i n a continuous aqueous phase consistent w i t h the mechanism proposed i n Figure 23. It should be pointed out t h a t other i q v e s t i g a t o r s (40-47) have proposed the p o s s i b i l i t y o f bicontinuous s t r u c t u r e o r t h e coexistance o f o i l external and water external microemulsions i n the middle phase. I n very high s u r f a c t a n t concentration systems, (15-20%) the existence o f anamalous s t r u c t u r e which are n e i t h e r conventional water external o r o i l ext e r n a l microemulsions have been proposed t o a.ccount f o r some unusual prop e r t i e s o f these systems (43-46). Figure 25 shows t h a t the t r a n s i t i o n l + m - c u i s not o n l y achieved by increasing the s a l i n i t y but i s also possible by changing any o f t h e other 8 variables.

7

20

Fig. 24

Freeze-fracture electron micrograph of the middle phase o f the Exxon system at the optimal salinity.

Oil

U

m

m

m

Brine

-

D

Parameter Increasing

The transition I

m --c u occurs by:

1. Increasing Salinity

2. 3. 4. 5. 6. 7. 8.

Fig. 25

Decreasing oil chain length Increasing alcohol concentration (C,, C,, C, ) Decreasing temperature Increasing total surfactant concentration Increasing brine/oil ratio Increasing surfactant solution/oil ratio Increasing molecular weight of surfactanf

Schematic illustration of the factors influencing the l + m + u transit ion in surf act ant /oi 1 /bri ne/al coho1 systems.

21

Thus, by choice of a suitable parameter, one can obtain the transition i n the structure of these microemulsions. A t optimal s a l i n i t y , the partition coefficient of surfactant i n the excess o i l and brine phases i s found to be near unity and the interfacial tension between the excess oil and excess brine is also m i n i m u n (19).

The importance of the optimal s a l i n i t y concept for enhanced oil recovery i s shown in the data i l l u s t r a t e d in Figure 26.

SURFACTANT SLUG =O.OS P.V. FLOODING RATEm2.3 ft/day DOW PUSHER 700:

SALINITY, NaCl w t 70

Fig. 26

Effect of s a l i n i t y on the capillary number and t e r t i a r y oil recovery i n sand packs.

I t i s evident that the o i l recovery is maximum at optimal s a l i n i t y f o r the systems reported here. An excellent correlation between the capillary number and oil recovery i s also evident from Figure 26 (48). In view of this observation, the surfactant formulation for a practical application should be designed such that the reservoir s a l i n i t y becomes the optimal s a l i n i t y under the given reservoir conditions. Figure 27 shows the effect of o i l chain length on optimal s a l i n i t y of the TRS 10-410 + isobutanol systems (49) and the corresponding interfacial tension at the optimal s a l i n i t y for dach o i l chain length. I t was observed that as the o i l chain length increases, the optimal s a l i n i t y i n creases and the volume of the middle phase decreases. The range over which the middle phase microemulsion exists also increases as the o i l

22

FFig. i g . 27 27

E f f e c t o f o i l chain length on t h e optimal s a l i n i t y and i n t e r f a c i a l tension a t t h e optimal s a l i n i t y .

chain length increases. It should be pointed out t h a t from extensive studies on mixed a1 kanes, the concept o f -Equivalent A1 kane Carbon Number (EACN) has been proposed t o c o r r e l a t e the i n t e r f a c i a l tension o f pure alkanes w i t h those o f the mixtures (50). Many l i g h t crude o i l s have been simulated by the mixtures o f pure hydrocarbons (51). Most l i g h t o i l s o r t h e EACN f o r most l i g h t crude o i l s were found t o be between C7 and c11. Figure 28 shows t h e c o r r e l a t i o n o f optimal s a l i n i t y i n t h e presence o f various alcohols w i t h t h e i r s o l u b i l i t y i n brine. F i g u r e 28 sumnarizes the data obtained by three research groups (49,52, 53). It i s i n t e r e s t i n g t h a t the optimal s a l i n i t y o f a given o i l and surf a c t a n t formulation l i e s near t h e i n t e r s e c t i o n o f the b r i n e s o l u b i l i t y . This c o r r e l a t i o n suggests t h a t i f one determines t h e optimal s a l i n i t y i n the presence o f 2 o r 3 alcohols, one can p r e d i c t the optimal s a l i n i t y i n t h e presence o f other alcohols from t h e i r b r i n e s o l u b i l i t y data. This i s a very useful c o r r e l a t i o n and eliminates t h e t i m e consuming and laborious procedure o f o b t a i n i n g t h e optimal s a l i n i t y i n t h e presence o f each alcohol.

E. TRANSIENT PROCESSES There are several t r a n s i e n t processes, such as the formation and coalescence o f drops as w e l l as t h e i r f l o w through porous media, t h a t a r e l i k e l y t o occur i n the surfactant-polymer f l o o d i n g process. Figure 29 shows the coalescence o r phase separation t i m e o f handshaken and sonicated macroemulsions as a f u n c t i o n o f s a l i n i t y .

Surfoclont

5 0 % TRS 10-410

40%

Alcohol

30%

0 7%

Brine

Variable

Vorioble

NoCl

01I

Dodecone

Wyomlng

Crude

WOR

I0

I0

Ref

Shah ond Hsleh, SPE 6594

Salter. SPE

BRINE SALINITY

(wt % NoCl 1

F i g . 28

NoCl

BRINE

Amoco

A A - Sulfonate

1.5 %

Xylene

Sulfonate

0. 5 % Variable

Oil

NaCl

90/10 lsopor

M/HAN

I .o

6843

SALINITY

(wt%

Puerto and Gale,

doc1 I

BRINE

SALINITY

A c o r r e l a t i o n o f optimal s a l i n i t y i n t h e presence of various alcohols w i t h t h e i r s o l u b i l i t y i n b r i n e .

SPE 5 8 1 4

( u t % No CI I

N W

24

16C

12c

8C E w

E l-

4c SONICATEO

C

0

2

4

6

SODIUM CHLORIDE CONCENTRATION, (b1T.X)

F i g . 29

E f f e c t o f s a l i n i t y on t h e phase separation o r coalescence r a t e o f sonicated and hand-shaken emulsions.

8

25

I t i s obvious that minimal phase separation time or the f a s t e s t coalescence r a t e occurs at the optimal s a l i n i t y (54). The rapid coalescence could contribute significantly to the formation of an oil bank from the mobilized oil ganglia. This also suggest that at the optimal s a l i n i t y the interfacial viscosity must be very low to promote the rapid coalescence. Figure 30 shows the pressure drop across a porous medium hhen emulsions prepared at various s a l i n i t i e s flow through i t . I t is evident that the minimum pressure drop occurs at and around the optimal s a l i n i t y of the surfactant formulation. T h i s also suggests that the interfacial tension is an important factor influencing the pressure drop across porous media ( 5 4 ) .

L

t

SONICATED EMULSION CONTAINING EQUAL VOLUME OF DODECANE AND AQUEOUS PHASE : TRS 10 -410 + IBA (5:3W/W) + NaCl +WATER

/

EMULSION FLOW RATE QE (rnl/rnin)

Fig. 30

Effect of s a l i n i t y on the pressure drop-flow r a t e curves of soni cated emu1 sions.

26

Figure 31 shows a very interesting and important correlation between the coalescence r a t e in enulsions and the apparent viscosity i n the flow through porous media. The minimun apparent viscosity for the flow of emulsions in porous media coincides with minimum phase separation time a t the optimal s a l i n i t y .

SYSTEM: SONICATED EMULSION CONTAINING TRS 10-410

30

1

0 1 0

t

IBA(5:3 W/W)

t

WATER

+ NaCl (x%) AND EQUAL VOLUME OF DODECANE

I

I

2

I

I

4

I

I

I

6

NaCl CONCENTRATiON (WT. %)

F i g . 31

A correlation between the apparent viscosity and coalescence r a t e of sonicated emulsions.

This correlation between the phenomena occurring in porous media and outside the porous medium allows us to use coalescence measurements as a screening criterion for many surfactant formulations for their possible behavior i n porous media. I t i s l i k e l y that a rapidly coalescing m u l sion will give a lower apparent viscosity for the flow i n porous media (54).

27

Figure 32 sumnarizes a l l the phenomena occurring a t t h e optimal s a l i n i t y i n r e l a t i o n t o enhanced o i l recovery by surfactant-polymer flooding.

yp

Oi I Recovery Efficiency

I

Apporent viscosity (or AP) of emulsions in porous media Coolescence or phase-seporotion time of emulsions

v

*VW

Surfoctont loss in Porous Media

vo

x

v

Solubilirotion of Oil and Brine in m+ microemulsions

w

lnterfociol tension

Ymo

-

OPTIMAL SALINITY

I/ Fig. 32

SALl NlTY A sumnary o f various phenomena occurring a t t h e optimal s a l i n i t y i n r e l a t i o n t o enhanced o i l recovery by surfactant-polymer flooding

.

It i s evident t h a t the maximum i n o i l recovery e f f i c i e n c y c o r r e l a t e s w e l l with t r a n s i e n t and equilibrium p r o p e r t i e s o f s u r f a c t a n t - o i l - b r i n e systems. I n our p r e l i m i n a r y studies, we have found t h a t t h e s u r f a c t a n t l o s s i n porous media i s also minimum a t t h e optimal s a l i h , i t y presumably due t o r e d u c t i o n i n the entrapment process f o r the surfactant phase. Therefore, the maximum i n o i l recovery at optimal s a l i n i t y might be a combined e f f e c t o f a l l these processes t a k i n g place a t the optimal s a l i n i t y .

Since optimal s a l i n i t y leads t o favorable conditions f o r optimal o i l recovery, one would l i k e t o design approaches t o a l t e r the optimal s a l i Figure 33 shows the n i t y o f a given s u r f a c t a n t formulation (55-57). optimal s a l i n i t y of a mixed s u r f a c t a n t formulation c o n s i s t i n g of a petroleum sutfonate and ethoxylated s u l f o n a t e (EOR-200).

28 I

1

I

SURFACTANT FORMULATION: TRS 10-410 t EOR-200

5.00/0

t

ISOBUTANOL

3.0%

4

2 I

I

TRSIO-410 €OR-200 I

Fig. 33.

5 C '0

4

1

1

I

2 3 4 3 2 I SURFACTANT CONCENTRATION wt.%

Increase i n the optimal s a l i n i t y o f surfactant formulation by a d d i t i o n o f EOR-200.

As one replaces petroleum sulfonates w i t h the ethoxylated s u l f o n a t e t h e optimal s a l i n i t y increases and can reach as h i g h as 32% NaCl brine. I n t e r e s t i n g l y , these formulations when e q u i l i b r a t e d with o i l produced middle phase microemulsions having very low i n t e r f a c i a l tension. Thus, the mixed s u r f a c t a n t formulations containing p e t r o l e m sulfonates and ethoxylated sulfonates o r alcohol are promising candidates f o r h i g h s a l i n i t y formulations ( 5 5 , 5 6 ) . Figure 34 shows t h e shape o f an o i l drop upon contacting a surfact a n t formulation c o n s i s t i n g o f 0.05% TRS 10-80 i n 1% NaCl. It i s e v i dent t h a t as s u r f a c t a n t molecules migrate from t h e aqueous phase t o the i n t e r f a c e and subsequently t o the o i l phase the i n t e r f a c i a l tension decreases and the spherical drop g r a d u a l l y f l a t t e n s out. This f l a t t e n i n g

29

Fig. 34.

An i l l u s t r a t i o n o f t h e drop f l a t t e n i n g phenomenon f o r a drop of octane i n an e q u i l i b r a t e d s o l u t r i o n o f 0.05% TRS 10-80 I n 1% NaCl

.

time r e f l e c t s the r a t e a t which molecules accumulate a t the o i l - b r i n e i n t e r f a c e . As shown i n Table 1, there i s a good c o r r e l a t i o n between the f l a t t e n i n g time, IFT and the o i l recovery. The reduction i n t h e f l a t t e n i n g time leads t o favorable o i l recovery efficiency (16,48).

30 TABLE 1

IFT, Flattening Time,and O i l Recovery Efficiency of 0. 052TRS 10-80 in I%NaCl vs. n-octane at 25OC

SYSTEM

IFT i m)

FLATTENING TIME*

1. II.

Ii1. IV.

Fresh Oilll% NaCl ~50.8* * FreshOillEquilibrated Surfactant 0.731 Solution Fresh OillFresh 0.627 Surfactant Solution EquilibratedOill% a 121 NaCl

V.

VI.

OILRECOVERY+

(seconds)

(m

(%OIP)

00

61-63

6600

44-52

480

15-11

900

83

w

EquilibratedOil/ Equilibrated Surfactant Solution

0.0267

240

EquilibratedOill Fresh Surfactant Solution

aOO209

15

*Flattening time i s defined as the time required for the n-octane drop to gradually flatten out

* *OctanelH@, 20'

C, IFT = 50.8 mNlm, "Interfacial Phenomenb', Davies and Rideal, Chapter 1, p. 17 Table I, Academic Press, N.Y. 1963.

+ San@ckdimension9 1. W'dia

x 7" long: Permeability= 3 darcy: flow rate:

2.3 f t /day.

I n general, a s u r f a c t a n t formulation f o r enhanced o i l recovery i n cludes a short chain alcohol. The p o s s i b l e e f f e c t o f alcohol can be t h e change i n v i s c o s i t y , lowering o f the i n t e r f a c i a l tension, r e d u c t i o n i n i n t e r f a c i a l v i s c o s i t y o r change i n s u r f a c t a n t p a r t i t i o n i n g and modifying the s o l u b i l i t y o f s u r f a c t a n t i n o i l o r b r i n e phase. I n t e r e s t i n g l y , we have observed t h a t the presence o f alcohol has a much more s t r i k i n g effect on the f l a t t e n i n g t i m e o f an o i l drop i n the presence o f a surfact a n t formulation. As shown i n Table 2 i t compares t h e many i n t e r f a c i a l properties, f l a t t e n i n g t i m e and o i l recovery e f f i c i e n c y i n the presence and absence o f alcohol (16). It i s evident t h a t the f l a t t e n i n g time decreases s t r i k i n g l y i n t h e presence o f alcohol suggesting t h a t t h e alcohol promotes the mass t r a n s f e r t o the i n t e r f a c e and a r a p i d r e d u c t i o n i n t h e magnitude o f the i n t e r f a c i a l tension. There are also time dependent changes i n the surface p r o p e r t i e s of a surfactant formulation. This include the chemical degradation (58,59), o r changes i n the aggregation process o f m i c e l l e s (60). Several i n v e s t i gators have show t h a t the i n t e r f a c i a l tension changes w i t h t i m e (61). We have also shown t h a t using several physical techniques t h a t molecular association also changes w i t h t i m e leading t o t h e aging e f f e c t s o f the surfactant formulation (58). The aging processes may occur over a period o f months o r years.

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32 F. SURFACTANT-POLYMER INCOMPATIBILITY Trushenski (17) has shown t h a t surfactant-polymer i n c o m p a t i b i l i t y can lead t o a considerable r e d u c t i o n i n the e f f i c i e n c y o f the process. The surfactant-polymer i n c o m p a t i b i l i t y manifests i t s e l f as a phase separ a t i o n and a l t e r a t i o n o f the v i s c o s i t y o f t h e separated phases. The entrapment o f the h i g h v i s c o s i t y phase w i l l e f f e c t i v e l y remove t h a t component from the f l o o d i n g process. The mixing o f the surfactant and polymer i n the porous medium occurs due t o both dispersion e f f e c t s as w e l l as excluded volume e f f e c t s f o r the f l o w o f polymer molecules i n porous media. Figure 35 shows the e f f e c t o f mixing surfactant and a polymer solut i o n i n the absence o f o i l .

Fig. 35.

E f f e c t o f a d d i t i o n o f polymer on t h e phase behavior o f aqueous s u r f actant solutions.

I t i s evident t h a t there are tho regions o f phase separation, one a t low s a l i n i t y and the other a t h i g h s a l i n i t y separated by a metastable c o l l o i d a l dispersion. We r e f e r t o the separation a t the lower s a l i n i t y as r e gion 1 and those a t h i g h s a l i n i t y as region 2. The separation o f a surf a c t a n t - r i c h phase i n r e g i o n 2 i s s i m i l a r t o t h a t i n coacervation process, h e r e a s t h e separation o f m i c e l l e s i n region 1 i s induced by the presence o f p o lymer molecules. The s u r f act ant -polymer incompat ib i 1it y shows up s t r i k i n g l y i n t h e formation o f region 1 (62).

The a d d i t i o n o f polymer t o an oillbrinelsurfactantlalcohol system shows t h a t the formation o f middle phase microemulsion i s promoted by the presence o f polymer (Figure 36). However, the t r a n s i t i o n middle phase t o upper phase microemulsion i s not influenced a t a l l by t h e presence o f polymer. We have f u r t h e r s h o w (62,63) t h a t t h e optimal s a l i n i t y i s n o t s i g n i f i c a n t l y influenced by the presence o f polymer i n t h e o i l l b r i n e l s u r f a c t a n t l a l c o h o l system.

33

1.0

-

0.8 -

0.6

-

0.4

-

0.2

0.0

5%

Polymer Concentration

W/V TRS 10-410

3% w/v IBA O i l : n-dodecane (MOR=l .O)

2500 ppm

-

1500 ppm

1.0 0.8

0.6 0.4 0.2 0.0

I

Fig. 36.

I

I

I

1

I

I

Effect of polymer concentration on the s a l i n i t y range f o r formation of middle-phase microemulsion.

Figure 37 shows the schematic explanation of the surfactant polymer incompati b i 1 it y and concomittant phase separation.

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36 surfactant slug i n porous media i s l a r g e l y determined by the s a l i n i t y o f t h e polymer s o l u t i o n (65). For b e t t e r m o b i l i t y c o n t r o l and minimal surfactant loss a two-slug design o f a s u r f a c t a n t formulation was employed (23). In t h i s design, the f i r s t surfactant s l u q has an optimal s a l i n i t y close t o the connate water s a l i n i t y and the second s u r f a c t a n t slug has a much lower optimal s a l i n i t y . The polymer s o l u t i o n s a l i n i t y i s made equal t o the optimal s a l i n i t y o f the second s u r f a c t a n t slug. With t h i s design, high o i l recovery i n berea cores can be obtained even i n the presence of h i g h s a l i n i t y (6% NaCl + 1% calcium c h l o r i d e ) connate water. The optimal s a l i n i t y concept i s f u r t h e r extended t o include t h e e f f e c t o f m o b i l i t y c o n t r o l and s u r f a c t a n t dispersion and entrappment i n porous media (65). The proposed s a l i n i t y shock design o f m o b i l i t y polymer s o l u t i o n s employs two slugs o f polymer s o l u t i o n s i n which t h e f i r s t polymer slug i s a t the optimal s a l i n i t y o f the preceeding s u r f a c t a n t f o r mulation and the second polymer slug i s at a much lower s a l i n i t y . INJECTION

PRODUCTION

c n

21

0

FLOW

A

c t

OPTIMAL SALINITY

Fig. 39.

SALINITY, %NaCI

Schematic representation o f the g r a d e d - s a l i n i t y design o f polymer b u f f e r s o l u t i o n f o r enhanced o i l recovery.

With t h i s unique design h i g h o i l recovery and h i g h s u r f a c t a n t recovery can be obtained f o r soluble o i l f l o o d i n g i n sandpacks, while t h e polymer consumption can be g r e a t l y reduced. Figure 40 schematically shows our r e s u l t s obtained using t h e s a l i n i ty shock design. The optimal s a l i n i t y f o r t h e s u r f a c t a n t f o r m u l a t i o n used was 2.1% NaCl and t h e r e s e r v o i r b r i n e was 3% NaCl p l u s 1% calcium c h l o r i d e . By the use o f two polymer slugs we were able t o o b t a i n i n berea cores 88% t e r t i a r y o i l recovery and 48% s u r f a c t a n t recovery. For aqueous micellar-polymer f l o o d i n g w i t h crude o i l i n Berea cores, i t has been shown (66-69) t h a t a c o n t r a s t s a l i n i t y design o f t h e p r e f l u s h micellar-polymer f l o o d i n g process may produce a b e t t e r o i l recovery than t h a t obtained from a constant s a l i n i t y process. In t h e c o n t r a s t s a l i n i t y design, the s a l i n i t y o f the p r e f l u s h water i s made higher while t h e s a l i n i t y o f the polyner s o l u t i o n i s made lower than the optimal s a l i n i t y o f the s u r f a c t a n t formulation. The r a t i o n a l e o f t h i s design i s t h a t an opt i m a l s a l i n i t y p r o f i l e can be established i n t h e v i c i n i t y o f the surfact a n t slug upon mixing o f t h e i n j e c t e d f l u i d s i n t h e porous medium.

37

1

CHASE WATER

~

~

~

a

~

L

u

G

.prrRI

'IiASE

POLYMER SLUG 0.05% NaCl

42 %

88 x

Fig. 40.

25 %

48 x

The e f f e c t o f s a l i n i t y shock o f polymer buffer s o l u t i o n an o i l displacement e f f i c i e n c y and surfactant loss.

I t i s hoped t h a t the experimental r e s u l t s presented i n t h i s paper c o n t r i b u t e i n a small way t o increasing our understanding of phenomena occurring i n porous media. It should be enphasized t h a t r e s u l t s we have obtained using laboratory scale experiments are n e i t h e r conducted nor intended t o be extrapolated t o the o i l f i e l d processes. It i s recognized t h a t the processes occurlng i n petroleun r e s e r v o i r s are f a r more complex than those t h a t we can design and c o n t r o l using a laboratory setup.

ACKNOWLEDGEMENTS The author wishes t o express h i s sincere thanks and appreciation t o the National Science Foundation RANN, ERDA and t h e Department of Energy (Grant No: DE-AC1979BC10075) and the consortium o f the f o l l o w i n g Indust r i a l Associates f o r t h e i r generous support o f t h e U n i v e r s i t y o f F l o r i d a Enhanced O i l Recovery Research Program during the past seven years: 1) A l b e r t a Research Council, Canada, 2) Pmerican Cyananid Co., 3 ) Ammo Production Co., 4) A t l a n t i c - R i c h f i e l d Co., 5 ) BASF-Wyandotte Co., 6 ) B r i t i s h Petroleum Co., England, 7) Calgon Corp., 8) C i t i e s Service O i l Co., 9) Continental O i l Co., 10) E t h y l Corp., 11) Exxon Production Research Co., 12) Getty O i l Co., 13) Gulf Research and Development Co., 14) Marathon O i l Co., 15) Mobil Research and Development Co., 16) Nalco Chemical Co., 17) P h i l l i p s Petroleum Co., 18) Shell Development Co., 19) Standard O i l o f Ohio Co., 20) Stepan Chemical Co., 21) Sun O i l Chemical Co. 22) Texaco, Inc., 23) Union Carbide Corp., 24) Union O i l Co., 25) Westvaco, Inc., 26) Witco Chemical Co., and the U n i v e r s i t y o f Florida. He also wishes t o convey h i s sincere thanks t o h i s Colleagues i n Chemical Engineering, Petroleum Engineering and I n s t i t u t e f o r Energy Studies o f Stanf o r d U n i v e r s i t y f o r t h e i r c o l l a b o r a t i o n during h i s s t a y a t Stanford University.

-

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40

38.

Chou, S. I.and Shah, D.O., ( 1981 )

J. C o l l o i d I n t e r f a c e Sci.,

39.

Chou, S. I. and Shah, D.O., (1981).

J. C o l l o i d I n t e r f a c e Sci

40.

Scriven, L.E.,

41.

Scriven, L.E., i n "Mice1 1i z a t i o n , Sol u b i l i z a t i o n and Microemulsions" ed. K.L. M i t t a l , Vol. 11, pp. 877, Plenum Press, N.Y. (1977).

42.

Ranachandran, C., 1561 (1980).

43.

Hwan, R., M i l l e r , C.A. 68, 221 (1979).

44.

Shinoda, K. J. C o l l o i d I n t e r f a c e Sci.,

45.

Shinoda, K. and Saito, H.,

46.

Friberg, S., Lapczynska, I. and Gilberg, G., Sci., 56, 19 (1976).

47.

M i l l e r , C.A., Hwan,.R., Benton, W.J. and Fort, T. Jr., J. C o l l o i d I n t e r f a c e Sci , 61 (3), 554 ( 1977).

48.

Chiang, M.Y.,

49.

"The E f f e c t o f Chain Length o f O i l and Hsieh, W.C. and Shah, D.O., Alcohol as w e l l as Surfactant t o Alcohol R a t i o on t h e S o l u b i l i z a tion, Phase Behavior and I n t e r f a c i a l Tension o f Oil/Brine/Surfactant/Alcohol Systems",SPE 6594, presented a t t h e 1977 SPE-AIME I n t l . Symposiun on O i l f i e l d and Geothermal Chemistry, LaJolla, CA, June 27-28, 1977.

50.

Morgan, J.C., Schechter, R.S. and Wade, W.H., i n "Improved O i l Recovery by Surfactant and Polymer Flooding", D.O. Shah and R.S. Schechter, eds., Acad. Press, Inc., N.Y. (1977).

51.

Cash, R.L., Cayias, J.L., Fournier, G., Jacobson, J.K., Schares, T., Schechter, R.S. and Wade, W.H., "Modeling Crude O i l s f o r Low I n t g r f a c i a l Tension", SPE 5813, presented a t t h e SPE Symposium on I m proved O i l Recovery, Tulsa, OK, March 22-24, 1979.

52.

Satter, S.J., "The I n f l u e n c e o f Type and Amount o f Alcohol on Surfact a n t - O i l - B r i n e Phase Behavior and Properties," SPE 6843, presented a t the 52nd Annual F a l l Conference and E x h i b i t i o n o f SPE-AIME, Denver Co., Oct. 9-12, 1977.

53.

"Estimation o f O p t i m a l S a l i n i t y and SolPuerto, M.C. and Gale, W.W., u b i l i z a t i o n Parameters f o r A l k y l Orthoxylene Sulfonate Mixtures", SPE 5814, presented a t the SPE Improved O i l Recovery Symposium, Tulsa, OK March 27-24, 1976.

54.

Vijayan, S., Ramachandran, C., Doshi, H. and D.O. Shah, i n "Surface Phenomena i n Enhanced O i l Recovery", D.O. Shah ed., pp. 327-376, Plenum Publishing Co., N.Y. ( i n press).

.

Nature,

-

263,

80(1), 49

., 80(2),

311

123 (1976).

Vijayan, S. and Shah, D.O., and Fort, T.

J. Phys. Chem.,

,

84,

Jr., J. C o l l o i d I n t e r f a c e Sci.,

24, 4

(1967).

J. C o l l o i d I n t e r f a c e Sci.,

g,70

(1968).

J. C o l l o i d I n t e r f a c e

.

Ph.D.

Dissertation, l k r i v e r s i t y o f F i o r i d a (1978).

41

650,451

55.

Bansal, V.K. (1978).

and Shah, D.O.,

J. C o l l o i d I n t e r f a c e Sci.,

56.

Bansal, V.K.

and Shah, D.O.,

SPE J.,

57.

Bansal, V.K. (1978).

and Shah, D.O.,

J. h. O i l Chemists SOC.,

58.

Vijayan, S., SOC.,

Ramachandran, C., (1981).

59.

Vijayan, S., SOC.,

Ramachandran, C. and Shah, D.O., (1981).

60.

Vijayan, S., Ramachandran, C. and Doshi, H., " U n i v e r s i t y of F l o r i d a Research on Chemical O i l Recovery Systems Semi-Annual Report", pp. Bl l -857, June, 1978.

61.

Cash, R.L., Cayias, J.L., Hayes, M., M c A l l i s t e r , D.J. %hares, J. Pet. Tech., 985 (Sept. 1976). Wade, W.H.,

62.

i n " U n i v e r s i t y o f F l o r i d a Research on Surfactant-Polymer Desai, N.N.; O i l Recovery Systems-Annual Report", pp. 127-149, Dec. 1979.

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Desai, N.N., i n " U n i v e r s i t y o f F l o r i d a Research on Surfactant-Polymer O i l Recovery Systems-Annual Report", pp. 135-1-48, Dec. 1980.

64.

Hesselink, F. Th. and Faber, M.J., i n "Surface Phenomena i n Enhanced O i l Recovery," D.O. Shah, ed., pp. 861-869, Plenum Publishing Co., N.Y. ( i n press).

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Chou, S . I . and Shah, D.O., covery", D.O. Shah, ed., ( i n press)

66.

Paul, G.W.

67.

Gupta, S.P.

68.

Nelson, R.C., "The S a l i n i t y Requirement Diagram-A Useful Tool i n Chemical Flooding Research Development1', SPE 8824, presented a t t h e SPE Improved O i l Recovery Symposium, Tulsa, OK, A p r i l 20-23, 1980.

69.

Hirasaki, G.J., Van Dmselaar, H.R. and Nelson, R.C., "Evaluation o f . t h e S a l i n i t y Gradient Concept i n Surfactant Flooding", SPE 8825, presented a t t h e SPE Improved O i l Recovery Symposium, Tulsa, OK, A p r i l 20-23, 1980.

167 (June, 1978).

and Shah, D.O.,

580,566

580,746

and Froning, H.R.,

55 (3), 367

J. h . O i l Chemists J. An. O i l Chemists

T. and

i n "Surface Phenomena i n Enhanced O i l Repp. 843-860, Plenum Publishing Co., N.Y. J. Pet. Tech.,

and Trushenski, S.P..

SPE J.,

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2, 116

(1973).

(1979)i

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This Page Intentionally Left Blank

44

The c h a r a c t e r i s t i c d a t a p e r t a i n i n g t o a s p e c i f i c g r o u p of res e r v o i r s must be e v a l u a t e d i n o r d e r t o p r o v i d e a r e p r e s e n t a t i v e s u r v e y o f t h e boundary c o n d i t i o n s r e q u i r e d f o r b o t h t h e r a p i d t e s t methods and t h e p r e l i m i n a r y f l o o d i n g e x p e r i m e n t s . C o n c l u s i o n s w i t h t h e most g e n e r a l a p p l i c a b i l i t y : S i n c e t h e r e s h o u l d be n o r e s t r i c t i o n t o one o i l r e s e r v o i r o n l y , t h e r e s u l t s s h o u l d be of t h e most g e n e r a l p o s s i b l e v a l i d i t y , and s u r f a c t a n t s o l u t i o n s w i t h a b r o a d r a n g e of a p p l i c a t i o n s h o u l d be s o u g h t . Hence, maximal demands s h o u l d be imposed on t h e f l o o d i n g media, i n o r d e r t o e n s u r e t e s t r e s u l t s which a r e a p p l i c a b l e t o a s many o i l r e s e r v o i r s a s p o s s i b l e . TEST PROGRAM/STANDARDIZATION Reproducible t e s t c o n d i t i o n s a r e always r e q u i r e d f o r i n v e s t i g a t i n g s u r f a c t a n t s , i n o r d e r t h a t v a r i o u s p r o d u c t s be a p p r a i s e d and compared. Such c o n d i t i o n s c a n be f u l f i l l e d o n l y by model s y s t e m s , s i n c e t h e p r o p e r t i e s of r e a l s y s t e m s ( r e s e r v o i r w a t e r , c r u d e o i l , reservoir rock) are usually subject t o variations. Hence a t e s t program r e q u i r e s t h e d e s i g n i n g of model s y s t e m s , i n which a s many p a r a m e t e r s of r e a l s y s t e m s a s p o s s i b l e a r e c o n s i d e red. S i n c e s u r f a c t a n t s a r e generally d i s s o l v e d i n w a t e r , t h e t o t a l s a l i n i t y and t h e c o m p o s i t i o n of r e s e r v o i r b r i n e a r e of u t m o s t i m p o r t a n c e f o r t h e s e l e c t i o n of s u i t a b l e s u r f a c t a n t s . Based on s e v e r a l hundred c h e m i c a l a n a l y s e s o f . w a t e r s a m p l e s from German o i l r e s e r v o i r s , a c l a s s i f i c a t i o n i n t o t h r e e b r i n e c a t e g o ries was p o s s i b l e : 1 t y p e AM ( l o w s a l i n i t y ) TDS < l o g.11 t y p e BM ( i n t e r m e d i a t e s a l i n i t y ) 1 0 .g-l-’C TDS (165 g.1t y p e CM ( h i g h l y s a l i n e ) TDS > 1 6 5 g.1-1

-

Observed s i g n i f i c a n t c h a r a c t e r i s t i c s of h i g h l y s a l i n e r e s e r v o i r brines are that many s a l t s o c c u r i n t h e d i s s o l v e d s t a t e a t c o n c e n t r a t i o n s exceeding t h e i r usual s o l u b i l i t y products 2+ a l l w a t e r s a m p l e s c o n t a i n heavy m e t a l i o n s , s u c h a s Fe t h e pH-values of b r i n e s BM and CM l i e i n a r e l a t i v e l y a c i d i c range (3,0-6,5) a l l b r i n e s show c o m p a r a t i v e l y h i g h s u l f a t e c o n t e n t s a l l b r i n e s c o n t a i n large q u a n t i t i e s of Ca2+ and Mg2+ i o n s and lower c o n c e n t r a t i o n s of Sr2+ and Ba2+.

-

T r a c e e l e m e n t s 0 1 0 mg.1-l) were n o t c o n s i d e r e d . A t r e s e r v o i r p r e s s u r e bgtween 50 and 100 b a r and r e s e r v o i r t e m p e r a t u r e s between 4 0 and 80 C a b o u t 4 g of C 0 2 d i s s o l v e s i n 100 g of w a t e r . However, above 6 b a r t h e pH-value of w a t e r c o n t a i n i n g CO a l r e a d y t e n d s t o ward a c o n s t a n t v a l u e of 3 , 3 / 1 5 / , which p r o b a b l y a l s o d o m i n a t e s i n most r e s e r v o i r b r i n e s of t y p e CM. For t h e s u r f a c t a n t i n v e s t i g a t i o n s a s t a t i s t i c a l c o m p o s i t i o n was a s c e r t a i n e d f o r a h i g h l y s a l i n e model r e s e r v o i r w a t e r CM ( t a b l e 1 ) . T h i s s t a n d a r d i z e d b r i n e CM was employed f e r a l l s u b s e q u e n t t e s t s , unless otherwise indicated. The p r i m a r y s c r e e n i n g c r i t e r i a of s u r f a c t a n t s f o r EOR p r o c e s s e s i n h i g h l y s a l i n e s y s t e m s may be l i s t e d a s f o l l o w s / l o / : s o l u b i l i t y i n r e s e r v o i r b r i n e (TDS >165 g . 1 - l ) long-term s t a b i l i t y i n t h e t e m p e r a t u r e r a n g e of 30-80°C low i n t e r f a c i a l t e n s i o n s i n t h e s y s t e m b r i n e / c ? u d e o i l (v< 1 mN.m-l)

-

45 Table 1: Composition of synthetic reservoir brine CM Salt

Concentrations in mg.1-l

NaCl CaC12

165 000 49 349 ( 2 5 O O O ) * 12 810 ( 6 O O O ) * 750 400 20 100

MgC12 KC1 KBr KJ LiCl NH4Cl SrC12 BaC12 NaHC03 Na2S04

. 6H20

. 6H20

350 1 681 ( 1 O O O ) * 58 ( SO)*

. 6H20 . 2H20 . 10H20

C02 injected for at least 1 h NaCQ3 4H20 FeS04 9H20

.

.

650 680 (

300)*

523 (

250)*

366 (

200)*

TDS: 200 070 mg.1-' *The concentration in parentheses refers to the quantity without water of crystallization Based on these fundamental requirements a standard test program for surfactants was developed (see fig. 1).

.solubility stobility wrfoctont in brine CM

ogoinst oil

,- nwhthenic

'T

swfoctont water soluble

interfociol tension Y e 1 mN.rn-1

1: 3a51.0 Y.

30 C' 60 'C

L poroninic

'1:

80 'C Figure 1: Test program for water-soluble surfactants

Besides the aforementioned criteria suitable surfactants should show further, - low adsorption on reservoir rock - favourable partition coefficients and. broad range of application.

-

'

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47

T a b l e 2 : Commercially a v a i l a b l e s u r f a c t a n t g r o u p s Structure

Des isnation

Ionic surfactants Na-salts of fatty acids Alkylbenzenesulfonate

R-CH,-COONa R-C,H,-S0,Na

Alkane sulfonate a-olefinsulfonate Hydroxyalkanesulfonate as byproduct

:)CH-SO,N~ R -CH,--CH=CH-CH,-SO,Na

+

R'-CH,-CH-(CH,)n-CH,-SO,Na OH

a-sulfa fatty acid ester

R-CH-C~' $O,Na'OCH' R-CH,-0-S0,Na

Fatty alcohol sulfate Fatty alcohol ether sulfate*

R; R,CH -O-(C,H,O),-SO,Nn

R -CH,-O-(C,H,O),

R',

+ /R'

-CH,COONa

Fatty alcohol ethoxylate acetate**

CP

(luaternary ammonium salts

R'/ N\R,

N o n I o n i c Surfadants R'

H

1. R=C,,, bei R'=H

R y - ~ - t ~ , ~ , ~ ) , - ~

n=3-15 2. R+R=C,,,, n=3-12

Primary or secondary alcohol ethoxylates

R-C,H.-O-(C,H.O)n-H

R=C,,,

Alkylphenol ethoxylates

n=7-10 YH, CA-Y+C' CH,

Amine oxides

h p l m l y t i c Surfactants R'

Sulfobetains R'

R' - m N -CH,-COO~ R'

Betains

* Fatty alcohol polyethylene glycol ether sulfate, Na-salt ** Fatty alcohol polyethylene glycol ether carboxymethylate,Na-salt

-

-

-

t y p e of c r u d e ( p a r a f f i n i c , n a p h t h e n i c , a r o m a t i c o r mixed t y p e ) c o l l o i d a l c h e m i s t r y of c r u d e ( c o n t e n t of a s p h a l t e n e s , r e s i n s , etc.) a d s o r p t i o n phenomena ( c o m p o s i t i o n of r e s e r v o i r r o c k ) c h a r a c t e r i s t i c s of r e s e r v o i r e n v i r o n m e n t (pH, t e m p e r a t u r e , wetting conditions, s a l i n i t y ) d i f f u s i o n phenomena ( r a p i d d i f f u s i o n t o t h e O / W - i n t e r f a c e ) .

The i m p o r t a n c e of t h e i n d i v i d u a l p a r a m e t e r s c a n v a r y g r e a t l y dep e n d i n g on t h e c o n d i t i o n s of a p p l i c a t i o n , and c a n n o t be g e n e r a l i z e d . For t h i s r e a s o n , two complex p a r a m e t e r s w i l l be d i s c u s s e d i n detai1. DIFFUSION PHENOMENA I t i s known from s t u d i e s on O/W s y s t e m s t h a t t h e d i f f u s i o n i s dep e n d e n t , among o t h e r s , on t h e s t r u c t u r e of s u r f a c t a n t s /l/. Y e t , t h e d i f f u s i o n c o e f f i c i e n t of s u r f a c t a n t s i t s e l f i s of d e c i s i v e imvortance. I n g e n e r a l , t h e following r e l a t i o n s h i p s apply:

48

-

t h e d i f f u s i o n c o e f f i c i e n t decreases w i t h i n c r e a s i n g d e g r e e of alkoxylation the d i f f u s i o n c o e f f i c i e n t increases with increasing concentrat i o n of s u r f a c t a n t ( u p t o c.m.c.) t h e d i f f u s i o n c o e f f i c i e n t i s d i r e c t l y p r o p o r t i o n a l t o temperature t h e d i f f u s i o n c o e f f i c i e n t f o r d i s s o l v e d s u r f a c t a n t s is i n v e r s e l v p r o p o r t i o n a l t o t h e v i s c o s i t y of t h e s o l v e n t branched b l o c k copolymers d i f f u s e more r e a d i l y t h a n l o n g - c h a i n l i n e a r types.

The s t r u c t u r e of t h e p o l y e t h e r c h a i n s of s y n t h e t i c s u r f a c t a n t s c a n a l s o be of i m p o r t a n c e f o r d i f f u s i o n p r o c e s s e s . I t is w e l l known t h a t p o l y e t h e r c h a i n s , depending on t h e d e g r e e of a l k o x y l a t i o n , c a n e x i s t i n t h e s o - c a l l e d z i g - z a g form o r i n t h e meander form ( s e e fig. 3 /2/).

Zig-zag form

Meander form

- F i g u r e 3 : Shapes of p o l y e t h e r c h a i n s / 2 / With i n c r e a s i n g EO number, t h e w i d t h / l e n g t h c o e f f i c i e n t of t h e noni o n i c s i n c r e a s e s , and d i f f u s i o n c o e f f i c i e n t t h u s d e c r e a s e s . By b l o c k i n g t h e p o l y e t h e r oxygen f o r h y d r a t i o n a s a r e s u l t of 0 4 H 2 d i p o l e f o r c e s , a change c a n a l s o o c c u r i n t h e c l o u d p o i n t s , t h e c r i t i c a l micelle f o r m a t i o n c o n c e n t r a t i o n (c.m.c.), and t h u s t h e i n t e r f a c i a l a c t i v i t y o r s o l u b i l i t y behavior / 3 / . ADSORPTION For t h e q u e s t i o n of a d s o r p t i o n phenomena a s a f u n c t i o n of s u r f a c t a n t s t r u c t u r e o r r e s e r v o i r r o c k , numerous f i n d i n g s a r e of importance /l, 9,12, l 4 / . GENERAL C R I T E R I A Swf aetants

-

Amphiphatic s u r f a c t a n t s a r e r e a d i l y a d s o r b e d on h y d r o p h o b i c r o c k s u r f a c e s , d e p e n d i n g on t h e i r s t r u c t u r e The g r e a t e r t h e s o l u b i l i t y of a s u r f a c t a n t , t h e s m a l l e r i s i t s a d s o r p t i o n ( g r e a t e s t a d s o r p t i o n of s u r f a c t a n t o c c u r s i n h i g h s a l i n i t y w a t e r b e c a u s e of diminished s o l u b i l i t y ) With i n c r e a s i n g t e m p e r a t u r e and v i s c o s i t y of t h e s o l v e n t a d s o r p tion decreases With i n c r e a s i n g s u r f a c t a n t c o n c e n t r a t i o n a d s o r p t i o n i n c r e a s e s

AIM:

Low t o t a l a d s o r p t i o n b u t h i g h r a t e of a d s o r p t i o n u p t o t h e s a turation concentration

R e s e r v o i r system

-

-

Hydrophilic e a s i l y water-wettable rocks: quartz, c l a y Hydrophobic, p o o r l y w a t e r - w e t t a b l e r o c k s : c a r b o n a t e s

49 SPECIAL CRITERIA Surf a c t a n t s

-

-

T o t a l a d s o r p t i o n d e c r e a s e s w i t h i n c r e a s i n g m o l e c u l a r mass of s u r f a c t a n t ( t h e t o t a l a r e a a c c e s s i b l e t o a d s o r p t i o n becomes smaller) Nonionic s u r f a c t a n t s / 9 / a r e adsorbed mostly i n unimolecular l a y e r s , a d s o r p t i o n d e c r e a s e s w i t h increasing EO d e g r e e , b u t a d s o r p t i o n i n c r e a s e s w i t h i n c r e a s i n g l e n g t h of t h e h y d r o c a r b o n c h a i n ; d e r i v a t i v e s w i t h an a l i p h a t i c h y d r o c a r b o n c h a i n a r e more s t r o n g l y a d s o r b e d t h a n d e r i v a t i v e s w i t h an a r o m a t i c h y d r o c a r b o n c h a i n I o n i c s u r f a c t a n t s a r e a d s o r b e d f o r t h e most p a r t i n polymolecul a r l a y e r s ( c a t i o n i c s : a b o u t 250 l a y e r s ) . Limiting concentration: s y n t h e t i c s u r f a c t a n t s (0.05-0.07 %) << n a t u r a l s u r f a c t a n t s (0.25 %).

Reservoir rock

-

C l a y : a d s o r p t i o n of u n s a t u r a t e d h y d r o c a r b o n s ( i n p a r t p o l y m e r i z e d ) > a r o m a t i c s > n a p h t h e n a t e s > a l k a n e s . C a t i o n i c s >>nonionics > anionics. S i l i c a t e s : s l i g h t a d s o r p t i o n of n o n i o n i c s ( o i l - w e t t e d > w a t e r w e t t e d ) , a d s o r p t i o n i n c r e a s e s with temperature; s t r o n g adsorpt i o n of c a t i o n i c s on q u a r t z ( l o w e r e d by a d d i t i o n of n o n i o n i c s ) .

The i n c r e a s e d a d s o r p t i o n of c a t i o n i c s , i n d e p e n d e n t of t h e reserv o i r r o c k i s t h s c l e a r l y e v i d e n t . A s a g u i d e , v a l u e s of a b o u t l o d 4 mg/cm c a n be g i v e n f o r t h e a d m i s s i b l e a d s o r p t i o n on 0,s quartz surfaces.

.

Y

PHYSICOCHEMICAL P R O P E R T I E S OF SURFACTANTS

P r i o r t o t e s t i n g , a f e w g e n e r a l l y - k n o w n r u l e s and some e m p i r i c a l d a t a from t h e c h e m i s t r y of s u r f a c t a n t s c a n be u s e d :

,:

range ( < C s m a l l m i c e l l e s , low Good w e t t i n g a c t i o n : C -C s u r f ace a c f i v $ $ y ) B r a n c h e a and s o l v a t a b l e g r o u p s s h o u l d l i e close t o t h e c e n t r e of t h e m o l e c u l e .

.

H y d r o p h i l i c c h a r a c t e r : 3 CH2 g r o u p s P 1 OH-group -$-NH-group P -0-group ( h y d r o g e n b r i d g i n g ) 3 CHp-groups

-

beginning water s o l u b i l i t y S o l u b i l i t y : n / 3 EO n / 2 EO -medium w a t e r s o l u b i l i t y 1 - 1 , 5 n EO-good water s o l u b i l i t y ( n = number of c a r b o n atoms i n h y d r o p h o b i c c h a i n ) Solubility decreases with r i s i n g temperature ( - c l o u d point/through dehydration and i n c r e a s i n g e l e c t r o l y t e c o n t e n t (see f i g . 4 / l / ) . HLB v a l u e : W/O e m u l s i f i e r s

3 -6

Wetting a g e n t s 7-9 O/W e m u l s i f i e r s 8-12 O/W d i s p e r s i n g a g e n t s , W/O demuls i f i e r s , solubilizing agents

/13

-18/

50

rurtactont nonylphsnol/l5 EO in water

0

1.o 2.0 3.0 electrolyte concentration /ma1 1-1

F i g u r e 4 : E f f e c t o f e l e c t r o l y t e c o n c e n t r a t i o n and t y p e o n c l o u d p o i n t TP / 7 / On t h e b a s i s o f t h i s p r e l i m i n a r y i n f o r m a t i o n , i t i s now a l r e a d y p o s s i b l e t o g e t the most i m p o r t a n t r e q u i r e m e n t s o n s u r f a c t a n t s f o r EOR p r o c e s s e s / 4 , 5 / : - Enrichment a t t h e i n t e r f a c e - Formation of o r i e n t e d monolayers - Permanent l o w e r i n g of i n t e r f a c i a l t e n s i o n i n t h e s y s t e m o i l / w a t e r t o (1 m N . m - 1 a t low s u r f a c t a n t c o n c e n t r a t i o n / 1 3 / - Tendency t o m i c e l l e f o r m a t i o n - Partial o i l solubility - S t a b i l i z a t i o n of O/W e m u l s i o n s Solubility or d i s p e r s a b i l i t y i n highly s a l i n e formation water - Long-term s t a b i l i t y ( 1 - 2 y e a r s ) u n d e r r e s e r v o i r c o n d i t i o n s - Low a d s o r p t i o n on r e s e r v o i r r o c k - Low c o s t c o u p l e d w i t h h i g h e f f e c t i v e n e s s

-

A l i s t of p o s s i b l e b u i l d i n g s t o n e s a v a i l a b l e c o m m e r c i a l l y f o r t h e s y n t h e s i s of s u r f a c t a n t s i s g i v e n i n t a b l e 3 . These c o n s i d e r a t i o n s t h e n l e a d t o classes of p r o m i s i n g p r o d u c t s , which i n p a r t s h o u l d e x h i b i t v e r y s t r o n g i n t e r f a c i a l a c t i v i t y and a r e described i n t h e U S - l i t e r a t u r e a s e f f e c t i v e f o r EOR p r o c e s s e s ( s e e t a b l e 4 and 5 ) .

T h e s e known s u r f a c t a n t s a r e s u i t a b l e p r i m a r i l y f o r low s a l i n i t i e s (1 % N a C l w i t h a b o u t 100-200 ppm Ca2+ and Mg2+ o n l y ) . W i t h o u t a p o l y e t h e r c h a i n w i t h s u f f i c i e n t d i s p e r s i n g power, however, t h e sol u b i l i t y i n h i g h s a l i n i t y s y s t e m s ( 1 5 - 2 5 % NaC1, 20 000-40 000 ppm C a 2 + and Mg2+) i s f o r t h e m o s t p a r t t o o low o r t h e e l e c t r o l y t e s e n s i t i v i t y t o a l k a l i n e e a r t h i o n s t o o h i g h . Even i n t h e case o f pol y e t h o x y l a t e s t h e e l e c t r o l y t e c o n t e n t of t h e r e s e r v o i r w a t e r c a n l o w e r t h e c l o u d p o i n t s t r o n g l y ( f i g . 4 ) and t h u s c a n b r i n g a b o u t a d e c r e a s e d s o l u b i l i t y as w e l l a s i n c r e a s e d a d s o r p t i o n and a p a r t i a l p a s s a g e o f t h e s u r f a c t a n t i n t o t h e o i l p h a s e /6/. I n g e n e r a l t h e i n t e r f a c i a l a c t i v i t y o f t h e anionics i s l i k e w i s e r e d u c e d s t r o n g l y i n water w i t h a h i g h e l e c t r o l y t e c o n t e n t / 5 / , F r e q u e n t l y a l s o s u r f a c t a n t m i x t u r e s f o r EOR p r o c e s s e s h a v e b e e n d e s c r i b e d and a p p l i e d . T h e r e r e m a i n s u n c l e a r t h e q u e s t i o n o f c h r o m a t o g r a p h i c phenomena i n t h e u s e of c o m p l i c a t e d s u r f a c t a n t m i x t u r e s i n r e s e r v o i r , i n which t h e q u i t e d i f f e r e n t components of t h e m i x t u r e c a n e x h i b i t c o m p l e t e l y d i f f e r e n t r a t e s of m i g r a t i o n .

51 T a b l e 3 : Possible b u i l d i n g s t o n e s f o r s u r f a c t a n t s Surfactant building stones a-olefins oligomeric alkenes fatty acids (saturated and unsaturated) and derivatives, natural oils alkanols (alfols, 0x0-alcohols, fatty alcohols) alkylaromatics isoalkylphenols alkylamines (fatty amines) polyalkylene glycol ethers polybutylene oxide (polypropylene oxide)

SO,, ( ~ O , ) , C I S O , H , , H,NSO,H,Na,SO,,NaHSO,

8 8-

),

HOC,H,SO,Na, ( C H , ) , < P ,

(CH2)(_So2\0

c'

H,O, (N), CICHFO,H, (HNO,) 1

0

/o\

(Formaldehyde, epichlorohydrin, RO-CHSH-CH,, aliphatic oligoamines, polyols, etc.)

A n i o n i c s u r f a c t a n t s f o r EOR p r o c e s s e s ( i n t e r n a t i o n a l literature)

Table 4 :

Anionic surfactants Chemical constitution

Designation

structural type

R'-FH-CO,R' SO,H (Na)

a-Sulfo fatty acid esters OH fatty acid sulfates

--T

R-CH,-CH-R-COONa OS0,Na R ~ C O N ~ ~ '

7

Sulfated amide oils

S0,Na R 2

Didecyldiphenyl ether disulfonates H H R-C -C,H,-N-CH,SO,Na bH N + S O , N ~

'c P %

R

R-N -R'-(OC,H,)xOSO,Na R PH R-CH,

RG@-o(c.H,,o)~R S0,Na (rnFXAC0) ,C,H,O-C-R HN' -C,H,O-C-R \ d H C,H,(OC,H,),OC-~-CH,-CO.Na

p

b sop

P

R-0-(CH,-CH,-0)"-P-ONa ONa

Hydroxyalkylaminosulfonic acids Alkenylsuccin-N-(alkyl)phenylimidesulfonates Dialkylamino polyether sulfates Alkenyl-, OH-Alkane sulfonates

7x -77 ).wv,

Sulfates of iosalkylphenyl polyether sulfonates Bisfatty acid esters of triethanolamine polyglycol ether sulfocarboxy lates Alkanol polyether phos-

-

52 T a b l e 5 : Amphoteric s u r f a c t a n t s f o r EOR p r o c e s s e s ( i n t e r n a t i o n a l literature) Amphoteric Surfactants Chemical constitution

Structural type Sulfobetains

R’ H R - ~ C H , - C -cH,-so,~

R’

Sulfobetains

4

Betain

--f.)

Alkylimidazoliniumbetains

-79

Amidoalkylbetains

-.-a

OH

YH’ H,,.,,c,,,:-I]I-cH,-coo~

CH,

R-&

HO-CH,~CH,/N\CH,~COO~ CH;

H,,,,-c,-co-NH-(cH,):-$-cH,-coo

e

CH,

O t h e r w i s e i t is p r o b a b l y p o s s i b l e t o i n c r e a s e , by t h e u s e of s u c h s u r f a c t a n t m i x t u r e s , t h e p a c k i n g d e n s i t y a t t h e i n t e r f a c e and t h u s t h e d e g r e e of w e t t i n g ( s e e f i g . 5 / l o / ) ; f u r t h e r , a l s o t h e format i o n of mixed micelles i s p o s s i b l e ( f i g . 6 /4/).

lipophilic port of molecule surfactant molecule

0 hydrophtlic part of mokcuie

F i g u r e 5 : I n c r e a s e d p a c k i n g d e n s i t y by s u r f a c t a n t m i x t u r e s a t O/W i n t e r f a c e s

When p u r e n o n i o n i c s a r e u s e d , s u c h a s i s o a l k y l p h e n o l e t h o x y l a t e s , a t t a i n m e n t of s a t i s f a c t o r y i n t e r f a c i a l a c t i v i t i e s demands a h i g h e r d e g r e e of a l k o x y l a t i o n . These p r o d u c t s a r e n o t e l e c t r o l y t e - s e n s i t i v e and h a v e a good s o l u b i l i t y i n b r i n e ( a r u l e of thumb i s t h a t a t 5OoC, o n l y n o n i o n i c s w i t h a d e g r e e of e t h o x y l a t i o n n of 1 0 o r more a r e s o l u b l e i n 1 0 % NaC1).

53 oure onionic surfoctont oil

011

transitional interface

L1

water

transitional interface

water

11 : 12

- 1.1

surfoctont mixture (anionics/nonionics I

F i g u r e 6 : a ) p a c k i n g d e n s i t y of p u r e a n i o n i c s u r f a c t a n t a t i n t e r face b ) p a c k i n g d e n s i t y of a n i o n i c - n o n i o n i c s u r f a c t a n t a t interface

EXPERIMENTAL

Under c o n s i d e r a t i o n of a s many s e l e c t i o n c r i t e r i a , physico-chemic a l p r o p e r t i e s and p o s s i b i l i t i e s of s u r f a c t a n t s y n t h e s i s a s poss i b l e more t h a n 1 2 0 0 s u r f a c t a n t s were t e s t e d f o r t h e i r a p p l i c a b i l i t y t o EOR p r o c e s s e s . The s c r e e n i n g of t h e s u r f a c t a n t s was c a r r i e d o u t a c c o r d i n g t o t h e r a p i d s c r e e n i n g program a l r e a d y i n troduced. F u r t h e r t e s t s on a s u r f a c t a n t w e r e proposed o n l y , i f i t had pass e d t h e s c r e e n i n g program. SOLUBILITY I N BRINE CM A l l e x p e c t a t i o n s on t h e s o l u b i l i t y of s u r f a c t a n t s i n h i g h - s a l i n i t y b r i n e s were c o n f i r m e d i n a l l r e s p e c t s . E s p e c i a l l y t h e s u r f a c t a n t s w i t h p o l y e t h e r c h a i n s and a n i o n i c g r o u p s have shown good s o l u b i l i t i e s up t o t h e mark. T a b l e 6 p r e s e n t s some t y p i c a l p r o d u c t s , which were s e l e c t e d on t h e b a s i s of t h e a b o v e - d e s c r i b e d s o l u b i l i ty criteriaa.

INTERFACIAL ACTIVITY

During t h e measurements of t h e i n t e r f a c i a l a c t i v i t y (Lecomte du Nouy) a s t r o n g dependence of t h e i n t e r f a c i a l t e n s i o n on t h e temper a t u r e and s a l i n i t y was e s t a b l i s h e d i n t h e system o i l / w a t e r w i t h o u t a d d i t i o n of any s u r f a c t a n t s ( s e e f i g . 7 ) . The e x p e r i m e n t s have shown t h a t a l l s t a n d a r d o i l s a r e c h a r a c t e r i z e d by a t y p i c a l i n t e r f a c i a l t e n sion - relationship - i n t e r f a c i a l t e n s i o n depends s t r o n g l y on t h e o i l c o m p o s i t i o n - n a p h t h e n i c o i l shows t h e h i g h e s t v a l u e s of i n t e r f a c i a l t e n s i o n against high-salinity brines - i n g e n e r a l an i n c r e a s e i n s a l i n i t y is accompanied by a d e c r e a s e i n i n t e r f a c i a l t e n s i o n / A minimum i n i n t e r f a c i a l t e n s i o n w i l l be passed. T h e r e s u l t s a r e summarized i n f i g u r e 7 .

-

54

T a b l e 6 : Some s u r f a c t a n t s w i t h good s o l u b i l i t y , t e s t e d i n h i g h salinity brine Chem. constitution

Designation

I-C,H,,~(C,H.OJ.,CH,CD,N~

Isoalkylphenylpolyether acetates Diisoalkylphenylpolyether sulfates

SO, Na

IC,H,.~O(C,H.OI,. l-C,Ha,

Rj-N/(C,H,O)x '(C,H,O), (2 x = 5 )

SO,Na S0,Na

Acylamidopolyether sulfates

fl

(R-C-~,H,-N/(C1H40)y ( 2 y t 1= 2 X I

'(C,H,Oly

(Esteramine polyether sulfates)

S0,Na)

i-C,,H,,~-CH,-~-CH,~(OC.H,.Jx SO,N~

Structural type-

( W n H x n)x O R

x-0-20 R'= H, SO,Na,

OR'

N

(Sulfone/sulfate-isoalkylphenylpolyethoxyglycerol ether)

-CH,COONa n=2,3

Ditert.-alkylphenyl polyethers

Isoalkylphenylpolyethers

I f s u r f a c t a n t s were added t o t h e s t a n d a r d o i l s , c h a r a c t e r i s t i c c u r ves r e s u l t e d f o r t h e f u n c t i o n i n t e r f a c i a l t e n s i o n y = f ( s u r f a c t a n t concentration CT). T h e s h a p e of t h e c u r v e s d e p e n d on - t y p e of o i l ( c o m p o s i t i o n ) - temper a t u r e - salinity - t y p e of s u r f a c t a n t and c o n c e n t r a t i o n of s u r f a c t a n t . T y p i c a l d i a g r a m s of s u r f a c t a n t m i x t u r e s ( a n i o n i c s - n o n i o n i c s ) a r e presented i n f i g u r e 8 a/b. -1 I f t h e i n t e r f a c i a l t e n s i o n r e a c h v a l u e s of < 1 mN.m , t h e accur a c y of t h e method of Lecomte d u Nouy i s no l o n g e r s u f f i c i e n t . Furt h e r t e s t s on " s u c c e s s f u l " s u r f a c t a n t s makes t h e a p p l i c a t i o n of a spinning-drop-tensiometer (SITE) n e c e s s a r y . A " s u c c e s s f u l " s u r f a c t a n t m u s t comely w i t h t h e f o l l o w i n q c r i t e r i o n : The i n t r f a c i a l t e n s i o n of a s u c c e s s f u l s u r f a c t a n t must be < 1 mN.m-f against a l l three standard o i l s i n the temperature range of 30-80°C. On t h e b a s i s of t h i s c r i t e r i o n a g e n e r a l t e m p e r a t u r e i n t e r f a c i a l t e n s i o n - r e l a t i o n s h i p was d e r i v e d f o r t h e s u r f a c t a n t s t e s t e d ( s e e fig. 9). By t h i s i t was e v i d e n t , t h a t a n i o n i c s ( w i t h an o p t i m a l c o n t e n t of nonionics) w i l l e x h i b i t the lowest i n t e r f a c i a l tension. TEMPERATURE STABILITY

For t h e i n v e s t i g a t i q n of t h e t e m p e r a t u r e s t a b i l i t y , s u r f a c t a n t s o l u t i o n s of v a r i o u s c o n c e n t r a t i o n s i n b r i n e CM were k e p t f o r

55

"I

Figure 7 : I n t e r f a c i a l tens i o n a s a f u n c t i o n o f temp e r a t u r e , s a l i n i t y and o i l composition (naphthenic, aromatic, p a r a f f i n i c )

N

20

Y ogoinst dist woter

6 month a t a t e m p e r a t u r e o f 8OoC. After t h i s t i m e the interf a c i a l a c t i v i t y was comp a r e d t o t h a t of a s t a n d a r d solution On t h e b a s i s of t h e s e e x periments, the following s t a t e m e n t was p o s s i b l e : ether Ether phosphates s u l f a t e s - e t h e r carboximethylates -ether sulfonates a r r o w i n d i r e c t i o n of increasing s t a b i l i t y

-

0

60

30

80

temperature 9/"C

20t

\:I y

= f(8.011 comp

1

Y against brine EM

s

12 10

5 8 .-

N

.-I

0 : .

0

20

t

1

v

.

I

.

I

.

,

80 temperot ure 8 / "C

30

60

-

SPECIAL FINDINGS

, -

P o l y e t h e r s u l f a t e s , -carbo x i m e t h y l a t e s and - s u l f o n a t e s of t h e f o l l o w i n g s t r u c ture are particularly suita b l e f o r EOR g r o c e s s e s : R(OC2H4)xY-Me (Fig.10).

y = t(;t.oil comp I

Numerous s u r f a c t a n t s w i t h e s p e c i a l l y low v a l u e s of t h e i n t e r f a c i a l t e n s i o n may be c l a s s i f i e d a s m i x e d s u r f a c t a n t s (Mischtenside) (ani o n i c / n o n i o n i c ) . The compos i t i o n of t h e m i x e d s u r f a c t a n t i s u s u a l l y g o v e r n e d by t h e manufacturing process o r t h e d e g r e e of c o n v e r s i o n . I n t h i s r e s p e c t i t was ob30 60 eo s e r v e d t h a t a d e g r e e of contemperature ;t/'C v e r s i o n o f 50 t o 8 0 p e r c e n t N naphthenic oil nonionic t o anionic surfacA aromottc oil t a n t g i v e s rise t o p a r t i c u P poroffinic oil l a r l y favourable surfactant p r o p e r t i e s . A t y p i c a l homoloaue d i s t r i b u t i o n f o r f o r s u c h a s u r f a c t a n t i s shown i n f i g u r e 11

Y agoinst brine CM

.

The f o l l o w i n g i m p o r t a n t d a t a and r e s e a r c h r e s u l t s a r e w o r t h mentioning: - The d i s t r i b u t i o n c u r v e f o r t h e s u r f a c t a n t homologs ( a l k o x i l a t e s ) s h o u l d be a s b r o a d a s p o s s i b l e (more p d l d i s p e r s e ) i . e . , a l k a l i catalyzed alkoxilation (not Lewis-acid catalyzed). - The d e g r e e of a l k o x i l a t i o n n m u s t be a d j u s t e d a c c o r d i n g t o t h e c r u d e type (and Y - ) . General r u l e s a r e HLB: 8-10 p a r a f f i n i c c r u d e s : n = 4 5 2 EO (partial o i l solubility) n a p h t h e n i c c r u d e s : n = 6 5 2 EO

56 rn namlhanic oil

oil

y = f (c,,

A poraflinic oil

type)

x ommolic oil suiodoni 63 tenpirniure ’ 30.C surfuianl in brine CM

Figure 8 a : I n t e r f a c i a l tension a s a funct i o n of o i l composition, surf a c t a n t concent r a t i o n and temp e r a t u r e (30°C) surfactant: C12/14-fatty alkohol-polyglycolether-(4,5 EO)-carboxmet h y l a t e , Na-salt

naphthanic oil

y = f (cT, oil type 1

10

A poraflinic oil

x oromalic oil surfactant 63 impKa1ua:I0.C surfoclani in brina CM

I

Figure 8 b: same a s f i g . 7a t e m p e r a t u r e 80 C

6

1n

1 A h htypical

onionics and mixed surfactants

high content of 1 nonionics

/

temperoture

area of spontaneous

a/

0;

emulsification

Figure 9 : Temperature/ i n t e r f a c i a l tension-rel a t i o n s h i p f o r some i m portant s u r f a c t a n t groups

57

hydrophobic chain

R

Polyether group

-+X+

fatty OlCOhd tatty ocid nonylphenol naphthenic ocid tatty ornines

ethyleneoxide propyleneoxide etc

polar hydrophilic group

counter ion

YQ

Z@

car boxylote sulfate sulphonate phosphate propionate etc

OlkOll earth alkali ornines etc

F i g u r e l o : S u r f a c t a n t s s u i t a b l e f o r EOR p r o c e s s e s

nonionic port

anionic part

Hal EO

Hol EO

F i g u r e 11: Q u a n t i t a t i v e a n a l y s i s of i-nonylphenol-polyglycole t h e r (6 E O ) - c a r b o x i m e t h y l a t e , Na s a l t , by HPLC aromatic crudes:

-

n

= 8 & 2 EO

( P r o p o x i l a t e s a r e i n g e n e r a l less e f f e c t i v e , a s a r e EO-PO ducts) The h y d r o p h o b i c c h a i n R must be t a i l o r e d w i t h p r e c i s i o n . p a r a f f i n i c c r u d e s : C14 5 4 ( s a t u r a t e d , u n b r a n c h e d ) naphthenic crudes: C,, + 2 arbmatic rudes: a k y l r o m a t i c s iiso-C8-12-alkyl). C a t i o n ( 2I) : Na', ,'K i'R4 o r NH4

ad-

The l e n g t h of t h e h y d r o p h o b i c and h y d r o p h i l i c m o l e c u l a r p a r t s s h o u l d be r o u g h l y i n t h e 1 : 1 r a t i o ( p a r t i a l o i l s o l u b i l i t y ) .

58 Example: C 1 2 , 1 4 - a l k y l p o l y g l y c o l

e t h e r s u l f a t e - ( 4 , 5 EO), N a - s a l t

( h y d r o p h o b i c : h y d r o p h i l i c c h a i n l e n g t h = 2 , 2 nm: 2 , 3 n m ) o r f o r n o n y l p h e n o l p o l y g l y c o l e t h e r s u l f a t e - ( 4 EO), Na-salt (hydrophobic: hydrophilic chain l e n g t h = 2,O: 2 , l nm ( s e e f i g . 1 2 ) .

oil

transitional interface

hydrophobic part A

water

hydrophilic port B

~~~

ratio at optimum A B - 1 1

-

F i g u r e 1 2 : Optimal c h a i n r a t i o of s u i t a b l e s u r f a c t a n t s f o r EOR p r o c e s s e s

The d e g r e e of c o n v e r s i o n of n o n i o n i c s i n t o s u l f a t e s , c a r b o x i m e t h y l a t e s , s u l f o n a t e s , e t c . , s h o u l d be 50-80 % ( m i x e d s u r f a c t a n t f o r m a t i o n f r o m n o n i o n i c s and a n i o n i c s ) .

The c a r a c t e r i s t i c b e h a v i o u r of a n i o n i c - n o n i o n i c m i x e d s u r f a c t a n t s w i t h t e m p e r a t u r e (minimum of i n t e r f a c i a l t e n s i o n ) c a n be e x p l a i n e d w i t h t h e h e l p of t h e p h a s e d i a g r a m f o r s u c h s y s t e m s ( s e e f i g u r e 13), w h e r e b y t h e o c c u r r e n c e o f a m i s c i b i l i t y g a p is d e c i s i v e .

A aI L aI

11 MST=T?

0% 100%

-nonionic surfnctant + c a n i o n i c surfactant -

100% 0%

MSTK

=

CK

= critical splitting -concentration of mixed micelles at MSTk

CX

= composition of mixed micelles

lower critical micell- splitting - temperature

MST=T2= splitting - temperature of mixed micelles

AT

=

a,p

= coexistent phases with concentrations c, and c ,

11 -12

F i g u r e 1 3 : Schematic p h a s e d i a g r a m f o r mixed surf actant (anionicn o n i o n i c ) w i t h miscib i l i t y gap

59

A s e p a r a t i o n i n t o w a t e r - / o i l - s o l u b l e s u r f a c t a n t s o c c u r s when t h e m i x e d m i c e l l e s formed from anionics & nonionics reach the micelle s p l i t t i n g t e m p e r a t u r e ( M S T ) . When t h e MST i s e x c e e d e d , v a r i o u s i n t e r e s t i n g phenomena may be o b s e r v e d ( s e e f i g u r e 1 4 ) ; t h e s e a r e accompanied by t r a n s p o r t p r o c e s s e s a t t h e i n t e r f a c e s .

t F i g u r e 1 4 : Phenomena a t the micelle-splitting t e m p e r a t u r e (MST) f o r m i x e d s u r f a c t a n t (nonionic-anionic)

CONCLUSIONS

With t h e t e c h n o l o g i c a l p o s s i b i l i t i e s t a k e n i n t o c o n s i d e r a t i o n , and w i t h t h e h e l p of a r a p i d t e s t p r o c e d u r e , i t was p o s s i b l e t o s e l e c t s u r f a c t a n t s s u i t e d f o r EOR p r o c e s s e s i n h i g h - s a l i n i t y s y s t e m s from a l a r g e number of p r o d u c t s . The s e l e c t e d s u r f a c t a n t s a r e ani o n i c s and b e l o n g t o t h e c l a s s e s of polyglycolethercarboximethyl a t e s and polyglycolethersulfonates. As a r e s u l t of t h e manufact u r i n g p r o c e s s , t h e s e p r o d u c t s may be c l a s s i f i e d a s mixed s u r f a c t a n t s ( n o n i o n i c - a n i o n i c ) . S i n c e m i x e d micelles a r e formed, t h e s e p r o d u c t s p o s s e s s s p e c i a l t e m p e r a t u r e - d e p e n d e n t p r o p e r t i e s which a r e i n t e r e s t i n g f o r EOR p r o c e s s e s . I n t h e long term, tailor-made p r o d u c t s , e s p e c i a l l y s u r f a c t a n t mixt u r e s o r mixed s u r f a c t a n t s , o f f e r s p e c i a l p r o m i s e from t h e economic p o i n t of view.

60

Nomenclature c .m .c CS

EO EOR

.

-

TDS

-

W/O

-

HLB HC OOIP O/W PO ppm

0

-

critical micelle formation concentration salinity/concentration of salts dissolved; g. 1-1 ethylene oxide enhanced oil recovery tertiary oil recovery phase) hydrophilic/lipophilic balance hydrocarbons original oil in place, % oil/water propylene oxide parts per million iota1 dissolved solids, % water-in-oil temperature, OC

Abbreviations for fiqures CT A1 # A 2

-

Au

-

L1 L2 Y

surfactant concentration in ppm or % distance between surfactant molecules at interface, nm thickness of transitional interface length of hydrophilic chain, nm length of hydrophobic chain, nm interfacial tension, mN.m-1

61 LITERATURE 1

Babalyan, G.A.:

Physicochemical p r o c e s s e s i n o i l prod u c t i o n , " P u b l i s h i n g House " N e d r a " , Moscow, 1974 ( i n R u s s i a n )

2

Rosch. M . :

The c o n f i g u r a t i o n of t h e p o l y e t h y l e n e o x i d e c h a i n of n o n i o n i c s u r f a c t a n t s ( p a r t 1 ti 2 ) ( i n German) Tenside Detergents ( 1 9 7 1 ) , pp. 302313 T e n s i d e D e t e r g e n t s 9 ( 1 9 7 2 ) , pp. 23-28

3

Schonfeldt, N.:

" G r e n z f l a c h e n a k t i v e E t h y l e n o x i d -Adduk-

t e " ( I n t e r f a c e - A c t i v e E t h y l e n e Oxide

Adducts) , Wiss. V e r l a g s GmbH, S t u t t g a r t Schick, M. J. :

"Nonionics Surf a c t a n t s " , M a r c e l Dekker, I n c . ,. N e w York, 1 9 6 7 / C h a p t e r 22

4

A k s t i n a t , M.H.:

V i s c o u s f l o o d i n g media f o r t e r t i a r y o i l recovery i n h i g h l y s a l i n e systems s e l e c t i o n c r i t e r i a , t e s t i n g methods and e x p e r i m e n t a l r e s u l t s ( i n German) Ph. D. t h e s i s , TU C l a u s t h a l 1 9 7 8

5

Gutscho, S.J.:

" S u r f a c t a n t s and S e q u e s t r a n t s " , Noyes Data Corp., Park Ridge, N . J . , 1977,

6

B a l z e r , D.; Kosswig , K . :

The p h a s e - i n v e r s i o n - t e m p e r a t u r e a s a c r i t e r i a f o r s e l e c t i o n of s u r f a c t a n t s f o r EOR ( i n German) T e n s i d e D e t e r g e n t s 16 ( 1 9 7 9 ) , pp. 256 261

7

Schick, M.J.:

-

-

S u r f a c e f i l m s of n o n i o n i c d e t e r g e n t s I. Surface tension study J. C o l l . Sci. ( 1 9 6 2 ) , p p . 801-813

17

8

Crook, E.H. ; F o r d y c e , D. B. ; T r e b b i , G.F.:

M o l e c u l a r w e i g h t d i s t r i b u t i o n of noni o n i c s u r f a c t a n t s / I I . P a r t i t i o n coeffic i e n t s o f n o r m a l d i s t r i b u t i o n and homogeneous p , t - Octylphenoxyethoxie t h a n o l s (OPES) J . C o l l . S c i . 20 ( 1 9 6 5 ) , p p . 191-204

9

Kravchenko, J . J . :

E f f e c t of t e m p e r a t u r e on t h e a d s o r p t i o n of n o n i o n i c s u r f a c e - a c t i v e subs t a n c e s on s o l i d a d s o r b e n t s C o l l . J. USRR 33. ( 1 9 7 1 ) , pp. 379-381

10

A k s t i n a t , M.H.:

Surface-active agents f o r t e r t i a r y

o i l r e c o v e r y : s e l e c t i o n c r i t e r i a and s e l e c t i o n m e t h o d s ( i n German) T e n s i d e D e t e r g e n t s 14 ( 1 9 7 7 ) , p p . 5763

62 11

Rieckmann, M . :

T e r t i a r y o i l r e c o v e r y methods ( i n German) Erdo14rdgas-Z. 91 ( 1 9 7 5 1 , pp. 348359

12

R u d i , V.P.; S o b k i v , E.R. :

I n f l u e n c e o f s u r f a c t a n t s on t h e p r o p e r t i e s of c l a y s ( i n R u s s i a n ) ( 1 9 6 6 ) , pp. 119-122 K o l l o i d Zh.

et al.:

S

Surfactant aging: a possible detriment t o t e r t i a r y o i l recovery 5 0 . SPE of AIME Ann. F a l l Mtg., 28.3.1.10.1975, Dallas/Tx. SPE-Paper 5564

13

Cash, R.L.

14

Trogus, F.J.

15

W r i g h t , C.C.:

The u s e o f C a r b o n D i o x i d e i n w a t e r floods A P I P r o d . D i v . P a c i f i c Coast D i s t r . Mtg., 2 1 . - 2 3 . 5 . 1 9 6 3 , Los A n g e l e s P r e p r i n t 801-39 k

16

Oppenlander , K. ; A k s t i n a t , M.H.; Murtada, H.:

S u r f a c t a n t s f o r enhanced o i l recovery i n hiqh-salinity systems - c r i t e r i a f o r t h e s u r f a c t a n t s e l e c t i o n and a p p l i cation Tenside Detergents 1 7 ( 1 9 8 0 ) , p p . 5767

et al.

A d s o r p t i o n of m i x e d s u r f a c t a n t s y s t e m s 5 2 . SPE of AIME A n n . F a l 1 Techn. Conf. & Exh., 9.-12.10.1977, Denver/Col. SPE-Paper 6845

63

CHEMICAL FLOODING

PRELIMINARY STUDIES OF THE BEHAVIOUR OF SOME COMMERCIALLY AVAILABLE SURFACTANTS IN HYDROCARBON-BRINE-MINERAL SYSTEMS C. ANDREWS, N. M. COLLEY and R. THAVER British Gas Corporation, London Research Station ABSTRACT Some commercial surfactants have been studied with a view to their usefulness for enhanced oil recovery applications. The following aspects of their behaviour have been assessed. 1.

Their interfacial tension behaviour with crude oil and pure alkanes.

2.

The variation of phase inversion temperature with different variables.

3.

Their adsorption onto rock surfaces

The interfacial tensions were measured by the spinning drop technique. As the temperature varies, the interfacial tension of a surfactant-brine- hydrocarbon mixture passes through a minimum. Some surfactants have given interfacial tensions approaching 10-3 dynes cm-1. We have found: 1.

The phase inversion temperature decreases with increasing salinity, the hydrocarbon and the surfactant concentration and composition remaining constant.

2.

For constant salinity and surfactant concentration phase inversion temperature increases with increasing equivalent alkane carbon number.

3.

The phase inversion temperature increases with ethylene oxide content of the surfactant, salinity and hydrocarbon remaining constant.

4.

The phase inversion temperature decreases with increasing lipophilic alcohol content of the systems.

5.

Static adsorption tests on reservoir rock show Langmuir adsorption isotherms.

Introduction London Research Station, the corporate laboratory of British Gas became involved in enhanced oil recovery after an invitation by the Department of Energy to take part in its research programme coordinated by A.E.E. Winfrith. After a review of information available to us on the reservoirs operated by British Gas Corporation

64

we decided that our resources would be most usefully employed studying micellar/polymer and miscible flooding. This paper describes the work we have performed so far to identify commercially available surfactants with interfacial tensions-lowering properties to suit the conditions prevailing in our reservoirs, and to assess their sensitivity to changes in reservoir variables, lack of sensitivity being a desirable (but attainable?) ideal. Measurements of phase inversion temperature (PIT), interfacial tensions and adsorption onto mineral surfaces have been made.

The Reservoir Conditions in the target reservoir are similar to those listed below: Oil type E.A.C.N.

7-a 10 43oc

(Reservoir) (Stock tank)

Temperature Formation water

90,000 mgNaCl/litre 1,300 mgCa/litre 500 mgMg/litre 30,000 mgNaCl/litre 400 mgCa/litre 1,200 mgMg/litre

Flood water (sea water)

Chemicals Surfactants. AG

.

Samples of the surfactants listed below were obtained from Hoeschst

Anionics: Hostapal" BV., an alkylaryl polyglycol ether sulphate

- Na

salt.

( 7 ethylene oxide (e.oJunits, 50% w/w active).

Surfactant A straight chain alkyl phenol ether acetate, 4 ethylene oxide units.

.

Surfactant B

Non ionics: units ) TlOO" "

.

1.

6 ethylene oxide units.

Sapogenate* T80 tri-butyl phenylpolyglycol ether(8 ethyleae oxide "(10 ethylene oxide units.) T110

'*

T130

'*

"

.- (11

ethylene

(13

ethylene

oxide units.) '*

oxide units.) Arkopal* NO60 Nonyl phenylpolyglycol ether (All 100% active).

(6 ethylene oxide units.)

Hydrocarbons used in this work were specified to be greater than 99% pure.

*

Hostapal, Sapogenate and Arkopal are trade marks of Hoechst AG.

65

Phase Inversion Temperature The phase inversion temperature, PIT, of a hydrocarbon/brine/ surfactant system indicates the existence of a minimum interfacial tension at that temperature. Since the lowering of interfacial tension is a requirement for the mobilisation of oil trapped in constricted capillaries and all oil reservoirs are essentially isothermal, PIT represents a useful parameter for the selection of surfactant for a given reservoir. For nonionic surfactants below the PIT the surfactant partitions preferentially into the aqueous phase and the emulsion formed between the two phases is predominately 'oil-in-water'. Above the PIT, it partitions mainly into the oleic phase and forms a 'water-in-oil' emulsion (Balzer and Kosswig,l979). Balzer and Kosswig (1979) have carried out some parametric studies of PIT with a range of anionic carboxy methylated nonyl phenol ethyoxylate surfactants. They found: 1. PIT increases with increasing equivalent alkane carbon number (EACN) of the oil and that aromatic hydrocarbons show very low values of EACN. Mixtures of aromatic compounds and alkanes give intermediate PITS. 2.

PIT increases with decreasing salinity.

3. PIT increases with increasing number of ethylene oxide groups in ethoxylated surfactants

We have extended this work to nonionic surfactants in studying the following variables on PIT. The effects of these variables must be considered if a surfactant flood is to maintain its oil mobilising properties as it passes through the reservoir. The parameters studied in this work are: 1. 2. 3.

4. 5. 6.

Oil type expressed as EACN. Surfactant type and concentration Salinity Co-surfactant type and concentration Phase ratio Number of ethylene oxide units in surfactant molecule.

1. The EACN for a given reservoir oil should be constant. The EACN of our reservoir crude has been assessed from measured EACN 6f stock tank crude and calculated from a well stream analysis. 2. The concentration of surfactant at some point away from the injection well is likely to change because of adsorption onto the reservoir rock surfaces. Adsorption measurements are therefore important.

3. The salinity of the brine in contact with residual crude in a waterflooded reservoir may vary from pure injection water to pure formation water.

4.

Co-surfactant effectiveness may change with concentration and type.

5. Variable oil/brine ratios will occur in a reservoir as a flood proceeds. must be taken into account when performing laboratory tests.

This

6 . The hydrophilic/lipophylic balance of a surfactant will depend upon its ethylene oxide content,(Shinoda 1965). Commercial surfactants are usually assigned a nominal ethylene oxide content, but actually contain a distribution of e.0. chain lengths. If PIT is dependent upon the number of e.0. units, then selective adsorbtion by reservoir rock will change PIT.

66 Interfacial Tension It is necessary to augment the data obtained from PIT measurements. The inversion of emulsions occurs over a small temperature range. For this to occur with minimum energy an interfacial tension minimum is implied. A typical plot of I.F.T. against temperature is sketched in Fig.1.

IFT, 10-L dynes/cm t0-L

V t I

lo-&

I I

J

PIT

T°C

Measurements have been made to determine the way IFT changes with temperature. Methods Phase Inversion Temperature was determined by means of electrical conductivity measurements (Baker and Kosswig 1979). For an oil-in- water emulsion with a non-ionic surfactant initially below the PIT the conductivity slowly increased with temperature but fell rapidly as the emulsions inverts and the aqueous phase became discontinuous and therefore non-conducting. Figure 2 shows a typical curve. More than one 'minimum' may occur for impure surfactants.

:tivity

T°C

Temperature

4'

(I

$ 4

*I

Figure 2 Adsorption The investigation consisted of a series of experiments to measure A, the adsorptive capacity of the reservoir rock for surfactant material. The method used was based on that of Somasundaran & Hannah (1979). The method of analysis for surface-active material was the titration procedure of Reid et al., (1967). Interfacial Tension Measurements were made at ambient pressure with the University of Texas spinning drop tensiometer.

67 TESTS, RESULTS AND DISCUSSION

Variation of PIT with EACN and determination of EACN value of the p h e n y u cyclohexyl groups.

1.

PITS were determined on the following mixtures at the phase ratios stated (brine/oil).

Brine

Hydrocarbons

10

Seawater

A+B

5 of each

T80

10

Surfactant

Concentration /litre

Phase Ratio brine/oil

Results

n-alkanes C7-C10

5: 1

Fig 3 line A

Seawater

n-heptane-toluene mixtures EACN 4 to 7

5:l

Fig 3 line B

Seawater

N-alkanes c6 to cll methylcyclohexane

5:l

~

A

T80

Fig 4 line A Fig 4 line B

As above after storage for 3 months at room temperature

T80

10

T80

50

30g /NaClI n-alkanes litre cg-cl1 11

**

1.

4: 1

Fig 5 line A Fig 5 line B

I.

TlOO

Fig 5 line C

TlOO

Fig 5 line D

TlOO

50

. . . I,

*.

.

butyl cyclohexane

4:l

Table 1

phenyl heptane

Table 1

phenyl octane

Table 1

Results and Discussion The results presented in Figs 3 to 5 show a linear relationship between EACN and PIT over the EACN range studied.

68

3

4

5

7

6

9

8

10 EACN

Figure 3: Variation of PIT with EACN for two different surfactant solutions.

PIT "C

70

60 50 40

30 20

I

I

4

I

I

I

I

6

5

7

I

I

8

9

I

I

1 0 1 1

12 EACN

Figure 4 :

Variation of PIT with EACN for log /1 Sapogenate T80 in seawater.

PIT "C

70

Line D

60 50 40

Line A

30 20 6

7

8

9

10

11

12

EACN Figure 5:

Variation of PIT with EACN; pure n-alkanes, 30 g /litre NaCl

69 The EACN of butyl cyclohexane was determined relative to the Fig 5 line B and line C, phenyl heptane and phenyl octane were determined relative to Fig 5 line C. The values found are listed in Table 1. TABLE I EACN found

Assigned EACN of ring

butylcyclohexane

6.5 (Fig 5 Line C) 6.75 fig 5 line B

phenyl heptane

5.0("

phenyl octane

6.0("

'.

")

"

")

-

2.6 -2.0 -2.0

Thus we are able to assign an EACN of 3.6 to methyl cyclohexane. This may enable us to dilute stocktank crude with hydrocarbons with rings to obtain mixtures of hydrocarbon at ambient pressures having EACNs more representative of reservoir crudes. A shift of PIT of 2 to 30C was observed on storage at room temperature for 3 months of the stock 50 gms TlO/litre solution from which line B fig 4 was obtained. No further change was observed on storage for a further 5 months, nor on a freshly prepared solution stored at 40OC for 3 weeks. At the higher concentration of T80 the dependance of PIT on EACN is reduced. affect is not as marked in the case of T100.

The

The difference in slopes shown between lines A and B, Fig 3 suggest the possibility of modifying the sensitivity of a system to change in temperature by the addition of another surfactant. Differential adsorption within a reservoir could cause problems in practice. PIT can change rapidly with EACN. Rates of change of PIT of up to 140C/EACN unit (line B Fig 3) are possible and the slope can change with surfactant concentration. Rates of change of PIT as low as 30C/EACN unit are possible (line A Fig 3).

2.

Variation of PIT with surfactant concentration

Tests

h e effect of increasing surfactant concentration was studied on the following mixtures.

Surfactant T80 T80 TlOO TlOO

Concentration 8 hitre Various 10 to 70

Brine g

Hydrocarbon

NaC111 30

Phase ratio brineloil

Results

heptane

4:1

Fig 6 Curve 1A

I.

*I

octane

4:1

Fig 6 Curve 1B

.*

I.

heptane

4:l

Fig 6 Curve 2A

I,

.I

octane

4:l

Fig 6 Curve 2B

I0

Results and Discussion The results are shown in Fig 6 . Both surfactants exhibit a non-linear relationship, with PIT increasing with decreasing surfactant concentration. This The rate of change of is in agreement with the work of Shinoda and Arai (1964). PIT is lower at high surfactant concentrations which indicates that a high concentration flood could be less susceptible to concentration changes.

PIT *C

60

50

40

30

20

I

'

16

o i

Figure 6:

3.

40 4b o;'

Qo 7 b ad Surfactant concentration, g /litre

Variation of PIT with concentration of Sapogenate T80 and T100.

Variation of PIT with Salinity Tests -

PIT'S were determined on the following mixtures.

Surfactant

Concentration g /litre

Brine

Hydrocarbon

Phase ratio brine/oil

Results

5:l

Fig 7 line A

hexane

4:l

Fig 7 line B

10

heptane

4:l

Fig 7 line C

10

octane

4:l

Fig 7

Ta0

10

T80

10

Ta0 T80

NaCl only Stock Tank (various Crude EACN 10 concentrations)

line D

71 Results and discussion For all hydrocarbons tested, the rate of change of The results are shown in Fig 7. PIT with salinity is independent of the hydrocarbon used. The decrease in PIT with increasing salinity is to be expected as the surfactant partitions more readily into the oleic phase as salinity increases (Knickerbocker et al, 1979).

60

.

50

-

40

-

PIT OC

\

Line A

30

2o

1 10

20

30 40

50

60

70

80

90

Brine concentration, NaCl/litre. Figure 7:,,Variation of PIT with brine salinity; 10 g /litre Sapogenate T80 solution.

g

4.

Variation of PIT with Alcohol (Cosurfactant) type and concentration

Tests -

Measurements were made on 50 g T100flitre brine. Brine concentration was 30 g /NaCl/litre and oil EACN 7.5 at a phase ratio of 4 : l . Alcohols studied were: (a)' iso-butanol (lipophilic) (b) is0 pentanol( " 1 (c) isopropanol (hydrophilic)

Results and discussion. The results shown in Fig 8 agree with trends predicted in the literature, (Knickerbocker et al, 1979), in that increasing the concentration of a lipophilic alcohol (lines A and B) will increase the partitioning of the surfactant into the oleic phase and tend to lower the PIT. The hydrophilic alcohol (line C) has the opposite affect but less pronounced. Increasing the concentration of hydrophilic alcohols has the opposite effect on PIT as increasing surfactant concentration. If an alcohol has to be used as a viscosity modifier then hydrophilic alcohols may be more manageable with respect to their effect on PIT than lipophilic alcohols.

72 PIT OC

60 50 g 30 g EACN

50

/litre Sapogenate TlOO /litre NaCl 7.5

40

30

10

20

40

30

50

Alcohol concentration, g /litre. Figure 8: Variation of PIT with alcohol concentration

5.

Variation of PIT with brine/oil phase ratio

Tests PITs were measured on the following mixtures to find out if PIT varied with phase ratio. Surfactant T80

50 g

/litre

T80

10 g

/litre

T80

.

T80

Brine

Concentration

I.

I.

.

. .

Hydrocarbon

Results

n heptane

Fig 9 line A

n hexane

Fig 9 line B

"

n heptane

Fig 9 line C

**

n octane

Fig. 9 line D

30 g Nacl /litre "

"

*.

"

*.

. .

Results and Discussions The possibility that PIT would depend upon phase ratio was indicated when PITs obtained from the measurements in the spinning drop tensiometer did not correspond exactly to those made by the conductivity measurements. The results show that PIT increases as the proportion of oleic phase increases. This is contrary to the findings of Balzer and Kosswig (1979) who reported smaller changes with the opposite slope. Arai (1965) reports the same effect as Balzer and Kosswig (op.cit.)

73

Line D '

PIT

60

Line C Line B

"C

50

40

Line A 30 20 10

20

30

40

50

Volume I hydrocarbon Figure 9: Variation of PIT with phase ratio.

6.

Variation of PIT with Ethylene Oxide (eo) content of surfactant

Tests

-

PITS were measured using a mixture of pure normal ,alkanes,EACN 7.5 with 30 g NaCl/litre brine containing 50 g of surfactant/litre. The surfactants used were Sapogenate T80,TlOO,T110 and T130 which contain (nominally) 8, 10, 11 and 13 ethylene oxide units respectively. Intermediate eo contents were obtained from mixtures of the adjacent surfactants as supplied and were calculated on a molar basis.

Results and Discussion

-

The results presented in Fig 10 show a linear relationship between PIT and the number of eo units per molecule. The deviation from linearity above eo 11 is probably due to evaporation of the hydrocarbon during the test. The change The findings are in agreement with those of Bourell et a1,(1980). in PIT is explained by the increased hydrophilic properties with increased eo content (Shinoda, 1965). The Arkopal series of surfactants probably exhibits a similar trend but only These gave PITS of two have been tried i.e. NO60 ( 6 eo's) and N080(8 eo's). about 30C and 70-75OC respectively at a concentration of 50 g /litre in the same brine/hydrocarbon system. The effect of the number of eo units is greater with the Arkopal series than the Sapogenates. Where a surfactant contains a spectrum of eo contents, selective adsorption by the reservoir rock may change its effective eo value and thus affect the PIT of the system.

74

PIT "C.

tion = 50 g

-

7.5

'Surfactant ethylene oxide number. Figure 10:

7.

Variation of PIT with surfactant ethylene oxide number

Variation of IFT with temperature

Tests Interfacial tension measurements were made between the upper and lower phases obtained from mixtures whose PIT'S had been determined in an attempt to confirm the presence of an IFT minimum at fhe PIT. Tests were performed with the following mixtures. ~~~

Concentration

Brine

T80

10 g /litre

T80

.

30 gm NAClf litre

Surfactants

NO60

1.

. .

I.

1.

*.

.

I.

*I

Hydrocarbons Phase ratio

PIT

Results Fig 11

n hexane

4: 1

39

**

n octane

4: 1

49.5

Fig 12

*'

Crude EACN =10 '

5: 1

23.5

Fig 13

Results and Discussion The results obtained are shown in Figs 11 to 13. The PITS obtained from conductivity measurements are included in the above table. Repeat determinations of 1.F.T. were usually found to agree within 2 5%. Figs 11 and 12 indicate that a minimum does occur at the PIT but that more than one 'minimum' can occur. This is supported by conductivity traces made during PIT measurements and is probably due to a proportion of surfactant having a different number of eo units than the stated nominal value. The equipment available only allowed for the transfer of phases into the tensiometer at room temperature. Measurements were made at various temperatures after heating

75

Oil : n-hexane Brine : 30g /litre NaCl Surfactant : Sapogenate T80, 1Og /litre

dynes/cm

30

34

38

42

46

Temperature, 'c Figure 11: Variation of IFT with temperature.

Oil : n-octane Brine : 30 g /litre NaCl Surfactant : Sapogenate T80,log /litre.

38

42

46

50

54

Temperature OC Figure 12:

Variation of IFT with temperature.

from room temperature. As one increases the temperature of the sample tube a third phase (microemulsion) begins to develop as the equilibrium is disturbed. In order to make meaningful measurements the middle phase is separated from the remaining oil drop. This was achieved with some difficulty especially in the case of colourless oils. Ideally, equilbratlon, sampling and measurements should be carried out at the same temperature.

16

d y n e s ; : 10-2

1

Oil : Dead crude Brine : 30 g /litre NaCl Surfactant : Arkopal N 6 0 , l O g /litre

J

lo-?

10-4

15

Figure 13:

20

25

30

Temperature ,OC Variation of IFT with temperature

Adsorption of Surfactants Tests This section describes the results obtained for adsorption of Hostapal BV on reservoir material in various states of disaggregation. Although work on Hostapal BV was terminated, (because optimal salinity falls outside the range of our interest), the results showed some of the-limitationsof static adsorption tests. Samples of reservoir rock were taken from cores and crushed in a ball mill 2 5 g of sample were taken and until the powder passed 180 sieve. equilibrated with 50 cm3 o various concentrations of Hostapal BV in The suspension was stirred constantly for 4 distilled water or sea-water. hours 40OC. The aqueous portion ws then decanted and centrifuged for 30 minutes, by which time, the supernatant liquid was clear. Analysis of this Hence the liquid then gave the remaining concentration of Hostapal BV. amount abstracted by the solids was calculated.

r

soo51 I

AdsorDtive

Adsorptive capacity,A

e o o 5 1

0.5 1 .o 0.5 1.0 Equilibrium concn., c,g / I Equilibrium concn,c,g /1 Figure 1 4 : Adsorption of Hostapal BV Figure 15: Adsorption of Hostapal BV Onto reservoir rock, Sample 1. onto reservoir rock,Sample 2.

Results and Discussion The tests performed are listed below and the results presented in Figs 14 to 18. Table 2 shows a typical sets of results. er a ."

water

0.5 1 .o Equilibrium concn., c,gr /I. Figure 16:

Adsorption of Hostapal BV onto reservoir rock,Sample 3.

TABLE 2 (SAMPLE 3) Initial surfactant concentration g /litre

Final (equilibrium) surfactant concentration,C g /litre

Adsorptive capacity A, g surfactantlg rock

0.25

0.0078

0.00048

0.50

0.033

0.00092

1.0

0.098

0.0018

1.75

0.164

0.0033

2.0

0.184

0.0036

2.5

0.193

0.0046

3.3

0.352

0.0059

5.0

0.957

0.0080

18

Adsorptive capacity A, g lg

.003

I

i

0.5

Figure 17:

-4

I

1 .o Equilibrium concn., c, g 11

Adsorption of Hostapal BV onto reservoir rock, sample 4.

-

1nA

-5

-

-6

-

-7

-

1

I

I

I

In c Figure 18:

Data from Figure 16 plotted logarithmically

79

All the figures show the tendency for A to tend towards a constant for a given Portions of Sample 3 (Fig 16) sample as the equilibrium concentration increases. were also equilibrated with the surfactant in seawater and the results appear to Sample 3 has similar permeability and show a much higher adsorptive capacity. porosity characteristics to the other samples. The curves have the same general form as the classical adsorption isotherms. A= adsorptive capacity A = Kc where c= final concentration K and n are constants or In A = In K + In C The data in Table 2 (sample 3 ) are plotted as In A against In C in Fig 18. There are indications in Fig 1 4 and 15 that adsorption may be proceeding in layers. A qualitative test of the effect of particle size on the equilibrium adsorption of surfactant was performed in a similar manner to those described above. The results obtained are shown in Table 3. Table 3 A g lg

<180~ 'fine powder 'coarse grains' cm size pieces

0.0036 0.0028 0.0022 0.0002

This would appear to limit the usefulness of static adsorption and calculation of a 'worst case' total adsorption capacity of a reservoir. More useful data would be obtained from core flood experiments.

CONCLUSIONS Phase inversion temperature can serve as a guide to the conditions under which a non ionic surfactant will give an interfacial tension minimum. Using the linear relationship between EACN and PIT it is possible to assign an EACN to; stock tanks crudes, and aliphatic and aliphatic cyclic hydrocarbons. It should then be possible to use cyclic hydrocarbons to lower the EACN of stock tank crude to that of reservoir crude for use in partitioning and phase studies at ambient pressure. If the way in which the parameters which affect surfactant properties change during the course of a flood can be assessed it should be possible to design a flood which will maintain it's properties. This, however, requires detailed knowledge of the reservoir.

Acknowledgements We would like to thank the British Gas Corporation for their permission to publish this paper.

80

BIBLIOGRAPHY Balzar, D, and Kosswig, K.; The phase inversion temperature as a criterion for the selection of survace active agents in the tertiary production of mineral oil. Tenside Det.

16 (1979),

5, pp 256-261.

Shinoda, K.; The comparison between the PIT system and the HLB value system to emulsifier selection.

-

Comptes rendus du 5 eme Congress International de la Detergence, Barcelona, (1965), pp 275-283. Somasundaran, P. and Hannah, reservoir rocks.

S.;

Adsorption of sulphonates on

SOC. Pet. Eng. Jour. August 979, pp 221-232. Reid, V.W., Longman, G.F. and Heinerth, E.; Determinaton of anionic active detergents by two-phase titration. Tenside Det.

4

(1967), pp 292-304.

Shinoda, K. and Arai, M. The correlation between phase inversion temperature in emulsion and clould point in solution of nonionic emulsifier. Jour. Phys. Chem.

68

(1964), 12, pp 3485-3490.

Knickerbocker, B.M., Pesheck, C.V., Scriven, L.E. and Davis, H.T. Phase behaviour of alcohol-hydrocarbon-brine mixtures.

Bourrel, M., Salager, J.L., Schechter, R.S. and Wade, W.H. correlation for phase behaviour of nonionic surfactants. Jour.Colloid Interface Sci.

(1980), 2, pp 451-461.

A

CHEMICAL FLOODING

81

THE PROVISION OF LABORATORY DATA FOR EOR SIMULATION C. E. BROWN and G. 0. LANGLEY Petroleum Engineering Branch, Exploration and Production Division, BP Research Centre, Sunburyen-names

Abstract Laboratory core tests are important in the development and assessment of EOR processes. It is vital that the core data obtained characterise the physical processes relevant to the field, and are appropriate to their use in field simulators. The key parameter of relative permeability is discussed, and its extension to low tension immiscible displacement assessed. The current status of these concepts is discussed with reference to oil slug propagation along a core.

1.

Introduction

Our overall aim is to obtain data from laboratory tests on core samples, to use these data for the prediction and analysis of field trial performance, and ultimately for the prediction of full field performance. There are many problems on the way from core tests to reservoir performance prediction, one of the biggest being reservoir description and identification of reservoir heterogeneity. In this paper we will limit our discussions to the topic of laboratory core data, and how this may be used to examine the physical processes involved in oil recovery. We will work bn the principal that if successful6,efficient displacement cannot be obtained from a core sample, then there will be little chance of obtaining success on the field scale. We will consider the theoretical aspects associated with oil bank propagation, and how the predictions are affected by the relative permeability input data. A brief discussion of methods of assessing potentially useful surfactant systems and possible artifacts associated with core tests on the laboratory scale is included. In this paper we will discuss low tension, immiscible floods only. Miscible flooding will not be considered. 2.

Laboratory core waterflood tests

Before considering low tension flooding, we will review the more conventional waterflood case, since this often forms the basis for enhanced oil recovery methods. Waterflood tests on core samples can be used to gain information on the efficiency of displacement of oil by water from actual reservoir rock. Laboratory displacement tests are usually confined to one dimension.

82

For stron&ywater-wet rocks the efficiency of displacement is good in the sense that the displacement appears piston-like; practically all of the oil is recovered before breakthrough of the flooding water. However, residual oil is trapped behind the waterflood front as insular globules of oil usually occupying the larger pore spaces (1). This residual oil level is dependent on the initial oil saturation; the relationship being influenced by pore structure. The scope for tertiary oil recovery may be high in this case. For strongly oil-wet rock the displacement does not appear to be efficient. Early breakthrough of water often occurs, and large amounts of oil are recovered after water breakthrough, at high fractional flow of water. Residual oil is less well defined in that oil is by-passed rather than trapped and occupies smaller pores and surface grooves. However, oil may continue to be produced until very low oil saturation is obtained ( 2 ) . The scope for tertiary oil recovery may be' low in this case. The contrast in the oil-wet and water-wet case is shown in Figure 1.

FIG. 1

I n order to predict waterflood performance, it would be convenient to generate a data set which could be used for the prediction of flood performance and which is a unique property of the rock.. The concept of relative permeability was introduced to fulfil this role, which has now become central to conventional numerical simulation of oil recovery processes.

3.

Relative Permeability

The basic concept of relative permeability is limited to movement of t w o o r m o r e continuous phases in the same direction through porous media at a steady saturation level. It assumes that it is valid to extend the Darcy equation for single phase f l o w to the multiphase case.

83

The concept is most likely to hold in the case of a sample which has initially 100% saturation of the wetting phase and where the saturation of the non-wetting phase is increasing. Relative permeability data can be generated either by a steady-state method (where both phases are injected simultaneously into the core sample and permeability measurements are made at a steady-state fractional flow), or by analysing flood data (e.g. using the Johnson, Bossler method (3) based on the Buckley-Leverett theory (4)). Some validation of the relative permeability concept comes in two ways:

1)

The steady-state and flood derived data are similar

2)

Data produced fr6m floods using different viscosity ratios give data which lie on the same curve, even though the recovery performance may be significantly different.

Figure 2 shows typical relative permeability curves for an oil flood of a water-wet rock. It is noted from Figure 2 that the relative permeability to oil increases quite rapidly, and that to water drops rapidly. The sum of the relative permeabilities througbuttheir range is very much less than unity indicating interference between the phases.

so

3.1

sw

Waterflooding - the oil-wet case

Parallel arguments apply to a waterflood of an oil-wet rock. Figure 3 shows typical relative permeability curves for the oil-wet case. Provided that capillary dispersion and end-effect problems are not involved, the waterflood performance (and hence the relative permeability obtained from waterflood data), does not appear to depend on flood rate ( 5 ) . Moreover, provided that the phases remain continuous and immiscible then, in concept, the relative permeabilities should not depend on interfacial tension.

a4

It is often suggested that the relative permeability curves will change shape as the interfacial tension is lowered, tending towards straight lines where the sum of the relative permeabilities is unity at all saturations ( 6 ) . This view often results from the study of miscible or partially miscible displacement tests where diffusion processes act to distribute the fluid components equally over the pore structure of the rock. Diffusion processes have the effect of improving the displacement efficiency. Theoretically, the flood efficiency can be improved by straightening the oil relative permeability curve to reduce the rate of change of fractional flow of water. The resulting relative permeability curves for these miscible displacements are pseudo-functions with little predictive capacity. Steady-state tests using miscible systems are likely to produce straight line relative permeability data since a mixture of the components slows in all conductive flow channels. As mentioned earlier, an alternative viewpoint for immiscible systems is that the oil drainage relative permeability curves will not change as interfacial tension is reduced. This would require that the oil recovery performance is independent of interfacial tension. Support for this view comes from the fact that increasing the capillary number (VL/y) has little effect (assuming constant viscosities) on recovery performance, provided that capillary dispersion and end-effects are negligible ( 5 ) . In addition, for oil-wet systems residual oil saturation is not a well defined quantity; in any case it is very low, provided that enough water has passed through the rock, and that endeffects are negligible. Reduction of interfacial tension will therefore have little effect on residual oil. The conceptual reasoning for the argument that relative permeability does not change as the capillary number increases is that the displacing fluid will preferentially occupy pore channels with higher flow capacity, irrespective of interfacial tension. More experimental work is neede& before definite conclusions can be drawn as to which relative permeability behaviour is relevant to low tension immiscible displacement.

3.2

Waterflooding - the water-wet case

For the case of waterflooding of a water-wet rock, the basic concepts of relative permeability are not strictly adhered t o ; principally because the non-wetting oil phase does not remain in communication. As mentioned earlier, the recovery performance of a waterflood on a water-wet core usually appears piston-like. Therefore no relative permeability data can be generated using conventional analysis of the flood performance, apart from end-point data. Relative permeability curves can be generated from steady-state tests, but the data can vary depending on the test method. A common method is to change the fractional flow in steps which results in a saturation front travelling down the sample. Perhaps a true steadystate test should avoid such saturation gradients in the core sample. This situation can be approached by gradually changing the fractional flow over a long period of time. Possible shapes of the relative permeability curves are shown in Figure 4. The residual oil values obtained by the two steady-state methods are not necessarily the same, and might not agree with that obtained from a flood.

85 The shape of the relative permeability curves may be considered to be academic in the water-wet case, since both sets of relative permeability curves shown in Figure 4 will probably predict plug displacement if the Buckley-Leverett theory is used. However, there may be differences of predicted flood performance when using coarse grid finite difference numerical models, but this is an artifact of the model and is usually overcome by empirically altering curves of type 1 to be more like type 2 . The truth of the matter is that we do not have a satisfactory theory to combine viscous and capillary flow effects, and we usually resort to some form of pseudo functions to match observation. The residual oil saturation obtained after a waterflood is a definite value, in that oil flow completely ceases (unlike the oil-wet case). The residual oil level is dependent on initial oil saturation and on flood rate. The distribution of residual oil is also dependent on flood rate (1). In addition, high flood rate can make a weakly ' water-wet rock appear oil-wet (7,8). It is noted from Figure 4 that the relative permeability to water at residual oil saturation is low, indicating that trapped oil occupies the largest pore channels. From the point of view of a field flood, this can be advantageous since water mobility following the flood front is kept low, thus suppressing viscous fingering on the reservoir scale. 1.0

FIG. 5

krw sw The residual oil saturation is also dependent on interfacial tension. The absence of imbibition in the case of very low interfacial tension can also make a water-wet sample look oil-wet. Considering the changes to the water-wet relative permeability curves as the interfacial tension is lowered, it is to be expected that significant changes will occur. Data obtained by the steady-state method (9) indicate that below an interfacial tension of 0.1 mN/m large changes in the water-wet curves occur. The tendancy is for the relative permeability curves to become straight lines, the sum of the relative permeabilities approaching unity at all saturations. As the interfacial tension is lowered during steady-state tests it is more likely that an emulsion of oil-in-water or water-in-oil will form.

86 As the interfacial tension decreases to very low levels the drop size is likely to become extremely small. A situation will be approached where the same fluid system is flowing in all conductive flow channels. In this situation straight line relative permeability data might be expected, although the basic concepts of relative permeability in fact no longer apply. Relative permeability data obtained from displacement tests have shown somewhat different results ( 9 ) . As the interfacial tension was lowered the relative permeability to water increased and that to oil decreased. At low interfacial tension (0.01 mN/m) the relative permeability curves resembled oil-wet data. This supports the proposal that oil drainage curves could be used as a first approximation for the back end of an oil bank even for a water-wet rock. Curves of residual oil saturation versus V/y viscosity) can be generated by two methods:

(for constant

i) Where each flood starts from the same initial oil saturation (curve A, Figure 5 ) . ii) Having established a residual oil saturation at low values of V/y we can increase V/y by increasing V or decreasing The residual oil saturation will eventually decrease y. as trapped oil is mobilised (curve B , Figure 5).

4.

Application of laboratory data to enhanced recovery prediction

Reduction of residual oil saturation is. a necessary but not sufficient condition for a successful tertiary recovery flood. It may be essential to develop and maintain an oil bank. Once an oil bank is developed, it is the mobilised oil which collects and mobilises residual oil at the front of an oil bank. Surfactant at the back of the bank prevents retrapping of the oil. We need to consider generation of secondary drainage relative permeability data, starting from the residual oil saturation left after primary imbibition, for application at the leading edge of the oil bank. Curves of the type shown in Figure 6 can be generated from steady-state tests. It has been suggested that the secondary drainage curves retrace the primary imbibition curves (10, 11, 12) but this needs confirmation, since it will depend on how the primary imbibition curves were obtained. Prediction of oil flood performance obtained using steady-state relative permeability data can be compared to oil flood data starting from residual oil saturation after the primary waterflood. If we work on the principal that the interfacial tension at the back end of the oil slug is low enough to prevent retrapping of oil, then as suggested earlier we might use oil-wet type relative permeability curves to describe fractional flow at the back end of the bank. The relative permeability set would then look like those shown in Figure 7. Theoretical predictions using this type of data will be discussed in the next section. Although many people have looked at the problem of generating relevant relative permeability data for low tension floods (13 - 21), there is still a need to obtain more data to clarify the position.

a7

FIG. 6

sw

AT WATER BREAKT!lROUGH

FIG. 9

Water Arrival

88

5.

OIL BANK PROPAGATION

In EOR processes the development and propagation of an oil bank is considered to be of importance; certainly the correct analysis of such phenomena is crucial to core testing. For highly complex EOR systems, analysis can only be carried out on the basis of assumptions which are difficult to validate, unless simplified systems can be studied. Curiously little work has been reported which attempts to do thin A recent paper by Gladfelter and Gupta ( 2 2 ) is valuable, in that it sets some experimental evidence against which current views of oil bank propagation may be weighed. One of the key findings is that a region of increased oil saturation (an oil bank) can be generated from the fractional flow properties, without invoking other mechanisms. The additional feature proposed to explain this behaviour was hysteresis of the relative permeability curves. The following outlines some features of oil bank propagation in two component, two phase (oil/water) displacement in cores as given by 1-D numerical simulation. This can be compared with the experimental results and Buckley-Leverett analysis of Gladfelteqand Gupta The test system simulated consists of a 45 cm core, divided (22). into forty grid blocks, with an oil/water ratio of 3:l. For each simulation run, a 0.0475 pore volume slug of oil was injected at high rate into the core, which was initially set at residual oil saturation. The relative permeability hysteresis set first used was as shown as curves A and B in Figure lO(a), with the arrows indicating which limb corresponds to which directional change in water saturation. The corresponding fractional flow curves are shown in Figure 10(b). The corresponding oil slug behaviour as simulated is shown in Figure ll(a), showing a series of oil bank profiles as it progresses along the core. The front of the oil bank progresses with a well defined front, but the size of the bank degrades as oil is 'lost' into the following tail. Use of the same relative permeability set, but with the hysteresis directions reversed gives the behaviour shown in Figure ll(b); in this the oil bank is not recognisably propagated since it is quickly dispersed. This result highlights the sensitivity of oil bank propagation behaviour to the relative permeability curves. They also show that numerical dispersion is not dominant in the present examples. Following the procedure of Gladfelter and Gupta ( 2 2 ) , injection of an oil and water mixture (in the present case, 25% oil) into a core at residual oil saturation gave the results depicted in Figure ll(c); a sharp oil front is formed, but without the presence of a bank of increased oil saturation as-experimentally observed. This result is as expected, since the numerical model moves incrementally up the relative permeability curves to the imposed injection composition; it cannot overshoot this point, as can be achieved with Rankine-Hugoniot shock front criteria as employed in a simple fractional flow analysis. However, the principal of an oil bank stabilised by relative permeability hysteresis can be demonstrated by simulating injection of an oil bank followed by injection of an oil/water mixture. This is shown in Figure ll(d). The importance of an oil bank induced by hysteresis effects extends not only to the valid identification of "enhancedt1oil, but also to the correct assignment of water-increasing or water-decreasing steady-state relative permeabilities; i.e. the presence of a transient bank may in fact involve changes in the direction reverse to that overall.

89

fw

0.3

- --

0,s c

(x/L)

1.0

90

91 More drastic disparity between the relative permeability curves used at the leading and trailing fronts of an oil bank can of course give stabilised bank propagation without an oil/water mixture being subsequently injected. Figure ll(e) shows this, using curves A and C of Figure lO(a). The straightening of curve A to give curve C follows the commonly assumed functional change in the relative permeability curve induced by reducing the interfacial tension. However, experimental verification of the relative permeability behaviour in eor systems is still limited, and the assumed curves may not offer a good description of the physical processes involved. If the immiscible displacement of oil by surfactant acts as a high rate water flood as suggested earlier (since in both cases capillary forces are dominated by viscous forces) the aqueous phase will preferentially travel through the larger pore channels. This could result in a relative permeability behaviour as shown in Figure 7, with an increased krw, but with a kro curve falling below the prior curve at high oil saturations, i.e. the low tension flood does not have the imbibition which in a water-flood case ensures the oleic phase preferentially occupies the larger pores of a water-wet medium. The simulation results for this case (Fig. ll(f)) once more show degradation of an injected oil slug. These simulation runs indicate the need to take proper account of relative permeability variations in the analysis and simulation of transient processes, and show that under certain conditions oil bank propagation will not occur. The use of assumed Ilideal" relative permeability data (i.e. straight line extrapolations) may artificially predict stable bank propagation.

6.

IRREVERSIBILITY AND HYSTERESIS IN CORE TESTS

In this section some modelling approaches to describe non-identity are outlined. Core tests can display a wide range of irreversible characteristics. Jones and Rozelle (23) consider that irreversibility results from the common "S" shaped fractional flow curve if the conventional tangent constructions are applied to waterflooding and oil flood respectively. However, in considering the Buckley-Leverett theory, it can be noted that two solutions to the problem are to be expected, since the material balance may be applied for either the waterflood or the oilflooding directions. The conclusion that the direction appropriate to the particular stage of an EOR process must be used still holds. A more fundamental problem is whether the fractional flow curve itself is a unique function of saturation.

6.

RELATIVE PERMEABILITY HYSTERESIS

6.1

Primary Hysteresis

The best documented tlhysteresisl' effects in relative permeability curves are associated with the irreversibility of the primary curves i.e. those curves which originate at initial conditions of complete saturation by a single phase. This hysteresis gives rise to residual (or irreducible) phase saturations. It is commonly assumed that essentially irreducible saturations can be established for both

92 wetting and non-wetting phases, although the distribution and properties of these phases are by definition functions of wettability. Thus it is usual to treat wetting and non-wetting phases asymmetrically. The irreducible water saturation and the residual oil saturation values are expected to be dependent on the initial saturation established prior to reduction to residual. For strongly wetting phases, the residual saturation tends to be ill-defined, so this effect is of little consequence. For the non-wetting phase, Land (12) has proposed a semiempirical relationship which correlates initial and residual non-wetting phase saturations; the Land relationship (taking water to be the wetting phase and oil the non-wetting phase) is

+

-1

(Sor)

+

where

-

+

Sor

=

Sor/(l- swi)

swi

=

Soi/(l- Swi)

+

-1

(Swi)

=

c

(1)

with C being a constant for a given system. Equations of this form have been used by Killough (24) to estimate hysteresis sets descending from the primary non-wetting relative permeability curve.

6.2

Secondary Hysteresis

The term secondary refers to those curves which start from the end points of the primary curves. This region is (in principle) fully accessible reversibly, that is in the saturation range Sw = Swi to (1-Sor). In fact, it is only within a reversible range that the term hysteresis can be truly applied. The characterisation of any hysteretic system can prove complex, and for relative permeability curves the lack of experimental precision and the probable dependence of data on experimental design (25) have so far prevented detailed analysis. In the absence of a scientific approach, empirical relationships are generally developed on the basis of plausibility and utility. It may be questioned whether the initial formulation of the multiphase flow relationships in the empirical Darcy-analogue form itself ensures that all subsequent analysis can be no more than empirical. A currently favoured parameterisation of relative permeability curves uses a scaled power law relationship;

kro

=

kro(Swi)*(S;)"o

krw

=

krw(Sor)*(S;)"w

So

=

(l-Sor-Sw)/(l-Swi-Sor)

* sw

=

(Sw-Swi)/(l-Swi-Sor)

where

*

I

93 The secondary hysteresis can then be conveniently described by exponents, as used by Evrenos and Comer (26) variation of the with an alternative different parameterisation scheme. A hysteresis parameter can be defined as

and similarly for the water exponents, where the superscript arrows denote increasing and decreasing water saturation. It can be noted that dependent on the value of Hi the hysteresis scan can occur in either direction, both types of behaviour being reported from experimental observations. The variation of the relative permeability curves for an EOR process requires detailed description if a numerical simulation of the process is to be made. For surfactant flooding, the paramaterised relative permeability curves are often modified in a systematic manner dependent on the new value of residual oil saturation (Sorc). Following this procedure with the hysteresis parameter, it is to be expected that the hysteresis becomes less pronounced as the residual

Sor = 0 . 2

FIG. 12

94

oil saturation is decreased (since any conceptual model of the hysteresis mechanism centres on irreversibility following loss of hydraulic connectivity during phase trapping). Paralleling other dependencies on Sorc, a logarithmic relationship between Hi and Sorc can be used, or more simply a power law expression. ( Sorc 1 a 1 - Hi (Sorc) = (4) (1 1 - Hi ( Sor I

Two of a family of relative permeability curves using this relationship isshown in Figure 12, with the dependence of the no exponent on Sorc being 1 - no (Sorc)

-

1 - n

6.3

Sorc

-

(5)

Sor

Scanning Hysteresis

Conventional oil recovery processes are usually described in terms of monotonic changes of saturation. Enhanced oil recovery processes aimed at mobilisation of post waterflood residual oil necessitate changes in the forms of the relative permeability curves and in the directions in which a process description scans them. In order to estimate how scanning from intermediate points of the secondary bounding curves will progress in the absence of definitive experimental evidence, parallels can be sought in other hysteretic systems. The other hysteretic process which is well established in petroleum engineering experience is the capillary pressure as a function of saturation. Since the same physical processgives rise both to relative permeability 2nd to capillary pressure hysteresis, it is to be expected that mutually consistent descriptions should be possible. . In order to compare the two sets of phenomena, the relative permeabilities need to be expressed as a single variable, and the fractional flow can be considered to be a state variable which offers more hope of comparability with other hysteresis phenomena. The most direct consistency relationship between capillary pressure scans and fractional flow scans would be if one set were directly mapable onto the other. However, since the fractional flow setis rigorously bounded whereas the capillary pressure set is asymptotically bounded, this can at best be an approximation. In addition, the commonly made approximation is also present in the comparison of equilibrium capillary pressure values with dynamic systems. Attempts to correlate primary capillary pressure curves with fractional flow curves have not to date proven sufficiently satisfactory to enable mapping of scanning curves from capillary pressure to fractional flow data. A less direct appeal to consistency can be made by application of similar functional forms to describe both capillary pressure and fractional flow hysteresis sets. The most general theory available to describe hysteresis systems is Independent Domain Theory, as propounded by Everett (27). Unfortunately, the theory has not proved quantitatively applicable (due to the prime assumptions i.e. the existence of domains and their independence, Topp and Miller ( 2 9 ) ) , but does provide a qualitative framework in which empirical relationships can be set.

95

In recent years a number of studies have been carried out in which unsaturated flow in porous aedia has been analysed numerically using empirical analytic hysteresis functions. However, these studies have concentrated on liquid/vapour systems of interest to hydrologists rather than on liquid/liquid systems and the hysteresis relationship examined has been between the saturation and flow potential. Applying an analogue of the empirical hysteresis function as recently used by Pickens and Gillham (29) to the fractional flow/saturation system gives

fw fi

I

cosh(Sw/S1)a

- (fi

cosh(SJS')a

- (fi - f .)/(fi+f

- f.)/(fi+fj) J .)

I

(6) J where S', a, f., and f. are fitting parameters which can be identified from sufficied data. =

J

The functional form of this relationship can reproduce fractional flow curves, and scans within those curves which accord with the expected hysteretic behaviour as described by independent domain theory. However, this equation is not convenient in that the relative permeability hysteresis set cannot be explicitly separated from this representation. A more flexible approach is to follow that which Killough ( 24) applied to capillary pressure hysteresis, by which scanning curves are described by a scaled combination of the bounding curves. Extending this to the relative permeability and fractional flow sets gives relationships of the type

.,

c

kri

=

0

fi

=

kri

.,

fi

+

+

+

+

- F(kri - kri) - F(fi

- fi)

0

where F

=

(Si

- Si + a)-

(Simax

1

(7a) (7b)

- l/a

- :S + a)-' -l/a

where the subscript refers to a scanning curve from point Si, the superscript arrows refer to the bounding curves, and a is a fitting parameter. Examples are shown in Figure 13.

96 The above discussion highlights the empirical way in which relative permeability hysteresis can be handled at present. For other. important factors, such as core end effects and oil saturation residual to surfactant flooding, the position is even less well defined

.

7.

DISPLACEMENT TESTS FOR ASSESSING POTENTIALLY USEFUL SURFACTANT SYSTEMS

7.1

Screening tests

Any potentially useful surfactant system must be able to reduce interfacial tension between oil and water by a significant amount (e.g. down to lo-' mN/m). Having found a surfactant capable of doing this, the next step is to conduct screening tests using glass bead or sand pack columns. If successful, the next step is to conduct core tests. As we have discussed, the wetting conditions of a core sample play a large part in the displacement characteristics. It is therefore of considerable importance to march reservoir wetting conditions when conducting core tests. In order to do this we use preserved core material which is carefully prepared in order to change the surface wetting as little as possible. Our present procedure involves the flushing of live crude oil through the core at reservoir temperature. The core is then left to ltageItin contact with crude oil for several weeks. A low rate waterflood is then conducted (e.g. 1 ft/day advance rate) to establish a residual oil saturation. Before injecting surfactant solution, the brine flow rate is increased to 200 ft/day. This is essential to ensure that oil left in the core is "trapped oil" and not oil retained by core end-effects. Surfactant is then injected into the core at 1 ft/day. Careful monitoring of the recovery performance enabled theoretical predictions to be tested. The theoretical work may show up reasons for lack of success in core flood tests or possible reasons why successful core tests may not necessarily lead to a successful field test.

-

7.2

-

Core scale artifacts

It is well known that laboratory tests on core samples can produce misleading information due to the small scale of the core plug in relation to reservoir scale. This is so even if the core plug represents a homogeneous reservoir rock. The recovery of oil from cores during laboratory waterflood tests is affected by capillary forces on the sample scale. For oil-wet cores flooded at low rate, tests on short cores result in early water breakthrough (5). The flood front is dispersed by capillary forces (Figure 8).

97

If the core length or flood velocity is increased or the interfacial tension is decreased, then the oil recovery at water breakthrough is improved. If a low rate flood test is carried out on a core sample, e.g. to match reservoir type flow rates, then the oil recovery at water breakthrough may show an increase as the interfacial tension is decreased. However, on the reservoir scale, the reduction of interfacial tension would have no effect, according to the curves in Figure 8. A similar situation arises in the case of residual oil saturation (i.e. after sufficient water has been passed through the core so that oil flow ceases). Capillary forces cause retention of oil at the outlet face of the core sample giving the impression of high residual oil saturation, particularly if the flood is carried out at rates representing reservoir flow rates. Reduction of interfacial tension can result in significant production of this end-effect oil which would not be representative of the reservoir scale. In order to improve the situation, to reduce the influence of end-effects. together to create a long core. Careful is necessary in order that relevant data

long cores are sometimes used Small core plugs may be butted arrangement of the small plugs is produced.

Turning to the water-wet case, the recovery of oil at waterbreakthrough is less affected by sample length than in the oil-wet case (8). Water may arrive early at the outlet end of the sample but capillary forces delay water-breakthrough (Figure 9). The representation given in Figure 9 only applies over a small region of flow rate and interfacial tension, where capillary forces completely dominate fluid distribution on the pore scale. Above a certain flow velocity or below a certain interfacial tension, viscous forces will start to take over as the dominant factor controlling fluid distribution. Increase of sample length, however, will have no effect on fluid distribution on the pore scale. The above discussion highlights the importance of careful interpretation of laboratory data if valid information is to be produced. In our discussions we have tended to consider the extreme case of oilwet and water-wet rocks. In practice rocks may have a variety of wetting conditions. Indeed not all of the pore surface may have the same wetting. We have also considered an ideal situation where clays within the porous media do not'effect the fluid flow characteristics. Adsorption of surfactants on to pore and clay surfaces has not been discussed. Full consideration of these interesting effects is outside the scope of this paper.

7.3

Simulation aspects

Preliminary analysis of core tests of EOR systems can be carried out with linear scaling relationships. Investigation of the sensivity to particular system properties in the optiiisation of a system requires the use of more detailed simulation methods. In particular, the separation of core scale effects as discussed above demand careful study if the experimental results are to characterise the physical processes relevant to the field. In all cases the data must be considered in terms of its relevance to its intended use on input to a field simulator, with the attendant changes in scale which can only be treated mathematically. An additional role of the simulation of core floods is provided by the greater degree of experimental accessibility,

98 and the ability to repeat laboratory work, as contrasted with the field situation. Despite the benefits of validation of a simulation model on the basis of laboratory results, there is no guarantee of success in the field (although, conversely, failure at the laboratory scale cannot easily be reconciled with confidence in subsequent field application). The simulation provides the language by which the dialogue between the laboratory and the field testing can proceed, and it is therefore important that it should be able to describe the real physical processes rather than aim at mere plausibility and utility. CONCLUSIONS 1. Despite its extensive use, the concept of relative permeability remains empirical. As with any empirical quantity, great care must be exercised when attempting to extend its area of applicability. In particular, the relative permeability functions which are appropriate to low tension immiscible displacement are as yet uncertain.

The behaviour of an oil slug injected into a core provides a prototype to assess many of the assumptions which are present when core data are prepared for simulation of EOR processes. The availability of a correctly defined set of relative permeability curves, complete with hysteresis, irreversibility and system changes is of great importance to the correct modelling of an oil bank. Although in field use, such concepts may be of secondary importance to the heterogeneity, they cannot be ignored in the provision of data from core tests. Currently available simulation schemes are empirical; they require development and experimental validation. 2.

3. Numerical schemes which essentially scan relative permeability curves demand that these curves are defined over the full saturation interval. The sensivity to these curves of oil bank stability (and presumably all multi-front systems) is such that plausibility alone is too weak a criterion for-acceptability. In addition, the behaviour of transient saturations associated with multiple shock fronts may not be adequately modelled. Acknowledgements Permission to publish this paper has been given by the British Petroleum Co. Ltd. The authors wish to thank Mr. J . F . Berry and Dr. I. White who carried out the simulation work described in this paper. List of Symbols kr S f V y

L x

relative permeability fractional saturation fractional flow superficial velocity interfacial tension core length distance along core it

a, C, F, fi, Hi, n, S+, S

, 0, -

parameters, defined in the text.

99

Subscripts oil water residual irreducible

o

w r i

References 1.

2.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

13*

-

14 15

*

L.L. Handy and P. Datta Fluid distributions during immiscible displacement in porous media. SOC. Pet. Eng. J, Sept. 1966 page 261. R.A. Salathiel Oil recovery by surface film drainage in mixed wettability rocks. SPE preprint 4104. Johnson, E.F., Bossler, D.P. and Naumann, V.O. Calculation of relative permeability from displacement experiments. Trans AIME (1959) 216, 370-372. Buckley, S.E. and Leverett, M.C. Mechanisms of fluid displacement in sands. Trans AIME (1942) 146, 107 - 116. L.A. Rapoport and W.J. Leas Properties of linear waterfloods. Trans AIME (1953) 198, 139 - 148. C. Bardon and D.G. Longeron Influence of very low interfacial tension on relative permeability. SOC. Pet. Eng. J, Oct 1980 page 391. F.F. Craig Jr. 1971.,The reservoir engineering aspects of waterflooding. spe Monograph Vol. 3 H.L. Doherty Series. Page 24. Kyte J.R. and Rapoport L.A. Linear waterflood behaviour and end effects in water-wet porous media. Trans AIME (1958) 213, 423 - 426. J.O. Amarefule and L.L. Handy 1981. The effect of interfacial tensions on relative oil-water relative permeabilities of consolidated porous media. SPE Preprint 9783 T.M. Geffen, W.W. Owens, D.R. Parrish and R.A. Morse Experimental investigation of factors affecting laboratory relative permeability measurements. Trans AIME (1951), vol. 192, page 99 - 110. C.R. Sandberg, L.S. Gournay and R.F. Sippel The effect of fluid-flow rate and viscosity on laboratory determinations of oil-water relative permeabilities. JPT, 1958, 36 - 43. C.S. Land. Comparison of calculated with experimental imbibition relative permeability SOC. Pet. Eng. J (Dec 1971) 419 - 425. M.C. Leverett Flow of oil-water mixtures through unconsolidated sands. Trans AIME (1939) 132, 149. N. Mungan Interfacial effects in immiscible liquidliquid displacement on porous media. SOC. Pet. Eng. J.(1966) 6, 247 - 253. A.W. Talash 1976. Experimental and calculated relative permeability data for systems containing tension additives. SPE preprint 5810.

100

16.

H.E. Gilliland and F.R. Conley. Surfactant waterflooding Proc. of 9th World Pet. Congress, Tokyo May 11-16, 1975.

17.

J.P. Batycky and F.G. McCaffery Low interfacial tension displacement studies. paper 78-29-26, 29th Annual Tech. meeting of the Pet. SOC. of CIM, Calgary, Canada (June 13-16,

19781. 18.

H. Asar Influence of interfacial tension on gas-oil relative permeability in gas-condensate systems. PhD dissertation University of Southern California (May 1980) C.P. Thomas, W.K. Winter and P.D. Flemings 1977. Application of a general multiphase multicomponent chemical flood model to ternary, two-phase surfactant systems. SPE preprint 6727.

20.

S.P. Gupta and S.P. Trushenski Micellar flooding compositional effects on oil displacement. SOC. Pet. Eng. J April 1979 116 - 128.

21.

G.A. Pope The application of fractional flow theory to enhanced oil recovery. SOC. Pet. Eng. J. (June 1980) 191 - 202. Gladfelter, R.E. and Gupta, S.P. Effects of Fractional Flow Hysteresis on Recovery of Tertiary Oil. SPE J (Dec. 1980) 508 - 520.

22.

Jones, S.C. and Rozelle W.O. Graphical Techniques for Determining Relative Permeability from Displacement Experiments. SPE J. (May 1978) 807 - 817. 24 *

Killough, J.E. Reservoir Simulation with History Dependent' Saturation Functions. SPE J (Feb. 1976) 37 - 48.

25.

Lin, C.Y. and Slattery, J.C. Three-Dimensional, Randomised Network Model for Two Phase Flow Through Porous Media. SPE 9803, 1981. Evrenos, A.I. and Comer, A.G. Numerical Simulation of Hysteretic Flow in Porous Media. SPE 2693, 1969. Everett, D.H. and Smith, F.W. A General Approach to Hysteresis. Trans. Faraday SOC. (1954) 50, 187 - 197.

26. 27 * 28.

Topp, G.C. and Miller, E.E., Hysteretic Moisture Characteristics and Hydraulic Conductivities for Glass Bead Media. Soil. Sci. SOC. Amer. Proc. (1966) 30, 156 - 162. Pickens, J.F. and Gillham, R.W., Finite Element Analysis of Solute Transport Under Hysteretic Unsaturated Flow Conditions Water Resour. Res. (1980) 16, 1071 - 1078.

101

CHEMICAL FLOODING

EXPERIMENTAL STUDY AND INTERPRETATION OF SURFACTANT RETENTION IN POROUS MEDIA J. NOVOSAD

Petroleum Recovery Institute CNgary,Alberta, CaMda T2L 2A6

ABSTRACT

T o t a l r e t e n t i o n of s u r f a c t a n t s i n a r e s e r v o i r d u r i n g chemical f l o o d s is probably one of t h e most important parameters i n t h a t i t determines the economic success o r f a i l u r e o f t h i s enhanced o i l recovery process. It is not, t h e r e f o r e , s u r p r i s i n g that a s u b s t a n t i a l r e s e a r c h e f f o r t has been devoted t o l a b o r a t o r y e v a l u a t i o n s of s u r f a c t a n t r e t e n t i o n i n porous media. Generally, t h e systems s t u d i e d are complex as they c o n t a i n a minimum of tw l i q u i d phases, an& no less t h a n f i v e components: s u r f a c t a n t , c o s u r f a c t a n t , e l e c t r o y t e , water, and o i l . The p r i n c i p a l o b j e c t i v e of t h i s paper is t o analyze and e v a l u a t e experimental procedures f o r determining s u r f a c t a n t a d s o r p t i o n and t o t a l s u r f a c t a n t r e t e n t i o n . It i s shown that t h e i n t e r p r e t i o n of experimental d a t a is n o t s t r a i g h t forward, and that extreme c a u t i o n must be exercised before any i n t e r p o l a t i o n o r e x t r a p o l a t i o n of a d s o r p t i o n o r r e t e n t i o n data is attempted. Laboratory d a t a on r e t e n t i o n of p u r e s u l f o n a t e (Texas # l ) , petroleum s u l f o n a t e (TRS 10-80). and s y n t h e t i c s u l f o n a t e (FA 400) are presented. These show t h e importance of experimental c o n d i t i o n s as similar experiments may y i e l d s u b s t a n t i a l l y d i f f e r e n t r e s u l t s when c o n d i t i o n s are v a r i e d . S p e c i f i c a l l y , t h e e f f e c t o f . p h a s e behavior on t o t a l s u r f a c t a n t r e t e n t i o n fs discussed and experimental procedures are o u t l i n e d so that a d i f f e r e n t i a t i o n can be made between l o s s e s of s u r f a c t a n t due t o unfavorable phase behavior and t h o s e due t o a d s o r p t i o n a t t h e s o l i d - l i q u i d i n t e r f a c e . An example of how experimental cond i t i o n s may a f f e c t t h e measured values of s u r f a c t a n t l o s s e s is shown by t h e e f f e c t of s u r f a c t a n t s l u g s i z e on t h e apparent l e v e l of r e t e n t i o n and adsorption.

INTRODUCTION

Adsorption of s u r f a c t a n t s considered f o r enhanced o i l recovery a p p l i c a t i o n s has been s t u d i e d e x t e n s i v e l y i n t h e last few years1’6 as it has been convincingly shown that i t is p o s s i b l e t o develop s u r f a c t a n t systems which d i s p l a c e o i l from porous media almost completely when used i n l a r g e q u a n t i t i e s . E f f e c t i v e o i l recovery by s u r f a c t a n t s is not a q u e s t i o n of p r i n c i p l e but r a t h e r a q u e s t i o n of economics. Since s u r f a c t a n t s are mre expensive than t h e crude o i l , development of a p r a c t i c a l enhanced oil recovery (EOR) technology depends on how much surf a c t a n t can be economically s a c r i f i c e d i n recovering a d d i t i o n a l crude o i l from a r e s e r v o i r . Therefore, i t is q u i t e clear why s u r f a c t a n t a d s o r p t i o n has always been considered c r i t i c a l t o t h e success OT f a i l u r e of t h i s EOR process.

102 It w a s recognized earlier t h a t physico-chemical a d s o r p t i o n may be only one of a number of f a c t o r s which c o n t r i b u t e t o t o t a l s u r f a c t a n t r e t e n t i o n . Other physico-chemical mechanisms may i n c l u d e s u r f a c t a n t entrapment i n a n immobile o i l phase5, s u r f a c t a n t p r e c i p i t a t i o n by d i v a l e n t i o n s 6 s u r f a c t a n t p r e c i p i t a t i o n caused by a s e p a r a t i o n o f c o s u r f a c t a n t from s u r f a c t a n t ' , and s u r f a c t a n t t a t i o n due t o chromatographic s e p a r a t i o n o f d i f f e r e n t s u r f a c t a n t s p e c i e s When complications a r i s i n g from ion-exchange phenomena u s u a l l y involved i n s u r f a c t a n t f l o o d i n g are i n c l u d e d , i t should not come a s a s u r p r i s e t h a t measured a d s o r p t i o n isotherms d i f f e r s u b s t a n t i a l l y from t h o s e p r e v i o u s l y observed f o r simpler s u r f a c t a n t systems.

yrecipi.

A p r i n c i p a l o b j e c t i v e o f t h i s work is t o e v a l u a t e t h e experimental techniques t h a t c a n be used f o r measuring s u r f a c t a n t a d s o r p t i o n and t o s t u d y experimentally two mechanisms r e s p o n s i b l e f o r s u r f a c t a n t r e t e n t i o n . S p e c i f i c a l l y , an a t t e m p t is made t o d i f f e r e n t i a t e between t h e a d s o r p t i o n of s u r f a c t a n t s a t t h e s o l i d - l i q u i d i n t e r f a c e and 'the r e t e n t i o n of s u r f a c t a n t s due t o t r a p p i n g i n t h e immobile hydrocarbon phase which remains w i t h i n t h e c o r e following a s u r f a c t a n t flood . PLUSCRMENT OF ADSORPTION AT THE SOLID-LIQUID INTERFACE

Previous a d s o r p t i o n measurements of s u r f a c t a n t s considered f o r enhanced o i l recovery produced a d s o r p t i o n isotherms of unusual shapes w i t h unexpectel f e a t u r e s . P r i m a r i l y , a n a d s o r p t i o n maximum has been observed when t o t a l s u r f a c t a n t r e t e n t i o n has been p l o t t e d a g a i n s t t h e c o n c e n t r a t i o n of i n j e c t e d s u r f a c t a n t . Numerous e x p l a n a t i o n s have been o f f e r e d f o r t h e s e peaks; such a s , a formation o f mixed micells6, t h e e f f e c t s o f " s t r u c t u r e forming" and " s t r u c t u r e breaking" c a t i o n s 8 , and t h e p r e c i p i t a t i o n and consequent r e d i s s o l u t i o n of d i v a l e n t i o n s 2 . Which of t h e s e e f f e c t s a r e r e s p o n s i b l e f o r t h e peaks i n a p a r t i c u l a r s i t u a t i o n and t h e i r r e l a t i v e impartance i s d i f f i c u l t t o asses. b w e v e r , i t seems t h a t , i n view of t h e number of processes t h a t are t a k i n g p l a c e s i m l t a n e o u s l y and t h e l a r g e number of components p r e s e n t i n most o f t h e systems s t u d i e d , one should n o t expect smooth monotonically i n c r e a s i n g isotherms t h a t a r e p a t t e r n e d a f t e r a d s o r p t i o n isotherms f o r only two p u r e components. Also, i t should be r e a l i z e d that most experimental procedures do not y i e l d a n amount of s u r f a c t a n t adsorbed b u t r a t h e r t h e s u r f a c e excess. I t i s shown n e x t that a n a d s o r p t i o n isotherm expressed i n terms o f t h e s u r f a c e excess a s a f u n c t i o n of a n e q u i l i b r i u m s u r f a c t a n t c o n c e n t r a t i o n must, by d e f i n i t i o n , c o n t a i n a maximum if t h e d a t a are measured over a s u f f i c i e n t l y wide range of c o n c e n t r a t i o n s . I t has been shown r e p e a t e d l y t h a t , f o r a d s o r p t i o n a t t h e s o l i d - l i q u i d i n t e r f a c e , the s u r f a c e excess i s t h e only c o n s i s t e n t l y defined experimental v a r i a b l e which should be used i n d e s c r i b i n g t h e p r e f e r e n t i a l uptake of one component over a n o t h e r i n t o t h e adsorbed layer'. The s u r f a c e excess is defined by Equation (1)L: 0

ne i where, no

n o = -(xi m

- Xi)

=

t o t a l mass o f t h e l i q u i d system ( g ) ,

xo i

=

x

=

r e l a t i v e concentration adsorption takes place r e l a t i v e concentration adsorption equilibrium

i

of component i i n t h e bulk phase b e f o r e (fraction), of component i i n t h e bulk phase a f t e r is a t t a i n e d ( f r a c t i o n ) ,

ne i

=

excess of mass of component i i n t h e adsorbed phase p e r mass u n i t o f adsorbent (g/g),

m

=

mass of adsorbent (g),

103

and a n a d s o r p t i o n isotherm is d e f i n e d a s t h e s u r f a c e e x c e s s dependence on e q u i l i b r i u m c o n c e n t r a t i o n o f component i i n t h e b u l k phase:

It should be clear from Equation ( 1 ) that t h e s u r f a c e excess must be equal t o z e r o f o r p u r e components ( x i = 0, x i = 1 ) and, t h e r e f o r e , a non-zero adsorpt i o n isotherm must c o n t a i n a t least one peak. This a p p l i e s t o f u l l y m i s c i b l e systems i n which a d s o r p t i o n isotherms are meaningful over t h e e n t i r e concentrat i o n range between pure component 1 and pure component 2 . However, s o l u b i l i t y l i m i t s of most s u r f a c t a n t s i n r e s e r v o i r b r i n e s a r e reached a t low c o n c e n t r a t i o n s , and measurements of a d s o r p t i o n above such c o n c e n t r a t i o n l e v e l s are meaningless a s s u r f a c t a n t p r e c i p i t a t i o n t a k e s p l a c e . Therefore, a presence o r a n absence of a maximum i n a n a d s o r p t i o n isotherm is dependent upon s u r f a c t a n t s o l u b i l i t y i n a b r i n e o r o t h e r continuous phase.

Equation (1) a p p l i e s a l s o t o multicomponent systems, however, such adsorption isotherms cannot be expressed g r a p h i c a l l y i n a two-dimensional form without s p e c i f y i n g a d i r e c t i o n i n which t h e a d s o r p t i o n s u r f a c e ( f o r three-component systems) is c u t f o r viewing i n two dimensions 4. It is not p r a c t i c a l t o perform a d s o r p t i o n experiments w i t h multicomponent systems i n such a way that t h e a d s o r p t i o n s u r f a c e is c u t i n a pre-determined way s i n c e i t i s n o t u s u a l l y known a p r i o r i w h a t t h e b u l k composition of i n d i v i d u a l components is going t o be a f t e r a d s o r p t i o n has taken place. This problem is even more complicated when d e s i g n i n g experiments w i t h surf a c t a n t mixtures which are considered f o r s u r f a c t a n t f l o o d i n g as i n d i v i d u a l components of t h e mixture are d i f f i c u l t t o s e p a r a t e and, consequently, t h e whole mixture is u s u a l l y t r e a t e d as a s i n g l e component. Even i f i t is assumed that a chosen a n a l y t i c a l method c a n determine t h e sum of s e v e r a l s u r f a c t a n t s a c c u r a t e l y , i t has been p r e v i o u s l y shown that isotherms f o r i n d i v i d u a l components may d i f f e r s u b s t a n t i a l l y from a n o v e r a l l i ~ o t h e r m . ~ This i s of importance f o r systems i n which each component w i t h i n t h e m i x t u r e s e r v e s a d i f f e r e n t f u n c t i o n , such a s e i t h e r a c h i e v i n g a n u l t r a low i n t e r f a c i a l t e n s i o n o r improving t h e s o l u b i l i t y of o t h e r components. The overa l l a d s o r p t i o n isotherm i s t h e n n o t s u i t a b l e f o r p r e d i c t i n g t h e system performance d u r i n g t h e f l o o d because d e p l e t i o n of i n d i v i d u a l components is not r e p r e s e n t e d by t h e o v e r a l l isotherm. T r e a t i n g t h e mixture as a s i n g l e component b r i n g s a d d i t i o n a l u n c e r t a i n t y t o a d s o r p t i o n experiments. As t h e i n d i v i d u a l components a r e adsorbed t o d i f f e r e n t e x t e n t s , t h e i r e q u i l i b r i u m c o n c e n t r a t i o n s become d i f f e r e n t from t h o s e o r i g i n a l l y p r e s e n t so t h a t they w i l l depend on s p e c i f i c experimental c o n d i t i o n s such as t h e a d s o r b e n t / s o l u t i o n r a t i o . The apparent a d s o r p t i o n l e v e l may vary S u b s t a n t i a l l y from one experiment t o a n o t h e r a s e q u i l i b r i u m c o n c e n t r a t i o n s may be moving on t h e a d s o r p t i o n s u r f a c e i n d i f f e r e n t d i r e c t i o n s depending on t h e s p e c i f i c c o n d i t i o n s of t h e experiment. These are t h e main r e a s o n s why experimental d a t a from d i f f e r e n t l a b o r a t o r i e s are so d i f f i c u l t t o compare and why a g r e a t d e a l of c a u t i o n should be e x e r c i s e d i n i n t e r p r e t i n g t h e shapes of isotherms which were determined i n experiments i n which t h e i n i t i a l r e l a t i v e c o n c e n t r a t i o n of each i n d i v i d u a l component was held c o n s t a n t w h i l e t h e t o t a l c o n c e n t r a t i o n w a s varied.

METHODS FOR WXjUREMENT OF ADSORPTION ISOTHERMS There a r e t w o d i s t , i n c t l y d i f f e r e n t approaches f o r measuring a d s o r p t i o n a t t h e s o l i d - l i q u i d i n t e r f a c e . The f i r s t , a b a t c h method, c o n s i s t s of measuring

104 s u r f a c t a n t c o n c e n t r a t i o n s i n t h e b u l k phase b e f o r e and a f t e r a d s o r p t i o n takes p l a c e , and a d s o r p t i o n is c a l c u l a t e d from Equation (1). S i n c e a l l measurements a r e performed i n t h e b u l k phase, t h e meaning of each v a r i a b l e i n Equation (1) is w i t h o u t ambiguity and t h e c a l c u l a t e d s u r f a c e excess is a v a l i d thermodynamic v a r i a b l e .

A main disadvantage of u s i n g t h e b a t c h method l i e s i n i t s poor accuracy a t h i g h e r s u r f a c t a n t c o n c e n t r a t i o n s . The measured change i n b u l k s u r f a c t a n t c o n c e n t r a t i o n due t o a d s o r p t i o n becomes small and a d s o r p t i o n i s obtained by s u b t r a c t i n g two numbers of s i m i l a r s i z e . It has been shown w i t h s u r f a c t a n t s y s t e m s considered f o r enhanced o i l recovery that exceedingly a c c u r a t e a n a l y t i c a l methods a r e r e q u i r e d f o r measurement of a d s o r p t i o n from s o l u t i o n s when s u r f a c t a n t c o n c e n t r a t i o n s exceeds one p e r c e n t . I n t h e second method, a dynamic one, the r e t e n t i o n of s u r f a c t a n t s i s determined from a flow-type experiment, and t h e l o s s e s of s u r f a c t a n t are c a l c u l a t e d e i t h e r from t h e d e l a y of t h e s u r f a c t a n t breakthrough c u r v e , i f t h e amount of s u r f a c t a n t i n j e c t e d is so l a r g e that t h e e f f l u e n t c o n c e n t r a t i o n r e a c h e s t h e i n j e c t e d c o n c e n t r a t i o n , o r from t h e material balance when a smaller amount of s u r f a c t a n t is i n j e c t e d (Figure 1). It should be r e a l i z e d t h a t , i f t h e s u r f a c t a n t c o n c e n t r a t i o n a t t h e c o r e o u t l e t does not r e a c h t h e i n j e c t e d c o n c e n t r a t i o n , t h e n t h e a d s o r p t i o n determined from a material balance is a t t a i n e d over a c o n c e n t r a t i o n range t h a t extends from t h e i n j e c t e d l e v e l a t t h e c o r e i n l e t t o t h e maximum e f f l u e n t c o n c e n t r a t i o n s measured a t t h e c o r e o u t l e t . For example, i f the i n j e c t i o n of a 20% PV s u r f a c t a n t s l u g r e s u l t s i n a maximum o u t l e t c o n c e n t r a t i o n corresponding t o 10% of t h e i n j e c t e d c o n c e n t r a t i o n , t h e average s u r f a c t a n t c o n c e n t r a t i o n w i t h i n t h e c o r e would be approximately 55% o f t h e i n j e c t e d l e v e l . A l a r g e r s l u g may g i v e a maximum o u t l e t c o n c e n t r a t i o n o f 90% r e s u l t i n g i n t h e average c o n c e n t r a t i o n w i t h i n t h e c o r e being about 95% of t h e i n j e c t e d c o n c e n t r a t i o n . Therefore, the r e t e n t i o n v a l u e s obtained from t h e s e two experiments would be r e l a t e d t o d i f f e r e n t c o n c e n t r a t i o n r e g i o n s , and t h e r e s u l t s would not be d i r e c t l y comparable. A similar argument c a n be made when a d i f f e r e n t degree of s e p a r a t i o n between a c o s u r f a c t a n t and a s u r f a c t a n t o c c u r s i n experiments i n which v a r y i n g s l u g sizes are used. An example of such a s e p a r a t i o n i s shown i n Figure 2, a n d a g a i n r e t e n t i o n r e s u l t s should be d i f f e r e n t s i n c e i t has been shown p r e v i o u s l y that alcohol concentrations a f f e c t s u r f act an t r et en tio n su b sta n tia lly .

There are two a d d i t i o n a l c o n s i d e r a t i o n s concerning measurements o f adsorpt i o n i n displacement experiments i n which a n o i l phase i s p r e s e n t and when i t i s d i s p l a c e d from a c o r e by a s u r f a c t a n t s o l u t i o n . I n t h i s c a s e , a d s o r p t i o n cannot be determined d i r e c t l y from t h e d e l a y of t h e breakthrough curve f o r two reasons. F i r s t l y , t h e pore volume a v a i l a b l e t o the s u r f a c t a n t is changing d u r i n g t h e flood a s o i l i s d i s p l a c e d . This makes t h e i n t e g r a t i o n i n d i c a t e d i n Figure l ( a ) mre d i f f i c u l t s i n c e t h e amount o f o i l recovered must be known a t each p o i n t i n t h e flood. Secondly, t h e p o s s i b i l i t y of s u r f a c t a n t being d i s t r i b u t e d between t h e b r i n e and hydrocarbon phases d u r i n g t h e flood, i n a way t h a t d i f f e r s from t h e i n j e c t e d s o l u t i o n , mst be considered. When t h i s o c c u r s , t h e s u r f a c t a n t flow v e l o c i t y becomes dependent n o t only on a d s o r p t i o n but also on two-phase flow c h a r a c t e r i s t i c s . Unless t h e s u r f a c t a n t d i s t r i b u t i o n is known p r e c i s e l y a t each s t a g e of t h e food, t h e d e l a y i n t h e breakthrough curve may be caused by e i t h e r of t h e two phenomena, and a d i s t i n c t i o n between them cannot be made. The previous paragraphs were intended t o show t h a t thermodynamically v a l i d a d s o r p t i o n measurements can be best performed i n batch experiments. However, s i n c e t h e i r s e n s i t i v i t y i s o f t e n n o t s u f f i c i e n t f o r measurements o f a d s o r p t i o n

105 from s u r f a c t a n t s o l u t i o n s of h i g h e r c o n c e n t r a t i o n s , displacement experiments must be used f o r such systems. It should, however, be r e a l i z e d that such tests measure averaged v a l u e s of a d s o r p t i o n over c o n c e n t r a t i o n s that r a n g e from t h e maximum e f f l u e n t c o n c e n t r a t i o n t o t h e i n j e c t e d c o n c e n t r a t i o n . The adsorption v a l u e s are also averaged over t h e range o f c o s u r f a c t a n t f s u r f a c t a n t ratios which depend on t h e s p e c i f i c characteristics o f t h e s u r f a c t a n t system. It f o l l o w s that even minor v a r i a t i o n s i n t h e displacement experiments can produce s u b s t a n t i a l l y d i f f e r e n t r e s u l t s i n terms of s u r f a c t a n t r e t e n t i o n and a d s o r p t i o n . Therefore, i t is i m p e r a t i v e t h a t e v e r y a d s o r p t i o n measurement be d e s c r i b e d i n d e t a i l so t h a t t h e r e s u l t s from d i f f e r e n t l a b o r a t o r i e s c a n be r e a l i s t i c a l l y compared. This is n o t p r e s e n t l y t h e case, a s manifested i n t h e r e c e n t paper by Meyer and S a l t e r ' who surveyed t h e l i t e r a t u r e t o determine t h e e f f e c t s of a n o i l presence o n s u r f a c t a n t r e t e n t i o n and found that a n i n c r e a s e , a d e c r e a s e , o r no e f f e c t had been observed. It is e n t i r e l y p o s s i b l e that t h e d i f f e r e n t experimental techniques and procedures could have been r e s p o n s i b l e f o r such d i v e r g e n t r e s u l t s .

Another phenomenon a f f e c t i n g t h e r e t e n t i o n of s u r f a c t a n t s should be t r e a t e d s e p a r a t e l y . S u r f a c t a n t s o l u b i l i t y i n r e s e r v o i r f l u i d s could p o s s i b l y be grouped w i t h i n t h e phase behavior categorv b u t , s i n c e it mav a f f e c t r e t e n t i o n of s u r f a c t a n t s so s u b s t a n t i a l l y , i t is d i s c u s s e d s e p a r a t e l y . I.o

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PORE VOLUME

Figure 1: Determination of S u r f a c t a n t Retention from Displacement Experiments It h a s been p r e v i o u s l y shown that t h e r e i s a n o r d e r o f magnitude d i f f e r e n c e i n t h e r e t e n t i o n of s u r f a c t a n t s from d i s p e r s e d s o l u t i o n s and from s o l u t i o n s i n which t h e s u r f a c t a n t s are t r u l y d i s s o l v e d Even though mst i n j e c t e d s u r f a c t a n t s o l u t i o n s used i n a d s o r p t i o n s t u d i e s c o n t a i n a l c o h o l s a s c o s u r f a c t a n t s i n order t o keep s u r f a c t a n t s f u l l y d i s s o l v e d , t h i s r a y n o t be t h e c a s e i n t h e l a t e r s t a g e s of a f l o o d . Alcohols propagate through t h e porous mediua a t d i f f e r e n t

'.

106 v e l o c i t i e s than s u r f a c t a n t s because they d i s t r i b u t e themselves between t h e o i l and t h e b r i n e d i f f e r e n t l y t h a n do t h e s u r f a c t a n t s (Figure 2 ) . Should t h i s happen, i t is l i k e l y that t h e s u r f a c t a n t l o s e s its: s o l u b i l i t y i n t h e b r i n e , p r e c i p i t a t e s , and l o s e s i t s a b i l i t y t o propagate through t h e core. This w i l l r e s u l t i n an a p p a r e n t i n c r e a s e i n s u r f a c t a n t r e t e n t i o n which cannot be e a s i l y d i s t i n g u i s h e d from e i t h e r a d s o r p t i o n o r t r a p p i n g in t h e hydrocarbon phase. Therefore, in most experiments d e s c r i b e d in t h i s work, a l c o h o l s were used i n e x c e s s q u a n t i t i e s thereby e l i m i n a t i n g o r s u b s t a n t i a l l y reducing t h i s p o s s i b i l i t y . I n a l l c a s e s , a l c o h o l c o n c e n t r a t i o n s i n t h e e f f l u e n t were monitored so that a p o t e n t i a l problem o f poor s u r f a c t a n t s o l u b i l i t y could be a s s e s s e d a t t h e end of eack flood.

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C o s u r f a c t a n t / S u r f a c t a n t Ratio a t t h e Core O u t l e t (10072 3’I n j e c t i o n of 2% 1 / 6 Texas !!l/ n-Propanol i n 1.5‘; N a C l Brine)

The main o b j e c t i v e o f t h i s work is t o determine s u r f a c t a n t r e t e n t i o n in & r e a c o r e s w i t h t h e main emphasis being t o d i s t i n g u i s h physico-chemical a d s o r p t i o n of s u r f a c t a n t s from l o s s e s of s u r f a c t a n t s due t o t r a p p i n g i n t h e i m o b i l e hydrocarbon phase t h a t is l e f t i n t h e c o r e a f t e r a flood. Chenical s Three types of s u r f a c t a n t s were used d u r i n g t h e c o u r s e of t h i s study. TXS 10-82 served a s a n example of a commercial q u a l i t y petroleum s u l f o n a t e which

107 is produced by a d i r e c t s u l f o n a t i o n of petroleum-based f e e d s t o c k s . PDM 337 w a s a n example o f a s y n t h e t i c s u l f o n a t e . and Texas 81 was a w e l l - d e f i n e d pure s u r f a c t a n t , t h e s t r u c t u r e o f which was p a t t e r n e d a f t e r typical molecules found i n petroleum-based f e e d s t o c k s .

-

Texas # I

PDM 337

-

TRS 10-80

Octane

sodium s a l t o f 8-phenyla-hexadecyl-p-sulfonate w a s obtained from P r o f e s s o r Wade o f t h e U n i v e r s i t y o f Texas and has been used as r e c e i v e d . According t o Frances e t a1.l1 t h e p u r i t y o f t h e sample exceeds 98%. monoethanol amine s a l t o f a l k y l o r t h o x y l e n e s u l f o n a t e s u p p l i e d by Exxon Chemicals, Houston, Texas. According t o t h e s u p p l i e r , i t is 84% a c t i v e w i t h a median a l k y l c h a i n s i z e of around C12. This s u r f a c t a n t was used a s r e c e i v e d .

-

petroleum s u l f o n a t e s u p p l i e d by Witco Chemicals. Samples were d e s a l t e d and d e o i l e d accord-ins t o t h e procedures d e s c r i b e d by Shah e t a1.12

-

t e c h n i c a l g r a d e s u p p l i e d by P h i l l i p s Petroieum Company.

Orthoxylene

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p o i n t r a n g e 143.5' Coleman and B e l l Co.

- 144.5"C

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Secondary Butyl a l c o h o l b o i l i n g p o i n t r a n g e 98" Eastman KDdak Company.

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Brine Adsorbent

s u p p l i e d by Matheson,

-

B e r e a s a n d s t o n e c o r e s w i t h a i r p e r m e a b i l i t y r a n g e o f 100 t o 1 , 2 0 0 md, s u p p l i e d by Cleveland Q u a r r i e s .

A n a l y t i c a l Methods The p r e c i s i o n o f a n a l y t i c a l methods is o f u t m s t importance i n a l l s t u d i e s of a d s o r p t i o n a t t h e s o l i d - l i q u i d i n t e r f a c e . The f o l l o w i n g methods have been e x t e n s i v e l y t e s t e d and employed f o r c o n c e n t r a t i o n d e t e r m i n a t i o n i n t h i s work. Surfactants

- W Spectrophotometry ( V a r i a n ' s Super Scan 3) - HF'LC u t i l i z i n g w a t e r - m e t h a n o l - a c e t o n i t r i l e - sodium phosphate s o l v e n t s '

3ihydro-

(Waters A s s o c i a t e s I n s t r u m e n t ) .

Octanelo-xylenefSecondary Suty: slcohol-GC emplo>-lng Chromosorb S packing and t h e thermal c o n d u c t i v i t y d e t e c t o r (Hewlett-Packard Instrument). Divalent Ions

- I o n i c Flame Spectrophometry - Chelatometric t i t r a t i o n

(Perkin-Elnrer

Instrument)

E i T e r i n e n t a l Procedures Berea a r e s (2.5 x 2.5 cm2 c r o s s - s e c t i o n ) were c u t t o 30 CGI l e n g t h s and d r i e d i n a vacuum oven a t ll0'C f o r 24 hours. They were t h e n s a t u r a t e d under vacuum w i t h degassed b r i n e , o i l flooded t o a connate water s a t u r a t i o n , and t h e n waterf l o o d e d t o a r e s i d u a l o i l s a t u r a t i o n u s u a l l y i n t h e range o f 30 t o 35% o f pore volume.

A s u r f a c t a n t s l u g w a s i n j e c t e d i n t o t h e cores a t r e s i d u a l o i l s a t u r a t i o n

a t c o n s t a n t rates of 2 ml/hour so that t h e a p p a r e n t f r o n t a l advance rate of the f l u i d d i d not exceed 30 cmlday. I n o r d e r t o eliminate e v a p o r a t i v e l o s s e s of v o l a t i l e components, t h e o u t l e t l i n e w a s f e d through a s y r i n g e n e e d l e p i e r c i n g t h e septum o f a c o l l e c t i o n tube. Synchronized movements of a f r a c t i o n c o l l e c t o r and t h e s y r i n g e n e e d l e were automated, t h u s a l l o w i n g u n i n t e r r u p t e d f l o o d i n g i n experiments l a s t i n g s e v e r a l days. S u r f a c t a n t f l o o d s were performed a s follows. During t h e s u r f a c t a n t flood and t h e subsequent b r i n e flood (no polymers o r v i s c o s i t y improving a g e n t s have been used i n t h i s work), t h e samples were c o l l e c t e d a t two-hour i n t e r v a l s which r e s u l t e d i n 5 t o 10% o f pore volume being c o l l e c t e d i n each sample. E f f l u e n t f l u i d s were t h e n analyzed f o r o i l , b r i n e , s u r f a c t a n t , and c o s u r f a c t a n t c o n t e n t . When t h e production of o i l , s u r f a c t a n t , and c o s u r f a c t a n t ceased, s e v e r a l pore volumes of a hydrocarbon phase were i n j e c t e d i n t o t h e c o r e i n a n a t t e m p t t o recover s u r f a c t a n t s trapped i n o i l remaining i n t h e c o r e . Liquid produced by t h i s hydrocarbon flood was analyzed f o r a l l components and recovered s u r f a c t a n t s were considered t o be s u r f a c t a n t s trapped i n t h e hydrocarbon phase d u r i n g t h e s u r f a c t a n t flood. I n some f l o o d s , o c t a n e w a s d i s p l a c e d by nonane o r decane so that a complete displacement of r e s i d u a l cil could be v e r i f i e d and a material balance 011 o i l c l o s e d . A f t e r a l l s u r f a c t a n t s trapped i n t h e o i l were d i s p l a c e d , t h e c o r e w a s flooded w i t h a s t r o n g s o l v e n t such a s e t h y l a l c o h o l o r i s o n r o p y l a l c o h o l i n a mixture w i t h b r i n e t o remove a l l remaining s u r f a c t a n t s from t h e core. This r e q u i r e d i n j e c t i o n o f 5 t o 1 0 pore volumes and t h e material balance on s u r f a c t a n t c l o s e d u s u a l l y between 90 t o 100% of i n j e c t e d s u r f a c t a n t . S u r f a c t a n t removed from t h e c o r e by a l c o h o l s o l v e n t s is considered t o be s u r f a c t a n t adsorbed on t h e rock d u r i n g t h e f l o o d . The f l o o d i n g sequence d e s c r i b e d above a l l o w s a d e t e r m i n a t i o n of t h e o v e r a l l s u r f a c t a n t r e t e n t i o n ( i . e . t h e amount o f s u r f a c t a n t l o s t d u r i n g t h e f l o o d ) from t h e d i f f e r e n c e between t h e amounts o f s u r f a c t a n t i n j e c t e d and recovered d u r i n g t h e s u r f a c t a n t and subsequent b r i n e i n j e c t i o n . The hydrocarbon flood g i v e s a amount of s u r f a c t a n t trapped i n t h e o i l phase due t o unfavorable phase behavior, and t h e adsorbed s u r f a c t a n t recovered i n t h e f i n a l s o l v e n t f l o o d completes t h e m a t e r i a l balance. This procedure i m p l i c i t l y assumes t h a t t h e hydrocarbon phase does n o t remove adsorbed s u r f a c t a n t from t h e core. This assumption was v e r i f i e d i n t h e following way: X 75X PV of 3% s u r f a c t a n t s l u g was i n j e c t e d i n a b r i n e - s a t u r a t e d c o r e and followed w i t h t h r e e a d d i t i o n a l pore volumes of b r i n e . S u r f a c t a n t l o s s was determined a t 0.6 mg/g. Then, o c t a n e was continuously i n j e c t e d and an e f f l u e n t was analyzed f o r s u r f a c t a n t s . A f t e r w r e than 5 P P o f throughput o n l y 0.06 mg of s u r f a c t a n t p e r one gram of rock w a s recovered. This i n d i c a t e s that a minor amount of adsorbed s u r f a c t a n t can be recovered by t h e o i l , and that t h e bulk of adsorbed s u r f a c t a n t w i l l n o t be desorbed. However, even c h i s small amount of adsorbed s u r f a c t a n t recovered by o i l is s u f f i c i e n t t o q u a l i f y t h i s method f o r d e t e r m i n a t i o n of trapped s u r f a c t a n t as q u a l i t a t i v e .

I n g e n e r a l , t h e b e s t m a t e r i a l balances were obtained i n f l o o d s w i t h TRS 10-80, a n d u s u a l l y t h e most i n a c c u r a t e results were obtained w i t h PDM 337. It seems reasonable t o suggest t h a t a degree of s u r f a c t a n t s o l u b i l i t y i n a l c o h o l s o l v e n t s could e x p l a i n t h i s t r e n d , however, no measurements of s u r f a c t a n t s o l u b i l i t i e s have been made.

109 I n o r d e r t o avoid experimental complications due t o t h e p o s s i b l e p r e c i p i t a t i o n of s u r f a c t a n t s by d i v a l e n t i o n s , sodium c h l o r i d e b r i n e s were used throughout t h i s study. Berea c o r e s were p r e f l u e h e d w i t h 5 t o 7 pore volumes of sodium c h l o r i d e b r i n e s i n o r d e r t o d i s p l a c e most of t h e exchangeable d i v a l e n t ions. Even w i t h t h e s e p r e c a u t i o n s , t h e r e i s a n i n c r e a s e i n d i v a l e n t c a t i o n c o n c e n t r a t i o n i n t h e propagating s u r f a c t a n t s l u g (Figure 3). I n our experiments, t h e s e l e v e l s have n o t exceeded 90 ppm. S e p a r a t e phase behavior experiments i n d i c a t e d that such low d i v a l e n t i o n c o n c e n t r a t i o n s a f f e c t e d t h e phase behavior o f s u r f a c t a n t s o l u t i o n s i n that a minor s h i f t toward upper phase microemulsions w a s n o t i c e d , but no s u r f a c t a n t p r e c i p i t a t i o n was observed.

loot

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1

PORE VOLUME F i g u r e 3:

DivaleDt Ions Content i n t h e E f f l u e n t ( I n j e c t i o n of 75% PV of 2% 110.5 TRS 10-8OlSBA i n 1%N a C l )

It should be noted h e r e that t h i s procedure f o r d i f f e r e n t i a t i n g trapped s u r f a c t a n t i n t h e hydrocarbon phase from t h e adsorbed s u r f a c t a n t is not a p p l i c a b l e t o a l l s i t u a t i o n s . For example, i n s u r f a c t a n t systems i n which t h e s u r f a c t a n t d i s t r i b u t i o n c o e f f i c i e n t is not a t extreme l e v e l s ( i . e . K = [ ( c s ) o i l / ( c s ) b r i n e l f o r upper phase microtends t o zero f o r lower phase microemulsions o r K + emulsions) t h e c h a s e b r i n e would b l e e d s u r f a c t a n t from t h e o i l phase and no s u r f a c t a n t would e v e r be found trapped i n the o i l .

-

RESLZTS Ah?) DISCUSSION

S t u d i e s of o i l recovery e f f i c i e n c y and s u r f a c t a n t r e t e n t i o n i n d i c a t e that b e t t e r , performing p r o c e s s e s a r e u s u a l l y accompanied by lower s u r f a c t a n t r e t e n t i o n even though lower r e t e n t i o n does n o t n e c e s s a r i l y mean higher o i l recoverp.14 Since our experimental technique can d i s t i n g u i s h between s u r f a c t a n t l o s s e s due t o a d s o r p t i o n and l o s s e s due t o unfavorable phase behavior, i t Qas thought t o be of i n t e r e s t t o perform s e v e r a l series of similar experiments and then o b s e r v e how t h e s e i n d i v i d u a l c o n t r i b u t i o n s t o t o t a l s u r f a c t a n t r e t e n t i o n are affected

.

110 E f f e c t of C o s u r f a c t a n t on S u r f a c t a n t R e t e n t i o n I t has been shown t h a n , i n systems c o n t a i n i n g no o i l ( i . e . systems c o n t a i n i n g o n l y s u r f a c t a n t , c o s u r f a c t a n t , and b r i n e ) , poor s u r f a c t a n t solub i l i t y may r e s u l t i n very high s u r f a c t a n t r e t e n t i o n i n Berea c o r e s . An a d d i t i o n a l c o s u r f a c t a n t helped t o d i s s o l v e t h e s u r f a c t a n t i n t h e b r i n e and t h e s u r f a c t a n t r e t e n t i o n w a s reduced by one o r d e r of m a g n i t ~ d e . ~I n systems c o n t a i n i n g o i l , poor s u r f a c t a n t s o l u b i l i t y may n o t r e s u l t i n s u r f a c t a n t molecule a g g r e g a t i o n b u t may l e a d t o a change in phase behavior i n which c a s e t h e s u r f a c t a n t d i s s o l v e s i n t h e upper hydrocarbon phase. I n that case t h e s u r f a c t a n t r e t e n t i o n would increase even though s u r f a c t a n t a d s o r p t i o n may e i t h e r not change a t a l l o r may even d e c r e a s e .

The PDM 337 s u r f a c t a n t w i t h secondary b u t y l a l c o h o l . a s a c o s u r f a c t a n t w a s s e l e c t e d f o r t h i s p a r t of t h e study. An i n c r e a s i n g c o s u r f a c t a n t c o n t e n t makes t h e s u r f a c t a n t s l i g h t l y -re b r i n e s o l u b l e and t h e phase behavior changes from a n upper t o a middle phase (Figure 4 ) .

SURFACTANT CONTAINING PHASE

VO.1

F i g u r e 4:

1/0.5

1/1.0

1/50

Phase Behavior of 3X PDM 337 S u r f a c t a n t (80120 volumetric r a t i o of 1.5% k C 1 / octane f o r d i f f e r e n t surfactantlsecondary butyl alcohol r a t i o s )

S u r f a c t a n t l c o s u r f a c t a n t r a t i o s of l:O.l, 1:0.5, 1:1, and 1:s were i n j e c t e d i n f o u r f l o o d s on Berea c o r e s t h a t had been waterflooded t o r e s i d u a l o i l s a t u r a t i o n s . The e f f l u e n t s were analyzed f o r s u r f a c t a n t , c o s u r f a c t a n t and o i l c o n t e n t . Typical examples of t h e d a t a c o l l e c t e d a r e shown i n F i g u r e s 5 t o 7 and t h e r e s u l t s of t h e s e f l o o d s are summarized i n Table 1. This series of f l o o d s c l e a r l y shows a l l of t h e d i f f i c u l t i e s which can be encountered when an a t t e m p t is made t o compare a d s o r p t i o n d a t a obtained from d i f f e r e n t displacement experiments.

111

PORE VOLUME Figure 5:

Surfactant and Cosurfactant Breakthrouzh Curves (Flood 112: 50% PV I n j e c t i o n o f 3%, 1:5 PDM 337lSBA i n 1.5% NaCl Brine)

6

-

0 MICROEMULSION f$jOIL

0 BRINE 5

4

s

Y

g3 3 J

0

' 2

I

0 0

I

2

PORE VOLUME Figure 6 :

Effluent Phase Behavior (Flood 112)

3

112

0.3

w

z u

k

0.2

LL

0

z

0 I-

2

0.1

K LL

0.0

PORE VOLUME F i g u r e 7:

F r a c t i o n a l Flow of O i l (Flood 1 1 2 )

Oil Recover).

Surfacuat co-surfacunc

Surfacunr Refention

u~uhtratio

4 1

lJO.1

1.2

110.5

1.2

111

1.0

115

0.7

losses Due to Adsorption ?hse BeUhvior

ulr

-

-

(c/c0)-

I MI?

Ull

z

(SorIf-

z

(foul2

52

15

17

1.2

.02

66

10

19

1.0

0.10

85

5

22

0.7

0.21

70

8

21

1.2

0

F i r s t , i t should be noted that, i n t h e f l o o d s w i t h s u r f a c t a n t r a t i o s of 1 : O . l and 1:0.5, e s s e n t i a l l y no s u r f a c t a n t is contained i n t h e e f f l u e n t . T h i s means t h a t n o t enough s u r f a c t a n t was i n j e c t e d t o s a t i s f y t h e a d s o r p t i o n c a p a c i t y o f t h e r o c k and t h a t t h e s u r f a c e s n e a r t h e end of the c o r e are probably n o t completely adsorbed w i t h s u r f a c t a n t . Floods w i t h the 1:l and 1:5 s u r f a c t a n t l c o s u r f a c t a n t r a t i o s have l e d t o t h e production of some s u r f a c t a n t ,

113 b u t t h e c o n c e n t r a t i o n peaks a t t h e c o r e o u t l e t s a r e s u b s t a n t i a l l y d i f f e r e n t

from each o t h e r and, consepuently, t h e a d s o r p t i o n v a l u e s f o r t h e two d i f f e r e n t average s u r f a c t a n t c o n c e n t r a t i o n s a r e n o t d i r e c t l y comparable. A l s o , as Figure 8 shows, t h e normalized r a t i o s of s u r f a c t a n t and c o s u r f a c t a n t concent r a t i o n s are q u i t e d i f f e r e n t f o r t h e two f l o o d s . Therefore, even though i t may b e tempting t o suggest t h a t t h e r e is enough d a t a i n Table 1 t o a s c e r t a i n t h e dependence of s u r f a c t a n t a d s o r p t i o n on a l c o h o l c o n t e n t , a c l o s e r l o o k shows that a comparison o f s u r f a c t a n t a d s o r p t i o n f o r t h e f o u r d i f f e r e n t systems cannot be nade w i t h o u t conducting a d d i t i o n a l experiments. The l a s t three c o l u m s of Table 1 c o n t a i n t h r e e i n d i c a t o r s o f t h e o i l recovery of each s u r f a c t a n t f l o o d . Results show that e f f i c i e n c y i n i t i a l l y i n c r e a s e s w i t h c o s u r f a c t a n t c o n t e n t , h w e v e r , t h e f i n a l f l o o d performs less e f f i c i e n t l y t h a n t h e p r e v i o u s one. This confirms a conclusion r e p o r t e d p r e v i o u s l y that lower s u r f a c t a n t r e t e n t i o n does n o t n e c e s s a r i l y l e a d t o t h e b e s t o i l recovery e f f i c i ~ n c y . ' ~

I

? I

I

5.0

I

I I I

4.0 Y

I I

,*olF; I I

I

0.0 0

Figure 8:

0.5

2.0 PORE VOLUME

1.0

3.0

>!ormalized C o s u r f a c t a n t / S u r f a c t a n t R a t i o s a t Core O u t l e t s

The E f f e c t of Slug S i z e on S u r f a c t a n t R e t e n t i o n The A similar series o f experiments w a s performed w i t h TRS 10-80. s u r f a c t a n t l c o s u r f a c t a n t r a t i o w a s v a r i e d from 1:O.S t o 1 : l O . Typical flooding r e s u l t s a r e shown i n F i g u r e s 9 t o 11, and Table 2 s u m a r i z e s t h e d a t a obtained i n t h e s e f i v e floods.

114

L

0 SURFACTANT

A

COSURFACTANT

1

PORE VOLUME Figure 9:

Surfactant and Cosurfactant Breakthrough Curves (Flood 69: 75% PV Injection of 2%, 1:0.5 TRS 10-80/ SBA in 1.0%NaC1)

0

2

PORE VOLUME Figure 10:

Effluent Phase Behavior

4

115

0.3

1

0 0.2 LL

0

z 2

5a

0.1

4

0.0 PORE VOLUME Figure 11:

Table 2:

Surf acUnc cesurfaeunt

Fractional Flow of O i l (Flood 69)

Summary of Flooding Results with 3% TRS 10-80/SBA i n 1.0% NaCl/Octane System

W

Injected

Retantien

x

nyh

Trapped Surfacunt =&It

Wl

1110

80

0.35

0.2

.1s

.so

115

94

0.50

0.4

0.10

0.95

113

150

0.2

-

0.15

1.0

113

75

0.3

0.1

0.20

0.85

Ill

75

0.5

0.48

0.8

110.5

75

0.6

0.55

1.0

-

Adsorption

(dc,),

116 It is i n t e r e s t i n g t o compare t h e s u r f a c t a n t r e t e n t i o n v a l u e s observed i n f l o o d s using a s u r f a c t a n t / c o s u r f a c t a n t r a t i o o f 1 : 3 i n which d i f f e r e n t s i z e s l u g s of i d e n t i c a l composition were i n j e c t e d . A 150% PV s l u g w a s s u f f i c i e n t l y l a r g e t o enable t h e e f f l u e n t c o n c e n t r a t i o n t o r e a c h t h e l e v e l of t h e i n j e c t e d concentration. The i n j e c t i o n volume i n t h e o t h e r comparable f l o o d w a s halved so t h a t t h e e f f l u e n t c o n c e n t r a t i o n reached o n l y 85% o f t h e i n j e c t e d concent r a t i o n . While t h e r e is a d i f f e r e n c e i n r e t e n t i o n , t h e d i f f e r e n c e i n adsorpt i o n i s smaller. This apparent discrepancy can b e explained i n terms o f t h e amount of o i l trapped i n t h e hydrocarbon phase. In t h e f i r s t f l o o d , t h e r e is no trapped s u r f a c t a n t , w h i l e i n t h e second about one-third of the s u r f a c t a n t l o s s i s due t o unfavorable phase behavior. T h i s example shows c l e a r l y that i n f o r n a t i o n r e f l e c t i n g o n l y o v e r a l l s u r f a c t a n t r e t e n t i o n may be very misleading.

Another series o f experiments w a s performed w i t h t h e pure Texas #I s u r f a c t a n t . F i g u r e s 12 t o 1 4 show a n example of t h e experimental d a t a and Table 3 p r e s e n t s a summary of t h e r e s u l t s . I n t h i s c a s e , even though b o t h o v e r a l l r e t e n t i o n and a d s o r p t i o n i n c r e a s e w i t h i n c r e a s i n g s l u g s i z e , they do so a t d i f f e r e n t rates. Again, i t is t h e 106s due t o t h e phase behavior which is a f f e c t e d more by t h e s i z e o f t h e s u r f a c t a n t s l u g .

0 SURFACTANT

A COSURFACTANT

/ 0.8 '*OI

p'

\ \ \

0.6

c'co 0.4

0.2 0.0 0

I

2

3

PORE VOLUME Figure 12:

S u r f a c t a n t and Cosurfactant Breakthrough Curves (Flood 99: 100% PV I n j e c t i o n of 2X, 1:6 Texas
117

0 MXROEMLILSION fQOIL

6

BRINE

5

-

- 4 E Y

g 3 J

0

>

2

1

I

L

0 0

Figure 13:

0.31

I

PORE VOLUME

Effluent Phase Behavior (Flood 99)

nn

PORE VOLUME Figure 14:

Fractional Flow of O i l (Flood 99)

118 Table 3:

Summary o f Flooding Experiments with 2 X , 1:6 Texas $l/n-Propanol in 1.5% ?;aCl/Octane I

011 Recovery

PV Injected

Rerention

bsses h e LO Phase Behavior

Adsorption 4

6

(c/co)ux

8

(fol*

ZROIP

(Sor)fLnal

x

x

2

22

.6/6

d

0.50

0.7

0.24

0.4

0.05

38

18

0.75

1.0

0.5

0.5

0.25

55

14

22

1.0

1.1

0.14

0.54

0.60

74

7

27

Experiments have beer? performed t o e v a l u a t e t h e e f f e c t o f c o s u r f a c t a n t p r e s e n c e w i t h i n t h e chase b r i n e o n t h e r e t e n t i o n o f s u r f a c t a n t s . Table 4 summarizes t h e r e s u l t s . Table 4:

Summary of Flooding R e s u l t s w i t h 3%, 1:1.75 PDM 337lSBA i n 1.5% NaCl/Octane System

Flood

Flood

I

Oewription

Retention WlK

lasses Due co M i o r p t i o n (clco)Phase k h v i o r ~

oil i n the core

86A

ti0

1.2

85

Surfacunr slug o n l y

0.8

82

Surfacunr

followed by one PV of 3Z S M in brlne 83

w/a

ma18 ~~~~~

~~~

~

1.2

0.65

0.15

0.5

1.0

0.5

0.20

0.3

0.5

0.8

0.L

0.4

1.0

79

5

36

I

s.U

am 85 bur at SLoyEll INJJLCTION

RATE

Flood 86A c o n t a i n e d no o i l , and a d s o r p t i o n of 1 . 2 mglg w a s observed. Flood 85 contained o i l a t r e s i d u a l o i l s a t u r a t i o n and a d s o r p t i o n of 0.5 mgfg was determined. I n a d d i t i o n , t h e r e was a l o s s of 0.15 mgfg s u r f a c t a n t due t o p h a s e behavior. The procedure used i n Flood 82 was t h e same a s f o r Flood 85 except t h a t i n Flood 82 t h e one PV o f t h e b r i n e t h a t followed t h e s u r f a c t a n t s l u g cont a i n e d 3% secondary b u t y l a l c o h o l . A s e x p e c t e d , t h e r e t e n t i o n and a d s o r p t i o n l e v e l s a r e both lower, however, t h e amount o f s u r f a c t a n t trapped in t h e oil phase d i d n o t change a p p r e c i a b l y . The o i l r e c o v e r y w a s b e t t e r a s t h e f i n a l o i l s a t u r a t i o n i s lowered from 1 4 % PI’ i n Flood 85 t o 5% PV i n Flood 82. Another i n t e r e s t i n g a s p e c t observed i n t h i s experiment was t h e s h a p e o f t h e s u r f a c t a n t breakthrough c u r v e s ( s e e F i g u r e 15). Even though t h e f l o o d s were r u n a t t h e same i n j e c t i o n rates, t h e shape of t h e curve in Flood 82 g i v e s t h e i m p r e s s i o n o f a much h i g h e r l e v e l of d i s p e r s i o n t h a n t h a t i n Flood 85. S e v e r a l e x p l a n a t i o n s are p o s s i b l e , b u t t h e l i m i t e d d a t a a v a i l a b l e do n o t a l l o w f o r a unique i n t e r p r e t a t i o n and

119 t h e r e f o r e none i s o f f e r e d . However, i t i s observed t h a t d a t a such a s t h e s e should be o f concern t o people d e a l i n g w i t h numerical models f o r chemical f l o o d i n g s i n c e t h e d a t a s u g g e s t t h a t t h e chemical composition of t h e s u r f a c t a n t s l u g may s u b s t a n t i a l l y a f f e c t t h e a p p a r e n t d i s p e r s i o n .

t-

0

I

I

2

3

4

PORE VOLUME F i g u r e 15:

S u r f a c t a n t Breakthrough Curves

A r e c e n t l y p u b l i s h e d paper d e s c r i b i n g s t a t i c a d s o r p t i o n e x p e r i m e n t s , among o t h e r r e s u l t s , i n d i c a t e d t h a n a n attainment of adsorption equilibrium required a l m o s t two weeks o f c o n t a c t between a s u r f a c t a n t s o l u t i o n and a s o l i d a d s 0 r b e n t . l An a t t e m p t has been made t o f i n d o u t i f similar phenomenon t a k e s p l a c e d u r i n g d i s p l a c e m e n t t e s t s i n Berea c o r e s . T h e r e f o r e , Flood 85 w a s r e p e a t e d b u t a t a n i n j e c t i o n r a t e t h a t w a s t e n times lower and e q u a l t o a n a p p a r e n t f r o n t a l v e l o c i t y of 3 cm/day. It took more t h a n 1 0 d a y s f o r t h e surf a c t a n t s l u g t o p r o p a g a t e through t h e c o r e . The o i l recovery was b e t t e r and a n a d d i t i o n a l 4% PV o f o i l was recovered which i s i n agreement w i t h t h e p r e v i o u s l y p u b l i s h e d d a t a o n t h i s t y p e of w p e r i m e n t . 1 5 The r e t e n t i o n l e v e l w a s t h e s a m e b u t t h e l o s s o f s u r f a c t a n t by t h e phase t r a p p i n g mechanism i n c r e a s e d s u b s t a n t i a l l y w h i l e t h e a d s o r p t i o n l o s s w a s s l i g h t l y lower. It t h e r e f o r e seems r e a s o n a b l e t o s u g g e s t t h a t t h e a d d i t i o n a l r e s i d e n c e time f o r t h e s u r f a c t a n t i n t h e c o r e allowed i t t o be more c o n c e n t r a t e d i n t h e o i l phase, b u t t h a n a n i n c r e a s e i n a d s o r p t i o n w a s n o t observed. I t has been noted b e f o r e t h a t , f o r s u r f a c t a n t systems which a r e n o t a t o p t i m a l f o r m u l a t i o n ( i . e . n o t a t a middle phase c o n f i g u r a t i o n ) , t h e time r e q u i r e d f o r a t t a i n m e n t o f phase e q u i l i b r i u m may b e s u b s t a n t i a l . Our experiments e n a b l e t h e s u g g e s t i o n that t h i s p r o c e s s ofs u r f a c t a n t r e d i s t r i b u t i o n among t h e p h a s e s may be more r e s p o n s i b l e f o r t h e time dependence o f r e t e n t i o n t h a n is t h e slow a t t a i n m e n t o f a d s o r p t i o n e q u i l i b r i u m a t the solid-liquid interface. T h i s s u g g e s t i o n i s supported by p r e v i o u s l y r e p o r t e d r e s u l t s o n a d s o r p t i o n measurements i n b a t c h experiments i n which, i n t h e absence of o i l , t h e a d s o r p t i o n always reached e q u i l i b r i u m w i t h i n 24 hours.4

120 SUIPlARY

Based upon more than one hundred displacement experiments w i t h t h r e e t y p e s of s u r f a c t a n t s i n Berea c o r e s , t h e following conclusions may be made:

1.

Thermodynamically v a l i d s u r f a c t a n t a d s o r p t i o n isotherms should be determined i n b a t c h experiments.

2.

Displacement experiments y i e l d s u r f a c t a n t r e t e n t i o n v a l u e s which i n v o l v e averaging s e v e r a l v a r i a b l e s . I f any theory developed f o r a d s o r p t i o n is a p p l i e d t o r e t e n t i o n d a t a obtained from displacement experiments, t h e o t h e r causes of s u r f a c t a n t l o s s e s must be accounted f o r so o n l y a d s o r p t i o n d a t a are used.

3.

Experimental procedures that permit d i f f e r e n t i a t i n g between s u r f a c t a n t l o s s e s due t o a d s o r p t i o n and t h o s c due t o unfavorable phase behavior have been developed and t e s t e d .

4.

Pure s u r f a c t a n t (Texas # 1 ) , s y n t h e t i c s u l f o n a t e (PDY 3 7 ) , and petroleum s u l f o n a t e (TRS 1@-80) g i v e comparable r e s u l t s f o r r e t e n t i o n and a d s o r p t i o n i n Berea cores.

5.

Adsorption of s u r f a c t a n t s can be reduced by t h e s d d i t i o n o f low molecular weight a l c o h o l s (sec-butyl a l c o h o l , n-propano'.?

6.

For t h e t h r e e s u r f a c t a n t s s t u d i e d , a d s o r p t i o n l e v e l s d i d not exceed 1.2 mg/g. I f t h e o v e r a l l r e t e n t i o n i s h i g h e r , s u r f a c t a n t l o s s e s due t o unfavorable phase behavior o r some o t h e r mechanism should be suspected.

.

ACKNOWLEDGEMENTS The a u t h o r wishes t o acknowledge t h e a s s i s t a n c e and d e d i c a t i o n of L a u r i e Baxter and G a i l Parker who performed t h e p r e c i s e experiments necessary f o r t h i s paper. S i n c e r e l y acknowledged a r e Bev Moore and G a i l Donaldson f o r t y p i n g t h i s manuscript.

REFERENCES

1.

MEYERS, K. 0. and SALTER, S. J.; "The E f f e c t of Oil-Brine R a t i o on S u r f a c t a n t Adsorption from Microemulsion", paper SPE 8989 presented a t t h e SPE 55th Annual F a l l Meeting, Dallas, Texas (September 21-24, 1980).

2.

CELIK, M. S., GOYAL, A., MANEV, E. and SOMASUNDURAN, P.; "The Role of S u r f a c t a n t P r e c i p i t a t i o n and R e d i s s o l u t i o n i n t h e Adsorption of S u l f o n a t e on Minerals", paper SPE 8263 presented a t t h e SPE 5 4 t h Annual F a l l Meeting, Las Vegas, Nevada, (September 23-26, 1979).

3.

KRUMRINE, P. A., CAMPBELL, T. C. and FALCONER, J. S.; "Surfactant Flooding I: The E f f e c t of A l k a l i n e Additives on IFT, S u r f a c t a n t Adsorption, and Recovery Efficiency", paper SPE 8298 p r e s e n t e d a t the 5 t h Symposium on O i l f i e l d and Geothermal Chemistry, Stanford, C a l i f o r n i a (May 28-30, 1980).

1 21 4.

NOVOSAD, J.; "Adsorption of P u r e S u r f a c t a n t and Petroleum Sulfonate a t t h e Solid-Liquid I n t e r f a c e " , P r o c e e d i n g s o f t h e 3 r d I n t e r n a t i o n a l Conference on S u r f a c e and C o l l o i d S c i e n c e s h e l d i n Stockholm, Sweden, (August 20-25, 1 9 7 9 ) , Plenum P u b l i s h i n g , New York (1981).

5.

GLOVER, C. J., PUERTO, M. C., MAERTER, J. M. and SANDVIK, E. I.; " S u r f a c t a n t Phase Behavior and R e t e n t i o n i n Porous Media", (June 1979) SPEJ 2, 183-193.

6.

"A h'ew I n t e r p r e t a t i o n TROGUS, F. J . , SCHECHTER, R. S. and WADE, W. H.; of A d s o r p t i o n Maxima and Minima", (June 1979) J. C o l l o i d S c i . 70, 293-305.

7.

GALE. W. W. and SANDVIK. E. I.: Petroleum S u l f o n a t e Composition 191-199.

8.

SOMASUNDARAN, P. and HANNA, H. S.; "Adsorption of S u l f o n a t e s on Reservoir Rocks", p a p e r SPE 7059 p r e s e n t e d a t t h e 5 t h Symposium on Improved Methods f o r O i l Recovery h e l d i n Tulsa, Oklahoma,(April 16-19, 1978).

9.

"Adsorption from Liquid SIRCAR, S., NOVOSAD, J. and MYERS, A. L.; M i x t u r e s on S o l i d s : Thermodynamics of Excess P r o p e r t i e s and T h e i r Temp e r a t u r e C o e f f i c i e n t s " , (May 1572) I & EC Fundamentals ll, 249-254.

" T e r t i a r v S u r f a c t a n t Floodinn: S t u d i e s " , (1973) SPEJ

- Efficac;

2,

10.

GILLILAND, W. E. and CONLEY, F. R. ; " S u r f a c t a n t Waterflooding".

11.

FRANCES, E. I . , DAVIS, H. T., MILLER, W. G . and SCRIVEN, L. E.; "Phase Behavior of a P u r e Alkyl A r y l S u l f o n a t e S u r f a c t a n t " , p r e s e n t e d a t t h e 1 7 5 t h ACS N a t i o n a l Meeting, Anaheim, C a l i f o r n i a (March 13-17, 1978).

12.

"Research on Chemical O i l Recovery SHAH, D. 0. and WALKER, R. D.; Systems", Semi-Annual Report, U n i v e r s i t y of F l o r i d a , G a i n e s v i l l e (June 1977).

13.

ZORNES, D. R., WILLHITE, G. P. and MICHXICK, M. J . ; "An Experimental I n v e s t i g a t i o n I n t o t h e Use of HPLC f o r t h e D e t e r m i n a t i o n of Petroleum S u l f o n a t e s " , (June 1978) SPEJ 18,207-218.

14.

TRUSHENSKI, S. P . , DAUBEN, D. L. and PARRISH, E. R.; %Micellar Flooding - F l u i d P r o p a g a t i o n , I n t e r a c t i o n and M o b i l i t y " , (1974) SPEJ l4, 633-644.

15.

HEALY', R. N., REED, R. L. and CARPENTER, C. W.; Nicroemulsion Flooding", (1975) SPEJ 15,87-100.

"A Laboratory Study of

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123

CHEMICAL FLOODING

THE EACN OF A CRUDE OIL: VARIATIONS WITH COSURFACTANT AND WATER OIL RATIO MIN KWAN THAM and PHILIP BOALT LORENZ

U.S.Department of Energy Bartlesville Energy Technology Center

ABSTRACT

The EACN concept, which allows the s u b s t i t u t i o n of a crude o i l by an alkane o r an alkane mixture f o r phase volume or i n t e r f a c i a l tension studies, has been gene r a l l y accepted. I n t h i s paper, i t was shown t h a t such parameters as alcohol type, crude o i l composition, and water-oil-ratio could have an e f f e c t on the EACN of a crude o i l . The p a r t i t i o n behavior of the alcohol was traced as one of the causes f o r t h i s aberration. Interaction of surfactant with heavy crude o i l components was thought t o be another. Experiments t e s t i n g the l a t e r hypothesis is i n progress.

INTRODUCTION

The term Equivalent Alkaf_e3Carbon Number (EACN), w a s coined by the researcn &--.up from University of Texas This concept a r i s e s from the observation t h a t the i n t e r f a c i a l properties of any o i l with a surfactant can be modeled by the behavi o r of alkanes. Thus, heptane, heptylbenzene, and butyl cyclohexane a l l exhibit "optimum" conditions, i.e., minimum i n t e r f a c i a l tension (IFT) f o r the same combinations of surfactant, cosurfactant, and s a l t concentration. I n general, the benzene r i n g appeared t o have EACN = 0 , and the cyclohexane r i n g EACN = 3. Inl-3 addition, the EACN of a mixture of hydrocarbons follows the simple mixing r u l e ,

.

(Em)mixture

=

11

xi

EACNi,

---(l)

i

where X i s the mole f r a c t i o n of component i. i

4

This concept was later found t o be applicable t o crude o i l s and pseudo crudes , whereby an alkane or alkane mixture can be found t o model the IFT behavior of a crude o i l . An important finding of t h e i r s is t h a t the EACN of an o i l (crude, pseudocrude, o r hydrocarbon) is independent of the surfactant formulation, and t h a t t h i s equivalence always holds. Crude o i l , being dark i n color and usually q u i t e viscous, can make equilibrium attainment very slow and phase volume observat i o n d i f f i c u l t . Replacing the crude with hydrocarbon w i l l f a c i l i t a t e screening of surfactant formulation, and therefore, the EACN concept is a very valuable one. Recently, the Texas group and Glinsmann5, extended t h e concept of equivalent optimal s a l i n i t y t o high concentration surfactant systems (> 2%). Here, also, the EACN of a crude o i l i s independent of the alcohols and surfactants i n the formulations.

124 As p a r t of our s u p p o r t i n g reseagch program f o r t h e DOE micellar-polymer

pilot test i n Nowata County, Oklahoma , w e determined t h e EACN of t h e Delaware-Childers (D.C.) o i l from t h a t f i e l d , u s i n g s e v e r a l s u r f a c t a n t systems, and a t e r - o i l r a t i o s (WOR). It w a s found t h a t t h e EACN w a s n o t a c o n s t a n t v a l u e This paper r e p o r t s t h e r e s u l t s i n our i n v e s t i g a t i o n on t h e p r o b a b l e c a u s e s f o r t h i s v a r i a tion.

Y.

5 Glinsmann's method of measuring t h e EACN of a n o i l was followed, i n which t h e o p t i m a l s a l i n i t i e s of a s u r f a c t a n t system w i t h a series of a l k a n e s w e r e d e t e r mined. By comparing t h e o p t i m a l s a l i n i t y of t h e c r u d e o i l w i t h t h e same s u r CN w a s determined. Of t h e d i f f e r e n t c r i t e r i a o d e f i n i n g f a c t a n t system, optimal s a l i n i t i ~ ! " ~ t h e one used h e r e w a s t h e e q u a l s o l u b i l i z a t i o n from phase volume measurements.

6

Various s u r f a c t a n t systems were s t u d i e d f i r s t , w i t h s p e c i a l emphasis on t h e e f f e c t of a l c o h o l type, becay&213tudies have shown t h e s t r o n g i n f l u e n c e of a l c o h o l s on phase behavior and IFT The e f f e c t of c r u d e o i l components w a s t h e n s t u d i e d . F i n a l l y , t h e e f f e c t of WOR w a s a l s o s t u d i e d .

.

EXPERIMENTAL Materials The s u r f a c t a n t s used (and t h e i r p r o p e r t i e s ) a r e l i s t e d i n Table I. used w i t h o u t p u r i f i c a t i o n .

They were

The a l k a n e s were pure-grade hydrocarbon from P h i l l i p s Chemical Company. phenyl dodecane w a s from Eastman Kodak Company.

The

Procedure For phase-volume s t u d i e s , s u r f a c t a n t s o l u t i o n s were mixed w i t h o i l i n g l a s s t u b e s ( p r e c i s i o n b o r e t o 0.474 5 0.001 cm i . d . ) , and shaken f o r one minute i n a mecha n i c a l s h a k e r (40 Hz). Except where noted o t h e r w i s e , t h e WOR w a s set a t u n i t y . The t u b e s were k e p t i n a n a i r b a t h a t 30' f o r e q u i l i b r a t i o n . Usually, one week t o s i x months were r e q u i r e d f o r complete e q u i l i b r a t i o n . Some of t h e s o l u t i o n s - e s p e c i a l l y t h o s e w i t h h i g h viscosity--were shaken a second t i m e t o e n s u r e thorough mixing. Table I.

P r o p e r t i e s of S u r f a c t a n t s TRS 10-410(a)

Suntech I (b)

Blend of petroleum s u l f o n a t e s mixed w i t h C o s u r f a c t a n t 122

Petroleum sulfonate

S u l f o n a t e s of mixed x y l e n e s and propylene tetramer

% Active

45

62

65

Equivalent WeAght

450

418

372

wide

400-450

344-390 (92%)

Floodaid 1 4 1

TY Pe

93"

Equivalent Weight Distribution

(80%)

(a) (b)

An e x p e r i m e n t a l s u l f p g a t e (Sample No. I , Suntech Lot 768511) prepared by

Witco Chemical Company.

(c)

Suntech Tech, Inc. Amoco C o s u r f a c t a n t 122 i s a m i x t u r e of e t h o x y l a t e d a l c o h o l s .

125 Phase volumes were measured with a cathetometer. Standard correction for the round-bottom end of the glass tubes, and for the oil and water menisci, were obtained by weight measurements. Solubilization calculations were fashioned after the work of Glinsmann. The following assumptions were made in the calculations: (a) all the surfactant and cosurfactant is in the surfactant phase (this is an incorrect assumption as can be seen later, but the effect on the phase volumes is negligible); (b) the volumes are additive. In the present work, surfactant and electrolyte concentrations refer to the concentration in the aqueous phase. Some experiments were performed with crude oil components. Distillation of crude oil into distillates and heavy ends were done at 400°F and 10 -Egg. Vacuum.

.

Asphatene Analysis for acids and bases was by column liquid chromatography determination was by pentane precipitation. Alcohol concentrations were measured with a gas chromatograph. RESULTS AND DISCUSSION

Optimal Salinities The optimal salinities for a number of systems with normal alkanes are plotted in The observed behavior is the same a8 that reported in the literature that is, the optimal salinity increases with increases in (1) hydrocarbon chain length, (2) water solubility of the cosurfactant (the solubilities are in the order IBA < TAA < Amoco 122), and (3) concentration of the water soluble cosurfactant.

I 000

'

I-

/ 5 7 0 T i3s 10- 410, 1.8% Amoco 122 ( E l

0

4% Suntech

z

-

\ U

600 8

o

o

G

.

I, 2%

TAA (A) %Amoco 122 (D)

0

!i i400 c I z

YZYO

FA 141 ( F )

U v)

-I

U

200

I

I ooc;' ,

80

*

I

7

I

8

I I I I 9 10 II 12 A L K A N E CARBON NUMBER

-

I

13

I

14

Figure 1. Optimal salinity of surfactant systems with normal alkanes. TAA = tertiary amyl alcohol; IBA = isobutyl alcohol: Amoco 122 Amoco Cosurfactant 122.

126

*

The observed l i n e a r re1 t nship of I n (S ) versus alkane carbon number (ACN) w a s reported by SalagergYfg, who found t h t t t h e s l o p e s f o r a l l t h e s u l f o n a t e systems were 0.16 5 0.01. The value f o r t h e 5 percent TRS 10-410 3 percent i s o b u t y l alcohol (IBA) system obtained by least square f i t is 0.17, which is i n good agreement with h i s values. However, t h e s l o p e s were 0.11 f o r t e r t i a r y amyl alcohol and 1.8 percent f o r c o s u r f a c t a n t 122, and 0.14 with 1.0 percent cosur-, f a c t a n t 122. This i s i n c o n t r a d i c t i o n t o t h e p r e d i c t i o n of S a l a g e r ' s equation , which p r e d i c t s s l o p e independent of t h e alcohol. The s l o p e s f o r t h e Suntech and Floodaid s u r f a c t a n t were 0.12 and 0.28, r e s p e c t i v e l y .

-

E f f e c t of S u r f a c t a n t Formulations on t h e EACN of Delaware-Childers O i l The EACN of D. C. o i l w a s determined by comparing i t s optimal s a l i n i t y with t h a t of t h e alkanes f o r a given s u r f a c t a n t formulation. The s e v e r a l s u r f a c t a n t systems w e r e used t o determine t h e constancy of i t s EACN. Table I1 shows t h e results. Table 11.

The optimal s a l i n i t y and EACN of D. C. o i l with d i f f e r e n t s u r f a c t a n t formulations

Surfactant system

Optimal s a l i n i t y meq/l N a C l

EACN

A

4% Suntech I 2% T e r t i a r y amyl alcohol (TW

680

9.5

B

5% TRS 10-410 3% TAA

197

9.3

C

5% TRS 10-410 3% I s o b u t y l alcohol

193

10.9

D

5% TRS 10-410 1% Amoco 122

410

6.15

E

5% TRS 10-410

590

6.2

222

7.7

1.8% Amoco 1 2 2 F

*

12% FA 141*

Sulfonate content equivalent t o 7.6% TRS 10-410 o r Suntech I

The spread of 4.7 u n i t s i n t h e values i n d i c a t e s t h a t EACN as u s u a l l y determined i s n o t a constant quantity. From Figure 1 and Table 11, i t is necessary t o conclude t h a t t h e c u r r e n t l y accepted concept apply only over a narrow range of

conditions. Thus, Systems A and B y with f a i r l y s i m i l a r s u r f a c t a n t s , g i v e n e a r l y i d e n t i c a l Also, i n Systems D and E , a twofold v a r i a t i o n i n alcohol concent r a t i o n has no i n f l u e n c e on EACN. But t h e t r a n s i t i o n from C t o B t o D (with a s i g n i f i c a n t i n c r e a s e i n water s o l u b i l i t y of t h e c o s u r f a c t a n t a t each s t e p ) shows t h a t t h e cosurfactant s p e c i e s has a major i n f l u e n c e on t h e r e s u l t s . There are two p r o p e r t i e s of System F t h a t could c o n t r i b u t e t o i t s d i f f e r e n t EACN value: a wide d i s t r i b u t i o n of equivalent weight and a d i f f e r e n t type of alcohol.

EACN values.

The EACN of an o i l w a s determined by comparing t h e optimal s a l i n i t y of t h e o i l with those of alkanes. The v a r i a t i o n i n EACN observed above, n e c e s s a r i l y r e f l e c t s d i f f e r e n c e s i n p r o p e r t i e s between t h e o i l and alkanes. It is t h e r e f o r e of i n t e r e s t t o study t h e e f f e c t of s u r f a c t a n t formulation on t h e EACN of a number of oils.

127 EACN of Several o i l s With Systems C and F S u r f a c t a n t s Systems C and F were used t o compare t h e b h of d i f f e r e n t o i l s . System C was chosen because i t has been widely s t u d i e d and because t h e optimal s a l i n i t i e s , phase behavior and EACN of most of t h e o i l s s t u d i e d with t h i s system followed a "regular" p a t t e r n . On t h e o t h e r hand, System F w a s chosen f o r its "irregularities". Table 111 lists t h e optimal s a l i n i t i e s and EACN of t h e s e systems with a number of o i l s . The E l Dorado o i l r e s u l t s show d i f f e r e n c e s i n t h e EACN between t h e two systems, even though t h e d e v i a t i o n i s n o t as l a r g e as t h e D. C. o i l case. Bradford o i l shows an even smaller difference. These v a r i a t i o n s among t h e various crude o i l s may be compared w i t h t h e d i f f e r e n c e s i n t h e crude o i l composition (Table I V ) . Bradford o i l i s high i n p a r a f f i n , and D. C . o i l contains a l a r g e r q u a n t i t y of heavy b28es and a c i d s . These heavy cornpounds are known t o complex with t h e s u l f o n a t e s

5*artna,

.

Table 111.

Optimal s a l i n i t i e s and EACN of crude o i l s and crude oil f r a c t i o n s System F

System C .

EACN

S*

EACN

S*

E l Dorado o i l

169

10.0

261

8.3

Bradford o i l

196

11.0

425

10.1

Bradford D i s tillates

130

8.2

197

7.3

Bradford heavyends + decanea D.

c.

Oil

D. C . digtillate

238

12.4 (20)

615

11.4 (15.8)

193

10.9

222

7.7

103

6.7

132.5

5.8

295

8.7 (4.6)

D. C. heavy-

ends + decanea

185

10.6 (12.5)

(a) Equal weight r a t i o of heavy ends and decane The behavior of t h e components of t h e s e crude o i l s is q u i t e revealing. The dist i l l a t e s show a downward s h i f t i n EACN as compared with t h a t of t h e whole crudes, as expected. I n t e r e s t i n g l y , t h e l a r g e d i f f e r e n c e s between Bradford and D. C. o i l s with r e s p e c t t o t h e s u r f a c t a n t Systems C and P disappeared. Both show a d i f f e r ence of 0.9 u n i t s w i t h t h e two systems, as compared t o 0.9 and 3.2 f o r t h e whole Bradford and D. C. o i l s , respectively. Y e t , t h e f a c t t h a t t h e d i s t i l l a t e s having d i f f e r e n t EACN with d i f f e r e n t s u r f a c t a n t systems i n d i c a t e s t h a t t h e r e are c e r t a i n components i n t h e d i s t i l l a t e s behaving d i f f e r e n t l y from t h e alkanes, which are t h e standards. Actually, i t has been recognized tQat t h e equivalence between There are d e v i a t i o n s i n t h e alkanes and o t h e r series of compounds i s n o t exact a l k y l benzene and a l k y l cyclohexane series t h a t are g r e a t e r , t h e f a r t h e r one m o v e s away from EACN of 8. Table V p r e s e n t s some f u r t h e r d a t a on t h i s , showing t h a t t h e d e v i a t i o n can be q u i t e l a r g e when less conventional materials are used. The mixing of benzene with phenyl dodecane ( t o g i v e an EACN of 8) shows normal EACN with System C. A downward s h i f t i n EACN w i t h System E, similar t o t h a t

.

1 28 Table I V .

Crude o i l p r o p e r t i e s

Delaware-Chllders o i l G r a v ity "AP I

Bradford o i l

31.9

44.3

E l Dorado o i l

36.0

Nitrogen, percent

0.07

0.01

0.07

X Aromatic through f r a c t i o n lza

4.04

3.82

5.50

X Acids17

2.17

0.13

-

17 X Bases

1.58

0.3

X T o t a l Asphaltenes

1.46

0.02

X P a r a f f i n through c u t 7

64.0

34.6

55.3

(a) Cut temperature 437°F a t 40 nun Hg. (corresponding t o molecular weight of 280). (b) Cut temperature 392°F (corresponding t o molecular weight of 150). Table V.

Optimal s a l i n i t i e s and EACN of a k y l benzenes .System C EACN

s,

-

*System E

s,

EACN

Benzene phenyl dodecane mixture, 1:2 molar r a t i o

110

7.9

360

1.9

Phenyl dodecane

145

9.0

557

5.9

with crude o i l s was ob e ved. On t h e o t h e r hand, phenyl dodecane does n o t observe the simple s c a l i n g l a w g s g f o r both s u r f a c t a n t systems. Under t h i s l a w , phenyl dodecane should have an EACN of 12. The observed EACN d i f f e r s g r e a t l y from this value and cannot be explained t o t a l y by t h e smaller d e v i a t i o n previously reported f o r t h e case without alcohol

€.

For p r a c t i The d a t a on t h e heavy ends in Table 111 are a l o t more "irregular". cal experlmental purposes, i t was necessary t o c u t t h e v i s c o s i t y by mixing with equal weights of decane. To g e t t h e EACN of t h e heavy ends by themselves from No v a l u e Equation ( l ) , an assumption was necessary on t h e molecular weight (MU). of MU could be found t h a t was c o n s i s t e n t with t h e EACN v a l u e s , even f o r "regular" System C. The d i s t i l l a t i o n temperature suggested a M J of 450, which corresponds t o an alkane of carbon No. 32, b u t gave EACN 20 f o r t h e Bradford heavy ends and 12.5 f o r those from D. C. The weight f r a c t i o n s of d i s t i l l a t e s and heavy ends from D. C. o i l (which l o s t only 4 wt-X I n d i s t i l l a t i o n ) required MW 254 (EACN 18) €or consistency with t h e whole-oil EACN. The EACN of t h e decane mixture obeyed equation (1) only w i t h MW = 160 (EACN 11.3) f o r heavy ends. It is obvious t h a t heavy ends are n o t equivalent a t a l l t o alkanes even with System C; and t h e d i s crepancy between Systems C and E are very large.

-

Alcohol P a r t i t i o n i n g and Its E f f e c t on EACN W e have shown earlier t h a t r e p l a c i n g i s o b u t y l alcohol w i t h Amoco 122 i n a s u r f a c t a n t formulation causes a downward s h i f t i n EACN. It is t h e r e f o r e of i n t e r e s t t o study the p a r t i t i o n i n g behavior of these alcohols, because alcohol p a r t i t i o n i n g is known t o be t h e prime determlnant of t h e phajts-&h2yior, i n t e r f a c i a l tension, and optimal s a l i n i t y of a s u r f a c t a n t - o i l system '

.

129 Since determination of alcohol concentrations in crude oil poses considerable problem due to its wide boiling range--choosing the right column is difficult-only the partition coefficients in hydrocarbons were measured. It was suspected that the large differences in behavior of alkanes and allcyl benzenes would be reflected in the alcohol partitioning and suggest one cause for the difference between alkanes and crude oils. The results of the partitioning experiments are listed in Table VI. The numbers are relevant only at optimal salinity, but data under other conditions are given for illustration. Partition coefficients are not very sensitive to salinity up to 3 percent; the table shows that the same value was obtained for Co-surfactant 122 in pure water and in System E at optimal salinity of 3.4 percent. The differences between the partition coefficients of Amoco 122 in octane and phenyl dodecane is striking. In addition, there is a strong preferential partitioning of the heavier alcohol compounds (components 2 and 3) into the oleic phase of the phenyl dodecane system (Table VII). Thus, in comparison with octane, the aqueous alcohol concentration in phenyl dodecane is lowered. It is not known what will be the effect of this change of alcohol composition and concentration on the optimal salinity and EACN. It is certain, however, such changes will make the effort to estimate a "true EACN" impossible. That is, it is not possible to modify the definition of EACN to account for thig2 change in alcohol concentration. In agreement with the findings of Tosh, s & , the presence of surfactant did not affect the alcohol partitioning behavior for the systems studied. Table VI.

Partition coefficients of alcohols ~

Octane

~~~~~

Phenyl dodecane

3% IBA

0.3ga

0.32b'd

1.8% Amoco 122

0.6aaSd

5.5C'd

-

a = alcohol originally in alcohol originally in b c = alcohol originally in d in the presence of 5%

-

Table VII.

deionized water. 0.9% NaC1. 3.3% NaC1. TRS 10-410 at optimal salinity.

Distribution of alcohol components, System E Alcohol concentration, %

Phase Octane

Upper Middle Lower

Component 1 0.26 0.5 0.3

Component 2 0.25 0.84 0.24

Partition coefficient

component 3

-

0.15 0.53 0.25 0.8

Alcohol concentration, % Phase Upper Phenyl Middle dodecane Lower

Component 1 0.26 0.6 0.19

Component 2 0.44 0.69
.

Partition coefficient

Component 3

0.4

-

0.69
130 Solubilization a t Optimal S a l i n i t y The g&)ilization a t optimal s a l i n i t y , being r e l a t e d t o the i n t e r f a c i a l tension , i s an i n t e r e s t i n g property t o examine further. Under optimal condition (vo/vs) = (vw/vs) (v/vs)S* The value decreases with increases i n alkane carbon

=

Hsieh and Shah” density.

Puerto and Gale”

found a correlation between (V/Vs)s* and alkane

related (V/Vs)s* and the s i d e chain lgngth of an a l k y l

*

orthoxylene sulfonate. Figure 2 is a p l o t bf (V/V ) versus alkane carbon number s$l i n e a r f o r alkanes. Such for System C. Within experimental e r r o r , the p l o t is l i n e a r i t y w a s @served a l s o i n the s o l u b i l i z a t i o n of alkanes i n micelles , according t o Klevens , who studied s o l u b i l i z a t i o n as a function of molar v o l v s , structure, and other c h a r a c t e r i s t i c s of the solubizates. Reed and Healy had a l s o noted some p a r a l l e l developments between o i l and water s o l u b i l i t y and s o l u b i l i zation i n micelles. I n t h i s work, we found t h a t the data f o r crude o i l s and crude o i l d i s t i l l a t e s a l s o f a l l on the alkane line. This shows t h a t with System C , o i l s modeled by optimal s a l i n i t y are a l s o modeled by the degree of solubilization.

o

7 .O

0

.

0

0

6 .O

\

0

Alkane Bradford oil D.C. oil Bradford light ends 0.C.-light ends

-

5 .O

4.0

\

3.0 +-s

->” v)

\

>

\

2.05 % TRS. 10-410

Y

I

I

- 3% IBA I

I

I

I

I

4

Figure 3 I s a similar p l o t f o r System F. Again a l i n e a r relationship f o r alkanes w a s observed. I n f a c t , Systems D and E a l s o give t h i s l i n e a r r e l a t i o n with alkanes (not shown), which shows t h a t t h i s relationship is q u i t e general. I n t h i s case, the crude o i l s and d i s t i l l a t e s do not f a l l on the line. I f the EACN values-

131 determined with System C are used, t h e f i t is much b e t t e r . This suggests t h a t degree of s o l u b i l i z a t i o n might give mre c o n s i s t e n t values of EACN than optimal s a l i n i t y . Even so, D. C. o i l does n o t f i t t h e c o r r e l a t i o n very w e l l , perhaps due t o i t s high content of a c i d s , bases, and asphaltenes.

"."

+'.

\

0-

8.0.

---

\

\

Alkane Bradford oil A D.C. oil Bradford - light ends 0 D. C. -light ends o

D

7 . 0. 6 . 0 .-

5 . 0 .-

\

4.0.

\

\

\

\

\ \

3.0.

2.0' 12% FA 141 I.

I

I

I

I

I

I

I

EACN Figure 3.

(V/Vs)s* versus equivalent alkane carbon number

Q Effect of Water-Oil-Ratio

on EACN

The e f f e c t of water-oil-ratio (WOR) can be seen from Figure 4. It is noted t h a t by i n c r e a s i n g t h e WOR from 1 t o 2, t h e p o s i t i o n of t h e octane and D. C. o i l l i n e s are interchanged. That is t h e EACN of crude o i l changed from 7.7 t o higher than 8, by simply i n c r e a s i n g t h e WOR. It is p l a u s i b l e t h a t t h e WOR e f f e c t is r e l a t e d t o alcohol p a r t i t i o n i n g . Consider t h e case of phenyl dodecane, with the d a t a of Table V I I . Increase of WOR reduces t h e proportion of t h e o i l phase, which would mean t h a t less of component l w o u l d b e e x t r a c t e d from t h e aqueous phase. The proportion of water-soluble component i n t h e aqueous phase,would Since increase. According t o Figure 1, t h i s should l e a d t o an i n c r e a s e i n S

4 .

t h e r e i s no such f r a c t i o n a t i o n with octane, and presumably w i t h o t h e r alkanes, the i n c r e a s e i n EACN is as expected.

132

30C

*,"

20c

A Octane o D.C. oil

I oc

I

0

2

3

WOR Figure 4.

Variation of optimal s a l i n i t y with water-oil-ratio CONCLUSIONS

The EACN concept was found t o be i n e r r o r +hen s y s t e m involving ethoxylated alcohols and/or aromatics were used. Alcohol p a r t i t i o n i n g is found t o be an important f a c t o r causing t h i s deviation. The higher boiling, non-hydrocarbon components of the crude o i l might have contributed p a r t i a l l y t o t h i s "abnormal" behavior. This is under investigation. W e would l i k e t o advise caution when applying the EACN concept. ACKNOWLEDGMENT The authors wish t o acknowlege the help of J. B. Green and J. Lacina f o r the analyses on crude o i l s components. NOMWCLATURe

Am

Alkane carbon number.

EACN

Equivalent alkane carbon number.

S*

Optimal s a l i n i t y f o r phase behavior, meq/l NaC1.

0

vO

vs vW

Volume of o i l solubilized i n the surfactant phase. Volume of surfactant i n the surfactant phase. Volume of water solubilized i n the surfactant phase. Volume of water o r o i l solubilized per u n i t volume of surfactant a t optimal s a l i n i t y .

133 REFERENCES Cash, R. L., Cayias, J. L., Fournier, R. G., Jacobson, J. K., Schares, T., Schechter, R. S., and Wade, W. H. "Modeling Crude O i l s f o r Low I n t e r f a c i a l Tension," Paper 5813 presented a t t h e SPE Symposium on Improved oil Recovery, held i n Tulsa, Okla., March 22-24, 1976. Cayias, J. L., Schechter, R. S., and Wade, W. H.: "The U t i l i z a t i o n of Petroleum Sulfonates f o r Producing Low I n t e r f a c i a l Tensions between Hydrocarbon and Water," J. Coll. I n t . Sci., 59, 31-38 (1977). Cash, L., Cayias, J. L., Fournier, G., MaCalllster, D., Schares, T., Schechter, R. S., and Wade, W. H.: "The Application of Low I n t e r f a c i a l Scaling Rules t o Binary Hydrocarbon Mixtures," J. Coll. I n t . Sci., 59, 3944 (1977). Cayias, J. L., Schechter, R. S., and Wade, W. B.: "Modeling Crude O i l s f o r Low I n t e r f a c i a l Tension," SPE J., l6, 351-357 (1976). Glinsmann, G. R.: "Surfactantflooding w i t h Microemulsions Formed I n s i t u E f f e c t of O i l Characteristics." Paper SPE 8326 presented a t t h e 54th Annual F a l l Technical Conference and Exhibition of t h e SPE-AIME, held i n Las Vegas, Nevada, September 23-26, 1979.

"ERDA's Walker, C. J., Burtch, F. W., Thomas, R. D., and Lorenz, P. B.: Micellar Polymer Flood P r o j e c t i n Nowata County." O i l and Gas J., 74, 6068 (1976). "Calcium E f f e c t i n t h e DOE SurfactantLorenz, P. B., and Tham, M. K.: Polymer P i l o t Test." O i l and G a s J. To be published. "Physicochemical Aspects of Microemulsion Reed, R. L. and Healy, R. N.: Flooding A Review," i n Improved O i l Recwery by S u r f a c t a n t and Polymer Flooding. Shah, D. 0. and Schechter, R. S., eds., Academic P r e s s (1977).

-

"OptiSalager, J. L., Morgan, J. C., Schechter, R. S., and Wade, W. H.: mum Formulation of SurfactantfWaterfOil Systems f o r Minimum I n t e r f a c i a l SPE J., 2,107-115 (1979). Tension o r Phase Behavior."

"Cosurfactants i n Micellar System Used (10) Jones, S. C. and Dreher, K. D.: SPE J., l6, 161-167 (1976). f o r T e r t i a r y O i l Recwery." (11) Salteli, S. J.: "The Influence of Type and Amount of Alcohol on SurfactantOil-Brine Phase Behavior and Properties." Paper 6843, presented a t t h e 52nd Annual F a l l Technical Conference and Exhibit of t h e SPE-AIME, i n Denver, Colorado, October 9-12, 1977. (12) Hsieh, W. C. and Shah, D. 0.: "The E f f e c t of Chain Length of O i l and Alcohol As W e l l Aa S u r f a c t a n t t o Alcohol Ratio on t h e S o l u b i l i z a t i o n , Phase Behavior, and I n t e r f a c i a l Tension of OilfBrinefSurf actantfAlcoho1 Systems." Paper SPE 6594, presented a t t h e SPE-AIME I n t e r n a t i o n a l S p p o sium on O i l f i e l d and Geothermal Chemistry, La J o l l a , C a l i f o r n i a , June 2728, 1977. (13) Wade, W. H., Morgan, J. C., Jacobson, J. K., Salager, J. L., and Schechter, R. S.: " I n t e r f a c i a l Tension and Phase Behavior of S u r f a c t a n t Systems." SPE J., la, 242-252 (1978). "The Influence of Alcohols (14) Baviere, M., Schechter, R., and Wade, W. H.: J. Coll. I n t . Sci., &&,266-279 (1981). on Microemulaion Composition."

134 (15) Dominguez, J. G., Willhite, G. P., and Green, D. W.: "Phase Behavior of Microemulsion Systems with Emphasis on Effects of Paraffinic Hydrocarbon and Alcohols," in Solution Chemistry of Surfactants. Vol. 2, Gttal, K. L., ed., Plenum, New York, pp. 673-697 (1979). (16) Malmberg, E. W.: "Large-Scale Samples of Sulfonates for Laboratory Studies in Tertiary Oil Recovery, Preparation and Related Studies," Report No. FE-2605-20, National Technical Information Service, U. S. Department of Commerce, Springfield, Virginia (1979). (17) Green, J. B. and Hoff, R. J.: "Liquid Chrometography on Silica Using Mobile Phases Containing Aliphatic Carboxylic Acids I1 Applications in Fossil Fuel Characterization," J. Chrom. 2,231-250 (1981).

-

(18) Salager, J. L.: "Physico-Chemical Properties of Surfactant-Water-Oil Mixtures---Phase Behavior, Microemulsion Formation and Interfacial Tension." Ph.D. Dissertation, The University of Texas at Austin, 1977. (19) Miller, C. A. and Fort, T. Jr.: "Low Interfacial Tension and Miscibility Studies for Surfactant Tertiary Oil Recovery Processes." Report No. DOE/BC/10007-4, National Technical Information Service, U.S. Department of Commerce, Springfield, Virginia 22161 (1979). (20) Clementz, D. M. and Gerbacia, W. E.: "Deactivation of Petroleum Sulfonates by Crude Oils." J. Pet. Tech., pp. 1091-1093, September 1977. (21) Puerto, M. C. and Gale, W. W.: "Estimation of Optimal Salinity and Solubilization Parameters for Alkylorthoxylene Sulfonate Mixtures." SPE J., 17, 193-200 (1977).

-

(22) Tosch, W. C., Jones, S. C., and Adamson, A. W.: "Distribution Equilibria in a Micellar Solution System." J. Coll. Int. Sci., 31, 297-306 (1969). (23) Healy, R. N., Reed, R. L., and Stenmark, D. G.: Systems." SPE J., 2,147-160 (1976).

"Multiphase Microemulsion

(24) Huh, C.: "Interfacial Tensions and Solubilizing Ability of a Microemulsion Phase That Co-exists With Oil and Brine." J. Coll. Int. Sci., 2, 408-426 (1979). (25) Fleming, P. D., 111, Vinatieri, J. E., and Glinsmann, G. R.: "Theory of Interfacial Tension in Multicomponent Systems." J. Phys. Chem., 84,15261531 (1980). (26) Klevens, H. B.:

"Solubilization."

Chem. Rev., 1-74, 1950.

135

CHEMICAL FLOODING

DYNAMIC INTERFACIAL PHENOMENA RELATED TO EOR J. H. CLINT, E. L. NEUSTADTER and T. J. JONES The British Petroleum Company Limited, BP Research Centre, Chertsey Road, Sunbutyen-Tharnes, Middlesex, TWI 6 7 WV

ABSTRACT The relevance of dynamic interfacial tension and interfacial rheology to EOR is discussed. A technique developed by BP, the "Drop Volume Dynamic Tensiometer" allows dynamic interfacial tension to be determined over a wide range of rate of fractional area change. The behaviour of aqueous surfactant systems against crude oil is very different for fresh systems compared with systems where the phases have been pre-equilibrated. The application of these measurements to EOR systems is illustrated with examples of surfactants which give widely different oil displacement profiles. new method for the measurement of interfacial dilatational rheological parameters of oil/water interfaces is described. This is the pulsed drop experiment which has experimental advantages over the interfacial trough method and allows parameters to be determined over a wider range of frequencies. The effect of interfacial dilatational rheology on coalescence phenomena is illustrated with data for water-in-oil demulsifiers.

A

The ease of oil bank formation is influenced by the kinetics of coalescence, which in turn is controlled by film drainage from between colliding droplets. For crude oil films in water, increasing interfacial shear viscosity greatly reduces the rate of thinning. For the reverse system, increasing interfacial shear viscosity can reduce coalescence rates for oil drops in water almost to zero. This would have a very adverse effect on oil bank formation.

INTRODUCTION

In an enhanced oil recovery process, oil ganglia which have been trapped at small pore throats are released by lowering the interfacial tension, prevented from being retrapped by maintaining a low tension (dynamic) and encouraged to coalesce to form an oil bank. In all except the initial release it could be argued that it is the dynamic properties of the interface such as the dynamic interfacial tension and the interfacial rheology which will govern each individual and hence the overall process. This paper reports some novel methods for measuring dynamic interfacial tension and interfacial dilatational rheology which work very well for crude oil-water systems. Techniques will be illustrated with results for pure oils as well as crude oils, and the significance of these data for EOR processes will be discussed.

136 DYNAMIC INTERFACIAL TENSION This technique is essentially an extension of the drop volume method for interfacial tension and is illustrated in Figure 1.

WATER JACKET

'k

(I

SYRINGE PUMP

SEPTUM CAP

FIGURE 1

- DROP VOLUME DYNAMIC TENSIOMETER

Oil from a syringe pump is pumped at an accurately known volume flow rate to a syringe needle inserted through a septum cap into a small glass cell surrounded by a water jacket. The tip'of the syringe needle is ground flat and the inside and outside diameters determined accurately. For convenience of observation an image of the tip and drops formed is obtained using a microscope and TV camera and displayed on a monitor screen. The experiment consists very simply of measuring the number of drops formed in a fixed period of time and repeating at a whole range of volume flow rates Q. If n is the number of drops per unit time then the volume of each drop I

Q

v = -

... (1)

n The interfacial tension y can then be calculated using the usual formula

...

(2)

137

-

where P P ' is the density difference between the oil and water phases, and R is the radius of the tip to which the drop is attached. The latter may be the inside or outside tip radius depending on the wetting conditions. If we make the assumption that the drops are spherical then the rate of fractional area change at the time when the drop detaches can be shown to be

...

(3)

Hence we are able to estimate both the interfacial tension and the rate of fractional area change simply by measuring the rate of formation of drops at a known volume flow rate. Figures 2 and 3 illustrate the type of results obtained using Forties crude oil against two different surfactant systems. The crude oil used was a well head sample free of any additives such as demulsifiers or corrosion inhibitors. All aqueous solutions were made up in filtered sea water. There were large differences in the results depending on whether the oil/water systems were preequilibrated or whether they were fresh. Figure 2 shows the dependence of dynamic interfacial tension on rate of fractional area change for a surfactant system "A" at 7OOC.

d

I

E

FIGURE 2

- DYNAMIC INTERFACIAL TENSION

-FORTIES CRUDE/SOOO PPM

SURFACTANT "A" AT 7OoC

138 The difference between fresh andpre-equilibrated systems is immediately apparent. The preequilibrated tension rises rapidly at moderate rates of area increase whereas the tension of the fresh system stays remarkably low until very high rates of area change are reached where the area is roughly doubling every second. In contrast to this is the behaviour of the surfactant system "B" shown in Figure 3.

6

5 d

I

E

0

1

FIGURE 3

- DYNAMIC INTERFACIAL TENSION I FORTIES CRUDE/50OO

PPM

SURFACTANT "B" AT 70OC

This time the pre-equilibrated system gave interfacial tensions which were very small and at time9 unmeasurably so (only the one which could be measured is shown). The dashed line indicates that the tension remains low even at high rates of area change. The tensions for the fresh system showed the normal dynamic effect rising rapidly with modest rates of area increase. The interesting point about these two systems is that they give totally different oil removal profiles when tested in a model sand column test. For surfactant "A" which gave low fresh tension but high equilibrium tensions, removal of oil was rapid but incomplete. About 35 per cent of residual crude oil was removed in less than 2 pore volumes (PV). For surfactant "B", which gave high fresh tensions but very low equilibrium tensions, removal of residual oil was Complete but required a very large number (15) of PV.

139 Admittedly the shape and duration of the oil displacement curve will be dependent on more than just the dynamic tension behaviour. Surface wettability and the degree of adsorption will also be important factors. However, the distinction between the two systems above is clear and the oil displacement behaviour is logically related to the dynamic tension properties.

INTERFACIAL DILATATIONAL RHEOLOGY For the measurement of interfacial dilatational rheology the method employed in the past has been that of dilatational modulus measurements at various frequencies using an interfacial film balance (1). The method involves propagation of longitudinal waves of the frequency of interest and measuring changes of interfacial tension with a Wilhelmy plate. These changes, together with the phase differences between them and the area changes, allow calculation of Ed# the dilatational elasticity and nd, and dilatational viscosity, at each frequency. This technique suffers from a number of disadvantages including (a) Measurements are reliable only at fairly low frequencies where the wavelength of longitudinal waves is long compared with the distance between oscillating barrier and Wilhelmy Plate. (b) Good results depend on the rapid response of the Wilhelmy plate and the maintenance of a well defined contact angle. (c) The method uses large quantities of oil with a large area exposed to air allowing loss of light ends. Also the apparatus is not easily used at temperatures much above ambient. We have developed a new technique which uses a small drop of oil pulsed in water. Area changes are calculated from drop diameters and the tip diameter, and tension is calculated by measuring the excess pressure inside the drop with a sensitive pressure transducer. The experimental arrangement is shown in Figure 4.

CHART RECORDER

SYRINGE PUMP

SENSITIVE PRESSURE TRANSDUCER

WATER FROM THERMOSTAT

FIGURE 4

-

PULSED DROP METHOD FOR INTERFACIAL DILATATIONAL RHWlLOGY

140 The oil drop is formed at a ground glass or stainless steel tip. The radius of tip needed depends on the region of interfacial tension being investigated. the excess pressure inside the drop was measured using a transducer from SE Labs (EMI) Ltd, type SE 1150/WG. Output from the transducer is displayed on a chart recorder. Instead of the conventional oscillatory method for dilatational modulus measurements, the single pulse Fourier transform method was used (2). When the cell containing the aqueous solution of interest is sufficiently well thermostatted the drop radius (rl) is measured, a fixed volume pulse is injected from the syringe pump over a short period of time which increases the radius to r2 and then the variation of pressure with time is followed on the chart recorder. The shape of a typical pressure trace is shown in Figure 5.

TIME/MINS

E'fGURE 5

- TRANSIENT PRESSURE INSIDE DROP FOLLOWING SUDDEN EXPANSION

The equilibrium pressure after the experiment is lower than that at the beginning because the drop radius is larger. All of the pressure trace after the rapid rise is assumed to take place at a constant drop radius, the final radius r ~ . Then the interfacial tension at any time Y (t) is given by

... (4)

141 The interfacial modulus is usually written:-

t*

=

dy/dlnA

=

t'

+

it"

...

(5)

Taking Fourier transforms of the numerator and denominator coverts the perturbation time function AA(t)/A and the response time function y(t), to the frequency function. Thus:-

€*(W) =

...

(6)

...

(7)

...

(8)

...

(9)

...

(10)

For a perfect step function (instantaneous area change):-

Therefore:-

~ A / A1, iw

t*(w)

=

f-

Ay(t) [cos wt

-

i sin otldt

The real part gives us the dilatational elasticity:-

=

Ed(w) =

[ :

Ay(t) sin wt dt

AA/A

The lmaginary part gives the dilatational viscosity:-

E"

= *wnd(w) =

w J:

m

AY(t) cos wt dt

W A where w = angular frequency (radians per second).

Equations 9 and 10 can be used to calculate td and n at any frequency from the decay curve. A desk top microcomputer is adequate afthough a little slow. It is convenient to take approximately 100 readings ffom the.decay curve for use in these computations. The method was evaluated using a model system of 10 ppm stearic acid dissolved in n-decane against distilled water adjusted to pH 2.5 to prevent ionisation of the acid. Results are shown in Figure6 for the real (elasticr damponent of the modulus and in Figure 7 for the imaginary (frequency x viscosity) component.

142

d

I

20

-

15

-

10

-

I I I I1111

I I I11111~

I

I111111

I I iiiirr

-

E

2

\

5 -

W

010-3

10-2

10-1

1

FREQUENCY/Hz FIGURE 6 - REAL PART OF INTERFACIAL DILATATIONAL MODULUS FOR 10 PPM STEARIC ACID IN n-DECANE/DISTIUED WATER pH 2.5 AT 25OC. OPEN CIRCLES - TROUGH METHOD. FILLED CIRCLES DROP METHOD

-

10

8

6 d

I

E

a

4

W

2

0 10-1

FREQUENCY/Hz

FIGURE 7

-

IMAGINARY PART OF INTERFACIAL DILATATIONALMDDULUS. SYSTEM AND SYMBOLS AS FOR FIGURE 6

1

143 In each case the results are shown in comparison with data obtained previously using the interfacial trough technique, also using the Fourier transform method. Each set of data is the average of three separate runs. Agreement between the drop and trough methods is very good over most of the frequency range except possibly for the values of E " at intermediate frequencies. The shapes of the curves of E ' and E" are very close to those expected for a single relaxation mechanism. This is illustrated more strikingly in Figure 8 where a Cole-Cole plot ( E " against E l ) is shown. A single relaxation mechanism has a semi-circular Cole-Cole plot and the data from interfacial trough experiments clearly follow a semi-circle quite closely. Again agreement with pulsed drop data is encouragingly good considering the great difference between the two techniques. The implication is that the techniques measure real dilatational parameters and not artefacts.

4

I

E

5

0

10 E ' / ~ N

15

20

m-l

-

COLE-COLE PLOT FOR INTERFACIAL DILATATIONAL MODULUS. FIGURE 8 10 PPM STEARIC ACID IN n-DECANE/DISTILLED WATER pH 2.5. OPEN CIRCLES TROUGH METHOD. FILLED CIRCLES DROP METHOD

-

-

The single relaxation mechanism implied by Figures 6 , 7 and 8 is presumably diffusion of the stearic acid from the interface into the bulk decane phase. The maximum in C'' which corresponds to the inflection point in E ' occurs at U = 0 . 0 0 2 5 Hz which is an angular frequency w = 2nu = 0.0157 s ' . This is the characteristic frequency of the relaxation process. The relaxation time 'I = l/w = 64 sec. This would seem to be a very reasonable relaxation time for a diffusion controlled mechanism in a dilute system [c = 10 p p = 3.5 x 10-5 mol am-31.

144 The main advantages of the drop method over the trough method are (a) The system can be enclosed so that loss of light ends from crude oils is avoided. (b) The system can easily be thermostatted at high temperatures. (c) The system is compact and very small quantities of materials are used.

EFFECT OF INTERFACIAL RHEOLCGY ON COALESCENCE PHENOMENA The pulsed drop method has not yet been used to investigate coalescence phenomena. However, as an illustration of how interfacial dilatational rheology is involved in coalescence processes which are essential to oil bank formation, dilatational parameters for the Forties crude oil/formation water interface can be quoted which were determined by the trough method. The influence of various water-in oil demulsifiers was investigated. Results are shown in Figure 9 for E " as a function of frequency and as a Cole-Cole plot in Figure 10.

6

0

5

A

4 rl

Ei

w

0

3

-

FORTIES/FORMATION WAT

-

+10 PPM DEM 1113

-

+10 PPM RP 968

-

+ 5 PPM CC

6601

2

1

0

1 FREQUENCY/Hz

FIGURE 9

- EFFECT OF VARIOUS DEMULSIFIERS ON

IMAGINARY (VISCOUS)

COMPONENT OF INTERFACI~RILATATIONAtMODULUS

FORTIES CRUDE/FORMATION WATER AT 25OC

145

4

2

0

6 E'/~N

FIGURE 10

8

10

12

m-l

- COLE-COLE

PLOT FOR SYSTBMS IN FIGURE 9. SYMBOLS AS IN FIGURE 9.

The interface without additives gives two separate peaks indicating two different relaxation mechanisms are involved. From the positions of the peak maxima we can calculate relaxation times for the two processes of 87 sec and 4 sec. These are compared with relaxation times for systems with low concentrations of three water-in-oil demulsifiers in the table below. Relaxation Time (Seconds) Forties crude/formation water 87 4

+ 5

ppn CC 6601

+10 ppm RP 968 +10 ppn DEM 1113

1

4.5 22 9

The major effect of the &emulsifiers is to remove the relaxation process characterised by a long relaxation time. Shorter relaxation times are expected to mean more rapid film drainage (3) and therefore more rapid coalescence. These demulsifiers are also found to reduce the interfacial shear viscosity of the crude oil/water interface. However, from Figure 9 it can be seen that at some frequencies the dilatational viscosity is reduced whereas at other, normally higher, frequencies the dilatational viscosity can be greatly increased. At this stage the mechanistic implications of these observations are not fully understood. Further work on this topic is planned.

146 MEASUREMENT OF DRAINAGE RATES FOR SINGLE OIL FILMS IN WATER Direct evidence for the influence of interfacial shear rheology on the kinetics of drainage of thin films has been obtained by measuring the thickness of crude oil films in distilled water. The technique was the same as that used to measure thickness of oil films in air ( 3 ) , but having the whole cell filled with water. Measurements of the intensity of light reflected from the single oil film were used to calculate film thickness as a function of time. Results for Iranian Heavy crude and for Forties crude in distilled water are shown in Figure 11.

4

0

0

0.5

1 .o

1.5

2.0

(t/min)-4 FIGURE 11

-

FILM DRAINAGE

-

CRUDE OIL FILMS IN DISTILLED WATER AT 25OC

For the Iranian Heavy case the thickness is proportional to t-+ in accordance with the Stephan-Reynolds equation indicating that drainage is essentially from between two rigid interfaces. In contrast the Forties crude in water film drainage curve is not a straight line and indicates much more rapid drainage of the film than can be accounted for by the lower bulk viscosity of Forties oil. This implies that the Forties crude/distilled water interface is much more fluid compared with the Iranian Heavy case. These implications are borne out by measurements of interfacial shear viscosity at the crude oil/water interface. Using the biconical bob shear rheometer the results shown in Figure 12 were obtained. Over a period of hours the shear viscosity of the Iranian Heavy/distilled water interface builds up to quite high values whereas that for the Forties/distilled water interface remains low. The reverse system, drainage of water films from between colliding oil droplets, is relevant to oil bank formation. Because crude oil is opaque it is not possible to perform experiments analogous to the single oil film drainage measurements outlined above. However, there is clear evidence in the literature for the reduction of coalescence rates for crude oil drops in water when interfacial shear viscosity is increased ( 4 ) .

4

E

P*

.6

\

E v)

8 v)

H

.4

3

3w X

v)

a

.2

H

V

2

FORTIES

a B

z H 0

1

2

3

I

I

4

5

INTERFACE AGE/HOURS FIGURE 12

- CRUDE OIL/WATER

INTERFACIAL, SHEAR VISCOSITIES AT 25OC

Clearly an important quality of an EOR surfactant will be the maintenance of low interfacial shear viscosity as an aid to oil bank formation.

CONCLUSIONS 1.

A dynamic drop volume technique can be used to determine dynamic

interfacial tension in crude oil/water systems as a function of rate of fractional area change. 2.

For different surfactant systems which have markedly different oil removal profiles from sand columns, dynamic interfacial tension behaviour can be completely different.

3.

A pulsing drop method has been devised which can measure the

interfacial dilatational rheological parameters for oil/water systems. The results agree well with those determined using an interfacial trough. Both systems can be used with the single step pulse Fourier transform method. 4.

For a pure system of stearic acid in n-decane against distilled water at pH 2.5, the complex dilatational modulus gives a semi-circular ColeCole plot indicating that relaxation at the interface is due to a single mechanism, presumably diffusion to and from the interface.

5.

For a Forties crude/oil formation water interface, two separate relaxation processes are detected, presumably diffusion and molecular rearrangement. Water in crude oil demulsifiers remove the mechanism with the longer relaxation time.

6.

Drainage of crude oils films in water can be followed by reflectance measurements of thickness. Drainage rate depends critically on interfacial shear viscosity.

148 NOMENCLATURE A

Q R V 9

n

AP t Y €*

E ' € "

Ed Ild U

P 'I

w

Area of interface (ma) Volumetric flow rate (m3 s-1) Tip radius (m) Volume of drop (m3) Acceleration due to gravity (m s - ~ ) Number of drops per unit time (s-l) Excess pressure inside drop (Nm-2) Time (s) Interfacial tension (Nrn-l) -1 Complex interfacial dilatational modulus (Nm ) Real part of dilatational modulus (Nm-1) Imaginary part of dilatational modulus (Nm-l) Interfacial dilatational elasticity (Nm-1) Interfacial dilatational viscosity (Ns m-l) Frequency (cyclic) (Hz) Density (kg N 3 ) Relaxation time ( 8 ) Angular frequency (s-1)

ACKNOWLEDGEMENT Permission to publish this paper has been glven by The British Petroleum Company Limited.

REFERENCES GRAHAM, D.E., JONES, T.J., NEUSTADTER, E.L. AND WHITTINGHAM, K.P. "Interfacial Rheological Properties of Crude Oil Water Systems", 3rd International Conference on Surface and Colloid Science, Stockholm, 1979, Plenum Press, in the press. LOGLIO, G., TESEI, U. AND CINI, R "Spectral Data of Surface Viscoelastic Modulus Acquired Via Digital Fourier Transformation" J. Colloid Interface Sci, (1979), 71, 316. CALLAGHAN, I.C. AND NEUSTADTER, E.L. "Foaming of Crude Oils: A Study of Non-Aqueous Foam Stability" Chemistry and Industry, 17.1.81, p 53. WASAN, D.T., McNAMARA, J.J., SHAH, S.M., SAMPATH, K. AND ADERANGI, N. "The Role of Coalescence Phenomena and Interfacial Rheological Properties in Enhanced Oil Recovery: An Overview" J. Rheology, (19791, 23, 181.

149

CHEMICAL FLOODING

BEHAVIOR OF SURFACTANTS IN EOR APPLICATIONS AT HIGH TEMPERATURES LYMAN L. HANDY Department of Petroleum Engineering University of Southern carifornrb

ABSTRACT Temperature sepsitive properties of some anionic and nonionic surfactants used in EOR operations have been measured. Of particular interest is the thermal stability. Those surfactants we investigated decomposed by first order kinetics. The stability can, therefore, be quantitatively expressed in terms of the half-life of the surfactant. At 180°C half-lifes for petroleum sulfonates varied from 1 to 11 days. Activation energies were measured and these data can be used to predict half-lifes at other temperatures. Solubility of nonionics is known to be affected by temperature. At the cloud point they dehydrate and become less soluble. Anionics appear to form precipitates with rock minerals. This problem increases with increasing temperature. Adsorption is temperature dependent although the experimental results for the anionics were obscured by precipitation. Adsorption of nonionics were observed to decrease with increasing temperature at low concentrations but to increase with temperature at high concentrations. Interfacial tensions have a l s o been measured as a function of temperature. The results vary with the surfactant. Mixtures of sulfonates, however, have all s h a m an order of magnitude reduction in interfacial tension at temperatures in excess of 120%.

INTRODUCTION Much of the unrecovered oil in the United States occurs in heavy oil deposits, mostly in California. Large accumulations of heavy oil are also known to occur in Venezuela, Mexico, Canada and elsewhere. To recover this oil the viscosity must be reduced by orders of magnitude. The only feasible way to accomplish this objective is to heat the oil in-place. This can be done by either steamflooding or in situ combustion. Steam injection is the most frequently used process. This has given rise to the investigation of various chemical additives which will improve the process. One of the problem with steam is that it tends to finger through the formation and to override the oil. Various organic chemicals have been investigated for use with steam as flow diverters to minimize gravity override. Surfactants are being evaluated as possible additives which will reduce the residual oil saturation in that portion of the reservoir which is flooded only with hot water during steam drive. Although the temperature requirements for chemicals to be used at steam tempiratures are much more rigorous, high temperatures are also encountered in the deeper reservoirs which are currently being considered for enhanced oil recovery. This has introduced additional requirements with respect to the temperature compatibility of chemicals used in these reservoirs.

150 In the present paper we are concerned, primarily, with surfactants, but problems are also encountered with polymers at high reservoir temperatures. Four aspects of the effect of temperature are considered: the effect on the stability of the surfactants, the effect on solubility, the effect on water-oil interfacial tensions and, finally, the effect on adsorption onto the solid matrix.

THERMAL STABILITY A limited number of studies have been reported in the literature on the stability of surfactants suitable for oilfield operations at temperatures in excess of 100°C. The most extensive of these is that of Handy et al.’ Data have also been reported by others for the petroleum sulfonate, TRS 10-80, but no temperatures were stated for those experiments.2 In our earlier report results were presented for anionic and nonionic surfactants. The anionics included sodium dodecylbenzene sulfonate, an acidic Dowfax sulfonate and several petroleum sulfonates. The petroleum sulfonates included TRS 10-80 manufactured by Witco and Petrostep 465 manufactured by Stepan Chemical Corporation. Dowfax 240 was from Dow Chemical Company. The nonionic was an alkylphenoxypolyethanol manufactured under the trademark of Igepal CO-850 by GAF.

The surfactants were mixed at various concentrations without salt and aged at elevated temperatures in Teflon containers in Parr Acid Digestion bombs. Particular care was taken to eliminate air from the bombs. Long term aging tests were conducted in sealed borosilicate glass vials. In comparing our work with that of others, a major factor is the method used for chemically analyzing for the active surfactant. The most common procedure is the Epton titration, which involves a dye transfer between two phases. We found the end points difficult to detect in this procedure. We used instead W spectrophotometry. The bond which ruptures during high temperature aging is the sulfur-aromatic ring bond. Disubstituted aromatic rings have a characteristic absorption wave lengths at 220-240 nm and 260-280 nm. When the sulfur-aromatic ring bond ruptures, the absorption at these characteristic wavelengths is decreased. The decrease in the concentration of the active surfactant can be measured quantitatively from the change in the peak heights. Concentrations were determined from a comparison of peak heights with those observed for solutions of known concentration. The alkylphenoxypolyethanols could also be analyzed by W absorption because these compounds also have a disubstituted aromatic ring. A modification of the Epton titration has been proposed by Mukerjee which is reported to be more quantitative than the original method. We have not tested that procedure. The decomposition reaction for the petroleum sulfonates is the following: ArSO;

+ 2H20

ArH

+ SO;

+ H30=

It would be possible, therefore, to monitor the reaction from a measurement of the pH. Representative data from reference 1 are given on Figures 1 and 2. The plot of the logarithm of concentration versus time was linear. pH versus time was also observed to be linear. The other anionic surfactants gave similar behavior. These results indicate that the decomposition reaction for the anionics is first order. The decomposition rate for a reaction following first order kinetics is

-

dC/dt = kt

151 c

=

c0c-kt

or log

c

=

-kt + 2.303

log co

In these equations C is concentration in moles per liter; C is the initial 0 concentration; t is time in days and k is the rate constant in days-'. The rate constant is determined from the slope of the semilog plot. One can also show that when C/Co 4, the elapsed time is equal to the half-life of the surfactant.

-

TRS 10-a0 C, = 243 x IU3M

70

I

0

99

OI 144 Ism HEATING TIME (HRS)

240

Fig. 1-Concentration of TKS 10-80 as function of heating time at 149°C and 204°C

Fig. 2 - pH of TRS 10-80 as function of heating time at 140'C

If one has rate constants at several different temperatures one can determine the activation energy for the reaction. With the activation energy one can determine rate constants and half-lifes at other temperatures. This is particularly useful in estimating the stability of surfactants at lower temperatures for which the decomposition rates are low and long times would be required to measure the half-lifes. Figure 3 is a plot of the log of the rate constant versus the reciprocal of the absolute temperature for TRS 10-80. This plot is typical of those obtained for the surfactants which were tested. In the equation log

a

-E a 2.303 RT +

Ea is the activation energy in cals/mole; R is 1.987 cals and T I s the absolute temperature in OK. From the slope of the plot one can determine the activation energy.

152 A summary of decomposition data for several surfactants is given in Table 1. At 180°C Petrostep 465 is the most stable of the surfactants we investigated. Because of its high activation energy relative to the other surfactants, this surfactant would have a half-life of about 16 years at 100°C. None of the surfactants have adequate stability for use at normal steam temperatures. These results would be expected to be representative for aryl sulfonates, but better stabilities have been informally reported for alkyl sulfonates.

I

1

I

1

TRS 10-80

I

w

0.7 0.5

SOLUBILITY 0.21 I 1 1 I I Quantitative data on the effect 2.0 21 ?A? 2.3 2.4 28 of temperature on the solubility of f IO~PK-IJ petroleum sulfonates have not been reported, but evidence has been cited Fig,. 3 - The rate constant (k) by several authors that precipitation 1 of the sulfonates occurs at the a s tunction of -(OK-') for T higher temperatures in natural sand'IKS 10-80 stones. * s 5 , This occurs not as a result of a direct temperature effect on the solubility of the surfactants but, apparently, as a result of an interaction with minerals in the porous media. Reed has measured a significant increase in the solubility of rock minerals at steam temperatures.' The petroleum sulfonate ions form precipitates with divalent cations. These precipitates are likely to decrease in solubility with increasing temperature. In general, the presence of salt in the solutions decreases the solubility of the sulfonates.

TABLE 1 SUMMARY OF DECOMPOSITION DATA FOR SURFACTANTS Surfactant

Mol. Wt.

Temp. "C

NaDDBS

348.5

130 180 150 180

Dowfax 2AO

500

177

TRS 10-80

415

149 204.5 180

Petrostep 465

465

130 157 180

Igepal CO-850

1100

130 180

t$(days) 6.13 .22 13.6 1.75 5.6(W) 6.9(pH) 17.4 3.0 7.0 444 108 11 .75 .22

Ea(kcals) 24.0 24.0 26.0 26.0 NA 12.4 12.4 12.4 25.2 25.2 25.2

8.84

8.84

Ziegler observed turbidity in the produced fluid from a Berea sand pack when sodium dodecylbenzene sulfonate solutions were injected at a concentration of 1400 pmols/liter. However, data in Figure 4 show that surfactant precipitated out of a 0.2 molar salt solution could be redissolved when distilled water was injected and when the temperature was increased. In this experiment the sand pack was flushed with 1374 pmols/liter surfactant In 0.2 M NaC1. Then the pack was flushed with salt solution only, with distilled water and. finallv. Fig. 4-Desorotion curve for NaDDBS with distilled wate; at 180'C. Distilled water redissolved sulfonate precipitated out of, brine and an increase in temperature to 180'C did redissolve sulfonate still precipitated at 40°C after the distilled waterflood. The solubility of nonionic surfactants is not as sensitive to salt concentration as that of the anionic surfactants. On the other hand, the solubility of the alkylphenoxypolyethanols shows a marked sensitivity to temperatures. At very specific temperatures called the cloud points, the ethoxy groups in these compounds lose associated water and the solubility decreases abruptly to form precipitates. The cloud point is a function of the molecular weight of the surfactant, the electrolyte composition and the concentration of the surfactant. Cloud points as a function of concentration for Igepal CO-850 are shown in Table 2. TABLE 2

SUMMARY OF PHYSICAL AND SORPTION PROPERTIES FOR IGEPAL CO-850 Molecular Weight

-

CMC = 100 w l / L

1,100

Cloud Points

cn trunOl/L)

Cloud Point ("C)

73

>180 113 106

366 640

Sorption Properties Temperature ("C)

Keq (dm'/pmol)

A (pmol/m2)

kl (dm'/pmol.h)

k2

(hours-')

45

5.78~

0.524

1.2 x

0.21

70

2.09 x lo-'

0.705

1.5 x

0.72

95

7.34 x lo-'

0.831

2.5x10-'

3.41

AHo (Id). -40.2

154 EFFECT OF TEMPERATURE ON SURFACTANT ADSORPTION If low concentration surfactants are to be used in combination with steamflooding or hot waterflooding in a reservoir. the effect of temperature on adsorption becomes a matter of considerable importance. Surfactant transport could be combined with heat transport through the reservoir. The surfactant concentration shock could either lead or trail the temperature shock. Data will be presented later which shows that interfacial tensions are reduced at higher temperatures. If this is the case, one would prefer to have the surfactant front remain in the heated portion of the reservoir. In steamflooding, however, it is well-established that the steam overrides the oil. The water transporting the surfactant is likely to be moving primarily in a heated region immediately below the steam zone. In that case the surfactant will be moving in a hot portion of the reservoir under isothermal conditions. Whichever mechanism prevails in the reservoir, adsorption isotherms will be required for the prevailing temperature at which the surfactant is being transported. Consequently, we have made an initial effort to determine adsorption Isotherms as a function of temperature for an anionic and a nonionic surfactant. An abundance of data exists in the literature for adsorption of surfactants onto various substrates at room temperature. These data normally obtained by equilibrating the surfactant solutions with the surfaces. Measuring adsorption isotherms at steam temperatures is a difficult problem.

various were solid much more

Ziegler et al. obtained data using a dynamic, chromatographic transport procedure. The porous medium was a disaggregated. fired Berea sandstone, packed in a core holder. The core was saturated with brine or distilled water and placed in an oven to maintain the temperature at the desired value. Surfactant solution was injected, starting at low concentrations. The pore volumes of solution required to move the surfactant through the core were measured. From chromatographic transport theory the quantity of surfactant adsorbed at this concentration could be calculated.

'

The surfactant concentration in the injected solution was increased stepwise and the volumes required to move each concentration step through the core was measured. The surface area of the sand had been measured by a variation of the BET method. From these data the adsorption isotherm

-

isotherms were also measured E 28' by the conventional static method at 25OC and 95OC. -24Dynamic and static adsorption data were obtained for sodium o 20dodecylbenzene sulfonate x (NaDDBS) and Igepal CO-850. 16: As discussed earlier, the NaDDBS has a low solubility in 0.2 molar NaCl and also tended to precipitate at the higher temperatures when in contact with the Berea sandstone. Consequently, only adsorption isotherms obtained by the static method are reported for NaDDBS. These data are shown at 25OC and 9SoC for concentrations up to 70 pmols/L on Figure 5. The results show

9 $

I

I

I

I

I

NoCl

=

I

02 Y

0

I

I

I

--

'

---

155 that adsorption decreases with increasing temperature as one would expect. Data obtained in the absence ot salt show less temperature dependence. Because of the precipitation problem, no dynamic data are reported for NaDDRS. 'Thc results o t desorption experimenLs are shown in Figure 4, but the slugs of surfactant being produced after reducing Lhe salt Concentration or after increasing the temperature had been explained earlier as being more the result of dissolving precipitated surlactant than desorption or adsorbed surfactant. The slug produced after increasing Llie temperature, however, may have resulted in part from decreased adsorption at elevated temperatures. This would be consistent with the limited static data showing a decrease in adsorption with temperature. The experiments with Igepal CO-850 were complicated by the cloud point, which is characteristic of this class of surfactants, and by the instability of this surfactant at high temperatures. Static results are given in Figure 6 . 28 Equilibration time for the ' 1 1 1 1 1 1 1 1 95OC curve was limited to E three hours. Degradation NeCl :O O M was a serious problem if significantly longer times were used. The results show a slight temperature depend- i ence. Figure 7 is an example I! 16 of results obtained by the dynamic method for Igepal CO-850. Surfactant was LEGEND injected at an initial con- ;oa + 25% centration of 67 pmols/L 2 -9- 95% and at two incremental coni~ centration higher than the initial. Consistent with a 2 1 1 1 1 1 1 1 ~ Langmuir-type isotherm, the O0 0 20 40 60 80 m pore volumes of injected SURFACTAM CONCENTRATION, M I 1 O6 surfactant required to produce the incremental step Fig. 6 - Static adsorption isotherms f o r in concentration decreased Igepal CO-830 with increasing concentration. Dynamic data were obtained at 45°C. 70°C and 95°C. Data were not obtained at higher I 1 I I I I I I I temperatures because of the 0 0 0 0 0 limit established by the cloud point's. Degradation of Igepal is not a problem in the dynamic procedure because the surfactant is LEGENO at an elevated temperaCo = 6?uM, v = 139 m/h ture only while moving -c- CO = 331uM, v 1 137 m/h through the core. 0

'

(v

-

-

-

<

The dynamic adsorption isotherms for Igepal are given qn Figure 8. At low concentrations adsorption decreases with temperature, but adsorption increases with temperature for concent.rations in excess of about 200 pmols/L. This effect is also associated

-

--+-

:597uM,

v = 139 m/h

:I8 a

LhMOLE- h

T=95%

NaCI = O O M

kl

02

00

o

4

a

12

16

x)

24

28

32

PORE VOLUMES INJECTED

Fig. 7 - Breakthrough curves f o r Igepal CO-850

156 with the cloua point. As the ethoxide groups lose their associated water, the surfactant becomes less soluble and would be expected to separate out onto the solid phase more readily. The Langmuir constants for Igcpal are given in Table 2. The results of the dynamic method with Igepal indicate that the method is suitable for determining adsorption isotherms at elevated temperatures, but the surfactants, Igepal and NaDDBS, were not suitable for testing the procedure at temperatures in excess of 100°C because of solubility problems. EFFECT OF TEMPERATURE ON INTERFACIAL TENSIONS Few results have been reported giving interfacial tensions of.oil0 loo 300 500 surfactant solutions as functiohs of SURFACTANT COWCLNTRMIOII, H I temperature. These data are required for any process using surfacFig. 8 - Dynamic adsorption tants in reservoirs but, particularly, isotherms for Igepal CO-850 for the high temperatures associated with steamflooding. We have used two methods for measuring interfacial tensions as functions of temperature and pressure. These are the-pendent drop and the spinning drop methods. The minimum interfacial tension that can be measured on the pendent drop equipment is about 0.1 mN/m and that is with low precision. The spinning drop reportedly gives data below 0.001 mN/m. If time is an important factor in establishing equilibrium between the surfactant solution and the oil, the pendent drop procedure is also less suitable than the spinning drop. In the pendent drop method a drop can be suspended at the most for one-half hour. On the other hand, a drop can be maintained indefinitely in a spinning drop apparatus. Normally, equilibrium times for surfactant solutions and refined oils are small. The problem arises with caustic solutions and crude oils. Some reports have indicated that equilibrium for these systems has not been established even in matter of days. Although the spinning drop would appear to be the preferred method, we have obtained data by both procedures.

'*'*'

We have modified the spinning drop equipment of Gash and Parrish for use at temperatures to 2OO0C and preseures to 30 The design of the spinning drop equipment is such that it is a simple matter to construct an air bath around the capillary tubes which contain the spinning drop. No bearings need to operate at thermostat temperatures. An epoxy was found that was effective in sealing the capillary tubes at the above temperatures and pressures. The epoxy can be easily drilled out of the tubes to permit using them again. Our equipment is easy and inexpensive to build, but it does not have the versatility of that developed at the Technical University of Clausthal. Their apparatus operates at higher pressures and temperatures and permits the exchange of fluids in the rotating capillary during the experiments. An important factor in measuring interfacial tensions by either the pendent drop or the spinning drop method is the density difference between the water and the oil. This becomes particularly critical when measuring interfacial tensions at elevated temperatures. The density of water decreases more rapidly with

157 temperature than that for oil. Consequently, the density difference between water and oil can become quite small at higher temperatures. A small error in estimating these densities can have a significant effect on the calculated interfacial tensions. This problem becomes particularly acute when the oil phase is a crude oil. For some crudes the density of the oil m y , in fact, become greater than that of the water. The spinning drop equipment cannot be used under those circumstances. Density data are readily available for water and can be generated easily for the surfactant and brine solutions. Densities for repined oils and pure hydrocarbons were determined using data from "Petroleum Refinery Engineering."' To correct crude oil densities for temperature, the volume correction factors from ASTM D-206-36, Group 1, were used. Density data for water and three crude oils taken from El-Gassier et al. are shown in Figure 9.

*

Kepresentative data obtained by the spinning drop method are shown on Figure 10. Interfacial tensions were measured between mineral oil No. 9 and TKS 10-80 in various concentrations of salt. The concentration of the TRS 10-80 was kept constant at 0.5 g/L. The interfacial tensions shared little dependence on temperature up to 18OoC, but they are affected substantially by the salt concentration. The lowest interfacial tensions were observed at salt concentrations of 5.0 g/L. The lower curves on this figure are duplicate runs and show reasonable agreement. Interfacial tensions for TRS 10-80 against a representative crude oil also showed little effect of temperature.

'

10 0 5.0

fo-doa$4 vs'. w&u

in^

NQ9

z ID r/L MOCI *Lo1)

-X-

0.7 10

' 50

'

API CWOE

fi WaCl

, , , ,

6rP,4PIFRUqE loo I50 x)o TEMPERATURE, "c

250

Fig. 9-Effect o f temperature on density of water and crude o i l s

0

3 o m s o l 2 o ~ m o ~ TEMPERATURE, 'Ic

Fig. 10- Effect of salt concentration and temperature on interfacial tension of 0.5 g/L TRS 10-80 versus mineral oil No. 9

The interfacial tension between the nonionic surfactant, Igepal DM-730 and a 15.9OAF'I California crude oil showed a marked minimum when plotted versus temperature as shown on Figure 11." No salt was present in this example but similar data were obtained with the surfactant in presence of salt. The interfacial tension minima for the nonionics coincided with the cloud point for the particular surfactant concentration. Since the cloud point indicates a decrease in the surfactant solubility, it is not surprising that the interfacial tension

158 decreases at tliis temperature. 'L'lie decrease in transparency 01 Llie aqiieous phase at the cloud point was a limiting factor in measuring interfacial tensions of nonionics as a I'unction 0 1 temperature by either tlic spinning drop or the pendent drop met hod.

100.0 500

A more detailed study of the efrects of surfactant concentration, E salt concentration and temperature on 1.0 interfacial tension against a crude E oil was made with the pendent drop b equipment. Although this equtpment is 0.2 not capable OP measuring the ultra low tensions it can show, at least qualitatively, the trend of the effect of these variables. Representative data 0.0 are shown on Figure 12. The surfactant in this case was TRS 10-80 and the oil was CaliPornia Wheeler.Ridge crude with an API gravity of 15.9". The temperature was 177OC. ?'he 10 50 100 I50 200 TEMPERATURE, OC results are interesting in that they Fig. 1 1 - Effect of surfactant indicate an optimum surfactant and concent rat ion and temperature salt concentration at 177°C to obtain on interfacial tension between a minimum interfacial tension. IHS 10-80 and criltle otl. Similar minima were observed for lower NaCl = 0.0 g / L temperatures but the minlmum interfacial tension increased with decreasing temperature. At 93°C the minimum intertacial tension was 0.1 mN/m as compared t o 0.005 mN/m at 177OC. Additional data have been obtained using a mixture of surINTERFACIAL TENSION CONTOURS I77.C factants against yure hydrocarbons and mineral oils. The equivalent alkane carbon number, FACN, for the surfactant mixtures was 0.5 calculated as recommended by 0 v = 0.005 nN/m Jacobson et a1.I5 As shown in c, Vigure 13, these mixtures stiow an abrupt decrease in interfacial tension at temperatures in excess of 120°C. The experiments are being extended to obtain data for several hydrocarbons and, thereby, evaluate the relation between the change in interfacial tensions with temperature and the FACN 1 I 1 1 1 1 concept

>

Y

1

0.02 0.I

.

0.5 ID 20 30 NoCl CONCENTRATION (WT %)

-

Fig. 12 Interfacial tensions as functions of NaCl and TKS 10-80 concentrations at 177OC

CONCLUSIONS The results of our experimental work and data reported by others suggests conclusions about

159 t h e behavior or surfacLants a t elevated temperature. Some ol these conclusions are quite specific and dependable for the systems to which they apply. Many are tentative. Certainly more work is required to extend the nuinber of sureactants wtiicla liavc been evaluated at high tempcratures.

I .o

as

1

I

1

1

1

I

MIXTURE OF ANIONIC SURFACTANT VS N-OOD€W

4a2

a5

Ei 1

05

-

1. The surfactants investigated 02 SURFACTANT were observed to decompose by Y TRS 10-80 first order kinetics. Therefore, & I)I PETROSTEP 465 . a quantitative measure of the E PETROSTEP 450 . stability of a surfactant at a f oo( NeCI CONC g/L given temperature is its Iialf0 2 0 life. Activation energies were rn determined for several surfactants. Stabilities can be estimated from these energies at 00; higher or lower temperatures than those used in the experiments. FIR. 13- Interfacial tensions as Ciinc2 . The anionic petroleum sulfotions o f temperature and salt concennates were observed to be more tration for lsurfactant mixtures against stable than the nonionics. The n- dodccanc stabilitv of the best sulfonate would be only marginally acceptable at temperatures to 180°C but other surfactants need,to be evaluated. All of the surfactants tested would be adequately stable at normal reservoir temperatures

.

3. Evidence suggests that the sulfonates may be precipitated at steam temperatures as a result of an interaction with solubilized rock minerals which show limited solubility at elevated temperatures. The solubility of the nonionics decreases abruptly at the characteristic cloud point. This limits the concentration at which these surfactants can hr uscad at higher temperatures.

4. Dynamic and static methods were used for evaluating the temperature effect on adsorption. The data suggest that adsorption decreases for both sodium dodecylbenzene sulfonate and for Igepal CO-850, but the effect is not as substantial as one might have expected. Additional data are required with other surfactants in consolidated sandstones.

5. A substantial amount of data is being accumulated relating interfacial tension and temperature. For specific types of petroleum sulfonates some data indicate little effect of temperature on interfacial tensions. On the other hand, pendent drop data do suggest a significant decrease in interfacial tension with temperature for optimum salt and surfactant concentrations. Other results show a decrease in interfacial tension with temperature for mixtures of sulfonates against pure hydrocarbon or mineral oil. The nonionic, Igepal DM-730, showed a sharp minimum in the int'erfacial tension at a specific temperature. That temperature appears to be related to the cloud point.

160 REFEKENCES 1.

HANDY, L. L., AMAEFULE, J. O., ZIECLER, V. M., and ERSHAGHI, I.; "Thermal Stability of Surfactants for Reservoir Application", paper SPE 7867 presented at SPE Fourth Intl. Symposium on Oilfield and Geothermal Chemistry, Houston, Jan. 22-24, 1979.

2.

ISAACS, E. E., PROWSE. D. R., and RANKINE, J. P.; "The Role of Surfactant Additives in the In Situ Recovery of Bitumen from Oil Sands", Paper No. 81-32-13, presented at the 32nd Annual Technical Meeting of the Petroleum Society of ClM, Calgary, May 3-6, 1981.

3.

MUKERJEE, P.; "Use of Ionic Dyes for the Analysis of Ionic Surfactants and Other Ionic Organic Compounds", Analytical Chemistry (May 1956) 2 (5) 870.

4.

ZIECLER, V. M. and HANDY, L. L.; "Effect of Temperature on Surfactant Adsorption In Porous Media", SOC. Pet. Engr. Jour. (April 1981) 21 (2) 218-226.

5.

CELIK, M., GOYAL, A., MANEV, E., and SOMASUNDARAN, P.; "The Role of Surfactant Precipitation and Redissolution in the Adsorption of Sulfonate on Minerals", paper SPE 8263 presented at the SPE 54th Annual Technical Conference and Exhibition, Las Vegas, Sept. 23-26, 1979.

6.

REED, M. G . ; "Gravel Pack and Formation Sandstone Dissolution During Steam Injection," J. Pet. Tech. (June 1980) 941-949.

7.

GOPALAKRISHNAN, P., BOREIS, S. A., and CAMBARNOUS, M.; "An Enhanced Oil Recovery Method -- Injection of Steam with Surfactant Solutions", Report of Group d'Etude IFP-IMF Sur lee Milieux Poreux Toulouse (1977).

8.

SANDVIK. E. I., GALE, W. W.. and DENEKAS, M. 0 . ; "Characterization of Petroleum Sulfonates", SOC. Pet. Engr. Jour. (June 1977) 184-192.

9.

McCAFFERY, F. G.; "Measurement of Interfacial Tensions and Contact Angles at High Temperature and Pressure", J. of Canadian Petroleum Technology (July 1972).

10.

GASH, B., and PARRISH, D. R.; "A Simple Spinning-Drop Interfacial Tensiometer", J. Pet. Technology (January 1977) 30-31.

11.

BURKOUSKY, M. and MAX. C.; "Applications for the Spinning Drop Technique for Determining Low Interfacial Tension", Tenside Detergents (1978) 15 (5) 247-251.

12.

NELSON, W. L. ; "Petroleum Refinery Engineering", (1958) 157-161.

13.

HANDY, L. L., EL-GASSIER, M. and ERSHAGHI, I.; "Interfacial Tension Properties of Surfactant-Oil Systems Measured by a Modified Spinning Drop Method at High Temperatures", paper SPE 9003 presented SPE Fifth Intl. SvaDosium on Oilfield and Geothermal Chemistry, Stanford University, May 28-30, 1980.

14.

ZEKRI, A.;

15.

JACOBSON, J. K., MORGEN, J. C., SCHECHTEX, R. S., and WADE, W. H.; "Low Interfacial Tensions Involving Mixtures of Surfactants", SOC. Pet. Engr. Jour. (1976) 122-128.

Personal Communication.

CHEMICAL FLOODING

161

SURFACTANT SLUG DISPLACEMENT EFFICIENCY IN RESERVOIRS; TRACER STUDIES IN 2-D LAYERED MODELS

ROBERT J. WRIGHT, RICHARD A. DAWE and COLIN G. WALL

Petroleum Engineering Section, Imperial College, London SW7 2AZ

ABSTRACT

The e f f e c t s of layering within porous material with regard t o basic flow mechanisms and chemical dispersion have been investigated. have been performed within unconsolidated g l a s s bead packs.

Experiments The

variables controlled were layer permeability and dimensions, f l u i d v i s c o s i t y and flow r a t e ; gravity and c a p i l l a r y pressure influences were eliminated by using model f l u i d s of matched density and complete miscibility.

The importance of channeling and crossflow e f f e c t s a r e emph-

asized by t h e r e s u l t s , and the behaviour of non-unit mobility r a t i o displacements i s predictable using r e l a t i v e l y simple conceptual/mathema t i c a l models.

The dispersion of chemical t r a c e r s between layers has

a l s o been modelled mathematically and t h e r e s u l t s have been applied t o laboratory t e s t s on heterogeneous cores.

162 INTRODUCTION

,

I t is well known that t h e n a t u r a l heterogeneity of petroleum reservoir material is one of the major problems i n chemical E.O.R. processes. Of p a r t i c u l a r consequence are the non-random v a r i a t i o n s i n permeability to be found within porous rocks. Layering s t r u c t u r e s a r e a common feature of sandstones and their e f f e c t s have been reviewed i n recent l i t e r a t u r e w i t h reference to f l u i d flow (1) and dispersion mechanism ( 2 ) . The efficiency of s u r f a c t a n t slugs is probably the most l i k e l y application of these considerations; however the fundamental problems a r e ocnmnon to a l l E.O.R. processes. We have investigated layered models, both conceptual/ mathematical and physical ( v i s u a l ) . Experimentally, flow mechanisms and dispersion e f f e c t s have been monitored using dye tracers. Displacements have been of an i d e a l miscible type and therefore represent p e r f e c t microscopic displacement efficiency. The properties peculiar t o surfactants such as adsorption, phase equilibrium and emulsification characte r i s t i c s have been excluded i n t h e present work. W e a r e taking the approach t h a t the gross f l u i d flow and dispersion e f f e c t s w i t h i n heterogeneous media shoald be b e t t e r understood before laboratory core-flood r e s u l t s and data from l i n e a r homogeneous packs can be applied t o the reservoir system. W e have attempted t o view miscible and immiscible displacement mechanisms on a common b a s i s s i n c e the two concepts merge i n ultra-low-tension systems.

The experimental work discussed here involved idealized layered models of packed Ballotini. The flow mechanics of displacements a t various (favourable and unfavourable) mobility r a t i o s were recorded by photographing dye t r a c e r boundaries under conditions of flow r a t e f o r which diffusion/dispersion e f f e c t s were small. To quantify dispersion phenomena we have considered equiviscous miscible displacements, and we describe here numerical predictions w i t h one example application. Conceptual models were developed, based on simple two layer-channel interactions. This approach follows contributions within the l i t e r a t u r e on dispersion ( 2 ) & (3) and crossflow ( 4 ) & ( 5 ) i n such model systems.

FLOW PATTERNS I N LAYERED MEDIA

I t has been found useful t o consider simple two-channel conceptual m o d e l s

i n order t o account f o r crossflow behauiour i n multilayered and s t r i a t e d media. CrosSflow d i r e c t i o n s and approximate magnitudes can be demons t r a t e d mathematically by considering t h e v a r i a t i o n of flow p o t e n t i a l along the axes of the channels. Figure l ( i )i l l u s t r a t e s two p a r a l l e l channels composed of homogeneous and continuous porous media; a high permeability channel ( a ) and a less permeable channel ( b ) . The displacement of f l u i d (1) by f l u i d ( 2 ) within this model ( i n t h e x direction) has resulted i n two displacement boundaries ( a t Xa and q). The instantaneous pressure p r o f i l e s a r e p l o t t e d f o r two d i f f e r e n t viscosity r a t i o s ; displacing f l u i d t h e more viscous i n F i g . l ( i i ) and the l e s s viscous i n F i g . l ( i i i ) .

163

t

(i) Displacement i n dual channel m o d e l

Y

1

P

ii

(ii) P r e s s u r e P r o f i l e s f o r !J2 > p1

0 1

P -

(iii) P r e s s u r e P r o f i l e s f o r

R

p2 < p 1

0 X+

L

x4

Figure 1.

This assumes no c a p i l l a r y p r e s s u r e , d i s p e r s i o n , g r a v i t y o r c c m p r e s s i b i l i t y e f f e c t s ; also f o r t h e moment, no crossflow between t h e channels (as i f s e p a r a t e d by a n i m p e r m e a b l e b a r r i e r ) . I t is, however, a u s e f u l method for r e p r e s e n t i n g local croltsflow tendencies as i n d i c a t e d by pressure drops ( a t f i x e d x) between the channel axes. C r o s s f l o w would therefore be s t r o n g e s t around t h e displacement f r o n t s a n d o c c u r s i n t h e d i r e c t i o n s i n d i c a t e d i n Table 1.

Table 1. Fig.

p2

Location.

l(iii)

>1

<1

Prom

Into

-

Channel:-

"b

(2)

a

b

X

(1)

b

a

"b

(1) E ( 2 )

b

a

X

(1) E (2)

a

b

P1 1(ii)

Fluids Crossflowing

Channe 1:

164 Experimental. Displacements w e r e performed i n a v i s u a l model composed of g l a s s beads packed t o form a c e n t r a l (high permeability) l a y e r surrounded by l e s s permeable packing. Channel widths were around 1 cm within a t o t a l model width of 10 cm., t h e length of t h e flow model was 20 an, the permeability r a t i o s between l a y e r s was 2.8, and p o r o s i t y was approximately 38%. Constant flow r a t e s were used and matched density aqueous s o l u t i o n s were employed. Glycerol/water mixtures and s o d i m chloride o r sodium sulphate s o l u t i o n s were used. The photographs ( P l a t e s 1 - 3 ) i l l u s t r a t e displacement p a t t e r n s with fluorescent t r a c e r s under t h r e e d i s t i n c t conditions of v i s c o s i t y r a t i o ; p2/p1 = 0.22 ( P l a t e 1 1 , 1.0 ( P l a t e 21, and 3 . O ( P l a t e 3 ) . Roughly 0 . 2 pare volumes of displacing f l u i d has been i n j ected, and flow is i n a l l cases from l e f t t o r i g h t .

P l a t e 1: unfavourable mobilities

P l a t e 2: equal m o b i l i t i e s

P l a t e 3: favourable mobilities

The d i f f e r e n t displacement boundary p a t t e r n s and t h e consequent differences i n displacement e f f i c i e n c y can be explained to sane e x t e n t by t h e a x i a l pressure gradients of Figs. l ( i i )and ( i i i ) , b u t t h e dominant influence is crossflow a s d e t a i l e d i n Table 1. Hence, when displacing f l u i d is less viscous (more mobile) the leading "finger" within the high permeability channel advances r a p i d l y due to crossflow i n t o t h e f i n g e r a t its base and o u t 06 t h e channel around i t s leading t i p . Crossflow is seen t o a l t e r t h e shape of t h e finger by swelling i t s f r o n t and squeezing i t s base. For "favourable" v i s c o s i t y r a t i o s these conditions a r e reversed; penetration i n t o t h e high permeability channel is retarded, t h e advancing Cusp being squeezed i n a t t h e f r o n t (with some t r a c e r dispersed ahead as a t h i n plume) and widened a t i t s base where it j o i n s t h e main displacement f r o n t . Smaller s c a l e differences a r e apparent around t h e main displacement boundary; l o c a l f i n g e r i n g i n t h e forme<>case and a sharp s t a b i l i z e d boundary i n t h e latter favourable mobil+&y case.

165 Quantitative Results:

Unfavourable Mobility Ratio Continuous Displacement

Crossflow can be quantified i n the two channel conceptual model described above by means of a numerical crossflow index:= A.-

.-

(Ax)2 d

kt ka

'

where A is the crossflow boundary surface area per u n i t volume of channel ( a ) , kt is the effective cross permeability between the channel axes, ka Is the permeability of channel ( a ) , Ax is the numerical inter-node fractional distance and d is the separation of the channel axes. For equal width s t r a i g h t layers of isotropic media,d is equal to the layer width and A

=

-kt

-

d

*

ka

2

1 + ka/kb

Fig. 2 i l l u s t r a t e s calculated instdtaneous channel (a) pressure profiles for xa = 0.5, xb 0 when p2/ p l = 0.1, for the mossflow indexes and layer aspect ratios given below:d &

Curve -

a (Ax =

layer z ( k b

0.02)

1

o.Ooo1

2.0

2

0.01

0.2

3

0.1

0.06

4

1.0

0.02

4,

These span the extremes of practically no crossfhw (curve 1) t o near m a x i m u m crossflow (almost zero resistance to flaw between channel centres, curve 4 ) .

Figure 2. Possible pressure distributions along channel ( a ) .

0

1

Numerical cdkculations of distance/time tracks have been performed based on incremental advances of a displacement front (Ax = 0 . 0 2 ) and estimation of pressure gradients, hence displacement velocities (as a function Of frontal position). For various values of "a" displacemant tracks were calculated for viscosity ratios of 0 . 5 (Fig.3),0.1 (Fig. 4) and 0.01 (Fig.5).

166

I L

02 '

Figure 3. = 0.5

lJ2/Pl 0.1 *

Figure 4.

P 2 h 1 = 0.1

E

l

I

Figure 5. lJ2/lJ1

Figs. 3

-

= 0.01

5 : Time/Distance t r a c k s f o r displacement f r o n t within high

permeability ChdMel; numerical c a l c u l a t i o n s .

Clearly, f o r mobility n a t i o s near u n i t y crossflow is unimportant and displacement v e l o c i t i e s a r e constant with t i m e . The l i m i t i n g l i n e a r t r a c k s f o r high a are approached q u i t e c l o s e l y f o r moderate values of The behaviour is only s e n s i t i v e v i s c o s i t y ratios and l a y e r aspect-ratio. to crossflow index when d/L > 0.1 and p2/p1 < 0.1, a s a general guide.

167 Experimental Results. Flow v i s u a l i z a t i o n experiments were conducted with matched d e n s i t y f l u i d p a i r s having " adverse" v i s c o s i t y ratios. The packed bead models were as described above. Experiments were d i s t i n g u i s h e d by t h e parameters given below:-

Experiment

0

1

*

3

*

2

0

4

kakD

d/L

1 1.:

1'/2'

}

0.33

2.8

0.22

.IS

-L xb

Figure 6. .I

R e l a t i v e Front Positions.

45

a a

"Mean f r o n t " p o s i t i o n s were e s t i m a t e d from c o l o u r photcgraphs t a k i n g i n t o account d i s p e r s i o n and local f i n g e r i n g . When p l o t t e d v e r s u s time,approxi m a t e l y s t r a i g h t l i n e t r a c k s were obtained; data scatter being n o t too serious. The r e s u l t s i n terms o f t h e l e a d i n g f r o n t displacement (xa) and are p l o t t e d on Fig. 6, along w i t h t h e numerically t h e main f r o n t (a) p r e d i c t e d curves using t h e parameters given i n Table 2. The c o r r e l a t i o n o f experiment and c d l c u l a t i o n s is encouraging. However, t h e s e p r e d i c t i o n s are based on equating xb/L to t h e dimensionldss t i m e (of Figs.3 - 5 ) which is n o t expected t o be a good approximation i n a l l cases. I t is n o t i c e a b l e t h a t t h e r e is a s i g n i f i c a n t dependence on v i s c o s i t y ratio: An i n t e r e s t i n g f e a t u r e o f m o s t experiments is the r e l a t i v e l y f a s t i n i t i a l p e n e t r a t i o n i n t o t h e high p e r m e a b i l i t y l a y e r , a d e t a i l c o n t r a d i c t e d by t h e n m e r i c a l r e s u l t s . S i m i l a r f i n d i n g s are d e s c r i b e d by Peaceman and Rachford (6) f o r vtscous f i n g e r i n g i n randomly v a r i a b l e porous media.

168 Discussion of Analytical Methods. I t is useful t o consider a t t h i s point the effectiveness of an a n a l y t i c a l solution method based on 1-dimensional flow theory and "pseudo" r e l a t i v e permeability functions ( 7 ) . These a r e b e t t e r described a s synthetic functions since they a r e derived by adding together t h e e f f e c t s of the individual layer properties. The r e l a t i v e permeabiliw t o displacing ( 2 ) and displaced (1) phases a r e p l o t t e d versus s a t u r a t i o n of phase ( 2 ) on Fig. 7 f o r the model parameters of experiments 3 and 4. Use of these functions is i d e a l l y r e s t r i c t e d to immiscible (no diffusion) processes; however they can be applied to miscible processes when the e f f e c t of dispersion is negligible. A useful feature of t h e present displacements is t h a t they should give r e s u l t s which a r e similar t o p e r f e c t ultra-lowtension displacements (having negligible c a p i l l a r y pressures and 100% microscopic displacement e f f i c i e n c y ) .

Predicted saturation/distance p r o f i l e s based on the above functions using the v i s c o s i t y r a t i o s of i n t e r e s t a r e given on Fig. 8 . These extended d i s t r i b u t i o n s a r e not found i n p r a c t i c e even when l o c a l fingering is taken i n t o account: however i t is only t h e averaged displacements w i t h i n 1.0) flowing regimes the f a s t (S2 = 0 0.14) and s l o w (S2 = 0.14 which w i l l be considered (dotted l i n e s ) . The r a t i o of displacement r a t e s

-

-

1.0

0.5

t 5,

0

s,

1

Fig. 7. Relative permeabilities.

0

-

0 X/L 0.5 Fig. 8 . Theoretical saturation distributions.

1.0

a r e predicted t o be 8.5 f o r a viscosity r a t i o of 0.33 and 12.9 f o r a These r e l a t i v e r a t e s a r e about a f a c t o r of two viscosity r a t i o of 0.22. g r e a t e r than those indicated i n Fig. 6 . I t is thought therefore t h a t 1dimensional flow theory exaggerates the e f f e c t of mobility r a t i o f o r reasons concerning crossflow mechanism. I t may therefore be possible, using convenient approrimations,to obtain predictions f o r miscible and low tension displacements w i t h i n layered media which a r e s i g n i f i c a n t l y b e t t e r than those provided by a n a l y t i c a l 1-dimensional methods. m t i u t i v e & s u i t s : Favourable Mobility Ratio Continuous Displacement. Crossflow is the p r i n c i p l e mechanism by which a displacement f r o n t may be s t a b i l i z e d against the influence of l o c a l permeability variations. The dual-channel pressure p r o f i l e s discussed above can be used to explain t h i s flow mechanism and t h e "shock front" concept of 1-dimensional displacement theory ( 5 ) .

169 I n sane preliminary work we used a packed bead model containing four f a s t flow channels (permeability r a t i o 13:l) of d i f f e r e n t width. The r e s u l t s r e f l e c t a considerable influence of g r a v i t y since t h e displacing f l u i d was more dense and was flowed v e r t i c a l l y upward. Pig. 9 i l l u s t r a t e s traced displacement f r o n t s ( f u l l l i n e s ) i n r e l a t i o n to t h e layer bounda r i e s (dashed) f o r three s t a g e s ( f r a c t i o n a l pore volrrmes i n j e c t e d indicated). Here l.12/l.11 = 5, Ap = 0.113 g/cm3; while on Fig. 10 are the observations f o r p2/p1 = 10,Ap = 0.149 9/cm3. Predictions based on s y n t h e t i c r e l a t i v e permeabilities f o r t h i s model lead t o the s i n g l e shock f r o n t s shown ( d o t t e d ) . The s u p e r f i c i a l flow r a t e was greater i n t h e l a t t e r case (1.8 x 10-3cm/sec, a s compared with 0.91 xlO-’an/sec) and the e f f e c t of t h i s is t o compensate t o some e x t e n t f o r the e f f e c t of a higher v i s c o s i t y r a t i o .

Fig. 9.

Fig. 10

Shock f r o n t formation is c l e a r l y not observed. The o s c i l l a t i o n s of f r o n t a l boundary appear t o increase i n amplitude with increase i n channel diameter ( t h e f a r r i g h t channel is r e a l l y a half-channel since there is a no-flow boundary a t i t s s i d e ) . I n t h e case of t h e higher v i s c o s i t y r a t i o displacement t h e r e is l i t t l e change i n t h e f r o n t a l shape with time. I t has been found t h a t the basic c h a r a c t e r i s t i c s of such s t a b i l i z e d displacement p a t t e r n s can be approximated by considering dual-channel pressure p r o f i l e s . Figure 11 i l l u s t r a t e s the form of such p r o f i l e s when viscous crossflow (but not gravity) is allowed f o r . The S t a b i l i z a t i o n

Figure 11. Pressure p r o f i l e s f o r favourable m o b i l i t i e s with crossflow.

Phenanenon, which tends t o discourage channeling i n t o the high permeability zone) depends upon the crossflow which i t s e l f i s governed by the region between t h e two p r o f i l e s . The geometry of t h i s region can be approximated by a t r i a n g l e enabling an expression t o be derived f o r a s t a b i l i z e d q),assuming the v e l o k i t i e s of the two f m n t e are separation “6”( = x a

-

170

IT. E . DANFORTM

I’aye 193 (2). Thermal Activation.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 (3). Decay of Enhanced Emission.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 (4). Activation by Reverse Current.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 (5). Effects of Products from Nearby Cathodes.. . . . . . . . . . . . . . . . . . . 198 3. Mechanisms of Disappearance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 a. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 b. Electrolysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 c. S p u t t e r i n g , . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 d. vapora at ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 4. Optical Phenomena in Crystalline Thorium Oxide., . . . . . . . . . . . . . . . . . . 202 5. Electrical Conductivity of Thorium Oxide.. . . . . . . . . . . . . . . . . . . . . . . . . 204 a. Powdered or Sintered Specimens.. . . . . . . . . . . . . . . . . . b. Crystalline Specimens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 210 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1). Three “Stateu of Activation”. . . . . . . . . . . . . . . . . . . . . . . . . .

I. INTRODUCTION The appearance of thorium oxide on the scene of high-powered tube engineering has been gradual over the past three decades, and was naturally accelerated by World War 11. I n general, it may be said t o be used in applications where barium-strontium oxide falls short in some aspect of ruggedness and where the extra heating power required by the thoria cathode is not impracticable. The present paper describes certain practical applications of thorium oxide emitters, outlines the outstanding problems and the types of research and development which are under way, and presents those rather fragmentary theoretical developments which research workers have succeeded in achieving a t the present writing. Even more than with barium oxide, the theory is still only semiquantitative, and decisive experiments are lacking. Comparing the thorium oxide situation with that of barium oxide one finds that less work with theoretical intent has been done in the former case. This is due to the fact that the latter has occupied a far more important commercial position for over a quarter of a century. Actually it may appear that, as a subject of research in semiconductor thermionics, the thorium oxide system is more amenable to quantitative understanding than is the barium oxide emitter. OXIDEAND PRACTICAL ELECTRONICS 11. THORIUM 1. Preliminary

The introduction of thorium oxide into the field of practical electronics came about because of its metallurgical as well as its thermionic properties.’ As a refractory material, insoluble in tungsten, quantities of the order of one percent are added t o tungsten t o control recrystallization

171 maxima covering t h e scatter of d a t a are p l o t t e d on Figure 13,along with crosses i n d i c a t i n g t h e s e p a r a t i o n s based on t h e p o s i t i o n a t which t h e channel is completely occupied by d i s p l a c i n g f l u i d . T h e o r e t i c a l curves applying to o u r model, and o t h e r p e r m e a b i l i t y ratios ( i n d i c a t e d on t h e curves) are included. These g i v e t h e e q u i l i b r i u m s t a b i l i z e d f r o n t a l s e p a r a t i o n s p r e d i c t e d using t h e above equations. Assuming t h e b a r s t o be a c c e p t a b l e a s an experimental estimate of t h i s parameter (remembering t h a t no p i s t o n - l i k e f r o n t is observed i n t h e high p e r m e a b i l i t y channel) then the u s e f u l n e s s of t h e mathematical approximation is supported. This should be viewed i n r e l a t i o n to the p r e d i c t i o n s o f 1-dimensional flow theory based on t h e s y n t h e t i c r e l a t i v e permeability f u n c t i o n s f o r t h e s e The a n a l y t i c a l models, Fig. 7 shows t h e s e f o r experiments 7 and 8 . s o l u t i o n i n d i c a t e s a s i n g l e shock f r o n t through t h e whole system f o r v i s c o s i t y ratios g r e a t e r than 2.82, i.e. 6 = 0. Our experimental r e s u l t s c l e a r l y demonstrate t h a t t h i s is n o t t h e case and w i l l be of more serious consequence t o displacement e f f i c i e n c y as Layer (or other channel) diameters i n c r e a s e .

5

b b

b

+

.

b

b m

8

b.

3

I

b.

.

Figure 12. F r o n t a l S e p a r a t i o n s , Experiment NOS. 0 5 , 0 6 ,

+ 7,

Figure 13. V i s c o s i t y R a t i o E f f e c t , experimental ( b a r s ) and theoretical ( l i n e s ) .

08.

172 SLUG DISPLACEMENTS I t has been found t h a t continuous i n j e c t i o n t e s t s model well t h e development of displacement boundaries a t f r o n t and rear of a "slug" up t o t h e time when overtaking occurs. P l a t e 4 shows a low v i s c o s i t y s l u g f i n g e r i n g and channelling ahead i n a similar way t o the displacements discussed abbve involving continuous i n j e c t i o n . Behind t h e slug we have a favourable r m b i l i t y r a t i o displacement of t y p i c a l pattern. The high v i s c o s i t y slug of P l a t e 5 shows a s t a b i l i z e d form a t i t s f r o n t . I t is pushed by a s i m i l a r liquid,without dye,exhibiting a t y p i c a l equiviscous displacement.

Plate 4

Plate 5

The permeability r a t i o was a s before (2.8) and the v i s c o s i t y r a t i o s involved i n t h e displacement of f l u i d (1) by f l u i d ( 2 ) by f l u i d (3) were f o r P l a t e 4, p3:p2:p1 = 3:1:3, and f o r P l a t e 5 , 4.6:4.6:1. Although the volumes of these s l u g s a r e about 20% of t h e pore volume, l o s s of slug i n t e g r i t y occurs. The low v i s c o s i t y slug ( P l a t e 6) is continuing to be squeezed from the low permeability medium i n t o t h e f a s t flow channel; however the slug is 'near being divided i n t o t h r e e portions. The high v i s c o s i t y slug ( P l a t e 7) has been s p l i t by t h e chase f l u i d which has channelled through and is crossflowing o u t of the high permeability layer, p a r t i c u l a r l y near the f r o n t o f t h e slug.

P l a t e 6.

Plate 7.

The breakdown of s l u g i n t e g r i t y could possibly be r e s i s t e d by chemicals, added t o t h e chase fluid.designed s p e c i f i c a l l y t o r e s i s t c e r t a i n crossflow processes and t h e mixing of out-of-sequence f l u i d s . An example could be the i n - s i t u g e l l i n g polymers which a r e s e n s i t i v e to s a l i n i t y environment ( 8 ) . This is a p o s s i b i l i t y which w i l l be i n v e s t i g a t e d i n f u t u r e modelling work. For s u r f a c t a h t s l u g s the f l u i a r e d i s t r i b u t i o n s discussed above w i l l be combined oith considerable adsorption, dispersion, mass-transfer and g r a v i t y e f f e c t s . Capillary pressure e f f e c t s could a l s o be important even though i n t e r f a c i a l tensions may be low, since mobilized o i l banks w i l l be p a r t l y o r wholly composed of discontinuous o i l whose flow w i l l be highly non-Newtonian. ( 9 ) .

173 DISPERSION I N LAYERED MEDIA

The s t a b i l i t y of chemical slugs w i t h i n channelled porous media can be strongly affected by diffusion/dispersion processes. Eere we consider a two-layer mode1,following the approach of Lake and IiraSaki ( 2 ) and Koonce and Blackwell ( 3 ) for chemical dispersion and Satman and Zolotukhin (10) for the analogous problem i n heat transfer. To scale these effects it is useful t o define a transverse dispersion number ( 2 ) :

14G. N~~

=

3 ,

d2 V

where L and d are the length and width of the system, Kt is the Mansverse dispersion doefficient, V is the superficial flow rate i n the high permeability layer. Lateral dispersion is insignificant when N T D < 0 . 2 , while when N T D > ~ composition is practically constant over any cross-section through the system and the behaviour can be represented by a single effective longitudinal dispersion coefficient ( 2 ) . W e examine here the intermediate range of NTD, between 0 . 2 and 5 , which could apply t o comon f i e l d conditions i f d is of the order of lm and to laboratory core tests i f layers of a few mrn width are present within the porous m e d i u m . W e consider flow parallel t o the layers and tracer dispersion normal t o t h i s direction (longitudinal dispersion coefficient is zero). The l a t e r a l dispersion coefficient has been taken to be constant,independent of concentration, position and flow rate. For reservoir r a t e s , i t is generally found to be of the order of the molecular diffusion coefficient (11). Figure 1 4 shows computed isoconcentration contours .(at 0..1 intervals) within a two layer system, the upper one (between Y values 0.5 and 1.0) flowing from l e f t t o right, the lower is stagnant but receives injected tracer by l a t e r a l dispersion from the permeable layer. Tracer injected a t u n i t concentration is dispersed as shown a t three values of the dimensionless t i m e : T Kt

t - -

d2

=

NTD

_.

14

where T is the absolute time from the s t a r t of the displacement. It is of i n t e r e s t to obtain convenient analytical approximations to the mean tracer concentration within a given cross-section of the flow channel (and of the non-flowing matrix). Figure 15 shows numerical points and analytical curves representing the distribution of average concentration w i t h distance i n the flow direction (normalized for t = 0 . 2 ) The analytical approximations were derived wing solutions t o the zeroconcentration-boundary-condition case ( 1 2 ) , evaluated for short dimensionless times. Expressions of s i d l a r form are applicable t o other channel geanetries (e.g. cylindrical) provided times are short. The approximations derived f o r the heat transfer problem (10) involve also a square root of time dependence; however these integral solutions are very complex because they are intended t o cope w i t h a large time range. Our approximation is:-

T I t l E = O -05 S

I?

I I.-,

?-

I I

-m

0-1

1.2

0.9

I

I

0.4

0.5

1

0.8

FRRCTIONAL OISTRNCE I N FLOY

0.7

0-1

0.)

I

OlRECTlON

-

I

T I t l E = O 10

I

I?

S

>

I *3 ‘

m

Z

t

a

O Z

25 N I 5

0.1

Figure 14.

0.2

0.s 0.a FRRCTIONAL OISTRNCE I N FLOY 0.9

0.4

0.1

0.m

0.)

OlRECTlON

Isoconcentration contours i n two layer system.

I

175 COnPUlEO

0 T=O.OS

A 1.0.10 1=0.15

.?

+

0

f 0

.

lu

0

_I

FITTED

-c; 1-2l'"I 1-1 I - x

I

I

a.1

-1

I

11-3

I

1

0.1

0.3

O.?

I

I

04

0.6

0.1

I

0.a

0-S

I I

FRRCTIONRL OISTRNCL

Figure 15.

E

=

Cross-sectional averaged concentrations i n flow channel.

1

-

2 . 0 t + (1

-

(1

- XI+)

where is t h e average i n j e c t e d tracer concentration w i t h i n t h e cross s e c t i o n ( a t X) of t h e flowing channel; X is t h e f r a c t i o n a l d i s t a n c e e q u a l t o x/V.i

.

similar method can be used t o approximate t h e averaged Concentrations w i t h i n t h e non-flowing matrix (Em) f o r the t w o equal-capacity l a y e r s h e r e considered:-

A

Em

=

2 . 0 t+ (1 -

x% .

Applications to a Multichannel Problem. One approach t o a multichannel problem is to consider each i n d i v i d u a l channel as i n t e r a c t i n g with a surrounding matrix which possesses t h e s u i t a b l y averaged p r o p e r t i e s o f t h e rest of t h e porous body. Generally a non-zero flow rate w i l l apply to t h e e x t e r n a l matrix i n c o n t r a s t t o t h e s t a g n a n t case as above. This n e c e s s i t a t e s c o n s i d e r a t i o n of the problem as one of r e l a t i v e flow rates using moving co-ordinate methods. Tracer e f f l u e n t p r o f i l e s have been analysed i n terms o f v a r i o u s models intended t o account f o r heterogeneity (13) ,(141, (15). Laboratory tracer tests on layered r e s e r v o i r materials are o f i n t e r e s t f o r t w o reasons; f i r s t , conventional methods f o r c h a r a c t e r i z i n g d i s p e r s i o n coe f f i c i e n t s f o r miscible displacement and r e l a t i v e p e r m e a b i l i t y f u n c t i o n s for l o w t e n s i o n immiscible d i s p l a c e m n t may be u n r e l i a b l e ; second, such l a b o r a t o r y Systems can model similar problems on t h e reservoir scale. To estimate mass t r a n s f e r rates f o r t h e channels (e.g.

layers) within a heterogeneous core sample displacement flow tests of d i f f e r e n t rates have t o be compared. Unfortunately, very l i t t l e r a w d a t a of this kind is to be found w i t h i n t h e petroleum l i t e r a t u r e . Our main source is t h e high q u a l i t y r e c e n t work o f Spence and WatJcins (16). Handy (17) has used d u a l tracers to e v a l u a t e d i f f u s i o n e f f e c t s and w e have begun tests on l a y e r e d sands t o n e s using u l t r a - v i o l e t a b s o r p t i o n monitoring techniques.

176 Using the above approximations, and the assumption t h a t flow within the matrix surrounding any given channel-"i" is approximated by the mean velocity oif the whole displacement (v), a method of effluent curve analy s i s has been derived (18). Thus i f the fractions of displacing fluid a t its moment of breakthrough a t the effluent end of the single channel j", (f (1) and f j ( 2 ) ) , a r e known from t w o experiments (1 and 2) performed :t difgerent rates, we can estimate the fractional cross section of the channel (6jS) and i t s effective mass transfer coefficient (M ) thus:j

= Vj

L/T,, L being the length of the test core.

W T j (1) M t = 4Kt/d2

= v

j ( 2 P j (2)

for a l a y e r .

These expressions can be applied to effluent eanposition values measured shortly a f t e r the f i r s t detected breakthrough of displacing phase from the multichannel system. This characterizes the f a s t e s t flow channel(s) of the sample. Subsequent tracer measurenmnts have t o be processed to allow for the ( t i m e dependent) contitbutions from a l l the faster-flowing channels. The gross composktion measured i n one experiment is F(a functibn of'.-) and the individual ("breakthrough") channel "j" contribution can be obtained using the following h1gorithm:-

The effluent profile is analyzed forward i n time as presented above for T C Lfi ; while for T > L f i s u p s are taken backward I n time redbfining F as the concentration of displaced fluid. Asatisfactory analysis can be performed with a proQramable calculator (a program suitable for an "BP 41C" Is available from the authors). Small t i m e steps should be avoided since errors due mainly to intralayer longitudinal dispersion, ignored i n the present analybls w i l l become impartant; ten t o twenty steps for each effluent curve have been found t o be satisfactory.

177 Example r e s u l t s based on some of the t r a c e r composition p r o f i l e s of Spence and Watkins a r e indicated on Figures 16 18. Mass t r a n s f e r coefficient d i s t r i b u t i o n over the cross section of t h e samples is given on Figure 16 f o r a sandstone and a carbonate. M values of lo-' and 1 0 - 4 could be i n t e r p r e t e d i n terms of layers of & o u t 2 . 0 cm and 0 . 5 an width respectively. Figure 1 7 gives the "no dispersion" velocity p r o f i l e s of the porous media. The l a t t e r can be represented as r e l a t i v e permeability functions (Fig. 18) applying to the i d e a l "no dispersion" case o r t o the i d e a l near-zero-interfacial tension immiscible displacement case. Predi c t i o n s of mobility r a t i o e f f e c t s could therefore be made using conventional 1-dimensional displacement theory. However, f o r Righly heterogeneous media allowance f o r crossflow e f f e c t s , as discussed above, should be included.

-

-

Figure 17.

Figure 16.

Mass t r a n s f e r coeffkcient d i s t r i b u t i o n s ~ ~ lines:"Sandstone 1 1 SS2" Dashed l i n e s : "Carbonate B 17"

Velocity d i s t r i b u t i o n s .

Figure 18. Miscible type r e l a t i v e penneabilities .

coNcLus10Ns Surfactant E.O.R. slugs w i l l be susceptible t o layer and streak permeabi l i t y heterogeneities found within reservoirs due t o disturbance of flow p a t t e r n s and increased dispersion. Mathematical approximations have been found which a r e capable of modelling the channelling and crossflow e f f e c t s present i n non-unit mobility ratio displacements. Experimentally, l o s s of i n t e g r i t y due to flow mechanism has been observed in slugs of around 20% pore volume. Diffusion/disper$ion e f f e c t s can be large, depending on the width of layers. For s h o r t dimensionless times it is possible to model khese phenamena a n a l y t i c a l l y to match numerical simulations and to analyze tracer t e s t data.

178 ACKNOWLEDGEMENTS Dr. M. Allmen is thanked f o r performing t h e d i s p e r s i o n computations and Mr. M. Hughes f o r t e c h n i c a l help. W e are g r a t e f u l t o t h e Department o f

Energy f o r f i n a n c i a l support.

REFERENCES

L.

WEBBER, K., Influence On F l u i d Flow of Conrmon Sedimentary S t r u c t u r e s I n Sand Bodies., S.P.E. Paper 9247

2.

LAKE, 11. & HIRASAKI. G. S.P.E. Paper 8436.

3.

KCONCE. T. & BLAQCWELL, R., I d e a l i z e d Behaviour of S o l v e n t Banks i n S t r a t i f i e d Reservoirs., S0c.Pet.Eng.J. (Dec. 1965) 2 , ( 6 ) , 318 - 328.

4.

HAWTWORNE, R.,

5.

WRIGHT, R. & DAWE.R., An Examination Of The Multiphase Darcy Model Of F l u i d Displacement I n Porous Media. Rev.Inst.Fr.du P e t r o l e (Nov-Dec 1980) 35, (N0.6) 1011 - 1024.

, Taylor's

Dispersion I n S t r a t i f i e d Porous Media.,

The E f f e c t of C a p i l l a r y P r e s s u r e I n a Multilayer Model of Porous Media. S0c.Pet.Eng.J. (Dec. 1975) Is, 467 476.

-

6.

PEACEMAN. D. & RACZiFORD, H., Numerical C a l c u l a t i o n of Multidimensional (Dec 1962) 2, 327 340. Miscible Displacement. S0c.Pet.Eng.J.

7.

€EARN. C.,

8. 9.

-

Simulation O f S t r a t i f i e d Waterflooding By Pseudo Relative Permeability Curves, ( J u l y 19711, 805 813.

g,

-

MACK, J., Process Technology Improves Oil Recovery, O i l & G a s J.(Oct.1979) No. 40, 67 - 71.

77, -

EGBOGAII, E. , WRIGHT, R. & DAWE, R., Porous Media, S.P.E. Paper 10115.

A Model Of O i l Ganglion Movement I n

10.

SATMAN, A. & Z O L O T W H I N , A., Application of the Time-Dependent O v e r a l l Heat T r a n s f e r C o e f f i c i e n t Concept t o Heat T r a n s f e r Problems I n Porous Media, S.P.E. Paper 8909.

11.

PERKINS, T. & JOHNSON, O., A Review o f Diffusion and Dispersion i n POrOUS Media, S0c.Pet.Eng.J. (March 1963) 2, 70 - 84.

12.

CRANK, J., The Mathematics o f Diffusion, Oxford Univ. Press.

13.

KOVAL, E., A Method For P r e d i c t i n g The Performance Of Unstable Miscible (June 196312,145-154. Displacements I n Heterogeneous Media, S0c.Pet.Eng.J.

14.

JOHNSON, C. & SWEENEY, S . , Q u a n t i t a t i v e Measurements Of Flow Heterogene i t y I n Laboratory Core Samples And Its E f f e c t On F l u i d Flow Characteris t i c s , S.P.E. Paper 3610:

15.

ROSMAN, A. & SIMON, R., Paper 5631.

16.

SPENCE, A.

17.

HANDY, L., An Evaluation O f Diffusion E f f e c t s I n Miscible Displacement, 65. Trans. AIME (1959) 216, 6 1

18.

WRICBT, R. et. a l . , Heterogeneous Porous Media; A Miscible Displacement Model;- t o be submitted f o r p u b l i c a t i o n .

1975,Sec.4.3.

Flow Heterogeneity I n Reservoir Rocks, S.P.E.

& WATKINS, R., The E f f e c t o f Miscfoscopic Core Heterogeneity On Miscible Flood Residual O i l S a t u r a t i o n , S.P.E. Paper 9229.

-

CHEMICAL FLOODING

179

SOME ASPECTS OF THE INJECTIVITY OF NON-NEWTONIAN FLUIDS IN POROUS MEDIA PETER VOGEL and GUNTER PUSCH Institut fur Tiefbohrkunde und Erdolgewinnung, Technical University Clausthal. West Germany

ABSTRACT In existing numerical models, the rheological behaviour of polymer solutions is commonly described by the power law, which is not satisfactory at very low shear rates and at relatively high shear rates. An improvement of the mathematical description was achieved by using the Carreau viscosity equation and deriving a filter law for porous media. The validity over a wide range of shear rates was proven by experimental results obtained from flood tests in sand packs with one typical product each of the three polymer classes (PAA, HEC, BPS) used in enhanced oil recovery. On the basis of typical reservoir data, the behaviour of an injection well during polymer injection is investigated by calculating the pressure profile around a wellbore. From these data, conclusions are drawn for the selection of polymers according to their rheological properties.

180

I NTRODUCTI ON Flooding with viscous media has aroused increasing interest in the field of enhanced o i l recovery. Numerous pilot projects are currently in progress or have already been terminated / 1 , 2 / . The importance which is at present attached to this field of research is thus evident. Chiefly aqueous polymer solutions are employed as viscous flooding media. A characteristic feature of these polymer solutions is that the decisive parameter for the description of their flow properties, the viscosity, varies as' a function of the shear rate. In general, the solutions exhibit pseudoplastic behaviour, that is, a decrease of the viscosity with augmenting shear stress. In the field of enhanced oil recovery, the viscous behaviour of polymer solutions in porous media has become of vital importance as far as their injectivity is concerned. The investigations were initiated by the following two questions:

-

-

How can the viscosity values indicated in a rheogramme be applied to flow processes in porous media? Can these polymer solutions be injected into the reservoir without exceeding the fracturing pressure of the rock?

In the following, a method which allows a calculation of the injectivity of polymer solutions on the basis of the rheogrammes and of the knowledge of the characteristic reservoir data is presented.

CHARACTERIZATION OF THE POLYMERS EMPLOYED

Information about the flow behaviour of non-NEWTONian fluids is provided by their rheogramme, that is, the plot of the viscosity as a function of the shear rate; this is both important and experimentally easy to obtain. All of the considerations discussed in the following are based exclusively on the information gained therefrom. To begin, the rheogrammes of the polymer solutions used here are presented. The liquids employed are aqueous solutions

181

Figure 1:

Figure 2:

Viscosity behaviour of a polysaccharide solution

viocosity behaviour of a hydroxyethylcelluloae solution

182

I

100

Figure 3:

Viscosity behaviour of a polyacrylamide solution

(original brine with a salt concentration of 1 0 0 g/l; reservoir temperature of 5OoC) of a typical, representative product in each of the three classes of polymers used in enhanced oil recovery. Polymer solutions which yield a mutually comparable additional oil recovery (p' of additional oil per m 3 of polymer solution consumed) in flooding tests were thereby selected. Figure 1 shows the rheogramme for a polysaccharide, figure 2 that for a hydroxyethylcellulose, and figure 3 that for a polyacrylamide solution. A double logarithmic scale has been chosen for the graphic representation. The three curves display characteristic features in common: A plateau occurs in the range of low shear rate; a linear decrease is observed at higher values. For the calculation of the flow behaviour of these nonNEWTONian fluids, an analytical expression for the dependence of the viscosity on the shear rate, which represents the experimental values of the rheogramme over a wide range of shear rate, is of special importance. The preceding figures show that the four-parameter equation found by CARREAU /3/

183 (1)

provides a good fit to the experimentally determined rheogramme for the polymer solutions under investigation here. The significance of the parameters in the CARREAU equation, as well as a simple method for determining them, are briefly explained. n o denotes the viscosity at the shear rate 0 = 0, and can be determined directly from the horizontal portion of the curve in the range of very low shear rates. By means of supplementary measurements performed in the range of high shear rates, values indicative of rl- are obtained. n-1 is the slope of the linearly decreasing part of the curve. The plateau for the range of low shear rate and the linearly decreasing part of the curve intersect at a point whose abscissa is approximately equal to 1/X. In the following, the essential steps in the development of a filter law for CARREAU fluids m d e s c r i h e d . The power law frequently employed in previous publications is considerably simpler to handle analytically, and is therefore preferred for the treatment of concrete problems. For the polymer solutions investigated in this work, however, a power-law dependence of the viscosity on the shear rate does not describe the experimentally observed behaviour with sufficient accuracy. Consequently, sizable errors can result in the description of the flow processes in porous media, as will be shown by means of an example. For a wide range of shear rates, an extension, as described in this work with respect to the viscosity model, is indispensable.

A F I LTER LAW FOR CARREAU FLUIDS Filter laws for non-NEWTONian fluids are known only for a few special cases / 4 , 5, 6, 7/. The procedure common to their derivations is as follows: First the capillary flow is treated analytically for the liquid in question, in order to obtain a filter law with the use of an appropriate capillary bundle model. This procedure is adopted in the following as well; a filter

184 law is thereby derived for CARREAU fluids, and the porous medium is replaced by a capillary bundle which is hydrodynamically equivalent with respect to porosity and permeabi 1ity

.

0

Figure 4:

Straight capillaric model of a porous medium

The simplest capillary model of a porous medium /a, 9 / consists of a bundle of circular cylindrical capillaries of equal radius R. Figure 4 illustrates this concept. A comparison of the DARCY filter law with the law of HAGEN-

POISEUILLE yields the "hydraulic equivalenceradius" for this simple model:

By means of this concept, the flow through a porous medium is related to the capillary flow of the liquid in question and can be treated accordingly. On the basis of can be derived. results. In the remarkable that

this theory, a filter law for CARREAU fluids The procedure is justified by experimental following considerations, it is no empirical corrections are required.

It is necessary first to calculate the flow behaviour of CARREAU fluids in capillaries; for this purpose the velocity profile and the averaqe velocity of the capillary flow must be known. For the derivation, a circular cylindrical capillary

185

.

1

Figure 5:

Flow throuqh a circular tube

of radius R and lensth L is considered - Figure 5 - and a cylindrical coordinate system is introduced. The z-axis and the capillary axis are identical; the direction of .flow is taken to be that of the positive z-axis. The differential equation for the radial velocity distribution v(r) is

(3)

whereby po - pL denotes the applied pressure difference. This differential equation is transcendental in the derivative of the function being souqht, v(r); this fact proved to be a considerable problem in the further course of the calculations. The introduction of the wall shear rate 0 , as a parameter is decisive for the solution of this problem. The calculation / l o / finally yields an analytical expression for the average velocity during capillary flow. By means of the hydraulic equivalence radius, this expression can be easily transformed to a filter law. In the case of the capillary bundle model used, the one-dimensional filter law takes the following form :

186

In order to save space, the following substitutions have been made :

With the exception of a correction factor, the external form of this filter law is identical to that of the DARCY law. This factor depends on the parameters of the CARREAU equation and on the maximal shear rate 9, occurring in the capillary bundle model. The maximal shear rate is obtained from the transcendental equation

which admits an iterative solution according to the BANACH fixed-point theorem. The algorithm necessary for the numerical solution of equations (4) and ( 6 ) requires the following steps: After the parameters of the CARREAU equation, as well as the permeability and porosity of the porous medium have been determined, q R is calculated from ( 6 ) for predetermined values of the pressure gradient, and the corresponding filter velocity is determined from ( 4 ) . COMPARISON OF THEORETICAL AND EXPERIMENTAL RESULTS

The theoretical results are verified by experiment; no empirical correction factors are thereby required. In order to carry out the required flood experiments, an apparatus similar to that already used by DARCY was employed. Sand packs of 50 percent porosity and 5 D permeability, compacted by vibration, served as porous media. If the DARCY equation is solved for the viscosity, the result is (7)

With the use of the present results, the effective viscosity in the porous medium was determined directly from the measured data according to ( 7 ) on the one hand, and by means of the previously derived filter law, on the other hand.

188

For comparison, polysaccharide and hydroxyethylcellulose, which exhibit a dominantly linear, decreasing range in their rheourammes, were treated as power-law fluids.

A OBSERVED VALUES CALCULATE0 - C A R R E N MODEL ----- CALCULATED-POWER -LAW MODEL o

10080.

-

I

c

u

10

D

.

.Z

.e

.'s

.4

t A

400. 300.

0

- ---

\ \

\

\

i'.z

t i

1:s

*

Effective viscosity for flow of polysaccharide solution in porous media'

Figure 6:

500.

1'.

VELOCITY Im/d)

\

OBSERVED VALUES CALCULATED - CARREAU MODEL CALCULATED -POWER -LAW-MODEL

'.

\

\

W

L

t

u

K

w

100 Figure 7:

-

VELOCITY ( m/dl

.Z

.C

.6

.8

1.

1.2

Effective viscosity for flow of hydroxyethylcellulose solution in porous media

189

t

100

Figure 8:

0

OBSERVED VALUES

- CALCULATED -CARREAU HODEL

Effective viscosity for flow of polyacrylamide solution in porous media

From the filter law for power-law fluids, the effective viscosity in a porous medium was likewise calculated. Figures 6, 7, and 8 show the dependence of the viscosity on the filter velocity and compare the experimental and theoretical results. For the CARREAU model, the deviation between the experimental and theoretical results is less than 10 percent for the polysaccharide and polyacrylamide solutions, and less than 15 percent for the hydroxyethylcellulose solution. Hence the agreement between theory and experiment can be regarded as qood. The power-law model describes the dependence of the viscosity on the filter velocity with sufficient accuracy in the case of polysaccharide, whereaa considerable deviation occurs for hydroxyethylcellulose. These examples demonstrate the advantages of the new filter law for the questions under investigation. CALCULATION OF THE INJECTIVITY BEHAVIOUR

During enhanced oil recovery, the pseudoplastic behaviour of the polymer solutions used exerts a pronounced influence on their injectivity. Once the questions concerning filtration .

190

adsorption, stability, etc. have been clarified for a given reservoir in the course of the product selection procedure, the question of the injectivity of the polymer solution involved remains to be answered by the reservoir engineer. A t this juncture, an important decision of whether or not a selected product is suitable for field application must be made; this is a vital cirterion because of the high financial risk involved. A method must be provided for predicting the behaviour in the field on the basis of laboratory data; thus a criterion for decision must be established. In the following, the flowing pressure and radial distribution of pressure around the injection well are calculated for an injector in a radially symmetric reservoir and for a predetermined injection rate, with the use of the filter law just presented. The multitude of influential parameters necessitates a restriction to a typical case encountered in practice. The following, realistic, qeometrical and physical reservoir data are employed for the model calculations: Reservoir: Permeability Porosity Effective reservoir thickness

K = 1000 d = 0.24 h = 4

mD m

Well : Cased with 7" diameter and ideally perforated in the reservoir zone Wellbore radius 0.069 m rW = Injection rate q = 100 m3/d Depth = 1000 m

FORMULATIONOF THE SELECTION C R I T E R I O N From the standpoint of reservoir engineering, the essential criterion for the injectivity of a polymer solution is that the fracturing pressure of the rock must not be exceeded during the injection. The predetermined injection rate and the average reservoir pressure also affect the decision. For a depth of 1000 m and under the assumption that the average reservoir pressure corresponds to the hydrostatic pressure ,

191

a value of 5 = 100 bar results. The order of magnitude of the fracturinu qradient typical for sedimentary rocks lies between 0.18 and 0.24 bar per metre of depth. For the injector under consideration here, this results in a maximal bottom-hole flowing pressure of 180 to 240 bar: hence the bottom hole flowing pressure may exceed the average reservoir pressure by a maximum of 80 to 140 bar durinq polymer injection. Furthermore, a radially symmetric reservoir is thereby assumed. The ranue of influence of the injector is selected at re = 200 m; the reservoir pressure of 100 bar is assumed to prevail at the outer boundary. Thus, the following criterion for decision is obtained: The polymer solution is injectable provided the pressure drop over a distance of 200 m from the bore hole does not exceed 80 to 140 bar.

CALCULAT IONAL PROCEDURE The object of the calculation is to determine the relationship between the pressure gradient and the distance from the well. This function is subsequently integrated. Because of the complicated structure of the filter law previously derived, the entire calculation is performed numerically. As a result of its structure, the filter law just developed

allows only the determination of the corresponding filter velocity for given values of the pressure gradient. With reference to / l l / , the following procedure is adopted for determining the locally prevailing pressure gradient. From the equation of continuity the following expression is obtained for the radial velocity distribution:

whereby r denotes the distance from the wellbore axis. This provides a possibility of determining the distance from the well corresponding to given values of the pressure gradient by means of the filter law and equation ( 8 ) . The calculation starts with the determination of the pressure

192 gradient at the bore hole. For this purpose, two values of the pressure gradient, of which one is smaller and one larqer than that prevailing at the well, are initially assumed. By nesting of intervals a sequence of pressure gradient values is constructed in such a way'that the values of the radius determined from the filter law and equatisn ( 8 ) converge toward the wellbore radius. The procedure is truncated as soon as the wellbore radius has been approached with the required accuracy. The value of the pressure gradient corresponding to the radius thus determined is then taken as the pressure gradient at the well. Subsequently, this value is decreased stepwise, and the corresponding values of the radius are determined from the filter law and equation ( 8 ) . Thus, a tabular representation of the pressure gradient as a function of the distance from the well is obtained. .The calculation of the total pressure drop is subsequently performed by means of numerical integration.

400.

1 POLYSACCHARIOE 2 POLYACRYLAMIDE 3mi 3 HYDROXYETHYLCELLULOSE 360.-

32 0-

-

200: 2(O:

0. Figure 9:

30.

60.

90. 120. 150. DISTANCE (M 1

180. 210.

Calculated pressure profile during polymer injection

193

RESULTS OF THE MODEL CALCULATION In figure 9, the pressure difference occurring during injection, as referred to the pressure at the injection well, is plotted as a function of the distance from the well for the three polymer solutions under investigation. Moreover, the maximal values of 80 and 140 bar for the injection overpressure are indicated. According to the criterion formulated here, the polymer solutions are suitable for injection provided the pressure difference remains less than 80 to 140 bar over a distance up to 200 m from the injection well. This condition is fulfilled for the polysaccharide, and partially fulfilled for the polyacrylamide in this case. In contrast, the hydroxyethylcellulose exhibits a decidedly deviating behaviour. The pressure difference, as referred to the well, already amounts to 140 bar at a distance of about 20 m, and increases to more than 350 bar over a distance of 200 m. It must be emphasized that this is a model calculation, whereby the effects described are attributed solely to the dependence of the viscosity on the filtration velocity. If, in a practically relevant case, the model calculations indicate that the maximal permissible injection pressure will be exceeded, the concentration of the polymer solution to be used must be reduced; the viscosity is thus decreased. The parameters of the CARREAU equation are then determined from the rheogramme, and the calculation is repeated with the use of these values.

is the purely theoretical plotting of rheogrammes for injectable fluids by the variation of parameters in the CARREAU equation.

A further possibility

CONCLUSIONS The rheological behaviour of aqueous polymer solutions is well described by the CARREAU model. A filter law derived for such fluids is described and experimentally verified. With.the use of the new filter law, the radial pressure distribution around the injection well during the injection

19 4

of polymer solution is calculated. A polymer solution is judged as suitable for injection as far as the bottom hole flowing pressure does not exceed the fracturing pressure of the rock at the bottom of the hole. Among the products investigated here, the polysaccharide solution fully, and the polyacrylamide solution conditionally satisfies this criterion under the given conditions.

NOMENCLATURE h K L n

-

P

Po q

r re rW

R V V

f

P YR ‘1 ‘10

1 ‘,

h

d

-

PL

Formation thickness Permeability Length Power-law index Average pressure Pressure drop Injection rate Radial coordinate External boundary radius Wellbore radius Radius of the tube Velocity Filtration velocity Shear rate Shear rate at the tube wall viscosity Zero-shear-rate viscosity Infinite-shear-rate viscosity Time constant Porosity

REFERENCES 1

CHANG, H. L.; Polymer Flooding Technology Yesterday and Tomorrow J. Pet. Tech. (Aug. 197818 1113 1128

-

-

195 2.

GRODDE, K.H., SCHAEFER, W.; "Experience with the Application of Polymer to Improve Water Flood Efficiency in Dogger Reservoirs of the Gifhorn Trough, Germany" Erdoel-Erdgas-Zeitschrift 94 (July 1978) 7 , 252 259

-

3.

CARREAU, J.P.; 'Rheological Equations from Molecular Network Theories" Ph.D. Thesis, Univ. of Wisconsin, Madison 1968

4.

BIRD, R.B., STEWART, W.E., LIGHTFOOT, E.N.; "Transport Phenomena" 207 J. Wiley a. Sons, New York ( 1 9 6 0 1 , 206

-

5.

SADOWSKI, T.J.; "Non-Newtonian Flow Through Porous Media" 271 Trans. SOC. Rheol. 9 ( 1 9 6 5 ) 2, 251

-

6.

SADOWSKI, T.J., BIRD, R.B.; "Non-Newtonian Flow Through Porous Media" Trans. SOC. Rheol. 9 ( 1 9 6 5 ) 2 , 243 250

-

7.

PARK, H.C., HAWLEY, M a c . , BLANKS, R.F.; "The Flow of Non-Newtonian Solutions Through Packed Beds" 773 Polym. Eng. Scie. (1975) 15, 761

-

8.

9.

SCHEIDEGGER, A.E.; "Theoretical Models of Porous Matter" Producers Monthly 17 (Aug. 1953) 10. 17

-

23

SCHEIDEGGER, A.E.; "The Physics of Flow Through Porous Media" University of Toronto Press ( 1 9 6 3 1 , 115 117

-

10. VOGEL, P.;

"Untersuchungen zur Berechnung des FlieSverhaltens wlSriger Polymerl6sungen in Sandpackungen" Ph.D. Thesis, TU Clausthal 1980, West Germany 11. BONDOR, P.L.,

HIRASAKI, G.J.r T H A M r M . J . ; "Mathematical Simulation of Polymer Flooding in Complex

Re servoirs" SOC. Pet. Eng. J. (Oct. 19721, 369

-

382

This Page Intentionally Left Blank

19 I

CHEMICAL FLOODING

BASIC RHEOLOGICAL BEHAVIOR OF XANTHAN POLYSACCHARIDE SOLUTIONS IN POROUS MEDIA: EFFECTS OF PORE SIZE AND POLYMER CONCENTRATION G. CHAWETEAU and A. ZAITOUN

Institut Francais du Pktrole, B.P. 31 I , 92500 Rueil Malmaison - France ABSTRACT

The b a s i c r h e o l o g i c a l behavior of xanthan polysaccharide s o l u t i o n s has been extensively i n v e s t i g a t e d by varying polymer concentration, pore s i z e and t h e chemical n a t u r e of porous media. The r h e o l o g i c a l c h a r a c t e r i z a t i o n of s o l u t i o n s h a s s h a m t h a t xanthan macromolecules behave l i k e r i g i d rods i n the s a l i n i t y conditions selected. A l l microgels were c a r e f u l l y removed from s o l u t i o n s i n order t o study t h e behavior f a r away from i n j e c t i o n wells. I n f i n e c y l i n d r i c a l pores, mobility reduction a t low shear r a t e s was found t o be constant and lower than the Newtonian v i s c o s i t y a t low shear r a t e s , except f o r pore diameters smaller than macromolecule length. Water permeability was not reduced a f t e r polymer flow, showing t h a t the r h e o l o g i c a l behavior was not influenced by r e t e n t i o n o r adsorption phenomena. The r a t i o between mobility reduction and r e l a t i v e v i s c o s i t y decreases a s pore s i z e decreases and polymer concentration increases. This i s explained by t h e e x i s t e n c e near t h e pore w a l l of a depleted l a y e r i n which polymer concentration and thus v i r c o s i t y i s smaller than i n t h e bulk. This d e p l e t i o n i s due t o s t e r i c e f f e c t s and does not depend on chemical n a t u r e and pore shape. A model based on t h i s physical hypothesis i s proposed f o r c a l c u l a t i n g mobility reduction a s a function of pore s i z e and polymer s o l u t i o n p r o p e r t i e s . The model's p r e d i c t i o n s a r e i n agreement with experimental r e s u l t s . I n various unconsolidated porous media, such as packs of g l a s s beads, carborundum p a r t i c l e s and.sand g r a i n s , t h e same behavior i s observed. The mobility reduction i r l e s s than i n l a r g e c a p i l l a r i e s and decreases with pore size. Moreover, the depleted l a y e r e f f e c t decreases with shear r a t e u n t i l i t vanishes a t high f l o w r a t e s . A comparison between flow curves and rheograms gives an estimation of e f f e c t i v e shear r a t e s i n pore t h r o a t s of porous media a s a f u n c t i o n of average velocity. The experiments c a r r i e d out i n Fontainebleau sandstones having d i f f e r e n t permeab i l i t i e s confirm t h i s observation and show t h a t pore t h r o a t diameters i n consolidated porous media a r e l a r g e r than predicted by the usual c a p i l l a r y models. I n a l l types of porous media, no d i l a t a n t behavior was detected even a t the highest flow r a t e s . The p r a c t i c a l a p p l i c a t i o n s of t h i s study f o r EOR a r e 1) w t h a n s o l u t i o n s a r e b e t t e r sweeping f l u i d s i n heterogeneous r e s e r v o i r s than conventional f l u i d s h v i n g the same average v i s c o r i t y ; 2) they can be ured i n l e s s permeable format i o n s than previously claimed; 3) very good i n j e c t a b i l i t y i s expected f o r microgelfree solutions.

198 INTRODUCTION Both hydrolyzed polyacrylamide and xanthan polysaccharide solutions are candidates for enhancing oil recovery. Up to now, hydrolyzed polyacrylamides have undoubtedly been more extensively studied in the laboratory and used in field applications. However, the macromolecular flexibility of this type of polymer causes several detrimental effects (1): 1) The viscosity decreases sharply as salinity increases, due to the screening of charged groups, particularly in the presence of bivalent ions. 2 ) The dilatant behavior at high flow rates which decreases injectability. This behavior isdue to the coil-stretch transition of macromolecules in converging zones of porous media ( 2 ) . 3 ) The mechanical degradation which occurs when hydrodynamic forces on the stretched molecules overcome the strength of carbon-carbon bonds ( 3 ) . Moreover, the hydrolysis of acrylamide groups at high temperatures, observed even in neutral conditions ( 4 1 , can lead to precipitation in the presence of calcium ions. So their use is limited to low salinity and temperature reservoirs. The rigid rodlike conformation of xanthan polysaccharide molecules in most reservoir conditions enables the problems mentioned above to be avoided. The viscosity is almost insensitive to salinity, except in a very low salinity range, and neither dilatant behavior nor mechanical degradation has been observed in oil recovery conditions. So this polymer is potentially very attractive, particularly for high salinity reservoirs. But, up to now, the poor quality of most industrial products available on the market has excluded xanthan polysaccharides from many field applications. The poor solubility of some products and the existence of both microgels and cellular debris, particularly in powders, is well documented (5). The influence of these microgels on their flow behavior has been extensively studied in well-defined porous media (6). However, recent improvements in manufacturing processes, particularly for fermentation broths, reduce to a great extent the risks of well plugging, so that xaqthan solutions could be widely used in the near future. These newly manufactured polymers contain so few microgels that they will be adsorbed or retained at a short distance from the injection well. In these conditions, most of the oil to be recovered which is located far from the injection well will be swept by a polymer solution without microgels. Thus knowing the basic rheological properties of such a solution in porous media is very important from a practical point of view. The first experiments carried out in porous media with a microgel-free solution (7) showed that the apparent viscosity or mobility reduction is less than the viscosity determined in a viscometer, mainly at the lowest shear rates in the Newtonian regime, Further experiments, performed with a well-characterized polymer solution and well-defined porous medium, showed that this phenomenon was related to the existence of a depleted layer near the wall, due to steric effects (8). The present investigation aims to study the influence of polymer concentration and rock permeability in order to estimate the effects of this depleted-layer phenomenon on the sweeping properties of xanthan solutions. POLYMER SOLUTIONS The xanthan polymer used is a sample manufactured in a fermentation-broth form by RhBne-Poulenc laboratories with a fermentation process specially designed to avoid microgel formation. Its molecular weight should be close to 0.8 x lo6. All solutions were obtained by dilution with salted water, clarified and filtered at very low shear rate to remove any possible remaining microgel with a method previously described (6). The addition of 400 ppm NaNg protected solutions against bacterial attack. In the conditions chosen (salinity = 5 g/l NaC1, pH = 7,

-

199 8 = 30°C), t h e polymer molecule was shown t o behave l i k e a r i g i d rod having a

0.62 pm length and 16.5

1 diameter

(8).

BULK RHEOLOGICAL PROPERTIES

Shear flow V i s c o s i t y measurements were performed with a s e r i e s o f g l a s s c a p i l l a r y viscometers, previously d e s c r i b e d , over a wide shear r a t e range ( 0 . 1 t o 3000 s-1) f o r various polymer concentrations (25 t o 2400 ppm) using Rabinowitch-Mooney c o r r e c t i o n f o r power-law f l u i d s . The p l o t s of shear v i s c o s i t y versus shear r a t e i n log-log coordinates (Fig.1) show how s o l u t i o n s behave i n pure shear flow. The following can be observed:

1) A Newtonian regime, a t very low shear r a t e s , i n which r e l a t i v e v i s c o s i t y 7, which i s t h e r a t i o between polymer s o l u t i o n and b r i n e v i s c o s i t i e s i s independent of shear r a t e and equal t o q r o . 2) A t r a n s i t i o n zone, c h a r a c t e r i z e d by a c r i t i c a l shear r a t e , equal t o the inverse of a r o t a t i o n a l r e l a x a t i o h time ir.

3 ) A shear-thinning regime, i n which r e l a t i v e v i s c o s i t y decreases with shear r a t e according t o a power l a w whose exponent is 2 m. Over t h e shear r a t e range t e s t e d , t h e experimental d a t a f i t very w e l l with the Cerreau model A ( 9 ) . '1 r o I

7r

= [1+ (

TrX

Y)

'3"

100: 50-

20+

lo: 5-

2

'L 1

Figure 1. Viscosity-shear r a t e curves f o r v a r i o u s polymer concentration

200

Converging flow An estimate of viscous f r i c t i o n i n converging flows can be made by measuring the apparent r e l a t i v e v i s c o s i t y i n a model c o n s i s t i n g of successive s h o r t c a p i l l a r i e s separated by c y l i n d r i c a l expansionsfm! which the geometry is shown i n Figure 2 .

Figure 2. Influence of converging flow zones on apparent v i s c o s i t y

The c a p i l l a r y r a d i u s was chosen s u f f i c i e n t l y small so a s t o avoid any i n e r t i a e f f e c t i n our expe imental conditions. For shear r a t e s l e s s than a c r i t i c a l value 600 s-i, t h e apparent v i s c o s i t y i n the model was found t o be equal t o the shear v i s c o s i t y , meaning t h a t r e l a t i v e v i s c o s i t i e s a r e equal i n both converging and shear flow. ForY > yf, t h e apparent v i s c o s i t y becomes g r e a t e r than shear v i s c o s i t y . This increased viscous f r i c t i o n occurring i n converging flow near the entrance t o t h e c a p i l l a r y is explained by t h e s t r o n g o r i e n t a t i o n of the rods i n t h e flow d i r e c t i o n when t h e product of r e l a x a t i o n time by elongat i o n r a t e is s u f f i c i e n t l y high (2) (10). However, this i n c r e a s e i n apparent v i s c o s i t y is very s m a l l , compared t o t h a t obtained with polyacrylamide s o l u t i o n Indeed, t h e polyacrylamide molecule is both with t h e same flow conditions ( 2 ) . s t r e t c h e d and o r i e n t a t e d i n the flow d i r e c t i o n by t h e converging flow. The high s t r e t c h i n g degree ( t h e s t r e t c h e d length may be ;O times t h e i n i t i a l c o i l diameter) explains t h e magnitude of t h e viscous f r i c t i o n i n c r e a s e with polyacrylamide, thus involving d i l a t a n t behavior.

o*=

201 WALL EFFECT I N FLOW THROUGH FINE CAPILLARIES The e f f e c t s of pore s i z e on apparent v i s c o s i t y were f i r s t i n v e s t i g a t e d i n a very simple system, namelywith a well-characterized r o d l i k e polymer s o l u t i o n flowing through f i n e c y l i n d r i c a l c a p i l l a r i e s , in order t o make t h e i n t e r p r e t a t i o n e a s i e r . Experimental f a c i l i t y Nuclepore membranes were s e l e c t e d f o r these experiments because t h e i r pores have a well-defined c y l i n d r i c a l shape. The average diameters and a r e a l pore d e n s i t i e s corresponding t o nominal diameters (ranging between 0.4 and 12 pm) were determined by e l e c t r o n microscopy (81, and the average diameters a r e given i n Figure 3.

4--+

3-

-3

2-

-2

_____ 500prn Copillories

-Nuclepore Membmnes

A s e r i e s of six f i l t e r holders, each one containing f i v e membranes separated by nylon g r i d s , was used t o o b t a i n s u f f i c i e n t pressure drops measured by oil-water manometers. The thickness of the Nuclepore membranes is constant and approximately equal t o 10 p m , so that t h e c a p i l l a r y length t o r a d i u s r a t i o l / r given i n Figure 3 depends on pore diameter. Results and discussion The r e s u l t s of flow experiments a r e shown i n Figure 3. Bulk r e l a t i v e v i s c o s i t y versus shear r a t e i s p l o t t e d a s a dashed l i n e . The s o l i d - l i n e curves show the v a r i a t i o n s of r e l a t i v e apparent v i s c o s i t y measured during flow through membranes having d i f f e r e n t pore diameters. The most importcmt r e s u l t is t h a t i n t h e Newtonian regime the apparent v i s c o s i t y in f i n e pores is found t o be lower than i n bulk s o l u t i o n s and decreases with pore

202 diameter, except f o r t h e s m a l l e s t one whose diameter (0.28 pm) i s l e s s than molecule length (0.62 pm). In t h i s l a s t case t h e macromolecules a r e r e t a i n e d on the upstream s i d e of t h e membrane, causing an extra-pressure drop and thus a curve upturn i n low shear range. A t t h e h i g h e s t shear r a t e s , t h e macromoleby hydrodynamic f o r c e s and can e a s i l y pass through t h e memcules are oriented branes. In a l l experiments, t h e water permeability was unchanged a f t e r polymer flow, showing t h a t flow p r o p e r t i e s were not d i s t u r b e d by a d s o r p t i o n o r r e t e n t i o n phenomena. It must be noted t h a t a comparison between apparent v i s c o s i t i e s i s v a l i d i n t h e Newtonian regime even f o r c y l i n d r i c a l pores having d i f f e r e n t length to-radius r a t i o s . A t higher shear r a t e s , t h e entrance e f f e c t s can i n c r e a s e apparent v i s c o s i t y i n r e l a t i v e l y s h o r t c a p i l l a r i e s (111, and t h e shear r a t e dependence must be s t u d i e d with models having s i m i l a r geometric shapes such as g l a s s bead packs ( s e e below). This decrease i n apparent v i s c o s i t y a s pore diameter decreases has been i n t e r preted ( 8 ) by t h e e x i s t e n c e of a depleted l a y e r near t h e pore.wal1. This deplet i o n i s due t o t h e s t e r i c hindrances which reduce t h e p r o b a b i l i t y t h a t t h e macromolecular c e n t e r of mass may be a t a d i s t a n c e less than one macromolecular h a l f length from t h e w a l l a s shown i n Figure 4. Thus, t h e polymer concentration w i l l i n c r e a s e from zero a t w a l l c o n t a c t up t o bulk c o n c e n t r a t i o n a t a d i s t a n c e c l o s e t o h a l f t h e l e n g t h of a macromolecule. Such a depleted-layer h a s been t h e o r e t i c a l l y p r e d i c t e d f o r both c o i l polymers (12) and r o d l i k e p a r t i c l e s (131, and i t p h y s i c a l l y explains t h e apparent s l i p a t t h e w a l l p r e d i c t e d f o r concentrated s o l u t i o n s (14). A s a consequence of t h i s d e p l e t e d l a y e r , the i n c r e a s e i n v i s c o s i t y due t o t h e polymer i s l e s s near t h e w a l l than i n t h e bulk, causing a lower o v e r a l l apparent v i s c o s i t y i n f i n e pores than i n t h e bulk. This e f f e c t i n c r e a s e s a s pore diameter decreases. A c o a x i a l two-fluid flow model has been proposed t o schematize polymer s o l u t i o n flow (Fig. 4 ) . The bulk s o l u t i o n with a r e l a t i v e v i s c o s i t y q r b flows i n t h e A depleted s o l u t i o n center of the c a p i l l a r y i n s i d e a r a d i u s equal t o ( r - 5 ) . having a r e l a t i v e v i s c o s i t y 'Iw flows i n an annulus having t h i c k n e s s 5 surrounding t h e bulk s o l u t i o n . The v e l o c i t y i s zero a t t h e w a l l and equal i n both

Allowed hsitiom of Rods

Ir Figure 4 Schemetic v i e w of polymer s o l u t i o n flow through f i n e pores w i t h a depleted l a y e r e f f e c t

203 the bulk solution and the depleted solution at a distance r - 6 from the axis. From this model, an analytical equation has been derived to calculate apparent relative viscosity 'Irp as a function of pore diameter 2 r:

rlrw

rlrFJ = where

p'

1

-

(1- 1/p ) (1- 6/r )

(2)

4

Trb' 1 ,'

Very good agreement between the experimental apparent relative viscosity in the Newtonian zone (Fig. 3) and the predictions of this model was found in choosing the following values for depleted layer characteristics:

I , '

8 = 0.3 pm

1.77

The value of 6 is close to half the length of a macromolecule (L/2 = 0.31pm), and the value of qrw is consistent with the physical hypothesis proposed. Moreover W B E R T and TIRRELL (15) have recently proposed a calculation based on the finitely extendable nonlinear elastic dumbbell as a molecular model and the exclusion of all molecule configurations intersecting the walls. Good agreement is found between their calculations and our experimental findings. Thus, the relation between the diameter dependence of apparent viscosity and the depleted- layer phenomenon seems to be very well established. Moreover, the same behavior was recently observed with polyacrylamide solutions when there are no effects of adsorption on flow properties ( 1 ) . FLOW THROUGH UNCONSOLIDATED POROVS MEDIA Pore size dependence Calibrated glass beads having different diameters (see Table 1) were packed to obtain porous media having similar pore shapes but different pore sizes. The flow experiments were performed with a 400 ppm xanthan solution, and the absence TABLE I

diameter

200-250

I

&I

Permeability k km2)

Apparent viscosity

tY

0

index

rP

137

0.40

36

0.40

I

3.90

0.185

3.75

0.180

8.4

0.175

40-50

2.4

0.160

20-3.0

0.66

10-20

0.21 0.11

0.41

I

2.97

1

1

1.7

I

43

0.130

1

0.110 0.080

of permeability reduction after polymer flow was checked for .very ascertain the absence of any adsorbed layer effect.

I

bead pack to

204

The flow-experiment r e s u l t s a r e q u i t e s i m i l a r t o those observed i n flow through c y l i n d r i c a l pores (Fig. 5 ) . The apparent v i s c o s i t y i n the Newtoqian zone is

XP5gA NoCl

4.

.

-4

1lSl 1361 1841

Glass Beod Pocks

12 41

3'

.3

I0161 IOZ1

10 111

2-

. -Apparent

Viscosity

(k) Permeobilily m

I,

-2

- - - .Bulk Sheor Vscosity .

.

.

a * . . .

\

prn' 8

,

'..--

,....''

. -1

Figure 5. Pore s i z e dependence of apparent v i s c o s i t y i n flow through glass-bead packs

found t o be lower than the bulk v i s c o s i t y and decreases with average pore s i z e evaluated by pack permeability a s shown i n Figure 5. The maximum w a l l shear r a t e i n the average pore t h r o a t diameter was c a l c u l a t e d by: -0.5 ? = 4 x 4 v (8 k 0 - 5 (3 1 Where a is a shape parameter c h a r a c t e r i s t i c o f t h e pore s t r u c t u r e . The value of a should be one f o r a bundle of c a p i l l a r i e s having the same diameters. For porous media, the value of P i s experimentally determined as being t h a t which gives t h e same c r i t i c a l y c corresponding t o the onset of shear-thinning behavior f o r both the shear viscosity-shear r a t e curve and the apparent viscosity-shear r a t e curve i n the porous medium under consideration. The a value was found t o be equal t o 1 . 7 f o r packs of l a r g e spheres having the same diameter (8). It decreases with the pore size-molecule length r a t i o and i n c r e a s e s a s pore s t r u c t u r e heterogeneity increases. This i s the case when t h e bead-diameter d i s t r i b u t i o n becomes wider o r when t h e consolidation degree of sands giving sandstones i n c r e a s e s (8). Due t o the s t a t i s t i c a l homothety of bead packs, t h e shear r a t e dependence of t h e depleted-layer e f f e c t can be deduced from flow experiments i n t h i s type of porous media. As expected, t h e rod o r i e n t a t i o n with $hear decreases t h e depleted l a y e r e f f e c t a s the flow r a t e i n c r e a s e s , and apparent v i s c o s i t y becomes independent of pore s i z e a t high shear r a t e s ( y 7 3000 s-1). A t t h e highest flow r a t e s , the apparent v i s c o s i t y overcomes t h e shear v i s c o s i t y . This can be explained by t h e . l n c r e a s e i n viscous f r i c t i o n i n converging zones of porous media where the macromolecules a r e o r i e n t a t e d i n t h e d i r e c t i o n of flow (Fig. 2).

205 As shown by results obtained with polymer flow through Nuclepore membranes, Equation (2) gives the relation between apparent viscosity and pore diameter. Thus an effective diameter can be calculated for each glass bead pack from the apparent viscosity measured. This effective diameter corresponds to an average hydrodynamic diameter of pore throats where polymer flows. On the other hand the mean pore size is proportional to the square root of the permeability for homothetic porous media. In Figure 9, the effective pore-throat diameter deduced ore diameter calculated from the polymer apparent viscosity is plotted versu from the simplest capillary model, 2 r = 2 ( 8 k 0-1)8". All the points corresponding to experiments performed with glass-bead packs are lined-up on the first bissectrix. So the average hydrodynamic diameter of pore throats is approxirmrtely equal to 2 ( 8 k 0-1)0.5 for homogeneous bead packs. Additional points deduced from experiments carried out in sand packs (8) are also lined-up on the same curve. polymer concentration effects The influence of polymer concentration was systematically studied by using a Carborundum pack having a permeability equal to 0.1 p m 2 , a porosity equal to 0.48 and an effective pore diameter of 2.6pm. The polymer concentration was varied from 200 ppm to 1600 ppm, and the absence of permeability reduction was checked after every polymer flow experiment.

7rP

r)r

10 -10

I

1

lo

'"%2

. .

'

..'

Figure 6. y'(seC-'1 The depleted-layer effect as a function of shear rate at different polymer concentrations incarborundum packs

206 Both shear v i s c o s i t i e s i n dashed l i n e s and apparent v i s c o s i t i e s i n s o l i d l i n e s a r e p l o t t e d i n Figure 6. The f i r s t observation i s t h a t t h e general behavior i s q u i t e s i m i l a r t o t h a t observed i n glass-bead packs. The depleted-layer e f f e c t appears t c be insens i t i v e t o t h e pore shape and chemical n a t u r e of porous media. This r e s u l t i s c o n s i s t e n t with t h e s t e r i c o r i g i n of t h e phenomenon. Moreover, t h e magnitude of the e f f e c t , i . e . t h e r a t i o between apparent v i s c o s i t y and shear v i s c o s i t y , i n c r e a s e s sharply with t h e polymer concentration, a t low shear r a t e s (Fig. 7 ) .

'7r

'7rP I

60-

1

I

I

XP 5911 NaCl pH=7 8 = 3 0 ° C

Corborundum Packs 40-

-40 / / 1

20-

0 0

400

800

1200

1600

C ( ppml Figure 7. The i n f l u e n c e of polymer concentration on t h e magnitude of depleted l a y e r e f f e c t

A t the h i g h e s t concentration t e s t e d ( c = 1600 ppm), t h e apparent v i s c o s i t y = 17.5) i s less than one t h i r d of bulk shear v i s c o s i t y ( 'Irb = 62). ( tlrp

This polymer concentration e f f e c t could a l s o be predicted. Indeed, a f t e r both d i v i s i o n by V r b and i n v e r s i o n , Equation (2) can be w r i t t e n :

207 For dilute solutions, the thickness of the depleted layer 6 is expected to be constant so that: (5) qrb’ qrp = k + (1 k ) P

-

-6

where k = (1 l 4 is a positive constant, always less than 1 for a given porous medium. &As a consequence , the depleted-layer effect incresses iinearly with p = ‘lrb . rlw In the concentration range tested, the Cb/Cw ratio is expected to be constant (13). Since the viscosity of these polymer solutions is roughly an exponential function of polymer concentration (81, the qrb/f)r,ratio increases very sharply with polymer concentration, thus explaining the concentration dependence observed for the depleted-layer effect. FLOW THROUGH SANDSTONES Permeability effects As shown above, the depleted-layer effect depends only on pore size for a given polymer solution. However, the well-known relation between pore size and permeability deduced from the simplest capillary model -1 0.5 (6) 2rc= 2 (8 k 0 is valid only for homothetic unconsolidated packs. For and are the

natural porous media such as sandstones, this relation is no longer valid, electron microscopy observations (16)hsve shown that pore throat diameters generally larger than those calculated by Equation (6). As a consequence, influence of permeability cannot be predicted by a simple model. TABLE I1

Flow through sand packs and sandstones (XP solution, 9, = 4.0, 2 m = 0.22) Perme-

Grain diameter Dg(pLm)

I

porosity

Apparent viscosity rP

abi1i3

k ( p

I

8 0 - 1 ~ ~ 5.0 Sand

I

0.38

I

3.5

Shearthinning

1

~

~~

I

Shear-rate Pore-thros;] constant diameter

0.165

2.5

21

0.165

1.4

15.7

Sand 2

I I I

I

0.087

0.119 Ssnd;tone

Sand:tone

I I I

I

0.0373 0.0206 0.0096 0.0033

1 I I

I

0.084 0.075 0.056 0.056

I I

I

I

2.95

0.062

2.83

0.060

2.69

0.056

2.49

-

I

4.2

I

13.6

I

I

9.1

I

6.0

I

14.3

4.4

208

some cores of quartzitic Fontainebleau sandstones having permeabilities ranging from 3x10'3 t o 0.4p1d (Table 11) were selected t o obtain a quantitative evaluation of the depleted-layer effects. A l l the cores were preflushed by a hydrochloric acid solution t o remove the slight quantity of iron contained i n the sample i n order t o avoid possible interaction8 with the polymer. After polymer flow experiments, the i n i t i a l permeability of each core was exactly restored, even for the l e s s permeable sample (3.3 x 10-3)Id).

The experimental r e s u l t s shown i n Figure 8 are similar t o those observed i n unconsolidated porous media. The apparent viscosity t s l e s s than in the bulk i n the Newtonian zone, which indicater a depleted-layer effect that increases as permeability decreases.

%

7)r

4

4

3

3

2

2

1

loo

1

10'

103

104

y(sec-1) Figure 8.

The depleted layer e f f e c t s in flow through Fontainebleau Sandrtoner

using polymersolution characteristics in the bulk ( '1 b = 4) and near the wall ( 8 = 0.3 p and q d l . 7 7 1 , deduced from experimantr vfth Nuclepore membranes, Equation (2) giver the effective diameter of pore throats 2 r am a fuoction of permability for Fontainebleau sandstones (Table 11). A8 e d c t e d , t U a e f + r-tive diameter 2 rp is always larger than 2 rc; and the r a t i o rp/rc increaaes a s $-me.b i l i t y &creaser, as shown in Figure 9, in which experimental point8 corresponding t o 8andrtones are plotted as solid circler. This trend is w r u i s t e n t with the secondary crystallization process which explains the decrease in permeability for Fontainebleau sandrtoner. The r a t i o rp/rc should be no l y one for Fontainebleau rand Pack8 having the same grain diameter (10
P

209

I

I

-

--I

/

I

(8.4)

0.3601, / p . 0 )

Sandpacks I 1. Sandstones I (k)Permeability in p m 2

i

i

I

Fontainebieau Sandstones 2r~=35(2r,)~~’

20-1

1 V

I

I

I

30.11)

2

5

16

. I

20 5‘ 100 2r or 2&mi

Figure 9 . Comparison of pore throat diameters detenrdned by polymer injection method with measured or calculated pore diameter i n various porous media

From a practical point of view, these r e s u l t s show t h a t xanthan solutions can pass very e a s i l y through even the low permeability zones of reservoirs. The lowest limit for use of such xanthan solutions should correspond t o pore throat diameters equal to_ycromolecular length ( k O . 6 pm) , i . e . t o permeability much lower than 10 p d f o r sandstones having a structure similar t o Fontainebleau sandstones. Practically, the use of such polymers is never limited by polymer dimensions.

Ddrodvnamic retention The f i r s t type of hydrodynamic retention, which is related to thermodpamic effects (17) and thus does not depend on pore-molecule r e l a t i v e dimensions, was found t o be almost negligible for these u n t h a n solutions having rodlibe molecules. As theoretically expected, the entropy difference. due t o molecular alignment are too small to induce large concentration differences between the different zones

2 10

of the porous medium. In high permeability sandstones, the concentration differences observed after sudden flow-rate changes (from Newtonian to shear-thinning regimes,namely from 6 to 700 sec’l) werE very small (m/q
-

-

CONCLUSIONS The basic rheological behavior of xanthan solutions in porous media has been studied with solutions without microgels, i.e. as they are in reservoirs far away from the injection wells. Indeed, the microgels contained in injected solutions are retained in a zone located around the injection well. The main conclusions of these investigations are the following: 1) The apparent viscosity of polymer solutions flowing through fine pores is always less than bulk shear viscosity at low shear rates in the Newtonian regime and decreases as pore size decreases. This phenomenon is interpreted by the existence near the pore wall of a depleted layer where average polymer concentration and viscosity are lower than in the bulk. 2 ) An analytical equation derived from a schematization of polymer solution flow as a two-fluid concentric flow is proposed to predict apparent viscosity as a function of pore size and polymer solution characteristics. F l o w experiments performed In well-calibrated cylindrical pores established the validity of this equation and provided the characteristics of the depleted layer. particularly, its thickness close to the half-length of the macromolecule is consistent with our interpretation of the origin of the depleted layer.

3 ) The depleted-layer effect decreases as shear rate increases so that, at the highest shear rates, the apparent viscosity becomes independent of pore size. Moreover, the rodlike conformation of xanthan molecules minimizes viscous friction in zones of converging flow inside the porous structure, so that w dilatant behavior is observed even at the highest flow rates such as those existing around the injection well. The injectability of microgel-free xanthan solutions should be excellent.

4 ) The depleted-layer effect is also observed in Nuclepore membranes, glass bead packs, Carborundum and sand packs,and Sandstones. Thus, this effect seems to be independent of the pore shape and chemical nature of porous media. This is consistent with the steric origin of this phenomenon.

5) The magnitude of the depleted-layer effect increases sharply with the polymer concentration, as predicted by our model, so that this effect becomes very significant from a practical point of view,

6) The magnitude of the depleted-layer effect increases as sandstone permeability decreases: Microgel-free ranthan solutions can pass easily, with a small apparent viscosity and without any permeability reduction, through sandstones having very low permeabilities.

211 7) The average hydrodynamic diameter of pore throats in a given sandstone can be deduced by measuring the apparent viscosity of a well-known polymer solution in the Newtonian regime. Thus polymer injection is a new method for investigating pore structure. 8 ) The effect of the depleted layer, which decreases apparent viscosity mainly in low permeability zones, enables xanthan solutions to sweep. o i l better in heterogeneous formations than conventional fluids having a viscosity that is independent of pore size.

Acknowledments This research was supported by the Association de Recherches sur les Techniques , and Rh6ne-Poulenc Industries provided d'Exploitarion du Petrole ( ARTEP the polymer sample. The authors wish to acknowledge the contribution of Ph. Delaplace and R. Tabary who performed laboratory experiments. . REFERENCES 1.

CHAUVETEAU, G.; 9'Molecular Interpretation of the Different Properties of Coil Polymer Solution Flow Through Porous Media in Oil Recovery Conditions", paper SPE 10 060 presented at the Annual Technical Conference and Exhibition, San Antonio, Oct. 4-7, 1981.

2.

CHAUVETEAU, G. and MOAN, M.; "The Onset of Dilatant Behavior in Non-Inertial Flow of Dilute Polymer Solutions through Channels with Varying Cross Sections", Journal de Physique-Lettres, 42 (1981) L-201 L-204.

-

3.

GHONIEM, S., MOAN, M. , CHAUVETEAU, G. and WOLFF, C.; "Mechanical Degradation of Semi-Dilute Polymer Solutions in Laminar Flowr",accepted for publication in Journal of Canadian Chemical Engineering.

4.

MULLER, G., FENYO, J.C., and SELEGNY, E.; "High Molecular weight Hydrolyzed Polyacrylamides. I11 Effects of Temperature on Chemical Stability", J. A w l . Pol. Sci., (19801, 25, 627-633. MULLER, G. ; "Thermal stability of High Molecular weight Polyacrylamide Aqueous Solutions", Polymer Bulletin (to be published).

5.

KOHLER, N. , and CHAUVETEAU, G. ; "Xanthan Polysaccharide Plugging Behavior in Porous Media: Preferential Use of Fermentation Broth", J. Pet. Techn. (Feb. 1981) 23, 349-358.

6.

CHAUVETEAU, G., and KOIILER, N.; "Influence of Microgels in Xanthan Polysaccharide Solutions on Their Flow Behavior Through Various Porous Media", Paper SPE 9295 presented at the 55th Annual Technical Conference and Exhibition, Dallas, Sept. 21-24, 1980.

7.

CHAUVETEAU, G.; "Ecoulement laminaire en milieu poreux de solutions de macromolecules de taille non negligeable devant les dimensions des pores", C.R. Aced. Sci. Paris, (Feb. 19791, 288, 107-110.

8.

CHAUVETEAU, G. ; "Rodlike Polymer Solution Flow through Fine Pores: Influence of Pore Size on Rheological Behavior", Submitted for publication in Journal of Rheology, 1981.

9.

C W U , P. J. ; "Rheological Equations from Molecular Network Theories", Trans. soc. Rheol., (19721, 16, 99-127.

2 12

10. HOA, N.T., CHAUVETEAU, G. , GAUDU, R. , and ANNE-ARCHARD, D.; "Relation entre le champ de vitesse dlelongation et l'apparition d'un comportement dilatant d'une solution de pol-re diluee dans un Ccoulement convergent non-inertiel", Submitted for publication in C.R. Acad. Sci. (1981). 11. MOAN, M. , CHAUVETEAU, G. , and GHONIEM, S.; "Entrance Effects in Capillary Flow of Dilute and Semi-Dilute Polymer Solutions", J. Non.Newt. Fluid. &&. , (19791, 5, 463-474. 12.

JOANNY, J.F., LEIBLER, L., and DE GENNES, P.G.; "Effects of Polymer Solutions J. of Pol. sc. (19791, 17, 1073-1084.

on colloid stability",

13. AUVRAY, L.; "Solutions de macromolecules rigides : Effete de paroi, de confinement et d'orientation uar un dcoulement", Journal de Physique (Janv. 19811, VOl. 42, 79-95. 14. DE GENNES , P.G. ; "Ecoulements viscosimetriques de polylderes enchevetres". C.R. Acad. Sci. Paris, (April 9, 19791, 288, B y 219-220. 15. AUBERT, J . H . , and TIRRELL, M. ; "Effective Viscosity of Dilute Polymer Solutions near Interfaces", ACS Polymer Preprint (1981) 22, 1, 82-83. 16. BATBA, V.K., and DULLIEN, F.A.L. ; "Correlation between Pore Structure of sandstones and Tertiary Oil Recovery", soc. Pet. Erin. J. (Oct. 19731, 13, 256-258. 17. METZNER, A.B. ; "Flow of Polymeric Solutions and Emulsions through Porous Media", in "Improved Oil Recovery by Surfactant and polvmer Floodinn", Acad. Press. Inc. , New-York (1977), 439-451. 18. CHAUVETEAU, G. , and KOHLER, N. ; "Polymer Flooding: the Essential Elements for Laboratory Evaluation", Paper S R 4745, presented at the Improved Oil Recovery Meeting, April 22-24 (1974). 19. WILLHITE, G.P., and DOHINGUEZ, J.C. ; %Mechanisms of Polymer Retention in Porous Media",in Jmroved Oil Recovery by Surfactmt and Polymer Floodinq, Acad. Press. Inc. New-York (1977),511-553. 20.

CHAUVETEAU , G. ; "The Effects of Rheological Properties and Polymer-Rock Dimension-Sensitive Interactions on Polyacrylamide Solution Flow through Porous Media", SOC. Rheol. Meeting, Houston, (1978) Oct. 22-26.

CHEMICAL FLOODING

213

THE CHATEAURENARD (FRANCE) POLYMER FLOOD FIELD TEST A. LABASTIE and L. VIO

ElfAquitaine ( M u c t i o n )

Abstract

A polymer flood is operated by Elf Aquitaine in the Chateaurenard (France) field, located in the Paris Basin. The pilot is developped with one injector and seven producers, in a layer of unconsolidated sand, 5 meters thick, at a depth of 600 m ; the 44 ha pattern enclosea a very important pore volume (700 000 m3). The oil is paraffinic and has a viscosity of 40 cPo at reservoir tenperkture (30OC). The water being almost fresh (0,4 g/l TDS) it has been decided to use hydropolyacrylamides. Several commercial products have been tested, mainly for viscosity and injectivity ; a liquid polymer, dissolved in produced water, is presently being used for the pilot. The water must be carefully treated before dissolution to avoid polymer degradation and formation plugging. The injection has been started in 1977 and on account of the quantities injected so far, we have not yet seen any response in the sir main producers (which are at a distance of 400 to 500 m from the injector). But the seventh intermadiate producer, drilled at a shorter distance (280 m) from the injector, has shown vexy interesting results with a sharp decrease of the WOR (WOO tons of tertiaq oil have been produced) ; this response is due to the effect of nobility control, maybe amplified by a local reservoir heterogeneity.

Field deBcriDtion The Chateaurenard field, outlined in Fig. 1, is part of the Neocomian (Lower Cretaceous) oil reservoirs, found in the southern part of the Paris Basin ; it is located 100 km SSE of Paris, and the oil eone extends over an area of 20 km2.

2 14

Fig. 1

-

Map of Chateaurenard field

2 15

Geol o m There are three distinct structures, separated by North-South faults with throws of 15 to 20 m. Situated at a depth of about 600m, the reservoir is formed of three layers of unconsolidated sands separated by shale as depicted on the type log of Fig. 2 ; the dip of these layers is very slight, about l o . The reservoir concerned by the polymer injection is formed by the two upper levels (R1 and R 2 , belonging to the Hauterivian stage of the Neocomian) of the central structure ; these two levels can be considered as a single reservoir, because the clay layer between them is discontinuous and does not form a tight barrier. The reservoir forms a roughly triangular monocline whose closures are a fault in the east and the wedgeout of the sands in the south.

-

The deposit of these sands is in the form of submarine channels ; this sedimentation type gives massifs with sharp lateral variations of facies.

T Y P E LOG

-

C H A T E A U R € N A R D St. FIRMIN. CHUtLLLS FIELDS

.-

Gamma-Ray

Fig. 2

Laieroloa

-

Type l o g

2 16

Characteristics of R1/R2 reservoir : fluid properties The reservoir is formed by uadonsolidated sand, with some amount of clay(2 to 15 k). The average total thickness in the pilot area is 5 metres, with a porosity of 30 $. This sandstone is relatively fine ained (average 150k), but with a wide g r a i n sine distribution (80 to 3 5 0 p Y The average permeabilitg ) 1 ( ), but with rather large and unforeseeable variations on is 1 Darcy m account of the channel type sedimentation system. The fluids are a relatively viscous oil (40 cPo at 30OC, reservoir temperature) of paraffinic type and without dissolved gas, and an almost fresh water ; the relevant characteristics are indicated in the folhing table : Depth, m (ft) Porosity, $ Permeability, mD Clay content, % Initial water saturation, $ Residual oil saturation, $ Current field avera e oil saturation, $ Temperature, OC ( O P T Oil gravity, g/cm3 (OAPI) Oil viscosity, aa.s (CPO) Water salinity (TDS), p m Water hardness (Ca + Mgp, ppm

600 (1970)

30 1000 2 to 15

30 30 55

30 (86) 089 (27) 40 (40) 400

70

Production history The field was discovered in 1958, initial oil in place was estimated at 1 1 Mm3 (69 millions bbl), with half f o r R1/R2 reservoir. I n 1980, cumulative production was 26 $ of OOIP, mainly through the action of an edge water drive. Because of very small dip a le and adverse mobility ratio (see kn Fig. 3 the relative permeability curve3 water appeared early in the production and water cut increased quickly ; in 1980, its average value for the field was 89 $. Peak oil production .reached 267 000 m3 in 1964 ; 1980 production was 95 000 m3.

- Relative permeabilities

2 17

POLYMER PILOT DESIGN Pattern selection The Chateaurenard field has been developped with an average well spacing of 400 m, and for this polymer pilot it has been decided to use this spacing. The R1/R2 was intergsting for this test, because of the two layers with a discontinuous separation, maybe responsible of poor sweeping efficiency ; but it was necessary that the two layers were not separated at the polymer injectca: well. After several interference tests, a seven spots pattern has been selected, with one injector (CR 9 bis) and six mpin producers (CR 3 - CR 6 CR 12 CR 16 - CR 19 Bis - CR 21 bis) at distances of 400 to 500 meters from the injector ; a seventh intermediate producer (CR 56) has been drilled at a shorter distance from the injector, in order to get an earlier response. This pattern is outlined in Fig. 4.

-

-Clay

Fig. 4

isopachs (separation R1

-

- R2)

- Polymer pilot pattern

The surface area of this pattern is 44 ha (110 acres), and it encloses a pore volume of 700 000 m3. The mobility ratio is very adverse and before polymer flood, after many years of waterflooding, the oil saturation was still 55 $.

Polymer choice and slug design The water being almost fresh and the temperature low, hydrolyzed polyacrylamides were selected. To dissolve polymer in produced water was the easiest for field operations, but it can Be detrimental for polyacrylamides stability (1). So we have studied the degradation of polymer in presence of oxygen and iron (little amounts are present in produced water). It has shown that we must avoid the presence of both iron and oxy en, but that little amounts of one of them is not detrimental (see Fig. 5 - 6 7 .

2 18

-

Fig. 6 A f t e r 2 hours Chemical ctegraduation of polyacrylamides : v i s c o s i t y ($ of i n i t i a l v i s c o s w y f u n c t i o n of Fe and 02 c o n t e n t

2 19 Commercial products were tested mainly for viscosity and injectivity. The injectivity test is a constant flow rate test through a 5,umilliporeR filter with pressure drop measurement ; the pore size (5p) is similar to the one of Chateaurenard reservoir, and the flow rate is chosen to give same shear rates as in the field flood. This is important because a plugging behaviour can be hidden if the fbw rate is to high, due to microgel deformations in impoktant pressure gradients ( 2 ) . This test seems a good screening procedure f o r comparison of products, even if sandpacks floods may be necessary for further investigation. Some results are given in Fig. 7 as an example. AP millibrn

I

l i l i r i 5.

f

64711

. . A

0

5

m

,

16

I (liqiil) I (liqiil) Sl(prlrr.2lk ritlltticl) G~(pmhr,iiritcitiw)

ZO

'tiw.h

It has been found that dry polymers (powder) need a retention of several hours after dissolution to become satisfactory on injectivity test. In this example, products A and C1 are good, products B and C2 are not satisfactory (plugging behaviour) ; product A is used for this operation. Polymer concentration and slug size have been determined by performance predictions with a reservoir model ; a slug of 0,33 PV with 700 ppm polymer has been chosen. The polymer slug will be followed by water injection, with viscosity decrease designed to prevent deleterious effects of viscous fingering (3). Surface installations The polymer solution is prepared with produced water, available in great quantities but not clean : it is contaminated by iron (Fe" and Fe+++), residual oil (1000 ppm), oxygen ( < 1 ppm) and clay particles. Removal of oil, clay and insoluble iron is carried out in a flotator using nitrogen, which also strips the water of oxygen traces ; a nitrogen blanket prevents anay oxygen entry. After treatment, the water is $ood for polymer dissolution, with low amounts of oil (< 3 ppm), oxygen (<0,01 ppm) and iron (< 5 ppm). A bacteria killing agent is added to the water, that is filtered before polymer dissolution.

2 20

At the beginning of the operation, dry powder polymer was used, with residence time between dissolution and injection to get good injectivity characteristics. It has been changed for liquid polymer (emulsion), easier to handle and good for injection immediately after dissolution. The fluid flow diagram of Fig. 8 outlines the equipment, that is designed for first dissolution of polymer in a concentrated master solution, and then final dilution ; polymer solution is 5rfiltered at the wellhead before injection, without any problem.

lil 151 I*

(IWW TIM

t t t t litqcc

PILOT PERFORMANCE : FIRST RESULTS The polymer injection has begun in 1977. Until 1979, the flow rate was 135 m3/day (850 bbl/day) ; since 1980, it has been increased to 250 m3/day (1 600 bbl/day) ; no injectivity problems were encountered with polymer solution. A slug of 235 000 m3 is to be i n j e M , with decreasing concentration at the rear front to prevent fingering, followed by water. Up to 'une 15, 172 700 m3 of polymer solution have been injected (24,7 $ pore volume?. The six main producers have not yet shown any response, which is normal on account of quantities injected so far. However, the seventh internlediate producer (CR 56) , has given very interesting results (see-fig. 9). This well, drilled at a distance of 280 m from the injector CR9 bis, has been put into production in 1978. Untgll mid 1979, the water cut was about 90 $, as in the other well of this area, then we observed a sharp decrease to 20 $ of the water cut, which is only 55 $ now (increasing).

9000 tons of tertiary oil have been produced. The time of oil bank breakthrough is in accordance with our predictions, but it is not possible to explain such an oil cut assuming an homo eneous repartition of permeabilities and saturations before polymer flodd fsee predicted and observed production in Fig. 9).

221 A very poorly waterflooded zone (of lower permeability) has been reached by

polymer flood, due to mobility control effect. This very good result would have not been possible without mobility control, so it must be attribuBed to the effect of polymer injection. However, this effect has been very important because 6f a local Eeservoir heterogeneity, so such a result cannot be generalized. But with this channel rtype sedimentation system, some other poorly water-d zones may exist, which can be swept by polymer flood in good conditions. We have now to wait for the response of other producers to have a good idea of polymer flodding performance in this field.

h

-.. b

b

.

07

0s b

0.2

b b b b

*

b

0

CONCLUSIONS 1

- The polymer solution is prepared without

2

-

3

-

problem using produced water, which is carefully treated. The solution is easily injected and does not show any plugging behaviour. A,significant decrease of WOR has been observed in the closest producer well ; a poorly waterflooded gone has been swept by polymers, due to mobility control effect. go00 tone of tertiary oil have been produced.

222

REFERENCES 1

-

2

-

3

-

G. Chauveteau et N. Kohler - Conditions de stabilit6 des solutions de polymkres lors d'une injection sup champs. International Symposium on hydrocarbon exploration, drilling and production technics (Paris, 10 - 12 dec. 1975). G. Chauveteau - The effect of rheological properties and polymer rock dimension sensitive interactions on polyacrylamide solution flow through porous media - 49th Annual Meeting of the Society of Rheology (1978). E. L. Claridge - A method of design of graded viscosity banks - Paper SPE 6848 presented at 52nd SPE Annual Fall Meeting (Oct. 1977).

223

CHEMICAL FLOODING

CAUSTIC FLOODING IN THE WILMINGTON FIELD, CALIFORNIA LABORATORY, MODELING, AND FIELD RESULTS VERNON S. BREIT

Scientific Software Cotporntion EDWARD H. MAYER

THUMSLong Beach Company JOHN D. CARMICHAEL

City of Long Beach Department of Oil PToperties'

ABSTRACT A c a u s t i c enhanced waterflood t e s t i s being conducted i n the Ranger Reservoir o f the Long Beach Unit, Wilmington Field, C a l i f o r n i a by t h e Department o f O i l Properties o f the City o f Long Beach and i t s f i e l d contractor, THUMS Long Beach Company, i n association w i t h the United States Department o f Energy. The purpose o f the p i l o t demonstration i s t o evaluate t h e e f f i c i e n c y o f t h e caustic displacement mechanism i n t h e environment o f a s t r a t i f i e d , heterogeneous, high o i l v i s c o s i t y r e s e r v o i r where primary waterflood recovery i s r e l a t i v e l y poor. The t e s t area i s located i n t h e Ranger Zone o f F a u l t Block V I I w i t h i n the Wilmington F i e l d . The p i l o t t e s t i n v o l v e s t h e i n j e c t i o n o f c a u s t i c s o l u t i o n i n t o a modified staggered l i n e d r i v e w e l l p a t t e r n c o n s i s t i n g o f e i g h t i n j e c t i o n w e l l s which surround eleven a c t i v e producers i n an area o f approximately ninety-three acres.

Laboratory i n v e s t i g a t i o n s conducted j o i n t l y by THUMS and the Department o f O i l Properties i n d i c a t e d t h a t Ranger Zone crude could be r e a d i l y emulsified i n the presence o f water containing as low as 0.1% b y weight sodium hydroxide. Additional o i l was recovered i n core f l o o d s when 1.0 weight percent sodium c h l o r i d e was added t o the a1k a l ine s o l u t i o n . The r e s u l t s o f t h e l a b o r a t o r y core t e s t work and t e s t s o f t h e r e a c t i o n between a l k a l i n e s o l u t i o n s and r e s e r v o i r sands used i n r e s e r v o i r simulations i n d i c a t e d o i l r a t e response and t o t a l incremental o i l recovery are v e r y dependent upon t h e caustic concentration and caustic s l u g size. A l k a l i n e consumption calculated t o be very large.

1.

Now w i t h X t r a Energy Corporation, Signal H i l l , C a l i f o r n i a .

224

This paper sumnarizes the r e s u l t s o f the caustic core f l o o d s which were performed t o evaluate t h e entrainment mechanism o f o i l displacement and l a b o r a t o r y t e s t s t o evaluate t h e long term consumption o f hydroxide ions by t h e r e s e r v o i r sands. The past performance o f the f i e l d and the r e s e r v o i r simulation history-match o f t h a t past performance are discussed. The predicted f u t u r e performance o f the f i e l d f o r both continued waterflooding and a caustic f l o o d i s sumnarized. A l k a l i n e f a c i l i t i e s were completed and placed i n operation on March 27, 1980. Pre-flush i n j e c t i o n consisted o f 11.5 m i l l i o n b a r r e l s o f softened f r e s h water w i t h an average o f 0.96 weight percent s a l t . The p r e - f l u s h amounted t o approximately 10 pore volume percent. A l k a l i n e s o l u t i o n containing 0.4 weight percent sodium o r t h o s i l i c a t e and 1.0 weight percent s a l t i n softened water i s being i n j e c t e d .

INTRODUCTION The Wilmington F i e l d i s the l a r g e s t f i e l d i n C a l i f o r n i a , Fig. 1. It has seven basic r e s e r v o i r zones w i t h crudes t h a t g e n e r a l l y have a r e l a t i v e l y low g r a v i t y , high v i s c o s i t y and high organic acid content. The recovery e f f i c i e n c y f o r the waterflood i n the Ranger Zone o f the Wilmington F i e l d has been low due p r i m a r i l y t o a h i g h l y unfavorable m o b i l i t y r a t i o between water and o i l and s i g n i f i c a n t r e s e r v o i r s t r a t i f ic a t ion.

FIGURE 1

- FIELD

LOCATION MAP

225

The concept o f a c t i v a t i n g the n a t u r a l surfactants present i n t h e crude o i l by contact w i t h a l k a l i n e water, although l i m i t e d t o r e s e r v o i r s w i t h s u i t a b l e crude o i l s , has p o t e n t i a l economic advantages over commercial surfactant flooding owing t o the high cost o f the s u r f a c t a n t s and t h e low cost o f a l k a l i n e materials. Several mechanisms have been postulated f o r t h e improved o i 1 recovery r e s u l t i n g from a l k a l i n e waterflooding. Included among these are emulsification and entrainment, wettability reversal, and emu1s i f i c a t i o n and entrapment1 The r e 1a t ionship between these p o s s i b l e mechanisms i s necessarily more complicated i n caustic waterflooding than surfactant i n j e c t i o n due t o the complexity o f the a l k a l i - c r u d e o i l r e a c t i o n which would take place i n the r e s e r v o i r . LABORATORY STUDIES Laboratory i n v e s t i g a t i o n s have been performed f o r t h i s a1 k a l i n e p i l o t p r o j e c t t o provide comparison core f l o o d t e s t s between waterflood and a l k a l i n e f l o o d recovery and d e f i n e the extent o f caustic consumption by the r e s e r v o i r rock. The comparative core f l o o d s were performed w i t h preserved core m a t e r i a l which was c u t p a r a l l e l t o the core axis. The plugs measured approximately two inches i n diameter by f i v e inches long. The long term a l k a l i n e comsumption t e s t s were performed w i t h sand packs * i c h were prepared i n L u c i t e columns and v a r i e d i n length from s i x t o twelve inches w i t h a diameter o f approximately one and a h a l f inches. Comparative Core Flood Studies Frozen preserved core samples were jacketed on coring i n p l a s t i c tubing. I n t h e l a b o r a t o r y the plugs were placed i n a modified Hassler sleeve apparatus, thawed and confined a t 1600 p s i overburden oressure. The cores were heated t o r e s e r v o i r temoerature o f 125'F and lQor , I . 1 ' , , ~.bor.iory namuitm dynamically driven t o 0 Phi. w,.r minimum water s a t u r a t i o n A C.nti. S*rllr using Ranger Zone crude --- S*l"l.,i.. I..*,. - CORE SAMPLt NO.21 oil. The samples were then water driven at a A I.-@ Q r a t e varying from s i x f e e t per day p r i o r t o do P water breakthrough t o one $0 f o o t per day a f t e r water 1% Ir breakthrough (the 9i reduction was done t o I@@: avoid excessive pressure s : I A: l B gradients within the 0 , 3 0 1' 1 ' core). The cores were 5 w0,,1 I waterf looded t o residual " , . z : H i . . , o i l s a t u r a t i o n (see Fig. 3' , , # A1 I 2). Then the cores were 1 I . 9' again dynamically driven 'L' )*on m u sI. A N.cL IOU Ito minimum water I OIL mv = s a t u r a t i o n using crude I I oil. The enhanced I I o r a l k a l i n e water drive I I tests were then . ' I I * I * 1 . ' SIL s ia n n be u 6s re performed. These t e s t s

--

!

I

#

f

-

;

-

a

'

a

0

-

226

1. 2.

3.

I n j e c t water t o breakthrough o r a pre-determined w a t e r / o i l ratio; I n j e c t a pre-flush containing 1%sodium c h l o r i d e b r i n e i n softened water; and Follow w i t h an a l k a l i n e - s o f t water s o l u t i o n containing sodium c h l o r i d e a t a concentration o f 1%. ( D i f f e r e n t a l k a l i n e concentrations were used i n the various t e s t s performed )

.

Figure 2 shows a t y p i c a l response t o t h i s t y p e entrainment mechanism a1 k a l i n e waterflooding. (Sixty-two comparative core flood t e s t s were performed.) On t h e average, improvement i n o i l recovery was approximately 10 pore volume percent. No strong c o r r e l a t i o n was found between improvement i n o i l recovery and t h e concentration of a l k a l i injected. Therefore, a l l o f the core f l o o d t e s t s were combined and analyzed t o o b t a i n a more s t a t i s t i c a l l y meaningful average core response t o a l k a l i n e flooding. These t e s t s were used t o o b t a i n r e l a t i v e p e r m e a b i l i t y t o o i l and water f o r both the waterflood and t h e a l k a l i n e f l o o d performance (Fig. 3). These r e l a t i v e p e r m e a b i l i t y phenomena were used i n r e s e r v o i r simulation matches o f i n d i v i d u a l core

FIGURE 3

- OIL/WATER RELATIVE PERMEABILITY

227

tests. They then were scaled f o r the two-dimensional s l u g size o p t i m i z a t i o n cases and f o r a three-dimensional model o f the p i l o t area f o r the caustic f l o o d p r e d i c t i o n cases. Long Term A l k a l i n e Consumption I n Reservoir Sands The e f f e c t o f a l k a l i n e consumption i s a c r i t i c a l economic consideration. As a r e s u l t , studies were undertaken i n an attempt t o d e f i n e the magnitude o f the caustic consumption which can be expected t o occur i n an a l k a l i n e f l o o d i n t h e Ranger Zone o f F a u l t Block VII. The t e s t s conducted included s t a t i c e q u i l i b r i u m tests, r e v e r s i b l e adsorption chemical consumption tests, s e n s i t i v i t y o f caustic consumption t o f l o w rate, and long-term f l o w t e s t s . I n the l a t t e r type t e s t s sand packs were prepared, and f o l l o w i n g waterflooding t o breakthrough, s o f t w a t e r - a l k a l i solutions w i t h 1%sodium c h l o r i d e were i n j e c t e d i n t o t h e sand packs f o r periods ranging between 30 and 104 days. S t a t i c periods o f varying length followed a f t e r which the a1 k a l i n e i n j e c t i o n was resumed. The o u t l e t c a u s t i c concentrations were measured d a i l y during the e n t i r e f l o w t e s t . It was evident from t h e t e s t s t h a t t h e consumption o f a l k a l i n e m a t e r i a l i s a long term phenomenon. The number o f pore volumes o f i n j e c t i o n required f o r concentration o f output s o l u t i o n t o reach t h e concentration o f t h e i n j e c t e d s o l u t i o n ranged upward t o 38 pore volumes. Reducing the f l o w r a t e o f t h e i n j e c t i o n increased the number o f pore volumes required t o reach an e f f l u e n t concentration n e a r l y equal t o t h e i n l e t concentration. The upper curve o f Fig. 4 shows t y p i c a l r e s u l t s f o r long term a l k a l i n e consumption r e s u l t s where t h e amount o f consumption, i n terms o f mass per u n i t volume i s p l o t t e d versus t h e concentration residence t i m e product. The consumption l a b o r a t o r y work i s described i n more d e t a i l i n t h e "Fourth Annual Report" o f t h i s p r o j e c t prepared f o r the U. S. Department o f Energy.2'

FIGURE 4

- LONG TERM ALKALINE COMSUMPTION RELATIONSHIPS

228

RESERVOIR

DESCRIPTION

The Wilmington f i e l d i s located i n the south-western p o r t i o n o f Los Angeles, C a l i f o r n i a as shown i n Fig. 1. It i s the l a r g e s t f i e l d i n C a l i f o r n i a and one o f t h e major f i e l d s i n North America. Cumulative o i l production t o date i s i n excess o f 1 b i l l i o n barrels. The f i e l d i s an asymnetrical a n t i c l i n e w i t h a north-west south-east axis broken by a series o f transverse normal f a u l t s . The f a u l t s d i v i d e the r e s e r v o i r i n t o pools and have proven t o be e f f e c t i v e b a r r i e r s t o f l u i d and pressure comnunication. Dips rang: from a maximum o f 20" on the northern f l a n k t o approximately 60 on the southern f l a n k . The e n t i r e s t r u c t u r e i s eleven miles long and t h r e e miles wide underlying approximately 13,000 acres. Produci.ng zones i n t h e F i e l d (Tar, Ranger, Upper Terminal, Lower Terminal, Union P a c i f i c , Ford, and 237) l i e between the depths o f 2,000 and 7,000 f e e t subsea and range i n age from l a t e Miocene t o Pliocene. The upper f o u r zones containing low g r a v i t y , high v i s c o s i t y crude are t h e major o i l reservoirs. The r e s e r v o i r rock i n a l l zones i s sandstone w i t h d i f f e r e n t degrees o f consolidation and varied s i l t and c l a y content. The p i l o t p a t t e r n area i s i n the eastern p o r t i o n o f t h e Long Beach U n i t o f Wilmington F i e l d between the Juniper0 and Temple Avenue F a u l t s i n t h e Ranger zone and i s shown i n Fig. 5.

FIGURE 5

- PATTERN AREA

SCHEMATIC

The modified l i n e d r i v e c o n f i g u r a t i o n of t h e p a t t e r n represents a t y p i c a l waterf lood we1 1 p a t t e r n f o r t h e Ranger Zone o f the Long Beach Unit. Ranger i s t h e l a r g e s t and most p r o l i f i c of the Unit's r e s e r v o i r s . It consists of several distinct intervals or subzones separated by impermeable shale sections (see Fig. 6). Each subzone i s an i n t e g r a t e d sequence of shales and unconsolidated to semi-consolidated, poorly sorted, medium-to-f i n e grained sands. These six subzones l i e at depths of 2,600 t o 3,400 f e e t w i t h a net thickness o f 305 feet. The p r o p e r t i e s o f each zone are sumnarized i n Table 1. Productive subzones underlying t h e p i l o t area contain crudes w i t h a wide range o f

229

TABLE 1 Ranger Subzone t0

SIMULATION YOWL LAYERS RANQEI ZONE PILOT AREA

-

FIGURE 6

- TYPE

LOG

- RESERVOIR CHARACTERISTICS BY ZONE

Porosity* Perm* ( f r a c t i o n ) (md) 260 270

Net Pay (feet)

Net Volume (Acre Feet)

109

9341

F

.274

321

52

4578

H

.246

179

41

3647

X

.265

173

48

4339

G

.289

220

29

2655

64

.270

131

26

2331

*

Based on 1600 P S I Confining Pressure Core Analysis Data and Special Logging Programs.

physical properties. The general c h a r a c t e r i s t i c s o f these p r o p e r t i e s are: an o i l g r a v i t y range o f 14'-27' API; t h e o i l g r a v i t y w i t h i n a subzone depends upon s t r u c t u r a l p o s i t i o n w i t h t h e higher subzone g r a v i t y a t the h i g h s t r u c t u r e p o s i t i o n s and low g r a v i t i e s a t the lower s t r u c t u r e p o s i t i o n s . From subzone t o subzone the o i l g r a v i t y depends upon geological age w i t h the lower ( o l d e r ) subzones containing higher g r a v i t y crude and t h e upper subzones containing t h e lower g r a v i t y crude. PRODUCTION HISTORY I n i t i a l development i n t h e p i l o t area began irr August 1967. A t t h e time o f the development, pressure gradients existed across the p a t t e r n w i t h t h e average r e s e r v o i r pressure being approximately 85% o f hydrostatic. This phenomenon i s due t o comnunication between the p i l o t and o l d e r producing areas i n t h e v i c i n i t y . Waterflooding operations began concurrently w i t h development. The modified three producing row l i n e d r i v e f l o o d p a t t e r n was aided by peripheral a q u i f e r injection. The i n i t i a l development o f t h e p a t t e r n was completed i n e a r l y 1975. O i l production f o r t h e p i l o t p a t t e r n area as o f September 30, 1980 was 11,490,000 STB. Cumulative water i n j e c t i o n by the e i g h t surrounding i n j e c t i o n w e l l s was 55,000,000 STB. O f t h i s amount, t h e p i l o t area had produced 38,000,000 STB o f water. (Performance o f the confined p a t t e r n i s shown i n F i g . 7.)

2 30

FIGURE 7

- PATTERN AREA OF PERFORMANCE HISTORY RESERVOIR SIMULATION HODELIN6

The formulation o f t h e caustic simulation model has been reported i n an e a r l i e r paper by B r e i t , e t al3. For enhanced waterflooding, t h e simulator accounts f o r t h e i n j e c t i o n and production o f up to s i x d i f f e r e n t a c t i v e agents i n an aqueous phase. Any o r a l l o f these agents may be caustic o r polymer type f l u i d s o r a combination o f these types o f f l u i d s . The primary displacement e f f e c t s o f a caustic f l u i d are represented by changes i n r e l a t i v e p e r m e a b i l i t i e s to o i l and water. This s i m p l i f i e d approach permits t h e modeling o f enhanced recovery p r o j e c t s without the necessity o f determining the exact mechanisms o f t h e displacement i n minute d e t a i l . The model also accounts f o r the consumption o f a c t i v e m a t e r i a l w i t h i n a caustic s l u g by three d i f f e r e n t mechanisms: The i n t e r a c t i o n between a caustic s l u g and formation water t o form p r e c i p i t a t e s o f d i v a l e n t cations, t h e instantaneous o r e q u i l i b r i u m adsorption o f c a u s t i c solution, and t h e long term k i n e t i c a l l y c o n t r o l l e d i n t e r a c t i o n between caustic and t h e rock m a t r i x i t s e l f . The p e r m e a b i l i t y changes r e s u l t i n g from t h e d i v a l e n t i o n p r e c i p i t a t i o n were not considered i n the simulator work f o r t h e Range V I I p i l o t . The s i m u l a t i o n work was based on t h e use o f t h e r e l a t i v e p e r m e a b i l i t y curves produced i n t h e l a b o r a t o r y experiments shown i n Fig. 2, an instantaneous c a u s t i c consumption o f 0.42 pounds and a maximum long term consumption o f 0.84 pounds per cubic foot. The match o f t h e l a b o r a t o r y response f o r core experiment No. 21 using these parameters i s shown i n Fig. 2.

231

Caustic Flood Optimization Study A small area o f the FQ subzone, Fig. 5, including two injectors was selected for s l u g optimization studies using the N-HANCE reservoir simulation model. Injection was scaled from the planned f i e l d injection r a t e of 34,000 STB per day. The reservoir and waterflood characteristics of this area are sumnarized i n Table 2. TABLE 2

-

ALKALINE SLUG OPTIMIZATION STUDIES BASE MTA FOR STUDY AREA

Reservoir Pore Volume o f Study Area I n i t i a l Oil in Place (TOIP) Waterflood Oil Recovery: TO 5-01-79 % TOIP e PV Waterflood O i l Recovery 5-01-79 To economic limit of 150 WOR (11-01-85) Cumulative Waterflood Oil Recovery % TOIP % PV Injection Rate 5-01-79 on to End (7.5 PV%/Yr.*) Preflush Injection 1.0% S a l t in Softened Water Solution (390 Days) % PV Start of Alkaline Injection 5-24-50

-

1,879,000 RB 1,231,000 STB 562,000 STB 45.65 29.91 84,000 STB 646,800 STB 52.54 34.42 4,806 B/D 1,874,340 STB 99.75

Performance of t h i s area of the f i e l d and simulator was characterized by rapid water breakthrough followed by a gradual r i s e i n WOR to i t s current average value of 50. Injection surveys have confirmed that over half the injection water i n these two injectors has entered the Fo subzone leaving it at a much higher average water saturation than lower zones. Results of the optimization study runs In a l l b u t one case, discussed are sumnarized in Table 3. subsequently, the r e l a t i v e permeability adjustment was made linearly between a1 kaline and waterflood behavior depending on the active alkaline concentration in each c e l l . The low alkaline concentration of 0.4 weight percent in the largest pore volume slug, 60%, produced the greatest amount. of incremental o i l . However, this. increase i n production tended to be at low rates, continuing on to l a t e i n the l i f e of the producers being modeled. In contrast, the higher concentration, smaller slug volume cases produced a m r e rapid oil r a t e response as can be seen in Fig. 8. T h i s figure also i l l u s t r a t e s the effect of long term caustic consumption on the projected results.

As can be seen by the results of the three 0.8 weight percent alkali cases, the incremental o i l recovery increases approximately 50% when no long term consumption is assumed to be present. In addition, the o i l r a t e reaches a maximum value approximately 15% higher in the absence of long term consumption. The r e l a t i v e success of an alkaline flood will be m r e dependent on the o i l recovery at wells f a r removed from the injection rows than of the wells d i r e c t l y adjacent to the injectors, because those areas

232 TABLE 3 Alkaline s1 ug Description

-

ALKALINE SLUG OPTIMIZATION S N D I E S O I L RECOVERY M T A

Long Term Consumption

-

Waterflood

MST Bbl.

Economic Limit (150 WOR) Date

M Bbl.

84.8

11-01-85

-

O i l Recovery

Incremental O i l Recovery Above Water Flood

Pro-Rated A l k a l i n e R e l a t i v e Permeability Adjustment % Accelerated 114.0 89.2 Rate 0.4% A l k a l i Accelerated 137.9 9-01-86 53.1 Rate 0.8% A l k a l i TFVT-Constant 143.5 6-05-86 58.7 0.8% A l k a l i Rate None 159.8 7-01-86 75.0 0.8% A l k a l i Accelerated 122.1 12-06-85 37.3 1.0% A l k a l i Rate 7TFv-TNone 142.3 10-21-85 57.5 1.0% A l k a l i 6 PV % Accel e r a t ed 162.0 2-16-88 77.5 Variable* Rate flinimum ’Threshold A l k a l i n e R e l a t i v e Permeability Adjustment % Accelerated 226.0 141.2 0.4% A l k a l i Rate

- -

3s PV

r

r

- -

*

% TOIP

% PV

-

-

7.25

4.75

4.31

2.83

4.77

3.12

6.09

3.99

3.03

1.99

4.67

3.05

6.30

4.12

11.47

7.51

0.4% o r t h o s i l i c a t e f o r f i r s t 1.5 years, 1.0% f o r next 1.0 year, 0.8% f o r 1.0 year, 0.4% f o r 1.0 year and 0.2% f o r 2.0 years.

FIGURE 8

-

OIL PRODUCTION RATES SLUG SIZE OPTIMIZATION

233 near the i n j e c t o r s have been more completely swept. The amount o f c a u s t i c t h a t can be t r a n s m i t t e d through these closer areas without being consumed i s o f considerable i n t e r e s t . The lower the long term consumption t h e greater i s t h e transmission o f t h e c a u s t i c through t h e area mear the i n j e c t o r s and out i n t o the r e s t o f the r e s e r v o i r , (Fig. 9). This long term consumption i s .dependent upon both t h e concentration o f the caustic i n an area and i t s residence time. Increased transmission r a t e s could also be expected f o r constant concentration s l u g i n j e c t i o n s at accelerated i n j e c t i o n rates.

FIGURE 9

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ACTIVE ALKALI TRANSMITTED THROUGH OPTIMIZATION STUDY AREA

Two a d d i t i o n a l v a r i a t i o n s from the constant concentration cases already discussed were run. F i r s t , a v a r i a b l e concentration case was r u n i n which t h e a l k a l i n e content was v a r i e d from t h e 0.4 weight percent c u r r e n t l y being i n j e c t e d i n the f i e l d t o a maximum o f 1.0 weight percent and then tapered back t o a concentration o f 0.2 weight percent. Total a l k a l i i n j e c t e d was the same as i n the p r i o r runs however. Although t h i s run d i d show some minor acceleration i n t h e o i l r a t e response, the cumulative production and the caustic moving o u t s i d e t h e area were both disappointing i n comparison t o the constant concentration i n j e c t i o n cases. S i m i l a r l y , another run was made i n which the change t o the enhanced recovery r e l a t i v e p e r m e a b i l i t y curves w i t h i n t h e model was made at a minimum threshold a1 k a l i concentration which corresponded t o t h e decrease i n i n t e r f a c i a l tension from the l a b o r a t o r y experiments. This case d i d show a considerably greater o i l production and a s i g n f i c a n t l y higher o i l production r a t e than t h e l i n e a r s h i f t i n from normal w a t e r / o i l r e l a t i v e p e r m e a b i l i t y curves t o caustic r e a t i v e p e r m e a b i l i t y curves. Currently, we are unable t o determine which o f

9

234 these two r e l a t i v e - p e r m e a b i l i t y s h i f t techniques more accurately represents t r u e r e s e r v o i r phenomena. Owing t o the f a c t t h a t t h e greatest cumulative o i l production was achieved f o r the continuous i n j e c t i o n o f 0.4 weight percent a l k a l i and the equipment l i m i t a t i o n s on i n j e c t i o n concentration and i t s r a t e i n the f i e l d , the 0.4 weight percent constant concentration cases were selected f o r p r e d i c t i o n o f the performance o f the e n t i r e p i l o t area.

Performance Match o f t h e P i l o t Area The h i s t o r i c a l performance o f the p a t t e r n area was matched using a black o i l r e s e r v o i r simulation model containing 1770 g r i d c e l l s i n seven layers, two w i t h i n the Fo subzone, and one layer. i n each o f t h e remaining subzones. The model included areas t o both the north and south o f t h e pattern, Fig.5. The i n j e c t i o n i n t o each subzone was s p e c i f i e d on the basis o f surveys o f the i n j e c t i o n wells. The performance shown i n Fig. 7 was matched by c o n t r o l l i n g t h e amount o f f l u i d which migrated o f f t h e p a t t e r n area t o the n o r t h and south, and by minimal changes i n the t r u n c a t i o n o f r e l a t i v e p e r m e a b i l i t y curves between the p a t t e r n and t h e areas t o the north and south.

Predicted Performance o f t h e P i l o t Area O i l recovery p r e d i c t i o n cases were run f o r continued waterflood operation and f o r t h e two caustic f l o o d cases. One o f these used t h e prorated a l k a l i n e f l o o d r e l a t i v e p e r m e a b i l i t y adjustment, Case I, and the other t h e minimum threshold a l k a l i n e r e l a t i v e p e r m e a b i l i t y adjustment, Case 11, o u t l i n e d i n an e a r l i e r section. The r e s u l t s of these p r e d i c t i o n s are sumnarized i n Table 4 and F i g . 10. The

mI

B II

FIGURE 10

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OIL PRODUCTION RATES, WATERFLaOD AND CAUSTIG FLOOD CASE I AND CASE I1

235 TABLE 4

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PATTERN AREA PREDICTED PERFORMME THROUGH OECEMBER, 1994 ~~

Subzone

F0H X (i

64 TOTAL

~

Waterflood Cum O i l MSTB

4390 2871 1742 3560 1787 699 lnmQ

A l k a l i Case I Cum O i l MSTB

4497 2990 1751 3580 1791 706 1 m

A l k a l i Case I 1 Cum O i l MSTB

4758 3048 1762 3622 1795 715

l??OU

predicted performance of the a l k a l i n e f l o o d i n comparison t o continued waterflood i n j e c t i o n i s disappointing. The runs i n d i c a t e t h a t those w e l l s i n the f i r s t row o f producers away from the i n j e c t i o n w e l l s do respond t o c a u s t i c i n j e c t i o n . However, these were w e l l swept by the i n j e c t i o n water p r i o r t o caustic i n j e c t i o n leaving l e s s o i l t o respond t o i n j e c t i o n o f caustic. A d d i t i o n a l l y , throughout the h i s t o r y o f t h e f i e l d , the Fo subzone has taken over h a l f o f the i n j e c t e d water. I n t h e p r e d i c t i o n cases h a l f t h e caustic water continued t o f l o w i n t o t h i s F subzone. Late i n the l i f e o f the f i e l d , s i g n i f i c a n t parts o f the o i f production from t h e w e l l s w i t h i n the p a t t e r n i s occurring from zones lower than t h e Fo subzone. As a consequence, the increase o r incremental production i n t h e Fo subzone i s overwhelmed o r masked by t h e production from lower zones.

mLusIoIIs The f i e l d performance t o date and t h e predicted performance from t h e s i m u l a t i o n studies i n d i c a t e t h a t t h e r e are many complicating f a c t o r s t o t h e successful a p p l i c a t i o n o f a l k a l i n e f l o o d i n g i n a heterogeneous r e s e r v o i r . The l a b o r a t o r y core t e s t s have confirmed the a p p l i c a b i l i t y o f a l k a l i n e f l o o d i n g t o Ranger Zone crude and r e s e r v o i r rock. However, the high degree o f consumption indicated b y l a b o r a t o r y work and simulation r e s u l t s can be a c o n t r o l l i n g f a c t o r i n t h e success o f any caustic i n j e c t i o n p r o j e c t . Actual f i e l d r e s u l t s are needed t o c a l i b r a t e t h e consumption parameters t o f i e l d conditions. Minimization of t h i s consumption appears p o s s i b l e by i n j e c t i n g t h e a l k a l i n e s o l u t i o n a t a higher concentration and/or i n j e c t i n g at a higher r a t e t o minimize t h e residence t i m e i n t h e r e s e r v o i r . Furthermore, the simulation experience has indicated the d e s i r a b i l i t y o f c o n t r o l o f t h e placement o f i n j e c t i o n f l u i d by subzone ( v e r t i c a l l y ) f o r a more e f f i c i e n t a l k a l i n e i n j e c t i o n p r o j e c t .

2 36

REFERENCES

J-

1.

Johnson, C.E.: "Status o f Caustic and Emulsion Methods". Pet. Tech. (January, 1976) 85-94.

2.

"Caustic Waterflooding Demonstration P r o j e c t , Ranger Zone, Long Beach Unit, Wilmington F i e l d , C a l i f o r n i a . Annual Report f o r t h e Prepared f o r Period June 1979 May, 1980." Report SAN/12047-4. DOE by t h e City o f Long Beach, Department o f O i l P r o p e r t i e s and THUMS Long Beach Company under Contract No. E-AC-03-76ET-12047.

-

3.

B r e i t , V.S., Mayer, E.H., and Carmichael, J.D.: "An E a s i l y Applied Black O i l Model o f Caustic Waterflooding". SPE Paper No. 7999, Presented a t the 1979 C a l i f o r n i a Regional Meeting of SPE o f AIME, Ventura, C a l i f o r n i a , A p r i l 18-20, 1979.

M I S C I B L E GAS D I S P L A C E M E N T

231

MISCIBLE DISPLACEMENT: ITS STATUS AND POTENTIAL FOR ENHANCED OIL RECOVERY

R.J. BLACKWELL Exxon Reduction Research Company

Miscible flooding continues to be one of the most intriguing enhanced oil recovery methods because of its potential for recovering all of the oil flushed by solvent; and one of the most exasperating, because only in rare instances have actual field performances come anywhere close to the high recovery efficiencies potentially possible from this process.

History The concept of miscible flooding is quite old. Its potential was generally recognized by the petroleum industry well over 50 years ago and several papers were published in the 1920's describing early research in this area. During the 1930's and early 1940's. interest in enhanced recovery techniques was low; however, following the end of World War 11, there was a dramatic increase in research directed toward improving our knowledge of what might be called the "physics and chemistry of fluid flow in porous media" and toward the development of the three basic areas of enhanced oil recovery--thermal, chemical, and miscible. Investigations into the use of miscible flooding techniques to improve oil recovery was a significant part of this increased effort. It was an exciting era. Laboratory tests were conducted to determine which fluids could be used for miscible flooding. Almost every available fluid including alcohols, ketones, propane, butane, LPG, nitrogen, carbon dioxide, methane and mixtures of many of the a ove were tested. Some of the first research was on completely misciblel~q (frequently called f irst-contact miscible) systems in which all mixtures of the solvent and oil form a single phase fluid. However, two multiple-contact methods of a hieving miscible displacements4 5 the high pressure or vaporizing gas method and the enriched gas process, were also developed during the 1950's. Both of the latter involve injection of a fluid which is initially not miscible with the crude, but is able to generate a solvent bank within the porous medium during the displacement process. In the high-pressure gas process, the injected gas is enriched with intermediate and higher molecular weight components vaporized from the first crude contacted. If the phase behavior of tht! gas oil system is favorable, a self sustaining solvent bank is formed le ing a small volume of denuded crude as residual in the reservoir. In the mriched-gas process, the enriching components in the injected gas transfer to the crude oil and generate a solvent bank consisting of a modified crude oil. In this process, essentially all of the oil (possibly excluding some asphaltenes) is flushed from the region contacted.

238 Following the discovery of these three basic approaches and the development of methods for determining the cond1tior.s that each must meet in order to have a miscible displacement, attention was turned (about 1954) to determining the conditions required for effective use of each method in field applications. Initially, the primary objective was to design miscible floods using the smallest amount of LPG or enriched gas possible. In order to do this, measurements of the amount of mixing that occurs as fluids flow through porous medin were needed and several companies including Exxon initiated work in this area. At about the same time, we and other research laboratories began our first experimental and theoretical studies of viscous fingering. It rapidly became apparent that, although the effects of mixing must be considered in any attempt to predict miscible flood performance, it was viscous fingering or solvent channeling that would likely dominate the behavior of a miscible flood.

Viscous fingering was studied in long models, short models, narrow models and wide models. Tests were conducted in Hele-Shaw models, in homogeneous sand or glass bead packs, and in models containing various permeability heterogeneities. In order to establish the physical principles responsible for viscous fingering and to quantify its effects, a number of floods were run in each model using fluid systems with different oil/solvent viscosity ratios, viscosity levels and fluid densities. At the beginning of this period, some people hoped that viscous fingering would turn out to be a "laboratory artifact" in the sense that it would be less of a problem in the field than it was in laboratory floods. However as confirmed later in many field tests, solvent channeling was a serious problem in field applications and at least as detrimental there as it was in laboratory floods.

Nevertheless, there was a general air of optimism during the middle 50's. Many believed that the remaining problems (such as viscous fingering) would soon be solved and that miscible flooding would usher in a new era of high enhanced oil recoveries. Because of this optimism, a number of field tests were initiated. However, incremental oil recoveries of only 5 to 10%. OOIP were obtained in many of these tests. These incremental recoveries not only fell far short of original expectations but were far from being economically attractive. The earlier optimism turned suddenly into pessimism.

The principal reason for the poorer than anticipated recovery efficiencies was severe channeling of the solvent banks. In some instances, the dominant cause of this channeling was reservoir heterogeneities such as permeability variations in different strata, fractures, etc. However, viscous fingering and gravity overriding were invariably major factors--either causing solvent channeling or aggravating the channeling associated with reservoir heterogeneity.

It is perhaps worthwhile to point out that viscous fingering and the closely rela ed gravity overridg phenomenum had been recognized sometime earlier. Hill in 1952 and Dietz in 1953 discussed gravity stabilization of displacement fronts and established the critical rate concept for the control of viscous fingering by gravity segregaticn. Unfortunately, practical production rates can be achieved in only a llmif d number of reeervoirs without exceeding the critical rate; hence the incentib for developing other methods of controlling solvent channeling was and remains quite high.

f

239 Several papers and patents were published during the late 50's and early 60's describing methods that might increase thz reservoir v o l y e swept by the solvent bank. One of the methods was gas-ucter injection which later became known as the WAG process. Another was thc use of foaming agents. Several other methods, including the use of polymers, were also investigated. Unfortunately, none appeared particularly attractive at that time; and with the growing disenchantment with miscible flooding, research in mobility control methods dropped to a low level. By default, the WAG approach became the generally "accepted" method for mobility control, but one with obvious deficiencies. In the middle 1970's, several laboratories renewed their research activity in this area and several new patents and papers describing the addition of various surfactants and other modifications to the WAG process have appeared recently. I regret to say however, that in my opinion, no dramatic breakthroughs have occurred to date and our ability to control solvent channeling has not changed much since 1960. Nevertheless, miscible flooding technology has advanced significantly during the past two decades. Results from both field applications and laboratory studies have provided additional insight into the dynamics of miscible displacement processes, particularly in the area of C02 miscible flooding. Numerical methods for simulating process performance have been developed along with better techniques for arriving at the critically important reservoir descriptions used for analysis of field results and in making predictions of the performance and economic viability of a miscible flood in a specific field.

-

Field Applications Miscible gas projects have provided the industry with valuable field data and operating experience during the past 15 years, particularly in the use of C02. Although detailed flood performance information is available from only a few of these projects, the results generally lead one to the same conclusions reached in 1950's--that is, high displacement efficiencies can be achieved in the regions flushed by solvent, but high volumetric sweep efficiencies are possible only if solvent channeling can be controlled effectively. The early breakthrough of C02 in the largest miscible-C02 flood in the United States, the 30,000 acre Sacroc project in the Kelly-Snyder field of West Texas, provides a dramatic illustration of the problem. C02 injection was initiated in this project in January 1972. Breakthrough occurred in June of the same year after injection of less than 2% HCPV of CO and increased rapidly. In November 1972, it became necessary to curtail injection when C02 production exceeded the capacity of the esisting gas plants to extract the C02 from produced gas. A paper by Kane describes in detail efforts to maintain control of CO 2 production. Two important steps were taken. First, the WAG ratio was increased from its initial value of about 0.5:l to 3:1, and then second, a zonal injection program was initiated to provide an improved distribution of the gas and water into all zones and thereby i m p r m e the overall sweep efficiency. C02 channeling and production cont iued to be an exasperating but manageable problem throughout the flood. N rertheless, the extra investment and operating costs involved in recovery, purifying, and reinjecting the produced C02 were significant factors in the 1977 decision to reduce the volume of C02 injected from 20% HCPV as planned originally to about 12% HCPV. The corresponding reduction in the estimated incremental oil recovery was from 107 million STB (8.1XOOIP) to 88 million STB (or 6.7XOOIP).

d2

240

In general, the performance of Sacroc and other field experience obtained to date suggests that incremental oil recoveries (over that. possible by water flooding) will most often fall in the range of only 6 to 30 percent of the original-oil-place (OOIP), less frequently in the 10 to 15% range, and will rarely exceed 15% OOIP. Current Laboratory Research At the present time, there are a number of industrial and university laboratories actively engaged in miscible displacement research. In recent years these research efforts have emphasized work on CO flooding, although there has been a limited amount of work on the use of ogher gases such as nitrogen, flue gas and C02 enriched with intermediate hydrocarbons such as propane, butane, etc. As mentioned earlier, several laboratories are investigating different methods for improving volumetric sweep. Several laboratories are engaged in fundamental studies of phase behavior and C02 flood performance often including measurements of the composition, density and viscosity of individual equilibrium phases of fluids produced during laboratory floods in slim tubes, or through reservoir cores. Equilibrated samples taken from PVT cells are also being analyzed and compared with he slim tube results. A recent U. S. Department of Energy report by Orr 5 et a1 is an excellent example of this type of study. The report describes their comprehensive study of the complex phase behavior of a particular C02crude oil system in some detail and carefully delineates the reservoir conditions under which liquid-liquid, liquid-liquid-vapor and liquid-vapor equilibrium mixtures were observed. It also describes their chromatographic analysis procedure which permits the characterization of the hydrocarbons present in the various fluid combinations described above throughout the CI1 C36 range (as well as the usual Cl Cl0 range).

-

-

-

Similar studies are being carried out in other laboratories using other C02 crude oil systems. Nevertheless, there is a need for additional carefully scaled experimental and theoretical studies of the interactions of phase . behavior, viscous fingering, gravity segregation, rock lithology and heterogeneity, and the relationship between oil remobilization and rock wettability. Research efforts to develop better mobility control techniques were mentioned earlier. The use of foams is again being investigated and some encouraging laboratory and field test results have recently been reported. Even though I remain skeptical that foam injection, as such, is the solution to the problem of viscous fingering, I feel additional research is merited. In recent years, the greatest strides in micellar-polymer technology have been made as the result of fundamental studies of the basic mechanisms involved. Similar comprehensive studies are needed using several C02, crude oi?., brine and classes of surfactants at pressures above and below the minimum miscibility pressure and temperatures spanning the range from 20' to 100°C. Mathematical Simulation Although worthwhile improvements in our numerical technique. for simulating miscible floods have occurred during the past 15 years, further improvements are greatly needed. The ideal computer program for modelling miscible C02 displacements, for example, must simulate the generation of the miscible rolvent bank, the potential precipitation of a solid (asphaltene) phase, and predict the amount and compositions of the various phases present in every

241 grid block each time step. Any grid block may contain a number of mobile and immobile immiscible hydrocarbon liquid phases (each containing over 30 components), and carbonated water. The simulator must be able to model block-toblock flow of both miscible and immiscible phases, and correctly model the dispersion or mixing of the miscible components transfer of components tetween immiscible phases. Compositional simulators with sophisticated phase behavior packages and other simulators with specialized capabilities have been developed to model miscible gas processes. Current compositional simulators can model most of the physical and chemical phenomena involved in a miscible flood; unfortunately, none provide all of the features that one might desire. Numerical dispersion remains a serious problem for the grid block sizes typically required in most reservoir studies; viscous fingering is difficult to model and is usually approximated empirically using a mixing parameter model; and computing costs are normally high because of the overall complexity of the simulator. Consequently, fully compositional models are frequently not as practical for field wide reservoir engineering studies as they are for special studies such as the simulation of the flood performance of a cross section or a small reservoir pattern area. A particularly important application is their use in conjunction with laboratory tests. This type of application is not only a good way to test the capability of the computer program, but it is also a good way to test our understanding of the chemical and physical processes involved in a miscible gas flood. Greatly simplified compositional simulators are frequently used for reservoir performance predictions, comparison of different gas injection programs, etc. These simplified simulators normally use a limited number of gas and pseudo components to represent the injected gas, and the natural gas and crude oil (including the asphaltenes). The number and composition of the required pseudo-oil components can be determined by comparing reservoir model results obtained by use of the simplified computer program with those obtained using a fully compositional simulator. Typical applications of the resulting simplified model include sensitivity studies of flood performance for various geological models of the reservoir, optimization of the WAG ratios, and large scale or field wide stud ies

.

Other types of simulators, such as modified black oil simulators, are also frequently useful for specialized applications. Effective use of these specialized simulators requires that the user understand the limitations of the various simulators since interpretation of results often complicated by the simplying assumptions used. A recent paper by Todd includes comparisons of the advantages and disadvantages of the principal types of "miscible" simulators.

fs

RESERVOIR DESCRIPTION The need for a reliable description of reservoir geology and other re !rvoir engineering data can hardly be overemphasized. No matter how well we mow the chemistry and physics involved in a miscible displacement, nor how precisely we are able to model these phenomena mathematically, it is not possible to make useful reservoir performance predictions of miscible processes without having a reliable reservoir description. It must be recognized that a much better reservoir description is required for predicting miscible

242

flood performance than is normally required for a comparable study of a water flood in the same field. Surprisingly small changes in the reservoir description can lead to significant differences in prediction of miscible flood performance and project economics; whereas, these same changes in reservoir description may be unimportant when predicting the performance and economics of a waterflood. In the past, the amount, type, and quality of routinely available reservoir description data have been dictated primarily by reservoir engineering needs for conventional primary and secondary recovery processes. Many of the same types of data are needed for predicting miscible flood performance. Useful geological input includes the depositional environment of the reservoir. Depositional environment data and information on subsequent diagenetic changes of rock matrix can be particularly valuable in predicting continuity of permeable zones, shale deposits or tight streaks, and the frequency and distribution of the openings (or windows) through these impermeable layers. Acquisition of this additional reservoir description data can be both difficult and costly, but its acquisition and careful interpretation is absolutely necessary.

EOR Potential For Miscible Processes United States: During the past decade, there have been numerous studies of the future potential of miscible gas processes and other enhanced recovery processes in the United States. Since the basic displacement mechanisms and phase behavior concepts used to predict miscible flood performance are well known, one might assume that the incremental oil recovery from miscible flooding could be easily estimated and that the incremental oil volumes predicted by the various studies would be similar in niagnitude with perhaps some differences in timing. However, this is not what one finds primarily because of the uncertainties in volumetric sweep caused by inadequate reservoir description data, in the estimates of the incremental oil recovery possible over waterflooding and in the economic assumptions used. Estimates of the incremental recovery over that possible from waterflooding, range from an "almost assured" 2 billion barrels* to "possibly optimistic" estimates of over 30 billion barrels. Our own estimates for the incremental reserves that can reasonably be added by the year 2000 fall into the 3 to 5 billion range. Hopefully, these estimates will turn out to be far too conservative. Despite this apparent conversatism, I believe that the United States and possibly Canada will begin to see significant production from miscible gas processes during this decade. Miscible processes have the most potential of the various enhanced oil recovery processes for near-term production of light But oil and could begin to make its contribution felt by the mid-1980's. timing for this increased production will be critically dependent on near term investments and development of C02 supplies. A recent study by Frost and Sullivan"

includes a breakdown of their projections of expenditures for enhanced oil recovery in the United States during the 10year period 1979-88. F6S predicts that expenditures for miscible gas processes will grow at a rate of about 25% per year from a level of about $0.7 billion per year in 1980 to $1.4 billion per year in 1984 and should reach a level of about $2.5 billion per year (of which $2.1 billion is for injected gases) in 1988. The total expenditure allotted to miscible gas processes during the *2 x 109 barrels

243 10-year period was $13.75 billion or 36% of the $38 billion projected for all EOR processes. These estimates include projections for oil field equipment and services as well as the cost of the injected fluids. Plans are gearing completion for three new pipelines which will bring over one billion(l0 scf/day of C02 to the Permian basin in West Texas from formations in Colorado and New Mexico. Current plans call for completion of the first two pipelines in early 1983. If we assume that injection of 10 k scf of CO will provide approximately one barrel of enhanced oil recovery production, tfen C02 from these pipelines would result in an oil production rate of 100 k B/D. This would more than double current U. S. production (currently about 70 k B/D) from all miscible gas projects. Most of the near term activity will continue to be concentrated in West Texas, but new miscible gas projects are also being considered for several other regions of the U. S., including Louisiana and the Mid-continent area. Most will employ CO although some projects will use nitrogen or methane enriched 2 with LPG. The use of nitrogen will usually be limited to deep high temperature reservoirs containing high gravity crudes because of miscibility pressure restrictions. For example, nitrogen will be used by Exxon in the 15400 foot, 285'F Jay and Black Jack Creek Fields in Florida. However, in some areas of the U. S. (e.g. in offshore reservoirs) or in Canada, acquisition of adequate supplies of COP at a reasonable cost may not be possible and miscible hydrocarbon gases may be used despite their high cost. Production of 100 k BID is not anticipated outside the Permian Basin of West Texas, until the late 1980's or early 1990's. Canada: In a recent (March 1980) study12 of the potential of enhanced oil recovery in Canada, it was estimated that miscible gas processes could increase oil recovery by 1.885 billion barrels, 1.352 from hydrocarbon miscible and 0.533 from CO This base case estimate was made for an assumed oil price of $20 per barref although higher prices ($25 and $100) were used in sensitivity studies. The study utilized the tax and royalty regulations of the federal government and the province of Alberta which were in place or announced in lY78. Consequently, the study will need to be updated when current negotiations betveen the federal and provincial governments have been completed.

.

The study found that the base case estimate of 1.885 billion barrels is extremely sensitive to small changes in the values assumed for recovery efficiency, operating costs, etc. For example, a reduction of only 15% in the assumed recovery efficiency reduced the estimated recovery to 0.476 billion barrels. This reduction of almost 75% indicates that a significant volume of marginally profitable (high risk) oil is included in the base case estimate. Past experience dictates that without significant increases in oil price, very few projects with marginal screening study economics remain as economically attractive prospects after more detailed studies have been completed. One reason is that early recovery estimates almost invariably drop as reservoir geology becomes better defined. Thus the potential for miscible flooding in Canada remains highly uncertain but it appears likely that an incremental production of about 1 billion barrels of oil could be achieved if current technical, economic, and political problems can be resolved.

244

North Sea: In recent years, consideration of potential applications of EOR processes frequently starts when a field is still in the early stages of its productive life. Thus it is not surprising that the evaluations of the potential of various EOR methods in the North Sea have already progressed past the screening stage and more detailed engineering studies are currently in progress for a number of fields. Although several reservoirs should be good miscible C02 flood candidates, the volume of C02 available is limited. Hence, the first miscible gas projects in the North Sea may, in fact, use hydrocarbon gases rather than C02. Until the C02 supply problem is resolved, it is premature to estimate probable incremental recoveries that can be attributed to future use of miscible gas processes. Other Areas: Although North America may have the largest number of existing or planned miscible-gag projects, the two largest miscible gas projects are in Libya and Algeria. Both are hydrocarbon miscible. The Intisar D project in Libya was started in 1969 and has been producing at approximately 100 k BID. The Hassi Messaoud project in Algeria was started in 1964 and has been producing at approximately 60 k B/D. There are several other small project in various parts of the world with a total production rate of perhaps 5001000 BID.

The ultimate potential for the use of EOR processes in the North Sea remains to be determined. However, I anticipate that several EOR projects will be initiated in North Sea fields before the end of the decade. Plans for a miscible C02 project onshore in a depleted East Midland oil field and a miscible hydrocarbon project offshore have already been announced. Similarly I understand that consideration is being given to a surfactant flooding pilot offshore. Undoubtedly, other projects will follow but the bulk of EOR activity in the North Sea will probably not occur until the next decade. I am optimistic about the future potential of EOR. Currently there is a shortage of trained scientists and engineers in the area. However, the number is increasing rapidly and the outlook for solving the remaining technical problems and designing economically attractive projects is promising. I feel that the thousands of man-years of research that the industry has devoted to the development of enhanced recovery technology are finally beginning to bear fruit. Interest and activity in applying miscible gas and other EOR processes are expanding rapidly throughout the world. The Industry is once again becoming increasingly optimistic about EOR potential. But there is a difference between the optimism of the 50's and that of the 80's; EOR technology of the 80's is more mature than it was then. We have a much better understanding of the capability and limitations of the various methods and the role that EOR can realistically be expected to play in our efforts to meet the world's energy needs. I recognize that significant and chal1engit:g problems remain to be solved, but I am confident that the solution to many of these problems can be found and that substantial volumes of EOR production will become economically feasible in the future. Miscible gas processes should make a significant contribution to this objective

.

245

REFERENCES 1.

Everett, J. P. et al: "Liquid-Liquid Displacement in Porous Media as Affected by the Liquid-Liquid Viscosity Ratio and Liquid-Liquid Miscibility," Trans., AIME 198 (1950) 215.

2.

Henderson, J. H.: "A Laboratory Investigation of Displacement From Porous Media by A Liquified Petroleum Gas" Trans., AIME 198 (1953) 33.

3.

Whorton, L. P., and Kieschnick, W. F.: "A Preliminary Report on Oil Recovery by High-Pressure Gas Injection," Drilling and Production Pract. ApI. 1950, 247.

4.

Stone, H. L. and Crump. J. S.: "The Effect of Gas Composition Upon Oil Recovery by Gas Drive," Trans., AIME (1956) 207, 105.

5.

Hill, S.:

6.

Dietz, D. N.:

7.

"Improving Miscible Displacement by Caudle, B. H., and Dyes, A. B.: Gas-Water Injection," Trans., AIME. 213, (1958), 281.

8.

Kane, A. V., "Performance Review of a Large Seale C02-WAG Project Sacroc Unit-Kelly Snyder Field," SPE 7091, Presented at Fifth Symposium on Improved Methods for Oil Recovery in Tulsa, Okla., April 1978.

9.

Orr, F. M., Taber, J. J. et al, U. S. DOEfETf12082-9, May 1981.

"Genie Chemique,"

Chem. Eng. Sci. (1952) I. NO. 6, p. 246.

Proc., Acad. Scie. Amst. B. (1953) 56, 83

"Displacement of Oil by Carbon Dioxide,"

10.

Todd, M. R.: "Modeling Requirements for Numerical Simulation of CO Recovery Processes," SPE 7998, presented at the 1979 Regional Meetlng of the SPE (AIME) in Ventura, Calif., April 1979.

11.

-,

12.

Prince, J. Philip, "Enhanced Oil Recovery Potential in Canada", Energy Research Institute ISBNO-0-920522-09-2, March 1980.

13.

Chierici, G. L.: "Enhanced Oil Recovery Techniques: State of the Art and Potential" presented at Seminar on Improved Techniaues For the Extraction of Primary Forms of Energy sponsored by United Nations Economic Commission for Europe, Vienna, Austria, Nov. 1980.

"#38 Billion Projected for Enhanced Recovery in '80s": Engineer International pages 98-100, Feb. 1981.

Petroleum Canadian

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MISCIBLE GAS DISPLACEMENT

247

THEORETICAL ASPECTS OF CALCULATING THE PERFORMANCE OF COZ AS AN EOR PROCESS IN NORTH SEA RESERVOIRS

DAVID S. HUGES, JOHN D. MATTHEWS,ROBERT E. MOTT AEE Winfrith,Dorchester, Dorset, DT2 8DH

ABSTRACT This paper examines some aspects of calculating the performance of COf as a prospective enhanced oil recovery agent in North Sea reservoirs. The paper falls into two areas. First the problems of predicting the phase behaviour of CO2 with reservoir oils are examined. Although experimental PVT data are available for C02-hydrocarbon systems, these are at lower pressures than prevail in the North Sea. The Peng-Robinson and Generalised Redlich-Kwong equations of state are compared for existing experimental data, and their predictions for miscibility are reviewed for North Sea reservoir conditions. Some of the problems of pseudo-components and interaction coefficients are discussed in this context. Second, results are presented of 3-D compositional simulations for a simplified reservoir model based on the Forties Field. The few component equilibrium factors in this model are adjusted to match the equation of state implications discussed above. Current reservoir conditions are found to give an immiscible Cop-displacement. Good sweep efficiencies are obtained in the watered-out reservoir from the immiscible COq-displacement calculations. This occurs because: (i) local displacement efficiency is good as a result of pi1 swelling and transfer of hydrocarbons into the gas stream and (ii) volumetric sweep is good with component exchange between gas and oil reducing viscosity and density differences. The reservoir pressure is then increased to achieve an MCM displacement. Three-dimensional results are obtained which compare the performance of the miscible and immiscible displacement processes. The immiscible results are slightly more attractive, but modelling approximations in both cases may be giving a false impression of the real comparability.

INTRODUCTION This paper examines some of the problems of predicting oil displacement behaviour by CO2 in the context of typical North Sea field characteristics. For this purpose we have considered both immiscible and miscible CO2 drive in a conceptual reservoir simulation with properties akin to the Forties field. The first part of the paper is concerned with problems of predicting phase behaviour using equations of state based on the Peng-Robinson and Generalised Redlich-Kwong formulations. Some preference for the latter is given because of its superior prediction of fluid densities. The use of the Redlich-Kwone

248 e q u a t i o n i n a few pseudo-component f o r m u l a t i o n i s i l l u s t r a t e d , w h i c h then d i c t a t e s t h e choice of an e q u i l i b r i u m K-factor c o r r e l a t i o n f o r use i n a compositional r e s e r v o i r s i m u l a t i o n code. I n t h e case of t h e F o r t i e s f i e l d t h e minimum m i s c i b i l i t y p r e s s u r e i s p r e d i c t e d t o be j u s t above t h e o p e r a t i n g p r e s s u r e , which i m p l i e s o p p o r t u n i t y t o c o n s i d e r b o t h immiscible o r m i s c i b l e C02-flooding of t h e r e s e r v o i r , f o l l o w i n g t h e p r e s e n t c o n v e n t i o n a l w a t e r f l o o d . The second p a r t of t h e paper examines both immiscible and m i s c i b l e o i l displacement by C02 i n a conceptual 5-spot p a t t e r n w i t h p r o p e r t i e s a k i n t o t h c F o r t i e s f i e l d . Various a l t e r n a t i v e COpJwater i n j e c t i o n s t r a t e g i e s a r e compared f o r immiscible displacement based on a v e r t i c a l two-dimensional scream-tube s e c t i o n . A n e a r optimum p r o c e s s i s then e v a l u a t e d i n a f u l l three-dimensional model. The p r e d i c t e d immiscible COz-drive i s found t o b e more a t t r a c t i v e than expected due t o i t s o i l s w e l l i n g and mass t r a n s f e r behaviour. M i s c i b l e c a l c u l a t i o n s f o r t h i s same three-dimensional model have a l s o been undertaken u s i n g t h e Todd and Longstaff mixing approximation i n t h e s i m u l a t i o n code. The d i f f e r e n c e s i n recovery e f f i c i e n c y between t h e s e two types of displacement a r e b e l i e v e d t o b e w i t h i n t h e u n c e r t a i n t y of t h e methods used. The f a c t o r s i n f l u e n c i n g t h e r e l a t i v e sweep e f f i c i e n c i e s under immiscible and m i s c i b l e drive a r e discussed.

PVT PROPERTIES OF C02 AND RESERVOIR OILS

Choice of Equation of S t a t e When p r e d i c t i n g PVT p r o p e r t i e s of r e s e r v o i r f l u i d s from a thermodynamic e q u a t i o n of s t a t e , a t y p i c a l approach i s t o use a two c o n s t a n t c u b i c e q u a t i o n based on t h e Redlich-Kwong e q u a t i o n (Ref I ) which g i v e s a s a t i s f a c t o r y compromise between s i m p l i c i t y and accuracy. The two e q u a t i o n s which a r e most commonly used, e s p e c i a l l y i n a p p l i c a t i o n s t o C02 systems, a r e t h e Peng-Robinson (PR) e q u a t i o n (Ref 2) and t h e G e n e r a l i s e d Redlich-Kwong (GRK) e q u a t i o n i n a form f i r s t proposed by Zudkevitch and J o f f e (Ref 3 ) . The Peng-Robinson e q u a t i o n t a k e s t h e form p = -RT \rb

-

a(T) 9

v'(v+b) + b(v-b)

a. = 0.45724 ai

ai = I + m ( 1

2

R

2

2 Tci/Pci

,

bi = 0.07780 R Tci/Pci

- Tr 11.

,

(3) (4)

2 m = 0.37464 + 1 . 5 4 2 2 6 ~ 0 . 2 6 9 9 2 ~

-

.

(5)

The o t h e r symbols have t h e i r c o n v e n t i o n a l d e f i n i t i o n s which a r e given a t t h e end of t h e paper.

,

249 I n t h e GRK e q u a t i o n

a

p = -RTv-b

T'v

(v+b)

,

and t h e mixing r u l e s ( 2 ) a r e used t o c a l c u l a t e a and b. R a i and S&i a r e temperature dependent f u n c t i o n s which a r e c a l c u l a t e d f o r each component by f i t t i n g t o t h e vapour p r e s s u r e and s a t u r a t e d l i q u i d d e n s i t y of t h e component a t t h e g i v e n temperature. For s u p e r c r i t i c a l t e m p e r a t u r e s Qa and are assumed t o t a k e t h e same v a l u e s as a t t h e c r i t i c a l temperature. The vapour p r e s s u r e and s a t u r a t e d l i q u i d d e n s i t y are normally d e r i v e d from c o r r e l a t i o n s i n terms of c r i t i c a l p r o p e r t i e s , normal b o i l i n g p o i n t and a c e n t r i c f a c t o r , a l o n g w i t h a l i q u i d d e n s i t y a t a s i n g l e r e f e r e n c e temperature. The a l t e r n a t i v e procedures s u g g e s t e d by Yarborough (Ref 4) and Coats (Ref 5 ) give broadly similar r e s u l t s . The i n t r o d u c t i o n of t h e %parameters i s t h e most s i g n i f i c a n t d i f f e r e n c e between t h e two e q u a t i o n s . I n t h e PR e q u a t i o n t h e c r i t i c a l Z-factor i s n e c e s s a r i l y 0.307 f o r a l l components, whereas f o r l i q u i d hydrocarbons t h e c r i t i c a l 2 - f a c t o r i s known t o be between 0.20 and 0.26. Thus t h e PR e q u a t i o n n e a r l y always u n d e r p r e d i c t s t h e d e n s i t y of hydrocarbon l i q u i d s . For example, a t 100°C t h e d e n s i t y of decane is u n d e r p r e d i c t e d by 6% and t h e d e n s i t y of pentadecane by 12%. The use of t h e %parameters i n t h e GRK e q u a t i o n overcomes t h i s problem ( a t t h e c o s t of a l o s s of s i m p l i c i t y ) and t h i s e q u a t i o n g e n e r a l l y g i v e s good p r e d i c t i o n s of l i q u i d d e n s i t i e s i f t h e %parameters are chosen a p p r o p r i a t e l y . Interaction Coefficients I n b o t h e q u a t i o n s t h e mixing r u l e f o r parameter ' a ' employs b i n a r y i n t e r a c t i o n c o e f f i c i e n t s 6 i which must be determined e m p i r i c a l l y . I n t e r a c t i o n c o e f f i c i e n t s f o r p a i r s of h y i r o c a r b o n components are g e n e r a l l y z e r o o r v e r y smill (except f o r methane-heavy hydrocarbon p a i r s ) b u t non-zero c o e f f i c i e n t s f o r hydrocarbon-C02 b i n a r i e s are e s s e n t i a l i f a c c u r a t e p r e d i c t i o n s are t o be o b t a i n e d , and t h e c h o i c e of i n t e r a c t i o n c o e f f i c i e n t s i s a major, problem when a p p l y i n g a n e q u a t i o n of s t a t e t o C02/hydrocarbon m i x t u r e s . The c o n v e n t i o n a l approach t o t h i s problem i s t o d e r i v e t h e i n t e r a c t i o n c o e f f i c i e n t s from d a t a on b i n a r y m i x t u r e s , b u t t h e p r e s s u r e s i n t h e s e b i n a r y systems are u s u a l l y much lower t h a n found i n r e s e r v o i r s , and t h e r e i s some evidence t h a t t h e r e s u l t i n g v a l u e s are n o t o p t i m a l f o r multi-component systems a t h i g h e r p r e s s u r e s . We have found t h a t an i n t e r a c t i o n c o e f f i c i e n t o f 0.10 f o r a l l C02-hydrocarbon b i n a r i e s g i v e s r e a s o n a b l e r e s u l t s i n t h e PR e q u a t i o n f o r t e r n a r y and multi-component systems, w h i l e b i n a r y d a t a s u g g e s t r a t h e r l a r g e r c o e f f i c i e n t s (eg. 0.13 f o r b u t a n e ) .

-

A more s y s t e m a t i c approach f o r C02-hydrocarbon m i x t u r e s h a s been proposed by Turek e t a1 (Ref 6 ) f o r t h e GRK e q u a t i o n . A second i n t e r a c t i o n c o e f f i c i e n t f o r C02-hydrocarbon b i n a r i e s was i n t r o d u c e d by modifying t h e mixing r u l e f o r t h e parameter ' b ' i n e q u a t i o n ( 2 ) , t o r e a d b =

1Z

. .

( 1 + Dij)

(bi + b . ) xi x j 3

'

2 50 This reduces t o e q u a t i o n (2) when D i j = 0. These i n t e r a c t i o n c o e f f i c i e n t s were assumed t o be r e s p e c t i v e l y q u a d r a t i c and c u b i c f u n c t i o n s of hydrocarbon a c e n t r i c f a c t o r , and a l s o Ra and f o r s u p e r c r i t i c a l C02 were assumed t o be q u a d r a t i c f u n c t i o n s of temperature. The polynomial parameters were t h e n determined by a r e g r e s s i o n a n a l y s i s u s i n g phase e q u i l i b r i u m d a t a on f i f t e e n C02-hydrocarbon b i n a r i e s . These developments t o t h e GRK e q u a t i o n have emphasised a c c u r a t e p r e d i c t i o n s of phase behaviour r a t h e r than d e n s i t i e s ; no d e n s i t y d a t a were used i n t h e r e g r e s s i o n a n a l y s i s . A consequence of t h e changes t o t h e C02-parameters from f i t t i n g t o b i n a r y d a t a i s t h e o v e r p r e d i c t i o n o f C02 d e n s i t i e s a t h i g h p r e s s u r e s ; f o r example, a t 100°C t h e d e n s i t y o f C02 i s o v e r p r e d i c t e d by 10% a t 200 b a r s and by 19% a t 300 b a r s . C 0 2 4 e n s i t i e s p r e d i c t e d by t h e PR e q u a t i o n a r e a c c u r a t e t o w i t h i n 5%, even a t high p r e s s u r e s . Thus,if t h i s form of t h e GRK e q u a t i o n i s t o be used t o c a l c u l a t e d e n s i t i e s i n a compositional s i m u l a t o r , some compensating adjustment of t h e R’s i s needed.

Comparison of P r e d i c t i o n s f o r C O ~ / S y n t h e t i cO i l Systems To i l l u s t r a t e some of t h e s e p o i n t s , t h e PR and GRK e q u a t i o n s have been used t o p r e d i c t s a t u r a t i o n p r e s s u r e s and d e r i s i t i e s of m i x t u r e s of Cog w i t h t h e I0 component s y n t h e t i c o i l whose composition i s g i v e n i n Table 1 . Experimental d a t a on t h i s system a t 48.9OC and 65.6OC i s g i v e n by Turek e t a l . The c a l c u l a t i o n s were c a r r i e d o u t u s i n g t h e VOLE phase e q u i l i b r i u m code (Ref 7) I n t h e c a l c u l a t i o n s w i t h t h e GRK e q u a t i o n t h e developed a t AEE W i n f r i t h . C02-interaction c o e f f i c i e n t s and ¶meters were t a k e n from Reference 6 , and i n t e r a c t i o n c o e f f i c i e n t s f o r a l l hydrocarbon p a i r s were s e t t o z e r o e x c e p t f o r C I - C I O and Cl-Ci4, where a v a l u e of 0.01 was used i n o r d e r t o match t h e observed bubble p o i n t s of t h e o r i g i n a l o i l . The PR c a l c u l a t i o n s used an i n t e r a c t i o n c o e f f i c i e n t of 0.10 f o r a l l C02-hydrocarbon p a i r s . I n t e r a c t i o n c o e f f i c i e n t s between C 1 , C2 and C3 w i t h C6’ hydrocarbons were taken from Katz and F i r o z a b a d i (Ref 8). e x c e p t t h a t t h e C I - C I O and C I - C ~ ~ c o e f f i c i e n t s had t o b e i n c r e a s e d by 0.01 t o f i t t h e observed bubble p o i n t However, t h e p r e d i c t e d bubble p o i n t was t h e n of t h e o r i g i n a l o i l a t 65.6W. i n e r r o r by 21: a t 48.9OC.

TABLE I COMPOSITION OF SYNTHETIC O I L (Ref 6 )

Component

Mole p e r c e n t 34.67

c2 c3 c4 c5

3. 13 3.96 5.95

4.06

Component ‘6 c7 c8

cIo ‘14

Mole p e r c e n t 3.06 4.95 4.97 30.21 5.04

251 Predicted s a t u r a t i o n p r e s s u r e s a r e shown i n Figure 1 . The GRK r e s u l t s agree q u i t e w e l l with the measurements except t h a t the p r e d i c t e d c r i t i c a l p o i n t s occur a t a r a t h e r higher C02 concentration. The PR p r e d i c t i o n s a r e r a t h e r less a c c u r a t e , e s p e c i a l l y a t the lower temperature, although some improvement could probably be made by a d j u s t i n g i n d i v i d u a l i n t e r a c t i o n c o e f f i c i e n t s .

MEASURED

414'C

0

DEW POINT

0

CALCULATED PR EOUAlION

L

GRK EOUAllON

0 ! i

6M.C

BUOBLE POINT 0

-- -

n

*

I

1

1

0

0.I

'

I

I

0.4 0.6 MOLE FRACTION Cq

06

1.0

FIG. 1. SAIURAIION PRESSURES IN THE COz- SYNlHElIC OIL SYSIEM. 700r

MEASURED

0

CALCULATED

---

CREOUAIION CRK EOUATION

b

\ t

I

0

0-2

FIG. 2.

I

I

0 .6 0.4 MOLE FRACTION CO2

I

I

0.6

1.0

DENBlllES OF SATURATED FLUID IN ;HE SYNTHEIIC OIL SYSTEM I&8.9'C 1

COz

-

Density p r e d i c t i o n s a t 48.9OC a r e shown i n Figure 2. The GRK equation is a c c u r a t e a t low C02 concentrations, b u t a t high C02-concentration the d e n s i t y i s overpredicted by lo%, s i n c e the d e n s i t y of pure C02 i s overestimated. The PR equation underpredicts d e n s i t i e s by 5 o r 6% a t 48.9OC. and by 3 o r 4% a t 65.6OC. This i s c o n s i s t e n t with the work of Sigmund e t a1 (Ref 9 ) . who found t h a t while l i q u i d d e n s i t i e s a r e underpredicted by the PR equation, t h e f r a c t i o n a l changes i n volume due t o the a d d i t i o n of COq t o o i l a r e represented q u i t e w e l l . From these r e s u l t s , and o t h e r c a l c u l a t i o n s on s y n t h e t i c o i l mixtures, i t appears t h a t n e i t h e r equation i s capable of accurate p r e d i c t i o n s of oilIC02 mixtures across the e n t i r e composition range. This implies t h a t some f i t t i n g of parameters t o experimental d a t a i s needed i f a c c u r a t e p r e d i c t i o n s of d e n s i t y and phase behaviour a r e t o be obtained simultaneously.

252 Pseudo Component R e p r e s e n t a t i o n of R e s e r v o i r O i l s The a p p l i c a t i o n of an e q u a t i o n of s t a t e t o s y n t h e t i c o i l s is r e l a t i v e l y s t r a i g h t f o r w a r d as i n d i v i d u a l components can be i d e n t i f i e d and r e p r e s e n t e d as such i n t h e t h e o r e t i c a l model. However, t h e heavy f r a c t i o n s of r e s e r v o i r f l u i d s c o n t a i n so many d i f f e r e n t isomers t h a t i t i s i m p o s s i b l e t o i d e n t i f y them i n d i v i d u a l l y , and i t i s n e c e s s a r y t o d i v i d e t h e heavy f r a c t i o n s (normally Cg and above) i n t o pseudo components, each pseudo component r e p r e s e n t i n g a group of components h a v i n g similar p r o p e r t i e s . The s e l e c t i o n of parameters f o r t h e s e pseudo components i s a s e v e r e problem when a p p l y i n g an e q u a t i o n of s t a t e t o r e s e r v o i r o i l s , and i s p a r t i c u l a r l y s i g n i f i c a n t i n C 0 2 / 0 i l systems, where t h e heavy f r a c t i o n s have a s t r o n g i n f l u e n c e on t h e phase behaviour a t h i g h p r e s s u r e . A comnon approach i s t o d i v i d e t h e heavy f r a c t i o n i n t o groups, each of which h a s i n d i v i d u a l components whoge b o i l i n g p o i n t l i e s w i t h i n a c e r t a i n range. This i s p a r t i c u l a r l y convenient i f a d i s t i l l a t i o n a n a l y s i s h a s been c a r r i e d o u t on t h e o i l , as one pseudo component can be a s s i g n e d t o each ' c u t ' i n t h e d i s t i l l a t i o n . S p e c i f i c g r a v i t y , average b o i l i n g p o i n t and molecular weight a r e normally determined f o r each ' c u t ' , b u t t h e e q u a t i o n of s t a t e model r e q u i r e s 'pseudo' c r i t i c a l p r o p e r t i e s as i n p u t . Various c o r r e l a t i o n s have been proposed f o r d e t e r m i n i n g t h e s e p r o p e r t i e s ; f o r example t h o s e o f C a v e t t (Ref 10) and Whitson (Ref 1 1 ) which are most convenient as they use s p e c i f i c g r a v i t y and average b o i l i n g p o i n t as c o r r e l a t i n g parameters.

A f u r t h e r problem i s t h e s e l e c t i o n of i n t e r a c t i o n c o e f f i c i e n t s f o r t h e s e pseudo components. The s y s t e m a t i c approach t o C02-hydrocarbon i n t e r a c t i o n c o e f f i c i e n t s d e s c r i b e d e a r l i e r h a s t h e advantage t h a t i t i s p o s s i b l e t o use t h e f u n c t i o n a l dependence on a c e n t r i c f a c t o r t o e x t r a p o l a t e t h e pseudc components. This r o u t e h a s been followed i n -the p r e s e n t work f o r t h e GRK e q u a t i o n , w h i l e f o r t h e PR e q u a t i o n a v a l u e o f 0.1 was used f o r a l l C02-hydrocarbon p a i r s . I n b o t h c a s e s t h e i n t e r a c t i o n c o e f f i c i e n t between methane and t h e h e a v i e s t f r a c t i o n s (c](j+) w a s a d j u s t e d t o match t h e observed bubble p o i n t of t h e o r i g i n a l o i l w i t h o u t C02. This c o e f f i c i e n t w a s always small (around 0.05) f o r t h e GRK e q u a t i o n , b u t when a p p l y i n g t h e PR e q u a t i o n t o North Sea o i l s , i t h a s always been found n e c e s s a r y t o use l a r g e methaneheavy hydrocarbon i n t e r a c t i o n c o e f f i c i e n t s (up t o 0.4) t o f i t t h e observed bubble p o i n t s ; t h e s e c o e f f i c i e n t s v a r i e d c o n s i d e r a b l y between d i f f e r e n t o i l s and d i d n o t f o l l o w any obvious s y s t e m a t i c t r e n d . C a l c u l a t i o n s on North Sea o i l s have shown t h a t t h e GRK e q u a t i o n p r e d i c t s t h e d e n s i t y of o i l w i t h o u t C02 t o w i t h i n a few p e r c e n t ; w h i l e t h e PR e q u a t i o n u n d e r e s t i m a t e s o i l d e n s i t y by between 10 and Z O X , depending on t h e c o r r e l a t i o n used t o c a l c u l a t e pseudo component p r o p e r t i e s . However, t o o b t a i n a c c u r a t e d e n s i t i e s w i t h t h e CRK e q u a t i o n i t was n e c e s s a r y t o use t h e measured d e n s i t y of each ' c u t ' when c a l c u l a t i n g t h e 0-parameters. A s s e s s i n g t h e v a r i o u s methods f o r c a l c u l a t i n g PVT p r o p e r t i e s f o r C 0 2 / r e s e r v o i r o i l systems i s d i f f i c u l t because o f t h e l a c k o f e x p e r i m e n t a l d a t a o n o i l s f o r which a comprehensive a n a l y s i s o f t h e h e a v i e r f r a c t i o n s i s a l s o a v a i l a b l e . F u r t h e r work is needed t o develop t h e e q u a t i o n of s t a t e method t o t h e s t a g e where i t can g i v e r e l i a b l e a p r i o r i p r e d i c t i o n s ( i e . w i t h o u t f i t t i n g t o e x p e r i m e n t a l d a t a ) of t h e s e p r o p e r t i e s . I n any case i t may prove s i m p l e r t o make a few PVT measurements on COZ/oil m i x t u r e s , t h a n t o c a r r y o u t the d e t a i l e d compositional a n a l y s i s required f o r i n p u t t o a p r e d i c t i v e e q u a t i o n o f s t a t e model.

253 P r e d i c t i o n of PVT P r o p e r t i e s of CO?/Forties O i l Mixtures A t the p r e s e n t time, no experimental phase behaviour d a t a a r e a v a i l a b l e f o r C02 and North Sea o i l s . I n the absence of such d a t a , d e t a i l e d equation of s t a t e c a l c u l a t i o n s have been performed t o generate PVT information f o r COZ/Forties o i l mixtures, and t o derive d a t a f o r a model with a small number of pseudo components with approximately the same e s s e n t i a l p r o p e r t i e s . Figures 3 and 4 show c a l c u l a t e d s a t u r a t i o n pressures and swelling f a c t o r s f o r COq/ F o r t i e s o i l , using the a l t e r n a t i v e PR and GRK equations i n an 18-component model i n the VOLE code (swelling f a c t o r i s defined a s the volume of o i l p l u s CO2 a t s a t u r a t i o n pressure r e l a t i v e t o volume of o r i g i n a l o i l a t i t s s a t u r a t i o n p r e s s u r e ) . Both the Whitson and Cavett c o r r e l a t i o n s were used f o r e s t i m a t i n g the p r o p e r t i e s of t h e twelve pseudo components t o r e p r e s e n t the C6+ f r a c t i o n . The two GRK c a l c u l a t i o n s p r e d i c t s i m i l a r s a t u r a t i o n p r e s s u r e s , while the two PR c a l c u l a t i o n s give s i g n i f i c a n t l y d i f f e r e n t s a t u r a t i o n p r e s s u r e s , depending on which c o r r e l a t i o n i s used f o r t h e pseudo component p r o p e r t i e s . I t i s t o be expected t h a t the GRK p r e d i c t i o n s a r e less s e n s i t i v e t o the pseudo component c o r r e l a t i o n because of the subsequent matching t o the measured density using the *parameters. The various methods give similar p r e d i c t i o n s f o r the o i l swelling f a c t o r s as a f u n c t i o n of Cop concentration. However, the swelling f a c t o r s f o r s a t u r a t e d o i l a t a t y p i c a l p r e s s u r e of 200 b a r s vary considerably, with values of 1.50 and 1.72 f o r t h e PR c a l c u l a t i o n s , and 1.58 and 1.64 from the GRK equation.

These c a l c u l a t i o n s have shown some s i g n i f i c a n t d i f f e r e n c e s between d i f f e r e n t methods f o r p r e d i c t i n g t h e PVT p r o p e r t i e s of r e s e r v o i r oil/CO2 mixtures. The choice of c o r r e l a t i o n f o r pseudo component p r o p e r t i e s appears t o be a t l e a s t as important a s the choice of equation of state. Experilqental d a t a a r e needed t o resolve the position.

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FIG. 3. CALCULATED SATURATION PRESSURES OF FORTIES OIL C02 MIXTURES

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FIG. 4. CALCULATED SWELLING OF SATURATED FORTIES OIL CO2 MIXTURES

The equations of s t a t e were used t o e s t i m a t e minimum m i s c i b i l i t y p r e s s u r e (MMP), using a s i m p l i f i e d model of the multi-step process leading t o m u l t i p l e c o n t a c t miscibility. In the numerical procedure adopted i n t h e VOLE code a t Winfrith, the f l u i d composition a t each s t a g e i s determined by mixing o r i g i n a l o i l with the gas phase from the previous s t a t e i n a multi-step process. The MMP f o r F o r t i e s w a s p r e d i c t e d by both PR and GRK models t o be between 210 and 220 b a r s , compared with a f i g u r e of 240 b a r s from the l a t e s t c o r r e l a t i o n of Holm and Josendal (Ref 12). In the F o r t i e s f i e l d the r e s e r v o i r p r e s s u r e w a s i n t i a l l y 220 b a r s , but has f a l l e n t o around 180 b a r s . Thus t h e c a l c u l a t i o n s suggest t h a t C02-injection i n F o r t i e s would give r i s e t o an i k s c i b l e displacement, but t h e pressure i s only j u s t below the MMP.

Few Component Representation of F o r t i e s O i l

To r e a l i s t i c a l l y r e p r e s e n t the PVT behaviour of r e s e r v o i r o i l s some 15 t o 40 d i f f e r e n t components ( o r pseudo components) a r e needed. However, when using a compositional s i m u l a t o r , i t i s e s s e n t i a l t o reduce the number of components so t h a t computing c o s t s a r e acceptable. When mathematically s i m u l a t i n g a COP flood, the methane and C02 a r e normally kept a s s i n g l e components, and between two and f o u r pseudo components a r e used t o r e p r e s e n t the C T - f r a c t i o n of t h e o i l . I t i s u n l i k e l y t h a t such a coarse r e p r e s e n t a t i o n w i l l give accurate results unless c e r t a i n parameters have been a d j u s t e d t o f i t d a t a from experiments, o r from more d e t a i l e d c a l c u l a t i o n s . This can be done by non-linear r e g r e s s i o n a n a l y s i s using an equation of s t a t e phase e q u i l i b r i u m code i n which t h e Q-parameters ( o r c r i t i c a l p r o p e r t i e s i n the PR equation), and i n t e r a c t i o n c o e f f i c i e n t s a r e a d j u s t e d u n t i l a good match i s obtained. When used i n a few component model w i t h i n a compositional s i m u l a t o r , t h e r e i s l i t t l e t o choose between d i f f e r e n t equations of s t a t e ; i n a l l cases i t should be p o s s i b l e t o o b t a i n an accurate r e p r e s e n t a t i o n by tuning a p p r o p r i a t e parameters. I n essence, the few component equation of s t a t e model becomes a s o p h i s t i c a t e d c o r r e l a t i o n with a wider range of v a l i d i t y than the K-value approach.

255 I n an i d s c i b l e C 0 2 f l o o d two main recovery mechanisms operate. They a r e the swelling of t h e o i l through s o l u t i o n of C02 and evaporation of c e r t a i n components from the o i l i n t o t h e produced gas stream. One-dimensional calculat i o n s using an equation of s t a t e compositional simulator which has r e c e n t l y been developed have demonstrated t h a t these phenomena could be a c c u r a t e l y represented i n a few component model. Two c a l c u l a t i o n s were performed f o r a C02 f l o o d i n a one-dimensional geometry. The f i r s t used an 18-component r e p r e s e n t a t i o n of the r e s e r v o i r o i l , and the second a 6-component r e p r e s e n t a t i o n i n which the parameters were obtained by an averaging procedure chosen t o give the same values of the equation of s t a t e ' a ' and 'b' c o e f f i c i e n t s . A f t e r some minor adjustments of the methane-heavy hydrocarbon i n t e r a c t i o n c o e f f i c i e n t s , t h e 6-component and 18-component p r e d i c t i o n s of d e n s i t y , v i s c o s i t y and bubble p o i n t s agreed everywhere t o w i t h i n I o r 2%. The o i l composition used was s i m i l a r t o t h a t found i n the F o r t i e s r e s e r v o i r , and the s i x components s e l e c t e d were COP, C 1 , C2-C5, c6-C1Os Cll-C19 and C20+. Figure 5 shows the o i l recovery and GOR a s a f u n c t i o n of the amount of Cog i n j e c t e d , f o r t h e two d i f f e r e n t r e p r e s e n t a t i o n s . There i s c l o s e agreement between t h e two cases, with o i l r e c o v e r i e s d i f f e r i n g by a t most 0.5%. The r e c o v e r i e s of i n d i v i d u a l components a r e a l s o i n c l o s e agreement. These r e s u l t s suggest t h a t a s i x component model can give an adequate r e p r e s e n t a t i o n of t h e PVT p r o p e r t i e s of the f l u i d s , so long as t h e parameters have been a d j u s t e d t o match d a t a from experiments o r more d e t a i l e d c a l c u l a t i o n s .

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FIG. 5. PREDICTED PERFORMANCE OF ONE DIMENSIONAL C02 DISPLACEMENT OF FORTIES OIL AT 210 BAR

THE DISPLACEMENT OF OIL BY C02 I N A CONCEPTUAL RESERVOIR C a l c u l a t i o n s of o i l displacement by C02 have been performed using a s i m p l i f i e d t h r e e dimensional conceptual r e s e r v o i r with p r o p e r t i e s broadly similar t o those found i n t h e F o r t i e s f i e l d (Ref 13). A repeated 5-spot p a t t e r n has been assumed i n a 100 m t h i c k sandstone w i t h uniform p o r o s i t y of 27% and permeab i l i t i e s of 400 mD i n t h e h o r i z o n t a l d i r e c t i o n and 40 mD i n the v e r t i c a l d i r e c t i o n . The assumed w e l l s e p a r a t i o n between an i n j e c t o r and a producer was a t y p i c a l value of 700 metres. The connate water s a t u r a t i o n was 23% and t h e r e s i d u a l o i l from waterflooding was 30%. Water v i s c o s i t y was 0.42 cp.

256 The assumption of homogenetity i n the 5-spot p a t t e r n allows e i g h t - f o l d symmetry t o be invoked and a three-dimensional r e p r e s e n t a t i o n of a symnetry s e c t o r was used i n the c a l c u l a t i o n s . To reduce mesh o r i e n t a t i o n e f f e c t s , a c u r v i l i n e a r a r e a l mesh p a t t e r n was adopted, based upon u n i t mobility p o t e n t i a l flow. This a r e a l mesh consisted of 4 stream tubes with 12 subdivisions along each tube the subdivisions being s e l e c t e d t o give equal a r e a s i n the s h o r t e s t stream tube (see Figure 7); t h i s reduces the t i m e s t e p penalty which occurs i n e x p l i c i t c a l c u l a t i o n s of s a t u r a t i o n s . In the v e r t i c a l c r o s s s e c t i o n , 6 v e r t i c a l l a y e r s were assumed, the thickness of the uppermost l a y e r s ( 6 . 7 and 13.3m) being smaller than t h a t of the lower l a y e r s (20 m) t o allow g r a v i t y o v e r r i d e t o be followed w h i l s t economising on the number of meshes. The broad adequacy of t h i s b a s i c mesh arrangement f o r the c u r r e n t comparative e x e r c i s e was examined by performing mesh refinement c a l c u l a t i o n s i n two dimensions. Before undertaking c a l c u l a t i o n s of o i l displacement by CO2 i n j e c t i o n , i t was f i r s t necessary t o define the s t a t e of the model r e s e r v o i r a f t e r waterflopding. Calculations of waterflood behaviour were performed assuming the 5-spot p a t t e r n t o be produced a t a constant r a t e of 5000 m3/day (31000 BPD) with an equal i n j e c t i o n of water i n t o each i n j e c t o r . R e l a t i v e p e r m e a b i l i t i e s were derived assuming t h a t t h e sandstone was predominantly water wet, and the Corey approximation (Ref 1 4 ) was used t o o b t a i n water r e l a t i v e p e r m e a b i l i t i e s . Imbibition o i l r e l a t i v e p e r m e a b i l i t i e s were derived by applying the Land concept of reduced f r e e s a t u r a t i o n s (Ref 15) t o the Corey drainage approximation. With the r a t h e r coarse l e v e l of mesh d e f i n i t i o n described above, i t was not thought necessary t o include the marginal e f f e c t s a s s o c i a t e d with the use of c a p i l l a r y pressure curve, b u t t h e c a l c u l a t e d d i s t r i b u t i o n of water s a t u r a t i o n s a r i s i n g from the model i s expected t o be t y p i c a l of a p o s s i b l e condition f o r a CO2 displacement process. The c a l c u l a t i o n s of waterflood behaviour were performed using t h e compositional simulator described l a t e r . Breakthrough of water occurs a t t h e producer a f t e r 1800 days, with a recovery of 51% of the o i l i n place. The water c u t rises t o 50% a t 2100 days when the recovery i s 59% of t h e o i l i n place. A t t h i s condition, most of t h e unswept o i l was confined t o the two o u t e r stream tubes around the production w e l l . Some underriding of o i l by water had occurred so t h a t the top two l a y e r s contained about h a l f of the unswept o i l . This condition when the water c u t reached 50% has been used a s the s t a r t i n g p o i n t f o r the CO2 displacement c a l c u l a t i o n s , s i n c e t h i s may be a t y p i c a l l i m i t i n g s i t u a t i o n f o r off-shore water handling. Modelling Assumptions Adopted i n Immiscible and Miscible Displacement Calculations Displacement of o i l by Cop i n the model r e s e r v o i r has been s t u d i e d under i d s c i b l e and miscible conditions by performing c a l c u l a t i o n s f o r p r e s s u r e s j u s t below and j u s t above the minimum m i s c i b i l i t y pressure. The Intercomp Composit i o n a l Reservoir Simulator, CRS, (Ref 16) used f o r t h e multi-dimensional immiscible displacement c a l c u l a t i o n s employs e q u i l i b r i u m K-value c o r r e l a t i o n s f o r c a l c u l a t i n g phase behaviour, with an equation of s t a t e f o r d e n s i t i e s . The s i x component r e p r e s e n t a t i o n of F o r t i e s o i l described e a r l i e r w a s used i n t h e study, t h e parameters i n the K-value c o r r e l a t i o n being adjusted t o match t h e s a t u r a t i o n pressure and swelling f a c t o r s of oil/CO2 mixtures p r e d i c t e d by the d e t a i l e d equation of s t a t e model ( s e e Figure 4), and t o match measured o i l d e n s i t i e s and v i s c o s i t i e s . The miscible c a l c u l a t i o n s were c a r r i e d o u t using the Todd and Longstaff mixing model (Ref 17). This i s a model f o r a two component, o i l and s o l v e n t , system which assumes d i r e c t m i s c i b i l i t y of t h e phases. The method r e l i e s on t h e assumption of an e f f e c t i v e o i l v i s c o s i t y and d e n s i t y , and an e f f e c t i v e gas v i s c o s i t y and d e n s i t y , using a mixing parameter, w, which has t o be defined by

257 empirical means. The CRS code was modified t o provide a s u i t a b l e v e h i c l e f o r t h i s mixing model. This involved bypassing the phase e q u i l i b r i u m c a l c u l a t i o n and i n c o r p o r a t i n g the Todd and Longstaff equations. Unmixed o i l and C02 p r o p e r t i e s were e n t e r e d i n t a b u l a r form. Using a value of W = 0.67, Todd and Longstaff c a l c u l a t e d the o i l displacement f o r an a r e a l bead pack system which gave good agreement with experimental d a t a obtained by Lacey (Ref 18). Good agreement with Lacey's r e s u l t s was a l s o obtained i n the p r e s e n t work using the modified CRS model with a c u r v i l i n e a r g r i d and w = 0.67. There i s , however, no experimental evidence t h a t t h e mixing model i s c o r r e c t f o r a v e r t i c a l c r o s s s e c t i o n geometry and the e f f e c t i v e d e n s i t i e s assumed i n the model may not be v a l i d . Whilst Todd and Longstaff recommend a value of w = 0.67 f o r a r e a l s t u d i e s , Warner (Ref 19) has recommended a value of w = 0.8 f o r v e r t i c a l cross s e c t i o n s and f o r 3-dimensional c a l c u l a t i o n s . I n the p r e s e n t s t u d i e s , a value W = 0.7 was used f o r most of the c a l c u l a t i o n s , b u t some c a l c u l a t i o n s were a l s o performed using w = 0.5 and w = 1.0 t o a s s e s s the s e n s i t i v i t y of the r e s u l t s t o changes i n t h i s f a c t o r . The r e l a t i v e permeability treatment i n the models f o r miscible and immiscible displacement a r e very d i f f e r e n t . For immiscible displacement, t h r e e phase r e l a t i v e p e r m e a b i l i t i e s a r e evaluated using Stone's second method (Ref 20). In t h i s approach, the water r e l a t i v e permeability i s a f u n c t i o n of the water s a t u r a t i o n only and the gas r e l a t i v e permeability is a f u n c t i o n of the gas s a t u r a t i o n only. The o i l r e l a t i v e permeability i s a f u n c t i o n of both water and gas s a t u r a t i o n s and is given by r lr 1

-

r

(9)

Each of the r e l a t i v e p e r m e a b i l i t i e s i n immiscible displacement a r e s u b j e c t t o three-phase h y s t e r e s i s e f f e c t s a s the flow regimes change (Ref 21). In a gas d r i v e t h e gas becomes mobile a t an i n i t i a l s a t u r a t i o n of about 0.05,whereas when gas i s displaced a trapped gas s a t u r a t i o n of 0.30 i s t y p i c a l (Ref 2 2 ) . F a i l u r e t o account f o r the h y s t e r e s i s i n gas r e l a t i v e p e r m e a b i l i t i e s r e s u l t s i n o p t i m i s t i c r e c o v e r i e s , s i n c e l i t t l e gas i s trapped. The CRS code was t h e r e f o r e modified t o allow f o r gas h y s t e r e s i s e f f e c t s . Gas r e l a t i v e p e r m e a b i l i t i e s were obtained by applying t h e Land method (Ref 15) t o t h e drainage curve c a l c u l a t e d from t h e Corey approximation (Ref 1 4 ) . The "free" gas s a t u r a t i o n .(SgF) defined by Land i s f i r s t computed a s a f u n c t i o n of the c u r r e n t gas s a t u r a t i o n (S ) and the h i g h e s t value of gas s a t u r a t i o n previously reached w i t h i n each g r i d f l o c k (Sgmax). The equations a r e

s* where

gF

- [s*g0.5

s -s

S*gr +/(s*g

- s* l 2 gr

+ 4(S*

g

-

s*gr)/c

I

A value of C = 1.86 was obtained from Equation 10 by s u b s t i t u t i n g a trapped gas s a t u r a t i o n (S ) of 0.30 when the maximum gas s a t u r a t i o n had reached 0.77 ( i e 1gr sWc): H y s t e r e s i s e f f e c t s i n the o i l and water r e l a t i v e p e r m e a b i l i t i e s were considered t o be small and were ignored.

258 The r e l a t i v e permeability treatment i n the Todd and Longstaff miscible model i s based upon the assumption t h a t o i l and s o l v e n t behave a s a s i n g l e phase. For consistency w i t h t h e waterflood. t h i s s i n g l e hydrocarbon/C02 phase uas given the same r e l a t i v e permeability (krhC) a s t h a t of o i l i n water. This implies a r e s i d u a l hydrocarbon/C02 s a t u r a t i o n a f t e r water d r i v e of 0 . 3 0 . The s e p a r a t e o i l and gas r e l a t i v e p e r m e a b i l i t i e s were then obtained by making the l i n e a r as sump t ion.

S

kro =

So S krhc g

(13)

Hysteresis e f f e c t s i n gas r e l a t i v e permeability were not included i n the miscible c a l c u l a t i o n s , i t being argued t h a t o i l and gas behave a s the same phase under miscible conditions. Two-Dimensional Studies A number of comparative imniscible displacement c a l c u l a t i o n s have been performed using a v e r t i c a l , two dimensional model t o examine various C02-injection s t r a t e g i e s a f t e r waterflood. This v e r t i c a l model c o n s i s t e d of the second longest of the f o u r stream tubes i n the mesh scheme i d e n t i f i e d previously. Continuous i n j e c t i o n of C02 (Case a ) was used a s t h e b a s i s of comparison. The following a l t e r n a t i v e s t r a t e g i e s were then examined f o r 0.22 PV of i n j e c t e d C02 followed by chase water u n t i l the produced water reaches 90%.

Case b

I n j e c t i o n of a s i n g l e s l u g of C02 over the f u l l h e i g h t of the s e c t i o n

Case c

A l t e r n a t i n g 100 day i n j e c t i o n s of Cog and water a c r o s s the f u l l h e i g h t of t h e s e c t i o n

Case d

Simultaneous i n j e c t i o n of C02 i n t o the lower h a l f of t h e s e c t i o n and water i n t o the upper h a l f

Case e

A l t e r n a t i n g 100 day i n j e c t i o n s of C02 and water, with the COP i n j e c t i o n r e s t r i c t e d t o the lower h a l f of t h e s e c t i o n and water i n j e c t i o n r e s t r i c t e d t o t h e upper h a l f .

Cases d and e , i f p r a c t i c a b l e , would both r e q u i r e dual completions with the i n j e c t e d C02 flowing down a c e n t r a l pipe and water through a surrounding annulus. The p r a c t i c a l problems of dual completions have not been considered i n d e t a i l . However, s e p a r a t i o n of C02 and water w i l l considerably reduce the corrosion problems a s s o c i a t e d w i t h a l t e r n a t i n g C02 and water i n j e c t i o n . The r e s u l t s of these c a l c u l a t i o n s a r e i l l u s t r a t e d i n Figure 6 . With Case a, the asymptotic value of o i l recovery is 45% of the t a r g e t , with only 15% of t h e o i l being recovered when 0.22 PV of C02 i s i n j e c t e d . I n c l u s i o n of chase water a f t e r 0.22 PV COP i n Case b i n c r e a s e s o i l production t o 34%, f o r two reasons, namely more of the swollen o i l i s d i s p l a c e d , and some of the C02 i s moved t o become e f f e c t i v e i n o t h e r p a r t s of t h e r e s e r v o i r . A l t e r n a t i n g water with t h e C02 i n Case c reduces t h e peak value of C02 s a t u r a t i o n a t t a i n e d i n any g r i d block, so t h a t t h e amount of C02 trapping i s a l s o reduced. A s a r e s u l t , more of t h e Cog can be mobilised during t h e subsequent chase water flood and t h e recovery i n c r e a s e s t o 39%.

259 In each of the above c a s e s , t h e r e i s a s i g n i f i c a n t amount of g r a v i t y override. By i n j e c t i n g C02 i n t o the lower h a l f of the r e s e r v o i r with water i n t o the upper h a l f , Case d, gas o v e r r i d e i s reduced and the o i l recovery i s increased t o 59% of the t a r g e t . A l t e r n a t i n g the gas and water i n j e c t i o n s , w h i l s t r e s t r i c t i n g t h e gas t o the lower h a l f of the r e s e r v o i r and water t o the upper h a l f , Case e , produces a f u r t h e r s l i g h t improvement i n o i l recovery t o 62% of t h e t a r g e t .

0

1ooo l l Y E (DAYS)

FlG.5 COMPARISON OF OIL RECOVFRIES FOR DIFFERENT If4JECTION SlHATEGIES

The c a l c u l a t i o n s f o r C02 i n j e c t i o n i n t o a v e r t i c a l two dimensional model r e s e r v o i r have been repeated f o r miscible displacement conditions. As shown i n Table 2 , the r e s u l t s showed the same trends as those f o r i m i s c i b l e displacement, with Case e again producing the h i g h e s t l e v e l of o i l recovery. The m i s c i b l e displacement c a l c u l a t i o n s produced o i l recoveries s l i g h t l y below the immiscible values. This trend i n d i f f e r e n c e between miscible and immiscible displacement was observed i n a l l of the c a l c u l a t i o n s reported i n t h i s paper. The c a l c u l a t i o n a l models described e a r l i e r f o r t h e two processes involve very d i f f e r e n t p h y s i c a l concepts. A s i s discussed l a t e r , c u r r e n t l i m i t a t i o n s i n r e p r e s e n t i n g these physical concepts a r e thought t o be the reason f o r the somewhat lower c a l c u l a t e d o i l r e c o v e r i e s f o r the miscible condition. Areal sweep e f f e c t s were examined f o r both m i s c i b l e and immiscible displacement of o i l when a t o t a l of 0.22 PV of C02 i s i n j e c t e d , with a l t e r n a t i n g 100 day s l u g s of gas and w a t e r , followed by chase water. For these c a l c u l a t i o n s , a two dimensional a r e a l model was used with a s i n g l e mesh block i n the v e r t i c a l d i r e c t i o n . The immiscible and miscible displacements showed o i l recoveries of 61% and 54% of t h e t a r g e t o i l r e s p e c t i v e l y . The r e s u l t i n g a r e a l d i s t r i b u t i o n s of o i l f o r the two processes a r e i l l u s t r a t e d i n Figure 7. It can be seen t h a t i n the immiscible case the C02 has been e f f e c t i v e f o r a g r e a t e r d i s t a n c e from the i n j e c t o r than i n the miscible case. This r e s u l t i s a d i r e c t consequence of the d i f f e r e n t treatments f o r gas and o i l r e l a t i v e permeabilities i n the two models, which produce d i f f e r e n t values f o r t h e r e s i d u a l gas

260 TABLE 2 COMPARISON OF IMMISCIBLE AND MISCIBLE DISPLACEMENT I N A VERTICAL, TWO DIMENSIONAL CROSS SECTION FOR A TOTAL INJECTION OF 0.22 PV OF CO2 ~

~~~~

O i l Recovery (2 of Target)

Strategy Immiscible

Miscible

a

Single s l u g i n j e c t i o n of C02

15

12

b

Single s l u g of C02 followed by chase water

34

29

A l t e r n a t i n g 100 day i n j e c t i o n s of C02 and water, followed by chase water

39

39

Simultaneous i n j e c t i o n of C 0 2 i n t o lower h a l f of r e s e r v o i r and water i n t o upper h a l f followed by chase water

59

51

I n j e c t i o n of C02 i n t o lower h a l f of r e s e r v o i r and water i n t o upper h a l f with a l t e r n a t i n g - 100 day cycles between C02 and water i n j e c t i o n , followed by chase water

62

52

c

d

e

-

.

s a t u r a t i o n s . This h i g h l i g h t s an important f a c t o r i n t h e mathematical r e p r e s e n t a t i o n of gas displacement processes which needs f u r t h e r t h e o r e t i c a development coupled with experimental information. The high a r e a l sweep e f f i c i e n c y obtained with the immiscible displacement i s caused by two e f f e c t s : ( i ) component exchange between o i l and gas reduces the i n i t i a l v i s c o s i t y r a t i o of 20:l t o 3.2:1 ( i i ) up t o one t h i r d of the gas d i s s o l v e s i n the o i l keeping gas s a t u r a t i o n s low and hence maintaining low gas m o b i l i t i e s . The e f f e c t of varying the Todd and Longstaff mixing parameter was examined i n the two dimensional s t u d i e s . Results of c a l c u l a t i o n s f o r w = 0 . 5 , 0 . 7 and 1.0 f o r a l t e r n a t i n g 100 day i n j e c t i o n s of Cop and water over t h e f u l l h e i g h t of the s e c t i o n . followed by chase water, a r e shown i n Table 3. I t might have TABLE 3

EFFECT OF VARYING TODD AND LONGSTAFF M I X I N G PARAMETER ON OIL RECOVERY FOR WATER ALTERNATING WITH GAS I N TWO DIMENSIONAL STUDIES

( X of t a r g e t )

V e r t i c a l Cross Section Areal Model

44

54

63

261

IMMISCIBLE

MISCIBLE

I

KEY EOUIVALENT HVDROCARBON

SO * 0 6

SATURATION

FIG 7

0.07-

0.16

0.15

0.24

-

RESIOUAL HYDROCARBON OlSTRlBUTlON 2 0 0 0 OAY WAG I N A R E A L MODEL

0.21-

0.33 RESULTING

FROM

been expected that the sensitivity to the value of w would be different in the horizontal and vertical planes, because in the latter the effective densities will influence the override behaviour. This has not occurred in an obvious manner, although the direct link between effective viscosities and densities in the Todd and Longstaff model may not be realistic.

Three-Dimensional Calculations Calculations of immiscible and miscible displacement of oil have been performed using the three-dimensional conceptual reservoir model described earlier. These calculations were performed assuming the Cop-injection strategy which produced the highest oil recovery in two dimensional studies; ie. injection of C02 restricted to the lower half of the reservoir and water injection restricted to the upper half with alternating 100 day injections of C02 and water, followed finally with chase water across the full height of the column. The results are presented in Figure 8. The calculated oil production for immiscible displacement was 56% of the oil remaining after waterflood, compared with 51% for miscible displacement. In both cases the water cut continued to rise immediately after initiation of CO2-injection,but decreased to a level of 50% for about 1000 days before it increased rapidly once more. Thus both processes imply a need to handle high water-cuts, but not as high as would be incurred from continued injection of water without C02. The distributionsof hydrocarbon in the vertical cross section along the second longest streamtube areshown in Figure 9 . These illustrate the effects of gravity on the recovery and show the additional penetration made by the C02

262

FIC. 8. COMPARISON OF IMMISCIBLE AN0 MISCIBLE DISPLACEMENTS FOR THE THREE OlMENSlONAL RESERVOIR MOOEL

(b) M I S C I I L DISPLACEMENT

FIG.9. MSTWEUTIONS OF HYDROCARBON IN A VERTICAL CROSS SECTION OF THE THREE DIMENSIONAL MODEL (HYOROCARBON MASS AS PERCENT WATER FLOOD RESICUAL)

263 during immiscible displacement. These results are broadly similar for both immiscible and miscible cases with the previous two-dimensional cross section calculations, and this indicates that selection of that model was a good basis for comparing general injection strategies. Modelling Factors Influencing the Calcu1atio:is The higher oil recovery calculated for immiscible displacement compared with miscible displacement was unexpected. However, there are a number of features in the simulation models which need further theoretical and experimental investigation. Although hysteresis has been introduced into the gas relative permeabilities for the immiscible calculation, the model adopted has certain limitations. The treatment used has considered variations in trapping of the gas phase only, whereas a full treatment should consider all non-wetting phases. However, this introduces new problems in estimating the proportions of oil and gas that are trapped, and there is no experimental evidence to resolve this problem. The relative permeability treatment for the immiscible case, which assumes distinct gas and oil phases, should also change as the displacement process approaches miscibility. In the mixing model for the miscible cases, only a single C02/hydrocarbon phase exists, and there is no equivalent to the hysterises in trapping of CO2 assumed in the immiscible relative permeability model. The mixing model used for the miscible calculations is designed to provide effective viscosities in the presence of viscous fingering, whereas the effects of viscous fingering are ignored in the multicomponent immiscible model.. Immiscible viscous fingering may well be important, particularly when miscibility conditions are approached. Predicted recoveries from the immiscible model are therefore likely to be optimistic. The method of calculating effective oil and solvent densities in the Todd and Longstaff model has not been validated. Gravity override is an important characteristic of miscible gas displacement processes and there is a need to develop and validate an independent mixing model for effective densities. Gravity override may be a partially stabilising influence on fingering in the areal plane.

The assumption of instantaneous equilibration over the whole grid block with the multicomponent model causes immiscible predictions to be optimistic. This phenomenon is particularly emFhasised in a coarse mesh arrangement, since it allows substantial amounts of C02 to dissolve in the oil ahead of the displacement front, causing the oil to swell artificially and consequently increasing the mobility ratio. Similarly, the formation of free gas behind the front is inhibited by the coarse mesh mixing. Oil recoveries with both processes are slightly optimistic because no allowance has been made for the solubility of CO2 in water. The effect of water blocking, preventing the CO2 from contacting some of the oil has also been neglected. All of the above factors require more detailed quantatative analysis supported by experimental measurements to allow more definitive comparisons to be made.

264 Nomenclature a,b

Parameters i n equations of s t a t e

C

Imbibition trapping constant

D

Binary i n t e r a c t i o n c o e f f i c i e n t f o r the parameter 'b'

K

Vapour-liquid

Kr

R e l a t i v e permeability

m

C h a r a c t e r i s a t i o n constant i n PR equation

P

Pressure

R

Universal gas constant

S

Saturation

T

Absolute temperature

V

Molar volume

X

Mole f r a c t i o n

a

Parameter i n PR equation

6

Binary i n t e r a c t i o n c o e f f i c i e n t f o r t h e parameter 'a'

w

Acentric f a c t o r ; empirical mixing par-ameter

n

Parameter i n GRK equation.

equilibrium p a r t i t i o n coefficient

(S* e f f e c t i v e s a t u r a t i o n )

Subscripts C r i t i c a l property Free gas c r i t i c a l gas hydrocarbon components maximum oi1 reduced property water connate water

265 Acknowledgement The work r e p o r t e d i n t h i s paper h a s been funded by t h e Department o f Energy. The a u t h o r s acknowledge t h e a d v i c e given by D r F J Fayers. D r T P F i s h l o c k and >lr R I Hawes and t h e h e l p of M r I R Hawkyard i n u n d e r t a k i n g computations. References I.

REDLICH, 0. and KWONG, J.N.S., "On t h e Thermodynamics of S o l u t i o n s . V. An Equation o f S t a t e . F u g a c i t i e s of Gaseous S o l u t i o n s " , Chemical Reviews. (February 1949), 44, 233-244.

2.

PENG, D.Y. and ROBINSON, D.B., "A New Two-Constant Equation of S t a t e " , Ind. Eng. Chem. Fundam. (1974) 15, 59-64.

3.

ZUDKEVITCH, D. and JOFFE, J . , " C o r r e l a t i o n and P r o d u c t i o n of Phase E q u i l i b r i a w i t h t h e Redlich-Kwong Equation of S t a t e " , AIChE J n l (19731, 16, 112-119. -

4.

YARBOROUGH, L.; " A p p l i c a t i o n of a G e n e r a l i s e d Equation of S t a t e t o Petroleum R e s e r v o i r F l u i d s " , i n "Equations of S t a t e i n Engineering", Advances i n Chemistry S e r i e s , American Chemical S o c i e t y , Washington DC. ( 1 9 7 9 ) , 385-435.

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COATS, K.H.; "An Equation of S t a t e Compositional Model", (October 1980). 363-376.

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TUREK, E.A. e t a l ; "Phase E q u i l i b r i a i n Carbon Dioxide - Multicomponent Hydrocarbon Systems: Experimental Data and an Improved P r e d i c t i o n Technique", p a p e r SPE 9231 p r e s e n t e d a t t h e SPE Annual F a l l Technical Conference and E x h i b i t i o n , Dallas, September 21-24 1980.

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MOTT, R.E., "Development and E v a l u a t i o n of a Method f o r C a l c u l a t i n g t h e Phase Behaviour o f Multi-Component Hydrocarbon Mixtures from a n Equation o f S t a t e " , AEEW R 1331 ( 1 9 8 0 ) .

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8.

KATZ, D.L. and FIROZAEADI, A; " P r e d i c t i n g Phase Behaviour of Condensatel Crude-Oil Systems u s i n g Methane I n t e r a c t i o n C o e f f i c i e n t s " . J. P e t . Tech. (November 1978), 1649-1655.

9.

SIGMUND, P.M. e t a l p "Laboratory C02 Floods and. t h e i r Computer Simulation", p a p e r PDlO(5) p r e s e n t e d a t t h e 10th World Petroleum Congress, Bucharest, 1979.

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10.

CAVETT, R.H., " P h y s i c a l Data f o r D i s t i l l a t i o n C a l c u l a t i o n s Vapour-Liquid Equilibrium", Proc. 2 7 t h API Mid-year Meeting, San F r a n c i s c o , 1962.

1I.

WHITSON, C.H., " C h a r a c t e r i z i n g Hydrocarbon P l u s F r a c t i o n s " , paper EUR 183 p r e s e n t e d a t t h e European Offshore Petroleum Conference and E x h i b i t i o n , London, October 1980.

12.

HOLM, L.WI and JOSENDAL, V.A.,

13.

HILLIER, G.R.K, COBB R.M., DIMMOCK, P.A.. "Reservoir Development Planning f o r t h e F o r t i e s F i e l d " , Paper EUR 9 8 p r e s e n t e d a t European Offshore Petroleum Conference and E x h i b i t i o n , London, October 1978.

" E f f e c t of O i l Composition on M i s c i b l e Type Displacement by Carbon Dioxide", p a p e r SPE 8814, p r e s e n t e d a t t h e 1st SPE/DOE Symposium on Enhanced O i l Recovery, T u l s a , A p r i l 1980.

266 14.

COREY, A.T., "The I n t e r - r e l a t i o n Between Gas and O i l R e l a t i v e Permeabilities", Producer's Monthly Vol X I X , I , Nov 1954.

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LAND, C.S., "Calculation of Imbibition R e l a t i v e Permeability f o r Two and Three Phase Flow From Rock Properties", Trans AIME ( 1 9 6 8 ) , 243, 149- 156.

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NOLEN, J.S., "Numerical Simulation of Compositional Phenomena i n Petroleum Reservoirs", SPE Reprint S e r i e s No I I , Numerical Simulation ( 1 9 7 3 ) , p 269-284.

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TODD, M.R. and LONGSTAFF, W . J . , "The Development, Testing and Application of a Numerical Simulator f o r P r e d i c t i n g Miscible Flood Performance", J. P e t . Tech. (July 1972), 874-882.

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LACEY, J . W . , FARIS, J . E . , BRINKMAN, F.H., "Effect of Bank S i z e on O i l Recovery i n High Pressure Gas-Driven LPG-Bank Process", J.Pet.Tech (August 1961). 806-816.

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WARNER, H.R., "An Evaluation of Miscible C02 Flooding i n a Waterflooded Sandstone Reservoir", J . P e t . Tech (Oct 1977), 1339-1347.

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STONE, H.L., "Estimation of Three Phase R e l a t i v e Permeability and Residual O i l Data", J. Can. Pet. Tech. (Oct 1973), 12, 53-61.

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BREIT, V.S. and GRAUE, D . J . , "Scaling of Flow Parameters f o r Miscible Gas Flood Simulation Studies", Paper SPE/DOE 9804, Presented a t the Second J o i n t Symposium on Enhanced O i l Recovery, Tulsa, A p r i l 1981.

22.

HOLMGREN, C.R. and MORSE, R.A., "Effect of Free Gas S a t u r a t i o n on O i l 135-140. Recovery by Waterflooding" Trans AIME ( 1 9 5 1 ) .

192,

267

MISCIBLE GAS DISPLACEMENT

OIL RECOVERY BY CARBON DIOXIDE THE RESULTS OF SCALED PHYSICAL MODELS AND FIELD PILOTS TODD M. DOSCHER, MAHGUIB EL ARABI, SIAVASH GHARIB and RICHARD OYEKAN Department of Petroleum Engineering, Universiq of Southern clllifornia. Los Angeles, Cdifornia 90007 I. ABSTRACT

C o n s i d e r a b l e e f f o r t s h a v e b e e n e x p e n d e d in t h e p a s t d e c a d e on t h e p o t e n t i a l u s e of c a r b o n d i o x i d e f o r t h e r e c o v e r y of r e s i d u a l c r u d e oil, however t h e r e s u l t s of f i e l d p i l o t o p e r a t i o n s have i n d i c a t e d t h a t very l a r g e q u a n t i t i e s of carbon d i o x i d e are r e q u i r e d t o r e c o v e r t h e r e s i d u a l oil. S c a l e d p h y s i c a l model s t u d i e s have been u n d e r t a k e n i n a n a t t e m p t t o d e t e r m i n e w h e t h e r t h e l a r g e r a t i o s of i n j e c t e d c a r b o n d i o x i d e t o produced c r u d e o i l . o b s e r v e d i n f i e l d d e m o n s t r a t i o n p r o j e c t s , are t o b e e x p e c t e d or a r e due t o some d e f e c t s in t h e a p p l i c a t i o n of t h e p r o c e s s i n t h e f i e l d . The r e s u l t s of t h i s s t u d y have r a t h e r u n e q u i v o c a l l y i n d i c a t e d t h a t t h e h i g h r a t i o s of i n j e c t e d c a r b o n d i o x i d e t o r e c o v e r e d c r u d e o i l s h o u l d i n f a c t be expected. The e x p e r i m e n t s have a l s o shown t h a t a v e r y h e i g h t e n e d e f f i c i e n c y of t h e p r o c e s s c a n b e a c h i e v e d by u s i n g a s l u g of c a r b o n d t o x t d e f o l l o w e d by water. However, t h e r e s u l t s need t o b e q u a l i f i e d by n o t i n g t h a t t h e protot y p e r e s e r v o i r s u s e d i n t h e s e s t u d i e s are v e r y f a v o r a b l e f o r t h e u s e of CO2* The r e c o v e r y mechanism a p p e a r s t o b e c h i e f l y t h e s o l u t i o n of carbon d i o x i d e i n t h e oil, i t s s w e l l i n g a n d c o n s e q u e n t i n c r e a s e i n m o b i l i t y , a n d t h e n t h e d i s p l a c e m e n t of t h e s w o l l e n , m o b i l e o i l by a g a s d r i v e ( i f carbon d i o x i d e is i n j e c t e d c o n t i n u o u s l y ) or by water i f a s l u g of carbon d i o x i d e is f o l l o w e d b y t h e l a t t e r . T h e e f f i c i e n c y o f t h e p r o c e s s is t h w a r t e d by t h e high m o b i l i t y of t h e carbon d i o x i d e which l e a d s t o v i s c o u s f i n g e r i n g and i t s low d e n s i t y , compared t o water, which l e a d s t o g r a v i t y s e g r e g a t i o n . E x p e r i m e n t s have i n d i c a t e d t h a t n i t r o u s o x i d e , which a l s o d i s p l a y s a h i g h s o l u b i l i t y i n o r g a n i c compounds, is as e f f e c t i v e as c a r b o n d i o x i d e i n t h e s e model s t u d i e s . 11. INTRODUCTION

Much of t h e o p t i m i s m c o n c e r n i n g t h e p o t e n t t a l of carbon d i o x i d e i n r e c o v e r i n g r e s i d u a l c r u d e o i l h a s been based on s l i m t u b e experiments. A 50 t o 100 f o o t l e n g t h of 3/8 i n c h t u b i n g i s packed w i t h sand, f i l l e d w i t h crude oil and d i s p l a c e d w i t h carbon d i o x i d e a t a h i g h p r e s s u r e , which changes b u t l i t t l e between e n t r a n c e and o u t l e t b e c a u s e of t h e h i g h p e r m e a b i l i t y of t h e system. A t y p i c a l r e s u l t of a s l i m t u b e e x p e r i m e n t is shown i n F i g u r e 1. On t h e same p l o t is shown t h e v a r i a t i o n i n d e n s i t y and v i s c o s i t y of t h e carbon d i o x i d e as a f u n c t i o n of t h e p r e s s u r e .

268 5.6.7 E a r l i e r i n v e s t i g a t o r s have def i n e d 1 * 2 s 3 * 4 ,and t h e n d e b a t e d , t h e p r e d i c t a b i l i t y of a "minimum m i s c i b i l i t y p r e s s u r e " ; t h a t p r e s s u r e a t which 95% of t h e o i l c o n t a i n e d in t h e s l i m t u b e is r e c o v e r e d b e f o r e carbon d i o x i d e breakthrough. There a p p e a r e d t o b e a n i m p l i c i t s u g g e s t i o n t h a t good recovery would be a c h i e v e d as l o n g as t h e d i s p l a c e m e n t p r e s s u r e was e q u a l t o o r g r e a t e r t h a n t h i s v a l u e . G a r d n e r , et.al.8 h o w e v e r s h o w e d t h a t t h e h i g h r e c o v e r i e s o b t a i n e d i n s l i m t u b e s is r e l a t e d t o t h e a t t a i n m e n t of a l o w p h y s i c a l d i s p e r s i o n c o e f f i c i e n t (D/vL), and i t c a n b e r e a d i l y shown t h a t t h e d i s p e r s i o n c o e f f i c i e n t s a c h i e v e d in s l i m t u b e s a r e v e r y d i f f e r e n t from t h e d i s p e r s i o n c o e f f i c i e n t s o b t a i n e d in r e a l r e s e r v o i r s 9 . E a r l i e r work o n v i s c o u s f i n g e r i n g of c o u r s e showed t h a t s t a b l e p i s t o n - l i k e d i s p l a c e m e n t of o n e f l u i d by a n o t h e r is e f f e c t e d w h e t h e r t h e f l u i d s a r e m i s c i b l e o r n o t ; even d e s p i t e a n a d v e r s e m o b i l i t y r a t i o i f t h e d i a m e t e r of t h e f l o w s y s t e m approaches t h e t h i c k n e s s of t h e f i n g e r s t h a t can be g e n e r a t e d in t h e s y s t e m u n d e r s t u d y l o . The j u x t a p o s i t i o n of t h e p h y s i c a l p r o p e r t i e s of c a r b o n d i o x i d e w i t h t h e s l i m t u b e r e c o v e r y a s a f u n c t i o n of p r e s s u r e in F i g u r e 1 c e r t a i n l y s u g g e s t s t h a t t h e i n c r e a s i n g r e c o v e r y is due t o g r a d u a l l y decreasi n g a d v e r s e m o b i l i t y and g r a v i t y r a t i o s .

'OOt

A

. \

400

800 PRCSSURC.

1200 PSI

1600

Fig. 1: THE EFFECT OF PRESSURE ON THE 5 ' CRUDE I N A SLIM TUBE DISPLACEMENT OF A 4 Warner'' s t u d i e d t h e n u m e r i c a l s i m u l a t i o n of c a r b o n d i o x i d e d i s p l a c e m e n t of r e s i d u a l c r u d e o i l w i t h a model t h a t depended on t h e mixing of t h e carbon d i o x i d e w i t h t h e o i l f o r i t s m o b i l i z a t i o n and t r a n s p o r t . No o i l bank was developed i n t h e s e s i m u l a t i o n s and t h e p a r a m e t e r t h a t e x e r c i s e d t h e c h i e f c o n t r o l o v e r t h e p r o c e s s w a s t h e g r a v i t y s e g r e g a t i o n of t h e i n j e c t e d carbon d i o x i d e i n t h e w a t e r - f i l l e d r e s e r v o i r . Warner's n u m e r i c a l r e s u l t s would have s t i l l been p o o r e r had h e i n c l u d e d t h e v e r y f i n e g r i d t h a t C l a r i d g e l 2 h a d e a r l i e r s h o w n was n e c e s s a r y f o r v i s c o u s f i n g e r i n g t o b e p r o p e r l y e x h i b i t e d in a n u m e r i c a l model. The p h a s e b e h a v i o r a s d e s c r i b e d in t h e c u r r e n t l i t e r a t u r e , e.g., R e f e r e n c e 8, shows t h e e x i s t e n c e of a m i s c i b i l i t y gap13 in carbon dioxidec r u d e o i l s y s t e m s . As t h e c a r b o n d i o x i d e c o n t e n t of t h e s y s t e m is inc r e a s e d , t h e s o l u t i o n of carbon d i o x i d e in t h e c r u d e f r a c t i o n a t e s i n t o two o r more phases. One is a s o l u t i o n of carbon d i o x i d e i n t h e heavy components of t h e c r u d e . F o r v i r t u a l l y a l l c r u d e o i l s t h a t h a v e b e e n s t u d i e d a n d r e p o r t e d i n t h e l i t e r a t u r e , t h e s o l u b i l i t y is a b o u t 60 m o l p e r c e n t c a r b o n d i o x i d e . The s e c o n d p h a s e is t h e m i x t u r e of t h e l i g h t c o m p o n e n t s of t h e crude and t h e e x c e s s carbon d i o x i d e in t h e system. The l a t t e r phase remains

269 a highly mobile f l u i d and can be expected t o f i n g e r through t h e r e s e r v o i r j u s t a s w o u l d any low v i s c o s i t y f l u i d . Even i n t h e a b s e n c e of v i s c o u s f i n g e r i n g , a Buckley L e v e r e t t a n a l y s i s 1 4 of t h e i n j e c t i o n of s o l v e n t i n t o a w a t e r e d o u t r e s e r v o i r shows t h a t e a r l y breakthrough of a mobile s o l v e n t s h o u l d be expected. The f i e l d p e r f o r m a n c e o f t e r t i a r y p i l o t o p e r a t i o n s have i n d i c a t e d t h a t i n d e e d carbon d i o x i d e can m o b i l i z e and d i s p l a c e r e s i d u a l crude o i l . The S a c r o c t e r t i a r y i l o t r e c o v e r e d 3% o f t h e r e s i d u a l o i l a t a CO /OIL r a t i o of 36 MSCF/BbllP. A t L i t t l e Creek, M i s s i s s i p p i , a s much as 60% 0% t h e o i l c o n t a i n e d i n a p i l o t p a t t e r n may have been r e c o v e r e d a t a r a t i o of 27.6 MSCF/Bb116. A t L i c k C r e e k , A r k a n s a s , a p i l o t o p e r a t i o n i n t h e Meakin s a n d i n d i c a t e s t h e r a t i o of recovered o i l t o i n j e c t e d carbon dioxide w i l l be 28.4 MSCF/Bbl, a n d t h e l a s t a v a i l a b l e f i u r e s f o r t h e Two F r e d s f i e l d i n West Texas i n d i c a t e a r a t i o of 18 MSCF/Bblq6. I f t h e s e r a t i o s are p r o j e c t e d t o b e v a l i d f o r f u l l s c a l e o p e r a t i o n , then t h e economic v i a b i l i t y of carbon dioxide i n j e c t i o n p r o j e c t s f o r t h e r e c o v e r y of r e s i d u a l o i l must b e re-examined. Even r e - i n j e c t i o n of produced carbon d i o x i d e , a f t e r r e q u i r e d p u r i f i c a t i o n and d r y i n g , and a c c o u n t i n g f o r i n t e r e s t c h a r g e s due t o t h e d e l a y b e t w e e n i n j e c t i n g c a r b o n d i o x i d e and r e c o v e r i n g t h e c r u d e 01, t h e c i t e d r a t i o s of c a r b o n d i o x i d e i n j e c t e d t o produced o i l would add o v e r $20 t o t h e c o s t of r e c o v e r i n g a b a r r e l of o i l by t h e i n j e c t i o n of carbon dioxide. These s t u d i e s were c a r r i e d o u t i n a n a t t e m p t t o d e t e r m i n e whether s u c h h i g h c a r b o n d i o x i d e / o i l r a t i o s a r e t o b e e x p e c t e d o r a r e due t o s p e c i f i c p e c u l i a r i t i e s of t h e p i l o t and d e m o n s t r a t i o n tests from which they have emenated.

111. RESULTS OF THE EXPERIMENTAL STUDIES The e x p e r i m e n t a l work was c a r r i e d o u t i n p h y s i c a l l y s c a l e d models of a d i r e c t l i n e d r i v e p a t t e r n , see T a b l e 1. T h e d e t a i l s of t h e s c a l i n g p r o c e d u r e s t h a t h a v e b e e n u s e d a n d t h e c o n s t r u c t i o n of t h e r e q u i r e d h i g h p r e s s u r e ( t o 5000 psi.), high t e m p e r a t u r e ( t o 250'F.) equipment i s d e s c r i b e d elsewhere9.. TABLE 1. PARAMETER PERMEABILITY, MDS. INJECTION PATTERN SPACING, INJECTOR TO PRODUCER, FT. RESERVOIR THICKNESS, FT.

MODEL VALUE

PROTOTYPE VALUE

3.000 LINE DRIVE

20. LINE DRIVF

3.08 0.1875

462. 28.2

The r e s e r v o i r chosen f o r t h i s p a r t i c u l a r set of e x p e r i m e n t s , i t can be s e e n , w a s one of r e l a t i v e l y low p e r m e a b i l i t y . T h i s was done t o minimize t h e e f f e c t s of g r a v i t y s e g r e g a t i o n and v l s c o u s f i n g e r i n g and t h u s s e c u r e a r e l a t i v e l y f a v o r a b l e performance.

2 70 A. The P r o d u c t i o n H i s t o r y of R e s i d u a l O i l R eco v er y by C ar b o n D i o x i d e Figures 2 through 4 present a t y p i c a l production h i s t o r y f o r the d i s p l a c e m e n t of r e s i d u a l c r u d e o i l by s u b - c r i t i c a l c a r b o n d i o x i d e a t 1400 p s i a n d 73OF. I t is r e a d i l y s e e n t h a t w a t e r a l o n e is p r o d u c e d a t f i r s t ; i t i s t h e o n l y m o b i l e p h a s e i n t h e r e s e r v o i r f o l l o w i n g a water f l o o d . Carbon d i o x i d e a p p e a r s a t t h e p r o d u c i n g end of t h e s y s t e m a f t e r t h e i n j e c t i o n of a b o u t 0.2 of a p o r e v o lu m e, a n d c r u d e oil p r o d u c t i o n is i n i t i a t e d s i m u l t a n e o u s l y w i t h t h a t of c a r b o n d i o x i d e .

COa INJECTED IPV)

F ig. 2. PRODUCTtON HISTORY FOR A TYPICAL C 0 2 DIS LACEMENT 45°A.P.I.CRUDE, S0=0.21. P11400 PSI. T=73

g

CO,

INJECTED

(PV1

F i g - 3 . CUMULATIVE RECOVERY OF OIL AND WATER FOR FXG. 2 The p r o d u c t i o n r a t e of oil r e a c h e s a maximum v a l u e w i t h i n 0.2 t o 0.3 o f a p o r e v o l u m e f o l l o w i n g b r e a k t h r o u g h , b u t t h e r a t i o o f oil t o c a r b o n d i o x i d e in t h e e f f l u e n t c o n t i n u o u s l y d e c r e a s e s a f t e r i t s f i r s t ap p ear an ce.

271

Fig. 4. PRODUCTION RATE HISTORY FOR FIG. 2

The recovery of t h e r e s i d u a l o i l is never c o m p l e t e even w i t h t h e i n j e c t i o n of s e v e r a l p o r e volumes of c a r b o n d i o x i d e , and t h i s i s t r u e even which a c o m p l e t e l y m i s c i b l e hydrocarbon (dodecane) i s s u b s t i t u t e d f o r t h e crude o i l . I t is i n f o r m a t i v e t o n o t e t h a t t h e a v e r a g e m o l a r c o n c e n t r a t i o n of c a r b o n d i o x i d e in t h e o i l p h a s e w i t h i n t h e m o d e l , c a l c u l a t e d by m a t e r i a l b a l a n c e , r e a c h e s a v a l u e of w e l l o v e r 0.6 by t h e time carbon d i o x i d e b r e a k s t h r o u g h in t h e e f f l u e n t , F i g u r e 5. The i m p o r t a n c e of t h i s o b s e r v a t i o n i n connectiom w i t h t h e r e l a t i o n s h i p of phase b e h a v i o r t o recovery w i l l be discussed later.

Fig. 5 . AVERAGE MOLAR CONCENTRATION OF CARBON D I O X I D E IN OIL PHASE FOR EXPERIMENT DESCRIBED BY FIGURE 2.

T h e e f f i c i e n c y o f t h e r e c o v e r y p r o c e s s , e x p r e s s e d i n terms of MSCF/Bbl, i s s h o w n i n F i g u r e 6 f o r v a r i o u s i n i t i a l s a t u r a t i o n s of c r u d e o i l . I t i s s e e n t h a t t h e C 0 2 / 0 1 1 r a t i o s a r e i n d e e d in t h e r a n g e of 20 t o 30 MSCF/Bbl when r e s i d u a l s a t u r a t i o n s of less t h a n 30% are b e i n g recovered.

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F i g . 6. THE EFFICIENCY OF OIL RECOVERY BY CARBON D I O X I D E AS A FUNCTION OF INITIAL OIL SATURATION, P=1400 P S I , T 73OF.

B. E f f e c t of T e m p e r a t u r e a n d P r e s s u r e The t e m p e r a t u r e a n d p r e s s u r e a f f e c t t h e d i s p l a c e m e n t of o i l by c a r b o n d i o x i d e i n two i m p o r t a n t a s p e c t s . The f i r s t is r e l a t e d t o t h e f a c t t h a t t h e s e parameters a f f e c t t h e p h y s i c a l p r o p e r t i e s , v i s c o s i t y and density, which, i n t u r n , a f f e c t f l u i d f l o w i n c l u d i n g t h e d i s p l a c e m e n t of o n e f l u i d by a n o t h e r . The s e c o n d i s t h e e f f e c t of t e m p e r a t u r e a n d p r e s s u r e on t h e s o l u b i l i t y of t h e c a r b o n d i o x i d e i n t h e c r u d e o i l . From c h e m i c a l t h e r m o d y n a m i c s i t i s known t h a t f o r t h e c a s e w h e r e t h e r e i s no n e t volume c h a n g e a t t e n d a n t upon mixing, s o l u b i l i t y of one l i q u i d i n a n o t h e r is n o t a p p r e c i a b l y a f f e c t e d by p r e s s u r e , a n d i s i n c r e a s e d by t e m p e r a t u r e . T h i s i n d e e d ' w a s f o u n d t o b e t h e case f o r t h e s o l u b i l i t y of l i q u i d c a r b o n d i o x i d e i n h y d r o ~ a r b o n s l ~ .The s o l u b i l i t y of s u p e r c r i t i c a l carbon d i o x i d e i n hydrocarbons i n c r e a s e s w i t h i n c r e a s i n 8 p r e s s u r e and d e c r e a s e s w i t h i n c r e a s i n g t e m p e r a t u r e . The s o l u b i l i t y of c a r b o n d i o x i d e i n t h e p r i n c i p a l c r u d e oil u s e d i n t h i s s t u d y is shown i n F i g u r e s 7 and 8.

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W i t h t h i s b a c k g r o u n d i n h a n d , s o m e t w e n t y r u n s were c o n d u c t e d t o e v a l u a t e t h e e f f e c t of t e m p e r a t u r e a n d p r e s s u r e on t h e d i s p l a c e m e n t of c r u d e o i l by c a r b o n d i o x i d e a s r e v e a l e d i n t h i s p h y s i c a l l y s c a l e d m o d e l s t u d y . Both c r u d e o i l a n d a m i s c i b l e h y d r o c a r b o n (dodecane) were u s e d a t r e s i d u a l a n d h i g h i n i t i a l s a t u r a t i o n s , a t t e m p e r a t u r e s t o 130°F., and o v e r t h e p r e s s u r e r a n g e o f 650 p s i . t o 2650 p s i . The e f f e c t of p r e s s u r e on t h e r e c o v e r y of t h e 45OA.P.I. c r u d e o i l a t s u b - c r i t i c a l t e m p e r a t u r e s is shown i n F i g u r e 9 f o r b o t h r e s i d u a l a n d h i g h i n i t i a l saturations. It i s a p p a r e n t t h a t t h e e f f e c t of p r e s s u r e a t a subc r i t i c a l t e m p e r a t u r e i s v e r y a i g n i f i c a n t i f t h e p r e s s u r e is l e s s t h a n t h e s a t u r a t i o n v a l u e ( a b o u t 900 p s i a t 75OF.), b u t a f u r t h e r p r e s s u r e i n c r e a s e above t h e s a t u r a t i o n v a l u e h a s o n l y a minor e f f e c t on recovery. For t h i s h i g h i n i t i a l o i l s a t u r a t i o n , t h e r e c o v e r y i n c r e a s e s f r o m a meager 20% t o o v e r 6 0 % u p o n i n c r e a s i n g t h e p r e s s u r e f r o m 6 5 0 p s i . t o 1,000 p s i , b u t i n c r e a s e s f r o m 63% t o o n l y 71% when t h e p r e s s u r e is i n c r e a s e d a n o t h e r 1000 p a l t o 2000 p s i . The d r a m a t i c i n c r e a s e i n t h e r e c o v e r y as t h e p r e s s u r e is i n c r e a s e d f r o m 6 5 0 p s i t o 1000 p s i a t 75OF. p a r a l l e l s a m a r k e d i n c r e a s e i n t h e d e n s i t y of c a r b o n d e n s i t y f r o m 0.11 t o 0.74 g/CC. The d e n s i t y of t h e c a r b o n d i o x i d e i n c r e a s e s f r o m 0.22 t o 0.70 t o 0.76 a s t h e p r e s s u r e i n c r e a s e s f r o m 1150 t o 2150 psi. and f i n a l l y t o 2650 p s i . This translates t o a density d i f f e r e n c e b e t w e e n d i s p l a c i n g f l u i d a n d d i s p l a c e d f l u i d ( w a t e r ) o f 0.78, 0.30, a n d 0.24 g/cc. A s i m p l e f o r c e b a l a n c e t h e n shows t h a t t h e same d e g r e e of g r a v i t y s e g r e g a t i o n t h a t o c c u r s a t a p r e s s u r e o f 2150 p s i c a n b e a c h i e v e d

274 a t 1 1 5 0 p s i o n l y by i n c r e s i n g t h e r a t e by a f a c t o r of t h r e e . H e n c e , t h e p o o r e r e f f i c i e n c y a t 1150 p s i as compared t o t h a t a t 2150 p s i is p r o b a b l y due p r i m a r i l y t o a g r e a t e r d e g r e e o f g r a v i t y s e g r e g a t i o n a t t h e l o w e r pressure. Between 2150 p s i and 1650 p s i , t h e small d i f f e r e n c e i n r e c o v e r y i s p r o b a b l y d u e t o t h e c o m b i n e d e f f e c t of s m a l l d i f f e r e n c e s i n b o t h s o l u b i l i t y and g r a v i t y segregation.

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Fig.9. THE EFFECT OF PRESSURE ON RECOVERY OF CRUDE O I L BY CARBON D I O X I D E AT 73'F* A t a s u p e r - c r i t i c a l t e m p e r a t u r e t h e e f f e c t o f p r e s s u r e on t h e r e c o v e r y of r e s i d u a l c r u d e o i l i s s i m i l a r t o i t s e f f e c t a t s u b - c r i t i c a l v a l u e s a l t h o u g h t h e r e c o v e r y l e v e l s a r e s o m e w h a t less t h a n a t t h e l o w e r t e m p e r a t u r e , F i g u r e 10.

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F i g . 10. THE EFFECT OF PRESSURE ON RECOVERY OF CRUDE OIL AT 130°F*

275 To f u r t h e r s t u d y t h e r o l e of d e n s i t y on t h e d i s p l a c e m e n t of carbon d i o x i d e , a set of e x p e r i m e n t s were performed o v e r a range of t e m p e r a t u r e s and p r e s s u r e s where t h e d e n s i t y c o u l d b e m a i n t a i n e d r e l a t i v e l y c o n s t a n t by m a n i p u l a t i n g t h e s e two p a r m e t e r s . A t 1 4 0 0 p s i . a n d 75’F. t h e d e n s i t y of c a r b o n d i o x i d e i s 0.82, a s i t i s a t 2700 p s i . a n d 125OF. e v e n t h o u g h t h e t e m p e r a t u r e s a r e below and above t h e c r i t i c a l t e m p e r a t u r e , r e s p e c t i v e l y . The r e s u l t s of two r u n s , one a t each of t h e f o r e g o i n g sets of p a r a m e t e r s , i s s h o w n i n F i g u r e 11 a n d i t i s r e a d i l y s e e n t h a t t h e r e s u l t s of t h e t w o r u n s can b e superimposed on each o t h e r . I

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Fig. 11. THE COMPENSATING EFFETS OF TEMPERATURE AND PRESSURE ON THE DISPLACEMENT OF RESIDUAL CRUDE O I L

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To g a i n s t i l l f u r t h e r i n s i g h t i n t o t h e d i s p l a c e m e n t of crude o i l by carbon d i o x i d e , t h e e f f e c t of p r e s s u r e on t h e d i s p l a c e m e n t of a c o m p l e t e l y m i s c i b l e hydrocarbon was i n v e s t i g a t e d as a f u n c t i o n of p r e s s u r e , F i g u r e 12. It i s a p p a r e n t t h a t t h e e f f e c t of p r e s s u r e is t h e same f o r t h e d i s p l a c e m e n t of d o d e c a n e a s i t i s f o r t h a t o f c r u d e o i l ; i t is t h e r a t e of c h a n g e of s o l u b i l i t y w i t h p r e s s u r e t h a t a f f e c t s t h e r a t e of change of recovery w i t h p r e s s u r e whether t h e d i s p l a c i n g f l u i d is r i s c i b l e or not.

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Fig. 1 2 . THE EFFECT OF PRESSURE ON THE DISPLACEMENT OF DODECANE BY CARBON D I O X I D E

276 C. E f f e c t of I n j e c t i o n Rate

E x p e r i m e n t s were c o n d u c t e d a t p r o t o t y p e v e l o c i t i e s v a r y i n g f r o m 0.05 t o 0.4 f o o t p e r day. F i g . 1 3 s h o w s t h a t i n c r e a s i n g t h e v e l o c i t y o v e r t h e However, t h e i n d i c a t e d r a n g e r e s u l t s i n a s l i g h t improvement i n recovery. e f f e c t is s e n s e d o n l y i n t h e l a t e r l i f e of t h e f l o o d . Some e x p e r i m e n t s were c o n d u c t e d a t s t i l l l o w e r r a t e , b u t g r a v i t y s e g r e g a t i o n dominated t h e s y s t e m and t h e c r u d e o i l recovery decreased rapidly. 80

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Fig. 13. THE EFFECT OF VELOCITY (OR INJECTION RATE) ON THE RECOVERY OF CRUDE O I L BY CARBON DIOXIDE

D. The E f f e c t of I n i t i a l Oil S a t u r a t i o n .

The i n i t i a l o i l s a t u r a t i o n h a s a very d i r e c t e f f e c t on b o t h t h e f r a c t i o n a l o i l r e c o v e r y , a n d t h e r e s u l t i n g c a r b o n d i o x i d e / o i l r a t i o , see Fig. 14. The o i l r e c o v e r y is o n l y 50% of t h e r e s i d u a l s a t u r a t i o n b u t c l i m b s t o 80% of t h e i n i t i a l o i l s a t u r a t i o n when t h e l a t t e r is 80%.

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277 The d i f f e r e n c e I n t h e e f f i c i e n c y of t h e d i s p l a c e m e n t is d i r e c t l y r e l a t e d t o t h e f a c t t h a t when a low o i l s a t u r a t i o n is d i s p l a c e d , much of t h e i n j e c t e d c a r b o n d i o x i d e is b e i n g u s e d m e r e l y t o d i s p l a c e t h e water i n t h e r e s e r v o i r (.which is n e c e s s a r y b e f o r e t h e c a r b o n d i o x i d e c a n c o n t a c t a n d d i s s o l v e i n t h e c r u d e o i l ) . When t h e i n i t i a l o i l s a t u r a t i o n is a b o v e t h e r e s i d u a l v a l u e , b o t h o i l a n d water a r e p r o d u c e d t h r o u g h o u t t h e run. The f l o w of o i l , e s p e c i a l l y a f t e r carbon d i o x i d e breakthrough, is much h i g h e r t h a n would be p r e d i c t e d from t h e r e l a t i v e p e r m e a b i l i t y r e l a t i o n s h i p f o r t h e o i l - w a t e r system; t h i s l e a d s t o t h e c o n c l u s i o n t h a t t h e m o b i l i t y of t h e o i l It IS obviously i n which carbon d i o x i d e h a s d i s s o l v e d h a s been increased. t h e v i s c o s i t y r e d u c t i o n and, perhaps, most i m p o r t a n t l y , t h e s w e l l i n g of t h e c r u d e o i l phase which c a u s e s t h i s i n c r e a s e i n m o b i l i t y . The s w e l l i n g of t h e 45' c r u d e oil u s e d i n t h i s s t u d y is shown i n F i g u r e 1 5 i t is s u b s t a n t i a l . The C 0 2 / 0 I L r a t i o is o n l y a b o u t 7 MSCF/Bbl f o r a n I n i t i a l s a t u r a t i o n of 0.77, b u t i n c r e a s e s to a v a l u e of 15 MSCF/Bbl when t h e i n i t i a l s a t u r a t i o n is d r o p p e d t o 0.29.

Fig. 15. THE SWELLING FACTOR OF A 45°A.P.I.

CRUDE BY CO2

E. The E f f e c t of O i l ComDosition

F o u r d i f f e r e n t " o i l s " were u s e d t o s t u d y t h e e f f e c t of o i l c o m p o s i t i o n : d o d e c a n e , w h i c h is c o m p l e t e l y m i s c i b l e , h e x a d e c a n e w h i c h d i s p l a y s a m i s c i b i l i t y g a p , t h e 4S0A.P.I. c r u d e , a n d a s o l u t i o n o f a 14O A.P.I. c r u d e i n t h e 45O c r u d e . The r e s u l t s a r e shown i n F i g u r e 16. The o v e r a l l recovery is h i g h e s t when carbon d i o x i d e is completely m i s c i b l e w i t h t h e o i l phase, viz., dodecane. However, o n l y a s l i g h t l y lower 0 1 1 r e c o v e r y is a c h i e v e d when h e x a d e c a n e is s u b s t i t u t e d f o r t h e dodecane. T h e r e is i n f a c t v i r t u a l l y no d i f f e r e n c e i n t h e r e c o v e r y of t h e o i l p h a s e , as l o n g as i t s v i s c o s i t y is less t h a n 6 c e n t i p o i s e s , m i s c i b l e o r not, d u r i n g t h e i n j e c t i o n of t h e f i r s t 0.5 p o r e v o l u m e of c a r b o n d i o x i d e . The s l i g h t d i f f e r e n c e s i n r e c o v e r y t h a t d e v e l o p u p o n t h e i n j e c t i o n of more c a r b o n d i o x i d e are perhaps b e s t understood by r e f e r r i n g t o t h e experiment u s i n g a m i x t u r e of 14O and 45O crude o i l s .

278 T h i s m i x t u r e had a v i s c o s i t y of 20 c e n t i p o i s e s and a g r a v i t y of ;'53 i t s r e c o v e r y by c o n t i n u o u s carbon d i o x i d e i n j e c t i o n was n o t i c e a b l y l e s s t h a n t h e r e c o v e r y w i t h t h e o t h e r o i l s w h i c h h a d a v i s c o s i t y of l e s s t h a n 6 centipoises. Exacerbated v i s c o u s f i n g e r i n g , l o w e r s o l u b i l i t y and s w e l l i n g probably a l l c o n t r i b u t e t o t h e l o w e r recovery f o r t h e more v i s c o u s c r u d e . I t is i n f o r m a t i v e t o n o t e , Fig. 17, t h a t most of t h e o i l t h a t is r e c o v e r e d h a s t h e same g r a v i t y a s t h a t of t h e m i x t u r e . O n l y a t t h e t a i l e n d of t h e r e c o v e r y is t h e r e some e v i d e n c e of t h e l i g h t e r f r a c t i o n b e i n g p r e f e r e n t i a l l y r e c o v e r e d . B e c a u s e o f t h e f r a c t i o n a t i o n of t h e s y s t e m i n t o t w o or m o r e phases when t h e c a r b o n d i o x i d e c o n t e n t of t h e s y s t e m exceeds a mol f r a c t i o n of 0.6 t o 0.7, t h e m o b i l e p h a s e c o n t a i n i n g a l a r g e f r a c t i o n of c a r b o n d i o x i d e a n d a s m a l l f r a c t i o n o f t h e l i g h t e n d s of t h e c r u d e o i l i s b e i n g p r e f e r e n t i a l l y produced. A d d i t i o n a l work h a s shown t h a t when a l i v e c r u d e oil i s u s e d , t h e r e s u l t s a r e n o t s i g n i f i c a n t l y d i f f e r e n t f r q m t h o s e t h a t have been d e s c r i b e d f o r t h e dead crude. Although a good p a r t of t h e methane a p p e a r s t o be s t r i p p e d from t h e c r u d e as t h e carbon d i o x i d e d i s s o l v e s i n i t , i t a l s o a p p e a r s t h a t f r a c t i o n a t i o n o c c u r s a t a somewhat l o w e r m o l a r concent r a t i o n of c a r b o n d i o x i d e a n d a more v o l a t i l e oil is p r o d u c e d s o m e w h a t e a r l i e r . However t h e o v e r a l l r e c o v e r y d o e s n o t seem t o b e s u b s t a n t i a l l y a f f e c t e d by t h e p r e s e n c e of moderate amounts of methane i n t h e c r u d e o i l .

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279 F. The E f f e c t of S l u g S i z e The e f f e c t of u s i n g s l u g s of c a r b o n d i o x i d e on t h e recovery of r e s i d u a l c r u d e oil was s t u d i e d , a n d t h e r e s u l t s a r e p r e s e n t e d i n F i g u r e s 18 a n d 19. The 4 5 O c r u d e w a s u s e d i n a l l t h e s e e x p e r i m e n t s , a n d t h e r e s i d u a l o i l s a t u r a t i o n w a s c o n s i s t e n t l y brought down t o 0.21 p.v. b e f o r e i n i t i a t i n g t h e test. I t is i m p o r t a n t t o n o t e i n t h e f o l l o w i n g d i s c u s s i o n , t h a t t h e comparis o n s t h a t w i l l b e made on t h e e f f i c i e n c y of t h e v a r i o u s s l u g s w i l l be f o r a ----l i m i t e d volume of t o t a l f l u i d i n j e c t e d , carbon d i o x i d e o r carbon d i o x i d e and water. F o r o p e r a t i n g c o n d i t i o n s of 1000 p s i . a n d 73OF. t h e oil r e c o v e r y i n c r e a s e s l i n e a r l y w i t h a n i n c r e s e i n s l u g s i z e f r o m 0.11 t o 0.22 p o r e volume f o r a t o t a l i n j e c t i o n of 1.0 t o 1.2 p o r e volumes. However, when t h e s i z e o f t h e s l u g i s i n c r e a s e d a b o v e 0.22 p o r e v o l u m e , a n d t h e t o t a l f l u i d i n j e c t e d i s k e p t c o n s t a n t a t a b o u t one p o r e volume, t h e recovery does n o t i n c r e a s e a n y f u r t h e r . A s a m a t t e r of f a c t , a s l o n g a s t h e t o t a l f l u i d i n j e c t e d is l i m i t e d t o 1.2 P.v., t h e r e c o v e r y a c t u a l l y d e c r e a s e s as t h e s l u g s i z e is i n c r e a s e d above a v a l u e of 0.22.

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2 80 Over t h e range of t e m p e r a t u r e s and p r e s s u r e s i n v e s t i g a t e d i n t h e s t u d y of t h e s l u g s of c a r b o n d i o x i d e , 7 3 O t o 130°F., a n d f r o m 1 0 0 0 p s i t o 1800 psi., t h e optimum s l u g s i z e showed no c o n s i s t e n t change; i t ranged from 0.20 t o 0.26 p o r e volume. I t i s h y p o t h e s i z e d t h a t t h e o p t i m u m s l u g s i z e i s t h a t v o l u m e of c a r b o n d i o x i d e w h i c h c a n b e i n j e c t e d i n t o t h e s y s t e m w i t h o u t e s t a b l i s h i n g a f r e e and c o n t i n u o u s s a t u r a t i o n throughout t h e e n t i r e model. Once such a mobile g a s s a t u r a t i o n is e s t a b l i s h e d , any f u r t h e r i n j e c t i o n of carbon d i o x i d e r e s u l t s i n t h e development of a (dense) gas d r i v e , which is r e l a t i v e l y i n e f f i c i e n t i n d i s p l a c i n g t h e s w o l l e n c r u d e o i l . On t h e o t h e r hand, i f carbon d i o x i d e i n j e c t i o n is h a l t e d b e f o r e a f r e e gas phase s a t u r a t i o n i s e s t a b l i s h e d throughout t h e model, t h e n t h e s w o l l e n crude o i l phase, rendered mobile by t h e i n c r e a s e i n i t s p o r e volume s a t u r a t i o n , w i l l be much more e f f i c i e n t l y d i s p l a c e d by a r e l a t i v e l y v i s c o u s f l u i d , v i z , water. The i n c r e a s e d e f f i c i e n c y of s l u g s o f c a r b o n d i o x i d e i n r e c o v e r i n g r e s i d u a l crude o i l is w e l l i l l u s t r a t e d by t h e r e s u l t s of t h i s work which are p l o t t e d i n F i g u r e 20. Again, i t m u s t be n o t e d t h a t t h e r e s e r v o l r p r o t o t y p e m o d e l l e d i n t h i s work i s o n e w h i c h s h o u l d show up c a r b o n d i o x i d e a t i t s very best. The e f f i c i e n c y of t h e u l t i m a t e d i s p l a c e m e n t c a n be i n c r e a s e d s l i g h t l y i f t h e v i s c o s i t y of t h e c h a s e w a t e r i s i n c r e a s e d by t h e a d d i t i o n of a g l y c o l o r a polymer. I f , f o l l o w i n g t h e i n j e c t i o n of a n optimum s l u g of c a r b o n d i o x i d e , n i t r o g e n is i n j e c t e d ; t h e n t h e r e s u l t i n g r e c o v e r y o f o i l is markedly reduced. The n i t r o g e n i s a n i n e f f i c i e n t d i s p l a c i n g f l u i d ; moreover It s t r i p s some of t h e d i s s o l v e d c a r b o n d i o x i d e f r om s o l u t i o n I n t h e c r u d e o i l , t h e r e b y d e f e a t i n g t h e e n t i r e p r o c e s s , see F i g u r e 21. 4

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r n o r d e r t o g a i n f u r t h e r c o r r o b o r a t i o n f o r t h e h y p o t h e s i s t h a t i t is t h e s w e l l i n g of t h e r e s i d u a l c r u d e o i l is t h e key f a c t o r i n t h e recovery of t h e l a t t e r by t h e i n j e c t i o n of carbon d i o x i d e , a s e a r c h . w a s made f o r o t h e r s u b s t a n c e s t h a t w o u l d d i s s o l v e t o t h e same e x t e n t a n d s w e l l t h e c r u d e o i l e q u i v a l e n t l y : n i t r o u s oxide h a s been d e s c r i b e d t o b e v i r t u a l l y e q u i v a l e n t t o c a r b o n d i o x i d e i n many p h y s i c a l p r o p e r t i e s 1 8 . Experiments proved t h a t n i t r o u s o x i d e performed i n t h e p h y s i c a l models i n a v i r t u a l l y i d e n t i c a l manner t o carbon dioxide. ( I t is a f a r more e x p e n s i v e substance.)

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IV. CONCLUSIONS P h y s i c a l l y s c a l e d m o d e l s t u d i e s of t h e d i s p l a c e m e n t a n d r e c o v e r y of c r u d e O i l by c a r b o n d i o x i d e y i e l d r e s u l t s w h i c h a r e c o n s i s t e n t w i t h t h e r e s u l t s of f i e l d d e m o n s t r t i o n and p i l o t p r o j e c t s . and c o n s i s t e n t w i t h t h e p r i n c i p l e s of f l u i d f l o w and phase behavior. Continuous i n j e c t i o n of c a r b o n d i o x i d e w i l l r e c o v e r a s i g n i f i c a n t f r a c t i o n of a w a t e r f l o o d r e s i d u a l o i l s a t u r a t i o n , b u t t h e r e s u l t i n g carbon d i o x i d e / o i l r a t i o s w i l l b e above 20 MSCF/B, and may b e as high as 30. The u s e of s l u g s of carbon d i o x i d e f o l l o w e d by water w i l l e f f e c t i v e l y reduce t h e r e s u l t i n g carbon d i o x i d e / o i l r a t i o w i t h o u t s e r i o u s l y a f f e c t i n g t h e amount of o i l t h a t can be r e c o v e r e d by t h e i n j e c t i o n of a t o t a l of about o n e p o r e v o l u m e o f f l u i d . A l t h o u g h v a l u e s a p p r o a c h i n g 5 MSCF/B h a v e b e e n a c h i e v e d i n t h e s e model s t u d i e s , i t is c a u t i o n e d t h a t t h e model used was a v e r y f a v o r a b l e one, viz., l o w p e r m e a b i l i t y , uniform and l i n e a r . Even minor h e t e r o g e n e i t y i n a f i e l d o p e r a t i o n w i l l encourage channeling, and t h e d e c r e a s e i n t h e v i s c o u s t o g r a v i t y f o r c e s encountered I n r a d i a l f l o w away from t h e w e l l b o r e s w i l l encourage g r a v i t y s e g r e g a t i o n . The performance of t h e d i s p l a c e m e n t e x p e r i m e n t s l e a d s t o t h e conclusion t h a t t h e mechanism by which carbon d i o x i d e d i s p l a c e s r e s i d u a l crude o i l is comprised of t h r e e s e q u e n t i a l s t e p s : 1) t h e i m m i s c i b l e d i s p l a c e m e n t of t h e o i l - o c c l u d i n g , mobile water, 2) t h e s o l u t i o n of carbon d i o x i d e i n t h e crude o i l and i t s subsequent s w e l l i n g t h a t develops o i l phase m o b i l i t y , and 3) t h e i m m i s c i b l e d i s p l a c e m e n t of t h e mobile s o l u t i o n of carbon d i o x i d e i n o i l by t h e c o n t i n u i n g f l o w of carbon d i o x i d e or water. Although t h e r e s i d u a l s a t u r a t i o n of t h e o i l phase ( a s o l u t i o n of carbon d i o x i d e i n o i l ) c a n b e l o w e r e d by c o n t i n u i n g t h e f l o w of c a r b o n d i o x i d e , r e s u l t i n g i n some c o n t i n u i n g e v a p o r a t i o n o f c r u d e o i l f r a c t i o n s , t h e

282 r e s u l t i n g i n c r e m e n t a l c a r b o n d i o x i d e / p r o d u c e d o i l r a t i o s w i l l b e v e r y high. The more p r a c t i c a l l i m i t t o t h e r e c o v e r y i s r e a c h e d when t h e r e s i d u a l s a t u r a t i o n of t h e low v i s c o s i t y o i l p h a s e t o t h e s u b s e q u e n t g a s o r water d r i v e i s approached. N i t r o u s o x i d e , which d i s s o l v e s i n a n d swells c r u d e o i l s s i m i l a r l y , i s as e f f e c t i v e as c a r b o n d i o x i d e i n r e c o v e r i n g c r u d e o i l . The s u b s t i t u t i o n of n i t r o g e n f o r water as a c h a s e f l u i d i n j u r e s t h e r e c o v e r y b e c a u s e t h e g a s i s n o t as good a d i s p l a c i n g a g e n t f o r t h e s w o l l e n c r u d e . The complex p h a s e b e h a v i o r of c a r b o n d i o x i d e w i t h c r u d e o i l a p p e a r s t o c o n t r i b u t e l i t t l e t o t h e r e c o v e r y p r o c e s s ; t h e e f f e c t of t h e f r a c t i o n a t i o n of t h e c r u d e i n t h e p r e s e n c e o f c a r b o n d i o x i d e r e s u l t s i n s o m e s l i g h t a d d i t i o n a l r e c o v e r y a t t h e t a i l e n d of t h e f l o o d . S l i m t u b e e x p e r i m e n t s s i n c e t h e y do n o t c o r r e c t l y model t h e d i s p e r s i o n c o e f f i c i e n t s a n d t h e r e l a t i o n s b e t w e e n g r a v i t y a n d v i s c o u s f o r c e s do n o t provide adequate i n s i g h t i n t o a r e s e r v o i r recovery process. The s o - c a l l e d minimum m i s c i b i l i t y p r e s s u r e a s i n t e r p r e t e d f r o m s u c h e x p e r i m e n t s i s a c t u a l l y t h e p r e s s u r e above w h i c h no s i g n i f i c a n t i n c r e a s e i n r e c o v e r y w i l l b e achieved. The r e c o v e r y mechanism is s t i l l e f f e c t i v e a t l o w e r p r e s s u r e s . ACKNOWLEDGEMENTS The work on t h i s p r o j e c t w a s s u p p o r t e d by t h e U n i t e d S t a t e s Department o f E n e r g y , G a r y E n e r g y Co., a n d e n d o w m e n t f u n d s a t t h e U n i v e r s i t y o f Southern C a l i f o r n i a .

REFERENCES

1. Beeson, D. M., a n d O r t l o f f , C.D., '!Laboratory I n v e s t i g a t i o n of t h e WaterD r i v e n Carbon D i o x i d e P r o c e s s f o r O i l Recovery", TRANS AIME (1959) 216, 38891 2. Holm, Law., "Carbon D i o x i d e f o r S o l v e n t F l o o d i n g f o r I n c r e a s e d O i l Recovery", TRANS AIME (1959) 216, 225-231 3. R a t h m e l l , J.J., S t a l k u p , F.I., a n d H a s s i n g e r , R.C., "A L a b o r a t o r y I n v e s t i g a t i o n o f M i s c i b l e D i s p l a c e m e n t b y C02", SPE 3 4 8 3 , 4 6 t h A n n u a l Meeting of SPE of AIME (1971) 4. Holm, L.W., and J o s e n d a h l , V.A., "Mechanism of O i l D i s p l a c e m e n t by Carbon Dioxide", JPT ( 1 9 7 4 ) , 1417-1438. 5. D u n n y s h k i n , I.I., a n d N a m o i t , A., " S t u d y o f C o n d i t i o n s o f P e t r o l e u m M i s c i b i l i t y w i t h Carbon Dioxide", N e f t . Khoz., ( 1 9 7 8 ) , v. 3, 59-61 6. N a t i o n a l P e t r o l e u m C o u n c i l , "Enhanced O i l Recovery An A n a l y s i s of t h e P o t e n t i a l f o r Enhanced O i l Recovery f r o m Known F i e l d s i n t h e U n i t e d S t a t e s 1976 t o 2000, Washington, D.C., (1976) 7. Y e l l i g , W.F. a n d M e t c a l f e , R.S., " D e t e r m i n a t i o n a n d P r e d i c t i o n o f C O P Minimum M i s c i b i l i t y P r e s s u r e " , JPT, ( 1 9 8 0 ) , 160-168. 8. G a r d n e r , J.W., Orr, P.M., a n d P a t e l , P.D., "The E f f e c t of P h a s e B e h a v i o r on CO2 Flood D i s p l a c e m e n t E f f i c i e n c y " , SPE 8367, 5 4 t h Annual M e e t i n g of SPE of AIME, L a s Vegas, (1979) 9. E l A r a b i , M., PbD. D i s s e r t a t i o n , U n i v e r s i t y of S o u t h e r n C a l i f o r n i a , J u n e 1981. 10. O f f e r i n g a , J., a n d v a n d e r P o e l , C., " D i s p l a c e m e n t o f O i l F r o m P o r o u s Media by M i s c i b l e L i q u i d s " , TRANS AIME (1954) 201, 310-317 11. W a r n e r , H. R., Jr., "An E v a l u a t i o n o f W i s c i b l e C02 F l o o d i n g i n W a t e r f l o o d e d S a n d s t o n e R e s e r v o i r s " , JPT, (1979), 1339-1347

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283 12. C l a r i d g e , E.L., " D i s c u s s i o n of t h e Use of C a p i l l a r y T u b e N e t w o r k s i n R e s e r v o i r Peformance S t u d i e s " , SPEJ ( 1 9 7 2 ) , 352-61 13. G l a s s t o n e , S., T e x t Book of P h y s i c a l C h e m i s t r y , p. 713, D. Van Nostrand, New York, 1940. 14. D o s c h e r , T. a n d G h a r i b , S., " P h y s i c a l l y S c a l e d M o d e l s S i m u l a t i n g t h e D i s p l a c e m e n t of R e s d i u a l Oil by M i s c i b l e CO2 i n L i n e a r Geometry", SPE 8896. 5 0 t h Annual C a l i f o r n i a R e g i o n a l M e e t i n g of SPE of AIME (1980) 1 5 , K a n e , A.V., " P e r f o r m a n c e Review o f a L a r g e S c a l e C a r b o n Dioxide-WAG P r o j e c t , SACROC U n i t - K e l l y S n i d e r F i e l d , SPE 7 0 9 1 , SPE I m p r o v e d O i l F i e l d Recovery Symposium, T u l s a 1978 16. G r u y F e d e r a l , Inc., " T a r g e t R e s e r v o i r s f o r C O P M i s c i b l e F l o o d i n g " , U.S.Department of Energy, Washington, D.C., (1980) 17. K a m a t h , K.I., C o m b e r i a t i , J.R., a n d Z a m m e r i l l i , A.M., "The R o l e of R e s e r v o i r T e m p e r a t u r e i n Carbon D i o x i d e F l o o d i n g " , P a p e r N4, p r e s e n t e d a t t h e U.S.Department of Energy Symposium, T u l s a , Oklahoma 1979 18. G e r r a r d , W., S o l u b i l i t y of Gases a n d L i q u i d s , A G r a p h i c A n a l y s i s , Plenum P r e s s , N e w Y o r k ( 1 9 7 6 ) . S e e a l s o , H i l d e b r a n d , J.H., a n d S c o t t , R.L., T h e S o l u b i l i t y of N o n - E l e c t r o l y t e s , R e i n h o l d , New York (1950).

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MISCIBLE GAS DISPLACEMENT

285

LABORATORY TESTING PROCEDURES FOR MISCIBLE FLOODS S. G. SAYEGH and F. G. McCAFFERY*

Petroleum Recovery Institute, Chlgury.Alberta, Gnuah T2L 2A6

ABSTRACT

The o b j e c t i v e of t h i s paper is t o provide a s t a t e - o f - t h e - a r t review and c r i t i q u e of l a b o r a t o r y t e s t i n g procedures f o r m i s c i b l e f l o o d i n g f o r r e s e a r c h e r s irr t h e f i e l d . An a d d i t i o n a l a i m of t h e paper is t o give r e s e r v o i r and production e n g i n e e r s i n s i g h t i n t o t h o s e procedures, 80 t h a t they may a p p r e c i a t e t h e i r p o t e n t i a l s and l i m i t a t i o n s , and be b e t t e r a b l e t o e v a l u a t e l a b o r a t o r y results i n l i g h t of t h e i r f i e l d experience. The t o p i c s t r e a t e d include s i n g l e - and multiple-contact phase behavior and p h y s i c a l p r o p e r t i e s measurements, and involve slim-tube and c o r e displacement t e s t s . General o b j e c t i v e s f o r each type of test are l i s t e d , recommended p r a c t i c e s are o u t l i n e d , and many examples from t h e l i t e r a t u r e are referenced. I n a d d i t i o n , g e n e r a l s c r e e n i n g criteria are presented f o r the s e l e c t i o n of s u i t a b l e candidate r e s e r v o i r s f o r m i s c i b l e flooding.

IXTRODUCTIOY One of t h e p r i n c i p a l enhanced recovery methods c u r r e n t l y under consideration f o r l i g h t o i l r e s e r v o i r s is miscible f l o o d i n g w i t h carbon dioxide and/or hydrocarbon s o l v e n t s . The process is complex and involves many parameters t h a t have t o be optimized so t h a t a flood can l e a d t o a t e c h n i c a l and economic success. Some of t h e f a c t o r s that have t o be s t u d i e d are t h e reservoir geology, o i l and o i l - s o l v e n t phase behavior, o i l solvent displacement characteristics, waterflood performance, as w e l l as r e s e r v o i r engineering a s p e c t s such as s o l v e n t production and o i l i n j e c t i o n s t r a t e g i e s , expected performance under b o t h water and solvent f l o o d i n g , apd economics. In t h i s paper, l a b o r a t o r y t e s t i n g procedures f o r m i s c i b l e flooding w i l l be d i s c u s s e d . These w i l l i n c l u d e t h e measurement of t h e phase behavior and d i s placenent d a t a of r e s e r v o i r crude o i l - s o l v e n t systems, and how such d a t a may be used in e v a l u a t i n g t h e s u i t a b i l i t y of a solvent flood f o r a p a r t i c u l a r a p p l i c a t i o n . The o b j e c t i v e of t h i s paper is t o provide a state-of-the-art review and c r i t i q u e f o r r e s e a r c h e r s i n the f i e l d . An a d d i t i o n a l aim of t h e paper is t o g i v e r e s e r v o i r and production engineers i n s i g h t i n t o l a b o r a t o r y t e s t i n g procedures SO that they may a p p r e c i a t e t h e i r p o t e n t i a l s and l i m i t a t i o n s and t h u s be b e t t e r a b l e t o e v a l u a t e l a b o r a t o r y results i n l i g h t of t h e i r f i e l d experience. For o t h e r

*

P r e s e n t address:

Occidental Research Cozporation, I r v i n e , C a l i f . 92713, U.S .A.

286 ze.:irvs of t h e E i s c i b l e f l o o d i n g process and i t s f i e l d a p p l i c a t i o n s , the reader is r s f e r r e d t o t h e works by Holm’, Stalkup2, Dosher e t a1.3, and M~ngan‘’~.

Burnett and DamC have reviewed s c r e e n i n g tests f o r a v a r i e t y of enhanced o i l recover:* p r o c e s s e s , PROCESS DESCRIPTION AND GENERAL SCREENING CRITERIA I n a m i s c i b l e f l o o d t h e s o l v e n t c o n t a c t s t h e o i l and a mixing zone is formed. I n t h e mixing zone, t h e r e is a gradual change in composition from o i l t o s o l v e n t , w i t h o u t a n i n t e r f a c e . For economic r e a s o n s , t h e s o l v e n t i s u s u a l l y n o t i n j e c t e d c o n t i n u o u s l y , b u t o f t e n i n the form of a s l u g t y p i c a l l y about 20-30% o f t h e hydrocarbon pore volume (HCPV). The s l u g is t h e n followed by a chase f l u i d , u s u a l l y water o r l e a n gas, t o d r i v e i t through t h e r e s e r v o i r towards t h e production w e l l s . The s l u g may be i n j e c t e d i n small p o r t i o n s a l t e r n a t i n g w i t h water, c o m n l y c a l l e d t h e water-alternating-gas (WAG) process. A l t e r n a t i v e l y , w a t e r may be co-injected w i t h t h e s o l v e n t . These latter i n j e c t i o n modes h e l p c o n t r o l t h e h i g h m o b i l i t y of t h e s o l v e n t . I t i s r a r e l y t e c h n i c a l l y or economically f e a s i b l e t o i n j e c t a s o l v e n t that i s d i r e c t l y m i s c i b l e w i t h t h e o i l . I n s t e a d , m i s c i b i l i t y is g e n e r a l l y achieved through what are known a s t h e m l t i p l e - c o n t a c t m i s c i b i l i t y (MCM) mechanisms7-13. Two such mechanisms can occur when gaseous or s u p e r c r i t i c a l s o l v e n t s a r e used: a condensation mechanism and a v a p o r i z a t i o n mechanism. When s u b c r i t i c a l s o l v e n t s a r e used a t p r e s s u r e s above t h e i r bubble p o i n t , t h e p r o c e s s is one of l i q u i d l i q u il e x t r a c t ion1 ’ 1 5 .

The high o i l recovery i n m i s c i b l e f l o o d s i s a t t r i b u t e d t o t h e following factors:

- high microscopic displacement - o i l e x t r a c t i o n by s o l v e n t - l o r i n t e r f a c i a l tension - o i l swelling - o i l viscosity reduction - blowdown recovery

efficiency

The s o l v e n t s used (C02 and hydrocarbons) are g e n e r a l l y less dense and v i s c o u s t h a n the o i l s . This c a u s e s t h e s o l v e n t t o o v e r r i d e t h e o i l and f i n g e r through i t . These are a d v e r s e f a c t o r s i n h o r i z o n t a l f l o o d s and lead t o e a r l y s o l v e n t breakthrough, poor sweep e f f i c i e n c y , and low o i l recovery. I n g e n e r a l , a good c a n d i d a t e r e s e r v o i r f o r h o r i z o n t a l m i s c i b l e f l o o d i n g should have t h e f o l l o v i n g characteristics:

- t h i n pay zone, up t o 5 m - good h o r i z o n t a l c o n t i n u i t y - r e l a t i v e l y homogeneous - low v e r t i c a l - t o - h o r i z o n t a l p e r m e a b i l i t y - Zot f r a c t u r e d - contains undersaturated o i l - c o n t a i n s no f r e e g a s s a t u r a t i o n - c o n t a i n s no mobile water

ratio

?ins s o l v e n t should be chosen such that i t :

- achieves m i s c i b i l i t y w i t h - is cheap - is readily available

t h e o i l a t r e s e r v o i r conditions

287 For v e r t i c a l downward displacements, t h e requirements a r e somewhat l e s s constraining:

- the - the

r e s e r v o i r should not c o n t a i n p e r m e a b i l i t y b a r r i e r s t o v e r t i c a l flow displacement should be c a r r i e d o u t a t a s u i t a b l e r a t e such that t h e flood is g r a v i t y s t a b l e

PHASE BEHAVIOR MEASUREMENTS Phase behavior measurements are c a r r i e d o u t f o r s e v e r a l purposes:

- to - to - to

c h a r a c t e r i z e t h e o i l - s o l v e n t system determine t h e mechanism by which m i s c i b i l i t y is achieved f i n e - t u n e t h e phase behavior packages i n compositional s i r m l a t o r s

I n g e n e r a l , t h e phase behavior s t u d i e s i n v o l v e t h e f o l l o w i n g measurements:

- solubilities - m u l t i p l e phase - densities - o i l swelling - viscosities

formation, i n c l u d i n g both l i q u i d and s o l i d phases

Phase Behavior Measurement Equipment High p r e s s u r e phase e q u i l i b r i u m experimental techniques f o r a v a r i e t y of a p p l i c a t i o n s have r e c e n t l y been reviewed by Eubank e t a1.16 Apparatuses used i n connection w i t h C02 and hydrocarbon systems were described by o t h e r , r e s e a r c h e r s . 17-26 A connuon t y p e o f a p p a r a t u s c o n s i s t s o f a windowed c e l l whose volume may be manipulated by means of a p i s t o n o r mercury from a p o s i t i v e displacement pump. The c e l l i s placed i n a t h e n m s t a t e d oven f o r temperature c o n t r o l . The d e s i r e d components of t h e mixture are loaded i n t o t h e cell and t h e n mixed. Mixing is u s u a l l y done w i t h a magnetically-coupled stirrer, by rocking t h e c e l l , o r by c i r c u l a t i n g t h e f l u i d s . Once e q u i l i b r i u m has been reached, v i s u a l o b s e r v a t i o n s of t h e c o e x i s t i n g phases may be c a r r i e d o u t . Samples of t h e s e phases may a l s o be withdrawn f o r d e n s i t y and v i s c o s i t y measurements, and f o r compositional a n a l y s e s . Constant composition expansions may a l s o be c a r r i e d o u t t o determine bubble and dew p o i n t s , and volumetric p r o p o r t i o n s of c o e x i s t i n g phases as f u n c t i o n s of p r e s s u r e .

The a p p a r a t u s d e s c r i b e d by LeeP3 and Sayegh e t a1.26 has two interconnected This g i v e s a greater f l e x i b i l i t y of o p e r a t i o n and p e r m i t s t h e measurement of v i s c o s i t y w i t h o u t using a s e p a r a t e viscometer. D. Robinson (personal communication) a t t h e U n i v e r s i t y of A l b e r t a has t h e c e l l constructed e n t i r e l y from sapphire. This p e r m i t s unhindered v i s u a l o b s e r v a t i o n o f t h e e n t i r e cont e n t s of the c e l l . The a p p a r a t u s e s of Orr e t a l . 2 4 , of Connor and Pope25, and of D. Robinson have t h e i r sampling l i n e s d i r e c t l y connected t o gas chromatographs f o r analysis. The a p p a r a t u s described by Orr e t a l . 2 4 d i f f e r s from t h e o t h e r s i n t h a t i t resembles a continuously s t i r r e d t a n k r e a c t o r .

cells.

288 Phase Behavior T e s t s t o C h a r a c t e r i z e t h e Crude O i l Typical t e s t s f o r t h e c h a r a c t e r i z a t i o n of t h e crude o i l involve t h e measurement of i t s composition, molecular weight, d e n s i t y , v i s c o s i t y , compressib i l i t y , bubble p o i n t , formation volume f a c t o r , g a s - o i l r a t i o , d i s t i l l a t i o n curve, d i f f e r e n t i a l l i b e r a t i o n , c o n s t a n t volume d e p l e t i o n , and c o n s t a n t composition expansion charac t e r i s tics. These tests are g e n e r a l l y c a r r i e d o u t a t r e s e r v o i r temperature using, f o r example, ASTM s t a n d a r d procedures and are p r e f e r a b l y c a r r i e d o u t w i t h bottomh o l e samples. T e s t i n g of o i l p r o p e r t i e s should b e p e r i o d i c a l l y repeated d u r i n g t h e production l i f e t i m e o f a r e s e r v o i r , and be c a r r i e d o u t on samples from t h e d i f f e r e n t producing zones o r horizons o f a pool t o determine i f t h e r e are any v a r i a t i o n s i n o i l p r o p e r t i e s . This is e s p e c i a l l y Important where t h e r e s e r v o i r p r e s s u r e f a l l s below t h e o r i g i n a l bubble p o i n t o f t h e o i l . Standingl’l and Henry e t a1.28 presented d e s c r i p t i o n s of bottomhole sampling procedures. I n g e n e r a l , t h e sampling w e l l should be s e l e c t e d so that i t is r e p r e s e n t a t i v e o f t h e average r e s e r v o i r c o n d i t i o n s . The w e l l should be produced a t a slow r a t e d u r i n g sampling t o minimize p r e s s u r e drawdown e f f e c t s and t h e r e s u l t a n t phase changes. Also, s u f f i c i e n t sampling time should be allowed t o ensure t h a t t h e sample bomb i s f i l l e d w i t h f r e s h oil. Large volumes of r e s e r v o i r f l u i d s a r e necessary t o c a r r y o u t a complete l a b o r a t o r y study of a m i s c i b l e flood. Thus, i t i s unreasonable t o u s e bottomhole samples f o r a l l t h e s e tests. The normal procedure i s t o t a k e l a r g e samples of s e p a r a t o r o i l and gas, then recombine them t o n a t c h t h e p r o p e r t i e s o f t h e bottomhole sample. 25

Phase Behavior Tests t o C h a r a c t e r i z e t h e Crude Oil-Solvent System The g e n e r a l phase behavior of hydrocarbon f l u i d s have been w e l l re~ i e w e d . ~ ”Data ~ ~ f o r hydrocarbon f l o o d s o f r e s e r v o i r crudes were presented by s e v e r a l author^^'^'^^'^^, w h i l e most of t h e r e c e n t l y published s t u d i e s have d e a l t with t h e phase behavior o f C02-011 systems.ll p12’14p18’23’24’26p30-38 This r e f l e c t s t h e growing i n t e r e s t i n u s i n g C02 as a m i s c i b l e f l o o d i n g a g e n t . The following d i s c u s s i o n w i l l c o n c e n t r a t e on C02-reservoir crude o i l systems s i n c e t h e s e are o f most i n t e r e s t t o t h e i n d u s t r y . The phase diagrams of C02crude o i l s stems a r e o f t e n presented i n t h e form o f t e r n a r y phase d i a g r a n s . 9 p 1 2 y Y 4 y 2 4Such a r e p r e s e n t a t i o n provides a convenient form f o r t h e v i s u a l i z a t i o n of t h e com o s i t i o n a l p a t h d u r i n g a c o n s t a n t temperature and p r e s s u r e d i s lacementl 11g7 and f o r determining t h e mechanism of a c h i e v i n g m i s c i b i l i t y . % It should, however, b e remembered t h a t t h e t e r n a r y r e p r e s e n t a t i o n is n o t thermodynamically r i g o r o u s and hence should n o t be i n t e r p r e t e d l i t e r a l l y . Nore a c c u r a t e p r e d i c t i o n s of t h e displacement p a t h may be made u s i n g a q u a t e r n a r y diagram. ’ A second type o f test is t h e c o n s t a n t c o n p o s i t i o n e ~ p a n s i o n . ~ ’ ~ ~ ’ ~ ~ ’ ~ ~ T n i s provides information on t h e phase b e t a v i o r of t h e C02-011 s y s t e m i n t h e v a r i o u s l o c a t i o n s of t h e r e s e r v o i r where t h e p r e s s u r e may vary. For example, a t c o c i i t i o n s where m l t i p l e l i q u i d phases appear. t h e s l u g could break down, while asp;laltene p r e c i p i t a t i o n could leqd t o a r e d u c t i o n i n r e s e r v o i r permeability.

289 The d e n s i t y , s w e l l i n g f a c t o r , and v i s c o s i t y of t h e C02-saturated 0 i 1 1 8 ’ 2 6 ’ 3 1 a r e u s u a l l y measured i n g a r a l l e l w i t h t h e phase-envelope measurements d e s c r i b e d above. Connor and Pope2 r e c e n t l y p r e s e n t e d such d a t a f o r h y d r o c a r b o n - o i l systems. I n g e n e r a l , as t h e p r e s s u r e i n c r e a s e s , more s o l v e n t g a s d i s s o l v e s i n t o t h e o i l c a u s i n g i t t o swell and t h u s t o reduce i t s d e n s i t y and v i s c o s i t y . Carbon d i o x i d e i s g e n e r a l l y more e f f e c t i v e i n t h i s r e g a r d t h a n hydrocarbon s o l v e n t g a s e s . j 6 A t v e r y h i g h p r e s s u r e s , t h e d e n s i t y and v i s c o s i t y curves could s t a r t i n c r e a s i n g because the e f f e c t o f p r e s s u r e on t h e f l u i d p r o p e r t i e s predominates o v e r t h e e f f e c t o f s o l v e n t d i s s o l u t i o n . Phase Behavior T e s t s t o Determine t h e Mechanism o f M u l t i p l e Contact M i s c i b i l i t y The tests mentioned p r e v i o u s l y are a l l s t a t i c , s i n g l e - c o n t a c t tests. The tests d e s c r i b e d i n t h i s s e c t i o n are designed t o s i m u l a t e t h e dynamic, m u l t i p l e c o n t a c t p r o c e s s o c c u r r i n g i n a r e s e r v o i r between t h e i n j e c t e d s o l v e n t and the r e s e r v o i r crude o i l . These tests are c a r r i e d o u t i n a c o n t r o l l e d manner i n a PVT c e l l , t h u s t h e p r o c e s s p a r a m e t e r s a r e w e l l d e f i n e d . The f i r s t t y p e o f t e s t is t h e g e n e r a t i o n o f a Benham p l o t by a stagewise approximation o f t h e continuous m u l t i p l e - c o n t a c t process.’ 2’ 9’ 24’2 5 ’ 39 I n t h i s procedure, a c e r t a i n p r o p o r t i o n o f o i l and s o l v e n t are mixed i n a PVT c e l l and allowed t o reach e q u i l i b r i u m . The p r o p o r t i o n s and p r o p e r t i e s o f t h e r e s u l t a n t vapor and l i q u i d a r e t h e n measured. I f a condensation p r o c e s s o c c u r s , t h e vapor phase is t h e n purged and a f r e s h b a t c h o f s o l v e n t is i n t r o d u c e d i n t o t h e c e l l . On t h e o t h e r hand, t h e l i q u i d phase i s purged i f , based on changes i n phase volume, a v a p o r i z a t i o n p r o c e s s is involved, and a f r e s h b a t c h o f o i l is i n t r o duced i n t o t h e c e l l . The e n t i r e p r o c e s s i s r e p e a t e d u n t i l o n l y one phase appears i n t h e c e l l , a t which p o i n t MCM h a s been a t t a i n e d .

’

The drawback o f t h i s method is t h a t i t is a s t a g e w i s e p r o c e s s , which o n l y approximates t h e continuous c o n t a c t s i n a r e s e r v o i r . As such, i t i s i m p l i c i t l y assumed t h a t t h e o i l and s o l v e n t i n t h e r e s e r v o i r have enough time t o reach e q u i l i b r i u m . T h i s is probably a r e a s o n a b l e assumption i n many cases s i n c e r e s e r v o i r flow rates a r e q u i t e low, b u t i f s e v e r e c h a n n e l l i n g , f i n g e r i n g , o r g r a v i t y s e g r e g a t i o n o c c u r i n t h e r e s e r v o i r , t r u e e q u i l i b r i u m may n o t be a t t a i n e d and t h e p r e d i c t i o n w i l l be o p t i m i s t i c . Another problem a s s o c i a t e d w i t h d e s i g n i n g t h i s t y p e o f batchwise experiment is t h e c h o i c e o f v o l u m e t r i c r a t i o s o f gas-to-liquid c o n t a c t e d i n each s t e p . R e s e n r o i r parameters such as t h e m o b i l i t i e s o f t h e h a s e s and flow rates should be taken i n t o account t o determine a realistic ratio. 39 The procedure d e s c r i b e d by O r r et a1.24 i s a v a r i a t i o n o f t h e above method i n t h a t t h e n u l t i p l e c o n t a c t s are c a r r i e d o u t c o n t i n u o u s l y . I n such a n e x p e r i ment, t h e rate o f s o l v e n t i n j e c t i o n i n t o t h e c e l l would have t o be c a r e f u l l y s e l e c t e d t o o b t a i n meaningful r e s u l t s .

LABORATORY DISPLACEMENT TESTS Laboratory displacement tests p r o v i d e i m p o r t a n t i n f o r m a t i o n on t h e behavior of r e s e r v o i r f l u i d / s o l v e n t systems under dynamic displacement c o n d i t i o n s . These tests a r e o f two t y p e s : slim-tube and c o r e d i s p l a c e m e n t s . It i s important t o c a r r y o u t b o t h t y p e s o f tests i n a l a b o r a t o r y s t u d y s i n c e each one p r o v i d e s d i f f e r e n t i n f o r m a t i o n n e c e s s a r y f o r t h e e v a l u a t i o n o f a f i e l d a p p l i c a t i o n . Each t y p e of t e s t w i l l now be d i s c u s s e d i n f u r t h e r d e t a i l .

Slim-Tube Displacement Tests Slim-tube displacement tests are l a b o r a t o r y tests that are c a r r i e d o u t i n a n i d e a l i z e d porous medium. As such, t h e y may be thought of a s b e i n g a n i n t e r mediate approximation t o r e s e r v o i r f l o o d s , l y i n g between t h e wre r e a l i s t i c c o r e f l o o d s and t h e more i d e a l i s t i c m u l t i p l e - c o n t a c t PVT c e l l tests. A s l i m tube t est is c a r r i e d o u t p r i m a r i l y t o determine i f a s o l v e n t a c h i e v e s m i s c i b i l i t y w i t h a n o i l a t a c e r t a i n temperature and p r e s s u r e . A l a b o r a t o r y i n v e s t i g a t i o n i n v o l v i n g a series o f r u n s ' c o u l d be done w i t h e i t h e r o r b o t h o f t h e f o l l o w i n g objectives :

- minimum m i s c i b i l i t y - solvent screening

p r e s s u r e (ME')d e t e r m i n a t i o n

Orr et al.24 have made a summary o f slim-tube displacement a p p a r a t u s e s used by v a r i o u s i n v e s t i g a t o r s . The s l i m t u b e is normally c o n s t r u c t e d from h o r i z o n t a l l y c o i l e d s t a i n l e s s steel t u b i n g . The t u b e i s 10-20 m l o n g , about 5 mu i n t e r n a l d i a m e t e r , and packed w i t h f i n e g l a s s beads o r s a n d s t o a p o r o s i t y o f about 30% and t o a p e r m e a b i l i t y of 3-15 urn2. The c o i l is f i r s t s a t u r a t e d w i t h o i l , t h e n flooded w i t h C O P . The e f f l u e n t from t h e slim-tube p a s s e s through a s i g h t g l a s s f o r visual o b s e r v a t i o n , i s sampled f o r a n a l y s i s , and is t h e n f l a s h e d t o a t m s p h e r i c p r e s s u r e through a b a c k p r e s s u r e r e g u l a t o r . Produced l i q u i d and gas phases are metered s e p a r a t e l y . The d a t a o b t a i n e d from t h e test i n c l u d e e f f l u e n t c o l o r , number o f p h a s e s , composition and g a s - o i l r a t i o , a s w e l l a s o i l recovery and p r e s s u r e drop a c r o s s t h e coil--each as a f u n c t i o n o f t h e volume o f solvent injected. The b a s i c assumption i n slim-tube tests i s that t h e displacement i s p i s t o n l i k e and t h a t l i t t l e o r no f i n g e r i n g o c c u r s . - T h i s i s due i n p a r t to t h e uniformi t y o f t h e packing and t h e dampening e f f e c t o f t h e t u b e ' s w a l l s . Accordingly, t h e c r i t e r i a f o r m i s c i b i l i t y b e i n g achieved i n a carbon d i o x i d e f l o o d a r e :

- no appearance o f -

-

a methane bank p r i o r t o . breakthrough l a t e s o l v e n t b r e a k t h r o u g h ( a t around 0.8 pore volumes o f s o l v e n t i n j e c t e d , or later) a s m o t h t r a n s i t i o n from o i l t o s o l v e n t i n t h e mixing zone w i t h o u t t h e a m e a r a n c e of a n i n t e r f a c e h i g h u l t i m a t e recovery ( g r e a t e r t h a n 95% o f t h e o r i g i n a l o i l - i n - p l a c e , . OOIP)

..

On t h e o t h e r hand, a n i m i s c i b l e displacement is c h a r a c t e r i z e d by:

- t h e appearance of a methane bank p r i o r t o s o l v e n t breakthrough - e a r l y breakthrough - t h e o b s e r v a t i o n o f a n i n t e r f a c e between t h e o i l - r i c h and s o l v e n t - r i c h p h a s e s i n t h e mixing zone - low u l t i m a t e r e c o v e r y A l l o f t h e above-noted symptoms o f a n immiscible displacement should appear i f t h e p r e s s u r e is w e l l below t h e MEip. This a l s o depends t o some e x t e n t on t h e c h a r a c t e r i s t i c s o f t h e s l i m t u b e i t s e l f ( t u b e d i a m e t e r , u n i f o r m i t y of bead s i z e and packing). I t would be i n s t r u c t i v e t o c a r r y o u t two i n i t i a l d i s p l a c e m e n t s t o c h a r a c t e r i z e t h e p a r t i c u l a r s l i m tube b e i n g used. The f i r s t f l o o d could be conducted under d e f i n i t e l y immiscible c o n d i t i o n s u s i n g n i t r o g e n , f o r example, a s t h e f l o o d i n g a g e n t , w h i l e t h e second f l o o d would i n v o l v e f i r s t - c o n t a c t m i s c i b l e c o n d i t i o n s u s i n g benzene, f o r example, as the d i s p l a c i n g a g e n t . For f u r t h e r d i s c u s s i o n s , t h e r e a d e r is r e f e r r e d t o o t h e r p u b l i s h e d works.24' 31'40'41 y 4 2

291 A v a r i e t y of s l i m t u b e l e n g t h s have been used by v a r i o u s researcher^.^^ I t would appear t h a t m u l t i p l e - c o n t a c t m i s c i b i l i t y i s achieved f a i r l y e a r l y i n t h e l i f e of t h e displacement ( w i t h i n t h e f i r s t two m e t e r s ) , o t h e r w i s e a high o i l recovery would not be o b t a i n e d . This is supported by t h e lower number of c o n t a c t s (about 1 0 ) r e q u i r e d i n PVT c e l l , m u l t i p l e - c o n t a c t experiments12’19’25 although, as mentioned p r e v i o u s l y , such experiments are open t o i n t e r p r e t a t i o n . On t h e o t h e r hand, Y e l l i g 1 5 concluded t h a t l o n g e r l e n g t h s (2.5 5 m) were required t o develop m i s c i b i l i t y when carbon d i o x i d e was i n the l i q u i d form. Thus, a s l i m tube l e n g t h between 10-20 1 is recommended. The r a t e a t which slim-tube d i s placements are r u n a f f e c t s t h e s t a b i l i t y o f t h e displacement f r o n t and t h e time allowed f o r c o n t a c t between t h e o i l and s o l v e n t . For t h i s reason, displacement rates are b e s t kept a t less t h a n 1 0 m/day. The u s e o f r e l a t i v e l y low rates a l s o minimizes t h e p r e s s u r e drop a c r o s s t h e slim tube, which provides f o r good d e f i n i t i o n o f t h e minimum m i s c i b i l i t y p r e s s u r e .

-

Benham e t a1.8 have presented c o r r e l a t i o n s f o r t h e minimum enrichment of d r y gas (by LPG) r e q u i r e d t o a c h i e v e m i s c i b i l i t y , w h i l e Jacobson43 s t u d i e d t h e c o n t r i b u t i o n o f a c i d g a s e s t o m i s c i b i l i t y . Other r e s e a r c h e r s 1 O S 3 l ’40’41 ’42’44 have i n v e s t i g a t e d t h e e f f e c t of t h e d i f f e r e n t p r o c e s s v a r i a b l e s on t h e carbon d i o x i d e MMP. I n g e n e r a l , t h e ME’ i n c r e a s e s w i t h d e c r e a s i n g o i l g r a v i t y and i t s C5 t o C30 c o n t e n t , and w i t h i n c r e a s i n g temperature and molecular weight of t h e o i l C5+ f r a c t i o n . Hydrogen s u l f i d e and LPG i n t h e carbon d i o x i d e decrease t h e I W , w h i l e n i t r o g e n and methane i n c r e a s e i t . I n a d d i t i o n t o studying dynamic m i s c i b i l i t y c o n d i t i o n s , t h e r e s u l t s of slim-tube experiments may be used t o c a l i b r a t e compositional s i m u l a t o r s . 39’45’46 Wang and L ~ c h ei n ~ v e~s t i g a t e d t h e r e l a t i v e e f f i c i e n c y of d i f f e r e n t watera l t e r n a t i n g - g a s c y c l e s and concluded t h a t t h e t o t a l o i l recovery w a s i n s i g n i f i c a n t l y a f f e c t e d by t h e i n j e c t i o n sequence provided t h a t t h e t o t a l amount of carbon d i o x i d e i n j e c t e d remained t h e same. I n summary, slim-tube displacement tests are an extremely u s e f u l t o o l f o r studying t h e m i s c i b i l i t y r e l a t i o n s h i p between o i l and s o l v e n t systems under c o n t r o l l e d dynamic c o n d i t i o n s . Caution must be e x e r c i s e d when t r a n s p o s i n g t h e r e s u l t s of such s t u d i e s t o r e s e r v o i r systems s i n c e t h e e f f e c t s of t h e r e s e r v o i r rock p r o p e r t i e s (homogeneity, r e l a t i v e p e r m e a b i l i t y , w e t t a b i l i t y , and pore geometry) have n o t been t a k e n i n t o account, hence displacement tests on r e s e r v o i r rocks must follow. The following s e c t i o n d e a l s w i t h c o r e displacement tests i n a n attempt t o provide more d e t a i l e d i n s i g h t i n t o t h e displacement behavior as i t may occur i n t h e r e s e r v o i r i n r e g i o n s contacted by t h e s o l v e n t . Core Displacement Tests Following slim-tube displacement t e s t s t o confirm t h e establishment of m i s c i b i l i t y w i t h t h e o i l f o r a given s o l v e n t a t a p p r o p r i a t e r e s e r v o i r c o n d i t i o n s of temperature and p r e s s u r e , c o r e f l o o d i n g measurements are g e n e r a l l y recommended. Such tests c a n be used t o e v a l u a t e a v a r i e t y of displacement phenomena t h a t have b e a r i n g o n t h e m i s c i b l e f l o o d i n g process. These i n c l u d e .

- recovery mechanisms9’1 9 - d i f f u s i o n and d i s p e r s i o n c o e f f i c i e n t s , and dead-end pore volume^^^-^^ - m i s c i b l e and compositional s i m u l a t o r tuning48’ 6 4 - chromatographic s e p a r a t i o n of components1 ’48 - water, o i l , and gas r e l a t i v e p e r r n e a b i l i t i e ~ ~ ” ~ ~ - r o c k i n t e r a c t i o n s w i t h gas and b r i n e - dynamic o i l - s o l v e n t phase behavior 5 8 - e f f e c t of t h e following f a c t o r s on displacement e f f i c i e n c y o r o i l recovery:

292

.. rsoocl vk e n t type’ 4’60

. water s a t u r a t i o n (secondary o r t e r t i a r y f l o o d i n g mode)59’60’63rC5 . phase behavior ( m u l t i l e l i q u i d and s o l i d phases)32 .. displacement p r e s s u r e ” ’’ solvent injection ratel5’6’

. water-solvent f l o o d i n g mode ( c o n t i n u o u s s o l v e n t i n j e c t i o n , s o l v e n t s l u g s i z e WAG, c o i n j e c t i o n , C02-foam and C02-polymer i n j e c t i o n ) b 2 ’ 6 3 . blowdown . low i n t e r f a c i a l

tension66

A c o r e d i s p l a c e m e n t a p p a r a t u s c o n s i s t s of a c o r e h o l d e r i n which t h e c o r e is placed under a c o n f i n i n g p r e s s u r e . The c o r e is connected t o r e s e r v o i r o i l and b r i n e , i n j e c t i o n water, and s o l v e n t c o n t a i n e r s . The. c o r e i s flooded a t r e s e r v o i r t e m p e r a t u r e and p r e s s u r e w i t h t h e s e f l u i d s i n t h e p r o p e r sequence, and t h e f l u i d p r o d u c t i o n and p r e s s u r e d r o p s are monitored. V i s u a l o b s e r v a t i o n o f t h e c o r e ’ s e f f l u e n t s c a n b e made through a s i g h t g l a s s .

It is recommended that c o r e from t h e a c t u a l r e s e r v o i r be used i n t h e d i s placement tests. Although o u t c r o p c o r e s may a l s o be used f o r c e r t a i n m e c h a n i s t i c s t u d i e s . The s e l e c t i o n of r e s e r v o i r c o r e s f o r t h e s e tests is a n important procedure which r e q u i r e s a n u n d e r s t a n d i n g o f t h e geology o f t h e e n t i r e r e s e r v o i r . The c o r e s should be sampled from t h e pay zone of i n t e r e s t and chosen t o p r o p e r l y r e p r e s e n t t h e main r o c k t y p e s o c c u r r i n g i n t h e r e s e r v o i r . Cores w i t h l a r g e h e t e r o g e n e i t i e s s u c h as f r a c t u t e s , vugs, and l a m i n a t i o n s would tend t o g i v e r e s u l t s that e x a g g e r a t e t h e e f f e c t s o f t h e h e t e r ~ g e n e i t i e s . ~S~t u d i e s of Rosman and Simon66, and Eatycky e t a1.67 have, however, shown t h a t t h e h e t e r o g e n e i t y e x h i b i t e d by i n d i v i d u a l c o r e segments d e c r e a s e s when t h e segments are b u t t e d t o g e t h e r t o form a l o n g e r c o r e assembly.

F u l l d i a m e t e r , v e r t i c a l c o r e s may be used f o r e v a l u a t i n g v e r t i c a l f l o o d s w h i l e , f o r h o r i z o n t a l f l o o d s , h o r i z o n t a l p l u g s have t o be d r i l l e d o u t of t h e f u l l d i a m e t e r c o r e . These p l u g s a r e t y p i c a l l y 2-3 cm i n d i a m e t e r and 6-10 cm long. About 20 p l u g s should be b u t t e d t o g e t h e r i n a c o r e h o l d e r t o g i v e a s u f f i c i e n t l y l o n g assembly f o r t h e d i s p l a c e m e n t t e s t , p a r t i c u l a r l y i f t h e development o f m u l t i p l e c o n t a c t m i s c i b i l i t y i s i n v o l v e d . To a c h i e v e good c a p i l l a r y c o n t a c t between t h e c o r e s , t h e c o r e f a c e s c a n be machined s q u a r e on a l a t h e , and t h e r e is t h e o p t i o n o f p l a c i n g f i l t e r paper between t h e c o r e f a c e s p r i o r .to mounting them i n a tiraxial c o r e h o l d e r . It i s recommended t h a t t h e plugs b e chosen s u c h that t h e y come from t h e same f a c i e s i n t h e r e s e r v o i r , and t h a t t h e y have similar and r e p r e s e n t a t i v e p o r o s i t y - p e r m e a b i l i t y c h a r a c t e r i s t i c s Combining p l u g s from d i f f e r e n t f a c i e s and w i t h w i d e l y v a r y i n g p r o p e r t i e s makes t h e i n t e r p r e t a t i o n of t h e d i s p l a c e m e n t r e s u l t s d i f f i c u l t and o f q u e s t i o n a b l e v a l u e a s i n p u t d a t a f o r s i m u l a t o r p r e d i c t i o n s of f i e l d performance. The c o r e s a v a i l a b l e f o r t e s t i n g may b e i n t h e preserved state o r , more l i k e l y , are i n a n aged c o n d i t i o n . I f p r e s e r v e d , t h e c o r e s can be used d i r e c t l y i n t h e displacement experiments. Non-preserved c o r e needs t o be cleaned thoroughly by e x t r a c t i o n or displacement w i t h s o l v e n t s such a s toluene-methano166, mounted d r y i n a c o r e h o l d e r , and t h e n have i t s w e t t a b i l i t y and i n i t i a : o i l s a t u r a t i o n r e - e s t a b l i s h e d by c o n t a c t w i t h t h e r e s e r v o i r f l u i d s . A t y p i c a l t e s t procedure u t i l i z e d w i t h c l e a n e d , non-preserved c o r e i n v o l v e s e v a c u a t i n g , s a t u r a t i n g w i t h r e s e r v o i r lsrine, and t h e n f l o o d i n g w i t h c r u d e o i l u n t i l t h e water s a t u r a t i o n approaches t h e connate water s a t u r a t i o n . I f t h i s procedure cannot p r o v i d e a s u f f i c i e n t l y low i n i t i a l water s a t u r a t i o n , t h e n methods u t i l i z i n g gas flow a n d / o r e v a p o r a t i o n c a n be Following placement of crude o i l i n t h e c o r e , i t is l e f t t o a g e f o r s e v e r a l d a y s f o r t h e purpose of

293 re-establishing t h e o r i g i n a l ~ e t t a b i l i t y ~A ~ f.t e r a g i n g , t h e c o r e is waterflooded w i t h i n j e c t i o n water down t o r e s i d u a l o i l s a t u r a t i o n . The w a t e r - o i l r e l a t i v e p e r m e a b i l i t y may be c a l c u l a t e d from t h e p r e s s u r e drop and production h i s t o r y o f t h e waterflood. F i n a l l y , t h e core i s s o l v e n t flooded. I f t h e s o l vent f l o o d is t o be a secondary one, t h e waterflood s t e p is then n a t u r a l l y omitted

.

The d i s t i n c t advantages of u s i n g non-preserved c o r e are its ease of handling d u r i n g t h e d r i l l i n g of p l u g s , and t h e a b i l i t y t o examine t h e cores and measure t h e i r p r o p e r t i e s (such as a i r p e r m e a b i l i t y and p o r o s i t y ) p r i o r t o t h e f l o o d tests. The disadvantage of u s i n g aged c o r e i s t h a t one is seldom s u r e of t h e adequacy o f t h e measures t a k e n t o r e s t o r e t h e c o r e t o its o r i g i n a l state. A prime r e a s o n f o r a t t e m p t i n g t o r e s t o r e t h e r e s e r v o i r w e t t i n g c o n d i t i o n i n t h e c o r e relates t o t h e r e p o r t e d t r a p p i n g o r s h i e l d i n g o f o i l by mobile water i n water-wet It is g e n e r a l l y b e l i e v e d that mixed o r i n t e r m e d i a t e l y w e t systems provide optimum t e r t i a r y recovery e f f i c i e n c i e s w i t h s o l v e n t floods. RECAPITULATION

The f i r s t s t e p i n t h e implementation of a f i e l d - s c a l e m i s c i b l e flood is t h e s e l e c t i o n o f s u i t a b l e c a n d i d a t e r e s e r v o i r s and s o l v e n t s . A set of t e c h n i c a l s c r e e n i n g criteria has been provided t o a i d i n t h e s e l e c t i o n . These should be augmented by o t h e r l i m i t a t i o n s and/or i n c e n t i v e s (e.g. economic) s p e c i f i c t o each locale. Once t h e p r e l i m i n a r y s e l e c t i o n has been made, l a b o r a t o r y tests can be c a r r i e d o u t t o reduce t h e t e c h n i c a l and economic u n c e r t a i n t i e s a s s o c i a t e d with f i e l d tests. The l a b o r a t o r y t e s t s should be supplemented w i t h g e o l o g i c a l ( r e s e r v o i r d e s c r i p t i o n ) and computer s i m u l a t i o n studies'. Laboratory t e s t s have been c a t e g o r i z e d i n t o s t a t i c and dynamic measurements, and d i f f e r e n t t y p e s of tests that may be c a r r i e d o u t under each category have been l i s t e d . S t a t i c phase behavior tests e n a b l e t h e measurement o f t h e p r o p e r t i e s of t h e o i l , s o l v e n t , and t h e i r m i x t u r e s under c o n t r o l l e d c o n d i t i o n s . Slim tube tests determine t h e dynamic m i s c i b i l i t y c h a r a c t e r i s t i c s of t h e o i l - s o l v e n t system. F i n a l l y , c o r e displacement tests h e l p determine t h e e f f e c t of t h e process c o n d i t i o n s and rock p r o p e r t i e s o n t h e displacement e f f i c i e n c y i n t h e swept zone of the reservoir. ACKNOIJLEDQ4ENI'S The a u t h o r s wish t o e x p r e s s t h e i r thanks t o P.M. Sigmund f o r c o n s u l t a t i o n s , and t o B. Moore f o r . t y p i n g t h e manuscript. REFERENCES 1.

HOLM, L.W.; "Status of C02 and Hydrocarbon Miscible O i l Recovery Methods", J . P e t . Tech. (January 1976) 76.

2.

STALKUP, F.I.; "Carbon Dioxide Miscible Flooding. P a s t , P r e s e n t and Outlook f o r t h e Future", J. P e t . Tech. (August 1978) 1102.

3.

DOSCHER, T.. e t a l ; "Carbon Dioxide f o r t h e Recovery of Crude O i l . A L i t e r a t u r e Search t o June 30, 1979 F i n a l Report", U.S. Dept. of Energy P u b l i c a t i o n No. DOE/BETC/5785-1 (1980).

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294 4.

INNGAN, N.; "Carbon D i o x i d e Flooding - Fundamentals", P e t . SOC. o f C I M paper no. 80-31-04, p r e s e n t e d a t 3 1 s t Annual T e c h n i c a l Meeting o f t h e P e t . SOC. of CIM, C a l g a r y , A l b e r t a (May 25-28, 1980).

5.

MNGAN, N.; "Carbon Dioxide Flooding A p p l i c a t i o n s " , P e t . SOC. o f CIM paper no. 81-31-22, p r e s e n t e d a t 31st Annual T e c h n i c a l Meeting o f t h e P e t . SOC. o f CIM, C a l g a r y , A l b e r t a (May 25-28, 1980).

6.

"Screening T e s t s f o r Enhanced O i l Recovery BURNETT, D.B. and DANN, 'M.W.; P r o j e c t s " , paper SPE 9710, p r e s e n t e d a t t h e 1981 Permian B a s i n O i l and Gas Recovery Symposium o f t h e SOC. o f P e t . Eng. o f AIME, Midland, Texas (March 12-13, 1981).

7.

HUTCHINSON, J R . , C.A. and BRAUN, P.H.; "Phase R e l a t i o n s of M i s c i b l e Displacement i n O i l Recovery", A.1.Ch.E. J. (1961), 7 (l), 64.

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BENHAM, A.L., DOWDEN, W.E., and KUNZMAN, W.J.; *'Miscible Flood Displacement P r e d i c t i o n o f M i s c i b i l i t y " , Trans. AIME (1960) 219, 229.

9.

"A L a b o r a t o r y I n v e s t i FATIWELL, J.J., STALKUP, F.I., and HASSINGER, R.C.; g a t i o n o f M i s c i b l e Displacement by Carbon Dioxide", paper SPE 3483, prepared f o r 4 6 t h Annual F a l l Meeting o f t h e SOC. o f P e t . Eng. o f A I I E , New O r l e a n s , L o u i s i a n a (October 3-6, 1971).

10.

-

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HOLM, L.W. and JOSENDAL, V.A.; " E f f e c t o f O i l Composition o n Miscible-Type Displacement by Carbon Dioxide", paper SPE 8814, p r e s e n t e d a t t h e F i r s t J o i n t SPE/DOE Symp. on Enhanced O i l Recovery, T u l s a , Oklahoma ( A p r i l 20-23, 1980),

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51.

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58.

HENRY, R.L. and METCALFE, R.S.; " M u l t i p l e Phase Generation During C02 Flooding", paper SPE 8812, p r e s e n t e d a t t h e F i r s t J o i n t SPE/DOE Symposium o n Enhanced O i l Recovery, T u l s a , Oklahoma ( A p r i l 20-23, 1980).

59.

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61.

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RANDALL, T.E., WANSLEEBEN, J . and SIGMUND, P.M.; " P h y s i c a l Model, West Wilmar R i c h Gas P i l o t " , P e t . Soc. of C M p a p e r no. 51-32-16, p r e s e n t e d a t t h e 32nd Annual T e c h n i c a l Meeting of t h e P e t . Soc. of CIM, Calgary, A l b e r t a (May 3-6, 1981).

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ROSMAN, A. and ZANA, E.; "Experimental S t u d i e s o f Low I n Displacement by C02 I n j e c t i o n " ; p a p e r SPE 6723, p r e s e n t e d a t t h e 52nd Annual F a l l T e c h n i c a l Conference and E x h i b i t i o n o f t h e Soc. of P e t . Eng. gf AIME, Denver, Colorado (October 9-12, 1977).

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BATYCKY, J.P., M I R K I N , M . I . , JACKSON, C.H., and BESSERER, G.J.; "Miscible and Immiscible Displacement S t u d i e s on Carbonate R e s e r v o i r Cores", J. Can. P e t . Tech. (1981) 20 (l), 104.

68.

"The Dependence of Water GRIST, D.M., LANGLEY, G.O., and NEUSTADTER, E.L.; P e r m e a b i l i t y on Core C l e a n i n g Methods i n t h e Case of Some Sandstone Samples", J. C a n P e t . Tech. (April-June 1975) 48.

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CUIEC, L., LONGERON, D . and PACSIXSZKY, J.; "On t h e N e c e s s i t y o f R e s p e c t i n g R e s e r v o i r C o n d i t i o n s i n L a b o r a t o r y Displacement S t u d i e s " , paper SPE 7785, p r e s e n t e d a t t h e Middle E a s t O i l T e c h n i c a l Conference of t h e Soc. of P e t . E n g . , Manama, Bahrain (March 25-29, 1979).

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HARVEY, JR., M.T., SHELTOM, J.L., a n d KELM, C.H.; "Field I n j e c t i v i t y Experiences With M i s c i b l e Recovery P r o j e c t s Using A l t e r n a t e Rich-Gas and Water I n j e c t i o n " , J. P e t . Tech., (September 1977) 1051.

299

MISCIBLE GAS DISPLACEMENT

COMPLEX STUDY OF COZ FJBODING IN HUNGARY

SANDOR DOLESCHALL, GABOR ACS, &VA FARKAS, TIBOR PAAL, JANOS TOROK Hungarian Hydrocarbon Institute

V A L ~ RBALINT General Contractingand Designing Office for the Oil Industry, “Olajterv”

ZOLTAN B I R ~ lhznsdanubian Oil and Gas Roduction Company

ABSTRACT A systematic program o f carbonated n a t u r a l gas f l o o d i n g has been c a r r i e d o u t i n Hungary, based on l a b o r a t o r y PVT and displacement studies, followed by composit i o n a l mathematical s i m u l a t i o n and. f i e l d experiment on depleted r e s e r v o i r . PVT s t u d i e s have proved t h a t gas c o n t a i n i n g 81 mole % carbon d i o x i d e can be used f o r EOR purposes. The s t u d i e s covered t h e v o l u m e t r i c and phase behaviour o f carbonated n a t u r a l gas f l o o d i n g under f i e l d c o n d i t i o n s and t h e r e s u l t s proved t h a t such f l o o d i n g was e f f i c i e n t even i f t h e gas i s n o t pure carbon dioxide. Based upon t h e o r e t i c a l c o n s i d e r a t i o n s a t e c h n o l o g i c a l scheme has been developed t o increase t h e sweep e f f i c i e n c y . A ten-component, three-phase mathematical model developed t o simulate carbon d i o x i d e f l o o d i n g i s s u i t a b l e f o r t r e a t i n g s i n g l e - and multi-phase systems. The d i f f e r e n c e equations handle t h e systems w i t h d i f f e r e n t number o f phases I n a u n i f o r m way, t h u s t h e generation and disappaerance o f phases can be followed by t h e model w i t h o u t d i f f i c u l t i e s . The computer model was used t o simulate p a r t i a l l y m i s c i b l e carbonated n a t u r a l gas f l o o d i n g i n t h e western area o f t h e Budafa o i l f i e l d . The production h i s t o r y match and p r e d i c t i o n agreed w e l l w i t h t h e f i e l d data.

INTRODUCTION The o i l resources o f Hungarian r e s e r v o i r s cover o n l y a small p a r t o f t h e country’s demand, and t h e import of crude o i l imposes a considerable economic burden on a c o u n t r y developing i t s i n d u s t r y . Apart from t h e n e e d - t o search f o r new o i l f i e l d s , it became e v i d e n t as long ago as t h e f i f t i e s t h a t it was important t o consider secondary and l a t e r t h e t e r t i a r y recovery methods. Among t h e o t h e r p o s s i b i l i t i e s t h e e f f e c t o f carbon d i o x i d e was a l s o studied, and

300 very soon most a t t e n t i o n focused on t h e questions o f C02 f l o o d i n g because i n Hungary t h e occurrence o f n a t u r a l carbon d i o x i d e i n h i g h carbon d i o x i d e content n a t u r a l gases i s more o f t e n found and t o a g r e a t e r e x t e n t than t h e world average. Some r e s u l t s o f C02 f l o o d i n g i n Hungary can be found i n Ref. 1 .

PVT AND PHASE BEHAVIOUR MEASUREMENTS F e a s i b i l i t y s t u d i e s o f t h e a p p l i c a t i o n p o s s i b i l i t i e s o f carbon d i o x i d e and carbonated n a t u r a l gases s t a r t e d i n 1955 w i t h a s e r i e s o f PVT measurements. The very f i r s t PVT s t u d i e s proved t h a t carbonated n a t u r a l gas a l t e r s t h e v i s c o s i t i e s and v o l u m e t r i c p r o p e r t i e s o f crudes w i t h very d i f f e r e n t d e n s i t i e s i n a favourable way compared w i t h t h e e f f e c t o f lean o r wet n a t u r a l gases under t h e same c o n d i t i o n s , mainly i f t h e carbon d i o x i d e c o n t e n t o f t h e d i s s o l v e d gas i s above 60 mole 5 . Based upon t h e r e s u l t s o f more d e t a i l e d PVT measurement, s e t s o f curves have been developed t o p r e d i c t t h e s o l u b i l i t y , s w e l l i n g and v i s c o s i t y o f monophase r e s e r v o i r oil--carbonated n a t u r a l gas systems. The a c t u a l PVT p r o p e r t i e s o f t h e o r i g i n a l gas saturated o i l were chosen as a reference s t a t e t o e l i m i n a t e t h e p o s s i b l e l a r g e e r r o r s coming from t h e unknown parameters o f such very complex systems, and o n l y t h e change o f t h e given p r o p e r t i e s was c o r r e l a t e d w i t h t h e d i s s o l v e d carbon d i o x i d e cont e n t . I n t h i s way simple, easy t o use equations w i t h good accuracy have been developed. For example, t h e p r e d i c t i o n o f v i s c o s i t i e s o f saturated and undersaturated crudes under d i f f e r e n t c o n d i t i o n s i s p o s s i b l e w i t h t h e use o f o n l y one measured v i s c o s i t y value.

I t has been proved t h a t i n t h e case o f Hungarian crude o i l s , bearing i n mind t h e a c t u a l r e s e r v o i r conditions, t h a t no complete m i s c i b i l i t y occurs even i f . t h e d i s s o l v e d gas i s pure carbon d i o x i d e . I n t h e course o f t h e thorough examination o f t h e PVT data "unusual" behaviour was observed. Repeated measurements i n a windowed PVT c e l l revealed t h e presence o f a carbon d i o x i d e r i c h second l i q u i d phase which e x i s t s w i t h i n a d e f i n i t e pressure-temperature range above a c e r t a i n gas--oil r a t i o . T h i s r e g i o n depends upon t h e t o t a l composition o f t h e system and t h e phenomenon i s connected w i t h t h e r e s t r i c t e d s o l u b i l i t y o f carbon d i o x i d e i n r e s e r v o i r o i l s . P a r t i t i o n o f l i g h t and intermediate hydrocarbons between t h e r e s e r v o i r o i l and t h e second l i q u i d phase has been proven i n agreement w i t h o t h e r experience. I n t h e case o f c e r t a i n Hungarian crude o i l s r e v e r s i b l e p r e c i p i t a t i o n o f semi-solid p a r t i c l e s has a l s o been observed b u t mostly under such circumstances which cannot be r e a l i z e d i n a c t u a l r e s e r v o i r s . I t i s i n t e r e s t i n g t h a t these phenomena occur i n t h e presence o f carbonated n a t u r a l gases, too, even i f they a r e r e l a t i v e l y r i c h I n l i g h t hydrocarbon f r a c t i o n . The existence o f t h e mentioned multiphase systems had t o be considered i n planning vapour--liquid e q u i l i b r i u m studies.

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The aim o f these s t u d i e s i s t o determine exact K values according t o t h e need o f compositional mathematical s i m u l a t i o n . E q u i l i b r i u m r a t i o s had been d e t e r mined f o r c h a r a c t e r i s t i c r e s e r v o i r oil--carbonated n a t u r a l gas as w e l l as r e s e r v o i r oil--water--carbonated n a t u r a l gas systems and a method f o r e s t i mation was developed. As a r e s u l t o f a d d i t i o n a l measurements and comparison of experimental w i t h computed data u s i n g d i f f e r e n t equations o f s t a t e i t i s concluded t h a t f u r t h e r improvements a r e necessary both f o r t h e development o f generalized K f u n c t i o n s and equations o f s t a t e t o g e t h e r w i t h t h e improvement o f interaction coefficients.

30 1 Judging by t h e r e s u l t s o f o t h e r studies, t h e i n t e r f a c i a l t e n s i o n decreases w i t h i n c r e a s i n g carbon d i o x i d e c o n t e n t i n gas--oil--water systems. Volumetric and phase behaviour as well as water c o n t e n t and hydrate forming c o n d i t i o n s o f carbonated n a t u r a l gases i n Hungary were a l s o s t u d i e d and t h e r e s u l t i n g data used t o formulate generalized r e l a t i o n s h i p s . Experimental data on s o l u b i l i t y , s w e l l i n g and v i s c o s i t y o f t y p i c a l r e s e r v o i r waters - s a t u r a t e d w i t h carbonated n a t u r a l gases having d i f f e r e n t composition, even i n t h e presence o f calcium carbonate and r e s e r v o i r rocks c o n t a i n i n g c l a y minerals t o g e t h e r w i t h vapour--liquid e q u i l i b r i u m r a t i o s supplied f u r t h e r i n f o r m a t i o n e n a b l i n g a b e t t e r understanding o f t h e mechanism o f carbonated n a t u r a l gas f l o o d i n g . I t has been pointed o u t t h a t because o f t h e i n t e r a c t i o n o f carbonated water and r e s e r v o i r rocks c e r t a i n c l a y m i n e r a l s c o n t r a c t and t h i s may improve t h e e f f i c i e n c y o f t h e process i n p r a c t i c e .

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A PVT model was used t o f o l l o w t h e change o f t h e v o l u m e t r i c and phase behaviour and t h e e q u i l i b r i u m composition o f phases i n t h e course o f f l o o d i n g . T h i s model contained water-, o i l - and gas-phases under r e s e r v o i r c o n d i t i o n s w i t h a r a t i o corresponding t o t h e a c t u a l s a t u r a t i o n a t a given, depleted f i e l d . The pressure was increased t o t h e o r i g i n a l r e s e r v o i r pressure d i r e c t l y by t h e i n j e c t i o n gas. I n another s e t o f experiments t h e f i n a l pressure was reached step by step, t h e vapour phase g r a d u a l l y being changed by t h e i n j e c t i o n gas a t each i n t e r mediate pressure u n t i l e q u i l i b r i u m composition was approached. These experiments were repeated f o r d i f f e r e n t f i e l d c o n d i t i o n s u s i n g i n j e c t i o n gases w i t h d i f f e r e n t carbon d i o x i d e content. I n t e r p r e t a t i o n o f t h e r e s u l t s revealed t h e Importance o f t h e dynamic pressure-increase process being a p p l i e d f o r carbonated n a t u r a l gas f l o o d i n g , t h e r o l e o f t h e l i g h t hydrocarbon f r a c t i o n present and supported t h e conclusion p r e v i o u s l y drawn on t h e b a s i s o f PVT s t u d i e s o f mono-and two-phase systems.

Taking i n t o c o n s i d e r a t i o n t h e composition o f t h e g r a d u a l l y displaced gas, i t has been concluded t h a t it i s n o t p o s s i b l e i n p r a c t i c e t o replace a l l t h e f r e e and d i s s o l v e d gas by a carbon d i o x i d e s l u g o f reasonable s i z e . I t has a l s o been found t h a t d e s p i t e t h e d i l u t i o n o f t h e s l u g by hydrocarbon gas i n t h e pores, r e l a t i v e l y s i g n i f i c a n t v a p o r i z a t i o n o f t h e o i l takes place i f t h e carbon d i o x i d e c o n t e n t o f t h e f r e e gas phase i s above a c e r t a i n c r i t i c a l concentration. T h i s c r i t i c a l value, which depends upon t h e pressure, temperature and t h e c h a r a c t e r i s t i c s o f t h e o i l , can a l s o be exceeded by using carbonated n a t u r a l gases f o r t h e i n j e c t i o n . These observations confirmed i n d i r e c t l y t h e idea about t h e probable formation o f a m i s c i b l e f r o n t i n t h e r e s e r v o i r under dynamic c o n d i t i o n s d u r i n g carbonated n a t u r a l gas f l o o d i n g . As t o t h e v o l u m e t r i c p r o p e r t i e s and v i s c o s i t i e s o f t h e e q u i l i b r i u m l i q u i d phases no s u b s t a n t i a l d i f f e r e n c e c o u l d be found on comparing t h e e f f e c t o f a carbon d i o x i d e s l u g and a l a r g e r volume o f carbonated n a t u r a l gas w i t h higher carbon d i o x i d e content.

LABORATORY DISPLACEMENT STUDIES F o l l o w i n g encouraging PVT r e s u l t s dynamical l a b o r a t o r y s t u d i e s were c a r r i e d o u t displacement processes. The l i n e a r model t o examine t h e e f f i c i e n c y o f C02 used f o r t h e measurements was 1 m long and 25 mm i n diameter. Nonconsolidated r e s e r v o i r sandstone cores and r e s e r v o i r f l u i d were used f o r these displacement t e s t s . T h i s technique i s s u i t a b l e f o r s t u d y i n g p r o d u c t i o n h i s t o r i e s , as well as f l o o d i n g and t h e a c t u a l mechanism o f t h e process. v a r i o u s forms o f C02

302 As a f i r s t s t e p t h e e f f e c t o f carbonated w a t e r was examined. Carbonated water s a t u r a t e d a t r e s e r v o i r p r e s s u r e and t e m p e r a t u r e was i n j e c t e d i n t o t h e p r e v i o u s l y water f l o o d e d c o r e . Carbon d i o x i d e appeared i n t h e e f f l u e n t a f t e r i n j e c t i n g one p o r e volume o f s a t u r a t e d w a t e r . To reach t h e i n j e c t e d e q u i l i b r i u m c o n c e n t r a t i o n o f t h e carbonated water i n t h e e f f l u e n t 4-8 p o r e volumes o f s a t u r a t e d water were necessary. Consequently, t h e a d d i t i o n a l o i l was produced w i t h a r a t h e r h i g h water c u t . The a d d i t i o n a l o i l was 5-7 % o f t h e o r i g i n a l o i l an p l a c e . Because o f t h e i n j e c t i o n o f a l a r g e volume o f w a t e r and t h e modest a d d i t i o n a l o i l recovery, t h i s method i s uneconomic. To i n c r e a s e t h e amount o f i n j e c t e d carbon d i o x i d e , o v e r s a t u r a t e d water was used i n t h e n e x t s e r i e s o f experiments. The a d d i t i o n a l o i l reached 10 % o f 0 . i . p . and f a v o u r a b l e e f f e c t s o f f r e e gas s a t u r a t i o n were observed, t o o . However even i n t h i s case, 3-5 p o r e volumes o f carbonated w a t e r were used t o obtain t h i s result. Gaseous carbon d i o x i d e was i n j e c t e d i n t o t h e model when s t u d y i n g t e r t i a r y r e c o v e r y methods f o r d e p l e t e d r e s e r v o i r s . Two d i f f e r e n t i n i t i a l s a t u r a t i o n c o n d i t i o n s were used as average r e s e r v o i r c o n d i t i o n s f o r m o d e l l i n g p r o d u c t i o n his t o r i e s : - t h e d e p l e t e d r e s e r v o i r has a h i g h gas s a t u r a t i o n , -25-35 %; - t h e d e p l e t e d r e s e r v o i r has a low gas s a t u r a t i o n and h i g h w a t e r s a t u r a t i o n , -50-60 $. The p r e s s u r e was increased t o t h e o r i g i n a l r e s e r v o i r p r e s s u r e by i n j e c t i n g carbon d i o x i d e gas. A f t e r t h e p r e s s u r e b u i l d - u p , d i f f e r e n t s i z e s o f C02 s l u g s were i n j e c t e d and f o l l o w e d by r e s e r v o i r w a t e r f l o o d i n g . The a d d i t i o n a l o i l r e c o v e r y a s a f u n c t i o n o f s l u g s i z e was s t u d i e d . The p r o b a b l e o p t i m a l s l u g s i z e was about 0.2 PV. Using t h i s , t h e a d d i t i o n a l o i l r e c o v e r y was 12-16 % o f t h e o r i g i n a l o i l i n p l a c e f o r systems h a v i n g a h i g h i n i t i a l gas s a t u r a t i o n and 8-12 % f o r t h e case o f h i g h i n i t i a l w a t e r s a t u r a t i o n . The a d d i t i o n a l o i l r e c o v e r y was always r e l a t e d t o t h e r e s i d u a l o i l s a t u r a t i o n o f t r a d i t i o n a l water f l o o d i n g . A l l o f t h e dynamic displacement t e s t s , mentioned above were performed w i t h p r a c t i c a l l y p u r e carbon d i o x i d e . T e s t s were conducted u s i n g carbonated n a t u r a l gases, t o o . The r e s u l t s showed t h a t t h e use o f c a r b o r a t e d n a t u r a l gases h a v i n g a CO c o n t e n t above 80 mole $, g i v e n o t worse, b u t b e t t e r r e s u l t s i n most 2 cases i f t h e p r o p e r d i s p l a c e m e n t t e c h n o l o g y i s used. Complex f l o w c o n d i t i o n s and physico-chemical processes e x i s t i n r e s e r v o i r o i l - - r e s e r v o i r water--carbon d i o x i d e - - r e s e r v o i r r o c k systems. The parameters i n f l u e n c i n g t h e e f f e c t i v e n e s s o f C02 f l o o d i n g must be i n d i v i d u a l l y determined f o r each p r o j e c t . I f t h e w e t t a b i l i t y o f r e s e r v o i r r o c k changes f r o m water-wet t o o i l - w e t t h e f a v o u r a b l e e f f e c t s o f f r e e gas s a t u r a t i o n and t h e l a t e r w a t e r f l o o d i n g a r e reduced. T h i s change of w e t t a b i l i t y depends upon many f a c t o r s among o t h e r s , on t h e q u a n t i t y o f i n j e c t e d C02 ( 2 ) . I f carbon d i o x i d e i s i n j e c t e d i n t o t h e d e p l e t e d o i l r e s e r v o i r i t i n t e r a c t s w i t h t h e r e s e r v o i r f l u i d and component mass t r a n s f e r s t a r t s among t h e phases. As a r e s u l t o f t h i s process t h e o i l phase w i l l be r i c h e r i n components h a v i n g h i g h e r m o l e c u l a r w e i g h t s . I n extreme cases some o f t h e components w i t h i n t e r f a c i a l a c t i v e c h a r a c t e r i s t i c s may adsorb on t h e r o c k s u r f a c e , t h e r e b y changing t h e w e t t a b i l i t y p r o p e r t i e s o f t h e system and l e a d i n g t o t h e r o c k becoming more o i l - w e t . A l t h o u g h t h e carbon d i o x i d e c o n t e n t o f t h e o i l phase decreases t h e v i s c o s i t y o f c r u d e r i c h i n h i g h m o l e c u l a r components and s w e l l s t h e o i l - p h a s e a possible increase i n the o i l - w e t character counteracts these favourable e f f e c t .

303 R e l a t i v e p e r m e a b i l i t y curves f o r saturated carbonated water systems were a l s o measured. The c h a r a c t e r o f r e l a t i v e p e r m e a b i l i t y curves j u s t i f i e d t h e e f f e c t mentioned above. Under some circumstances t h e porous medium became more o i l - w e t . Decreasing o i l and i n c r e a s i n g water p e r m e a b i l i t i e s c o u l d be observed i n c e r t a i n s a t u r a t i o n ranges, depending upon t h e CO content o f t h e gas used. The increase 2 i n r e s i d u a l o i l s a t u r a t i o n was a l s o observed w i t h i n c r e a s i n g C02 content. The bases o f comparison were t h e r e l a t i v e curves o f hydrocarbon gas saturated s y s terns.

COMPUTER MODEL A three-phase, ten-component mathematical model has been developed t o study carbon d i o x i d e displacement experiments and t o p r e d i c t performances (3, P a r t I . ) . The governing d i f f e r e n t i a l equations o f t h e compositional model w r i t t e n i n a usual form a r e as f o l l o w s :

=

div

[5 2 j

kjfj

Aj

C. (grad p j Jti

+

$9 grad z)

+

@zSjSjDj,igrad

C

j

+

9i

i = l,Z,

...,I0

j = gas, o i l ,

water

The b a s i s o f t h e c a l c u l a t i o n s i s t h e assumption t h a t local thermodynamic e q u i l i b r i u m e x i s t s d u r i n g displacement. I n t h i s way, t h e r e l a t i o n s h i p s c o r r e l a t e d w i t h l a b o r a t o r y PVT and e q u i l i b r i u m measurements can d i r e c t l y be employed. I n accordance w i t h t h e l a b o r a t o r y measurements, t h e formation f l u i d o f Budafa o i l f i e l d was considered as a ten-component system. The components a r e : seven hydrocarbon components /C,, C2, C3, C4, C5, C6, C /, nitrogen, carbon d i x i d e 7+ and water. As t h e water phase e x i s t s everywhere i n t h e formation, and d u r i n g t h e water

i n j e c t i o n a g r e a t amount of carbon d i o x i d e i s t o be transported by water, t h e s o l u t i o n o f t h e carbon d i o x i d e component i n t h e water phase cannot be neglected. Besides three-phase regions, two-, moreover one-phase regions occur d u r i n g t h e processes, thus a method has been developed t h a t a l l o w s one t o e a s i l y c a l c u l a t e a change i n t h e number o f phases. The three-phase e q u i l i b r i u m was i n t e r p r e t e d as t h e simultaneous existence o f two two-phase e q u i l i b r i u m s . To s i m p l i f y t h e e q u i l i b r i u m c a l c u l a t i o n s t h e f o l l o w i n g assumptions were made: - t h e gas and o i l phases do n o t c o n t a i n a water component, - t h e d i s s o l v e d gas i n t h e water phase c o n s i s t s o f carbon d i o x i d e o n l y . /When checking t h e c a l c u l a t i o n s t h e d i s s o l v e d gas i n t h e water phase contained methane, as well, b u t t h e l i t t l e i n f l u e n c e o f t h i s on t h e phase e q u i l i b r i u m made i t reasonable t o n e g l e c t it./

304 When c a l c u l a t i n g t h e phase e q u i l i b r i u m , f l a s h c a l c u l a t i . o n s a r e used t o d e t e r mine t h e mole f r a c t i o n s o f t h e phases; however, t h e c a l c u l a t i o n o f three-phase e q u i l i b r i u m make i t necessary t o s o l v e a coupled system o f two n o n l i n e a r a l gebraic equations. Occasionally, mainly when t h e number o f phases changes, convergence problems o f i t e r a t i v e techniques occur. The system was transformed i n t o one n o n l i n e a r a l g e b r a i c equation, and a numerical procedure combining t h e Newton-method and t h e method o f halving, ensure f a s t convergence i n every case. The d e n s i t y o f t h e gas phase i s c a l c u l a t e d using t h e Redlich-Kwong equation o f s t a t e . When determining d e n s i t i e s o f t h e f l u i d phases t h e labor a t o r y c o r r e l a t i o n s a r e applied. I n accordance w i t h these c o r r e l a t i o n s t h e formation volume f a c t o r i s c a l c u l a t e d as a f u n c t i o n o f t h e d i s s o l v e d g a s / f l u i d r a t i o f o r both f l u i d phases. Thus t h e q u a n t i t y o f t h e dissolved gas has t o be known. Because t h e composition o f t h e phases i s known, t h e d i s s o l v e d g a s / o i I r a t i o can be determined from t h e composition o f t h e o i l phase by normal f l a s h c a l c u l a t i o n . As f o r t h e dissolved gas/water r a t i o , i t was assumed t h a t water i n i t s normal s t a t e i s f r e e o f gas. I n order t o check t h e PVT and e q u i l i b r i u m c a l c u l a t i o n s l a b o r a t o r y pressure-build-up measurements were simulated by a one-volume element model. Very good matches could be achieved by modifying t h e molecular weight o f t h e C7+ component by 5 $.

FIELD EXPERIMENT A f t e r some p i l o t t e s t s t h e f i r s t large-scale process was s t a r t e d i n t h e western area o f t h e Budafa o i l f i e l d i n 1972. The area i s a s e c t i o n o f t h e Lower-Pannonian /Lower-Pliocene/ Budafa r e s e r v o i r which c o n s i s t s o f f o u r separable sequences o f s t r a t a o f t h e same hydrodynamic system. The formations a r e heterogeneous v e r t i c a l l y and h o r i z o n t a l l y . The e f f e c t i v e formation t h i c k n e s s v a r i e s from 1-2 m t 30 m. The average p o r o s i t y i s 21 $, t h e average h o r i z o n t a l 9 p e r m e a b i l i t y 0.1 pm

.

The sandstone formations o c c u r r i n g a t an average depth o f 850 m have a temp e r a t u r e o f 64 OC. The i n i t i a l pressure level j u d g i n g by t h e h y d r o s t a t i c c o n d i t i o n a t t h e beginning o f p r o d u c t i o n was 9800 kPa. The producgd crude i s o f an i n ermed a t e - p a r a f f i n character, i t s average d e n s i t y a t 20 C being 0.817.10' kg/mf. The r e s e r v o i r o i I was i n i t i a l l y saturated, t h e two upper sequences o r i g i n a l l y had an e x t e n s i v e gas cap. T h i s accumulation was unfavourable from t h e p o i n t o f view o f t e r t i a r y recovery because t h e o i l zones o f t h e two lower l a y e r s were s i t u a t e d under t h e gas caps o f t h e two upper I ayers. Production was begun i n J u l y o f 1937. F o l l o w i n g t h e r a i d increase i n t h e !? number o f wells, crude p r o d u c t i o n amounted t o 89,800 m /year i n t941 which was t h e peak p r o d u c t i o n o f t h i s area. The energy o f the formation decreased because o f t h e h i g h p r o d u c t i o n l e v e l and r e s t r i c t e d egge water d r i v e . I n o r d e r t o overcome t h e energy reduction, 139 m i l l i o n m hydrocarbon gas was i n j e c t e d i n t o t h e r e s e r v o i r from 1942 t o 1958. During t h e primary and secondary displacements t h e s o l u t i o n gas d r i v e , t h e energy o f gas caps and, t o a s l i g h t extent, edge water d r i v e worked w h i l e t h e formation pressure decreased t o an average level o f 2900 kP3, which was considered as an 3 abandon pressure. A t o t a l o f 1 m i l l i o n m o i l and 600 m i l l i o n m gas was produced. The average recovery e f f i c i e n c y was 22.6 $.

305

I

306 A t t h e b e g i n n i n g o f t e r t i a r y r e c o v e r y t h e o i l zones o f t h e a r e a had a h i g h gas s a t u r a t i o n . T e r t i a r y r e c o v e r y by carbonated n a t u r a l gas was r e a l i z e d by u s i n g 41 i n j e c t i o n , 71 p r o d u c t i o n and 9 o b s e r v a t i o n w e l l s . When d e s i g n i n g t h e technology, t h e e x i s t i n g w e l l s i n t h e a r e a were t a k e n i n t o account, and t h e system c o u l d be c h a r a c t e r i z e d by an i r r e g u l a r m u l t i - s p o t p a t t e r n . The w e l l p a t t e r n used i s shown i n F i g . 1. I n t h e f i r s t phase o f t h e t e r t i a r y recovery, carbonated n a t u r a l gas was i n j e c t e d i n t o t h e f o r m a t i o n d u r i n g which c o n t r o l l e d p r o d u c t i o n was r e a l i z e d . The carbonated n a t u r a l gas used was produced f r o m a h i g h p r e s s u r e r e s e r v o i r d i s c o v e r e d i n t h e a c t u a l area o f Budafa. T h i s gas - h a v i n g a carbon d i o x i d e c o n t e n t o f 81 m l e % and l i g h t hydrocarbons - was i n j e c t e d i n t o t h e low p r e s s u r e o i l r e s e r v o i r by means o f n a t u r a l energy. The carbon d i o x i d e appeared i n t h e p r o d u c t i o n w e l l s 1-2 months a f t e r t h e b e g i n n i n g o f i n j e c t i o n . Data r e l a t i n g t o i n j e c t i o n and p r o d u c t f o n 3 r a t e s / F i g . 2/ show t h a t t h e GOR amounted t o a v e r y h i g h l e v e l /3000-5000 m /m / d u r i n g t h e i n j e c t i o n . T h i s disadvantageous e f f e c t was caused by t h e h i g h gas s a t u r a t i o n d a t i n g back t o t h e p r i m a r y and secondary r e c o v e r y . No o i l bank f o r m a t i o n c o u l d be observed i n any o f t h e p r o d u c t i o n w e l l s . Gas and l i q u i d f l o w always o c c u r r e d s i m u l t a n e o u s l y i n t h e l a y e r s . I n o r d e r t o d i m i n i s h t h e h i g h GOR v a l u e o f t h e p r o duced f l u i d , w a t e r i n j e c t i o n was s t a r t e d a t t h e g a s - o i l c o n t a c t o f t h e two upper l a y e r s i n t h e autumn o f 1974, and t h e whole a r e a was w a t e r f l o o d e d f r o m t h e summer o f 1975. A t t h a t t i m e t h e averag? p r e s s u r e o f t h e r e s e r v o i r was 10,900 kPa, t h e water i n j e c t i o n r a t e f 5 0 0 m /day. GOR response t o w a t e r f l o o d i n g was observed f r o m t h e end o f 1974 when t h e c h a r a c t e r o f p r o d u c t i o n changed remarkably. Along w i t h i n c r e a s i n g o i l p r o d u c t i o 3 r y t e , t h e g a s / o i I r a i o decreased f r o m t h e p r e v i o u s y e a r s ’ l e v e l o f 5000 m /m t o a b o u t 600 m3/$. The changed c o n d i t i o n s can be seen i n F i g . 2. The carbon d i o x i d e c o n t e n t o f t h e produced gas remained above 65 mole % d u r i n g t h e w a t e r i n j e c t i o n , which made i t e v i d e n t t h a t i n j e c t i o n o f a d d i t i o n a l c rbonated n a t u r a l gas was n o t necessary. U n t f I 1 s t January 1981, 694 m i l l i o n m carbonated n a t u r a l gas and 3.013 m i l l i o n m w a t e r had been i n j e c t e d i n t o t h e f o r m a t i o n . I t should be mentioned t h a t t h e g r e a t e r p a r t o f t 9 e i n j e c t e d gas was used t o f i l l up t h e gas caps. By January 1981, 173,000 m o i l and 3 1.072 m i l l i o n m w a t e r had been produced and t h e average r e c o v e r y e f f i c i e n c y had been 27.5 %, t h u s t e r t i a r y r e c o v e r y r e s u l t e d i n a d d i t i o n a l o i l o f 3.9 T h i s amount o f a d d i t i o n a l o i l i s , however, an average v a l u e . For example, t h e a d d i t i o n a l o i l from Section I I . q u i t e considerable i n t h a t t h e e a r l i e r value was ‘12.7 % 0 . i . p . The method has proved t o be s u c c e s s f u l f o r one-layer, r e l a t i v e l y homogeneous s e c t i o n s h a v i n g low w a t e r s a t u r a t i o n , and t h e e f f e c t i v e n e s s was poor, a b o u t 1-2 % f o r t h e m u l t i - l a y e r s f o r m a t i o n under t h e gas caps. The d i s p l a c e m e n t i s s t i l l c o n t i n u i n g . The f i n a l amount o f a d d i t i o n a l The p r o d u c t i o n o f a d d i t i o n a l o i l proved t o be economo i l expected i s 5.7 I. i c a l l y worth w h i l e .

3

%.

HISTORY MATCH AND PREDICTION The f i e l d e x p e r i m e n t was analysed by s i m u l a t i o n o f performance h i s t o r y (3, P a r t I I.). The r e s e r v o i r i s t h i n , heterogeneous, laminated and n e a r l y h o r i z o n t a l , t h u s an a r e a l model was used and t h e e f f e c t s o f c a p i l l a r i t y and g r a v i t a t i o n were n e g l e c t e d . Because of t h e complex p e t r o g r a p h i c and h e t e r ogeneous s a t u r a t i o n c o n d i t i o n s , t h e Budafa-West m u l t i - l a y e r r e s e r v o i r

L---n I

Grp Butlofa-West

Unit

performcnce

history

307

FIGURE 2

308 c o n s t i t u t e s a c o m p l i c a t e d system. For t h i s reason an e a s i l y separable, one- l a y e r s e c t i o n o f t h e r e s e r v o i r was examined b e l o n g i n g t o t h a t a r e a where t h e h i g h e s t amount o f o i l o r i g i n a t e d from. /Primary and secondary displacement r e s u l t e d i n 45.2 % f o r t h i s s e c t i o n . / The s e c t i o n i s shown i s F i g . ‘I as Section 1 1 . Because o f computer r e s t r i c t i o n /an ICT 1905 computer w i t h a memory o f 32 Kwords was used/, we c o u l d n o t d e s c r i b e a l l t h e i n j e c t i o n and p r o d u c t i o n w e l l s o f t h e s e c t i o n ; o u r i n t e n t i o n was t o o b t a i n an o v e r a l l p i c t u r e o f t h e process. / I t i s t o be noted t h a t d e t a i l e d d a t a on f o r m a t i o n parameters were a l s o i n a c c e s s i b l e . / The s e c t i o n was c o n s i d e r e d t o be o f c o n s t a n t t h i c k n e s s , h o r i z o n t a l , and t h e average r o c k parameters and i n i t i a l s a t u r a t i o n r e f e r r i n g t o t h e b e g i n n i n g o f t h e t e r t a r y r e c o v e r y were used. We wished t o make use o f a l l t h e measured data, t h e r e f o r e on t h e bases o f a v e r a g i n g t h e d i s t a n c e s o f t h e i n j e c t i o n and p r o d u c t i o n w e l l s o f t h e s e c t i o n an e i g h t h o f a f i v e - s p o t element was cons t r u c t e d . The i n j e c t i o n and t h e p r o d u c t i o n d a t a o f t h e model were c a l c u l a t e d from t h e c u m u l a t i v e d a t a o f t h e s e c t i o n u s i n g t h e p o r e volume r a t i o o f t h e s e c t i o n and t h o s e o f t h e e i g h t h o f t h e f i v e - s p o t element. R e l a t i v e p e r m e a b i l i t y c u r v e s f o r three-phase carbonated systems were n o t a v a i l a b l e . Based upon l a b o r a t o r y measurements and p u b l i s h e d d a t a a s i m p l e f o r m o f p a r a m e t r i c r e l a t i v e p e r m e a b i l i t y c u r v e s were c o n s t r u c t e d , and parameters o f t h e c u r v e s were determined by h i s t o r y matching. P r e s s u r e and p r o d u c t i o n d a t a o f 5.5 y e a r s /2.5 y e a r s o f gas i n j e c t i o n , 3 y e a r s o f water i n j e c t i o n / were used. I t seemed t h a t no parameter group can be chosen t o s i m u l a t e e a r l y breakthrough o f carbon d i o x i d e . A n a l y s i s o f h o r i z o n t a l p e r m e a b i l i t y d i s t r i b u t i o n i n t o v e r t i c a l d i r e c t i o n u s i n g c o n t i n u o u s c o r e samples o f t h e r p s e r v o i r examined showed t h a t 20 % o f t h e p e r m e a b i l i t y d a t a were above 0.31 pm which d i f f e r e d remarkably f r o m t h e average v a l u e . The f l o o d i n g process i s v e r y s t r o n g l y i n f l u e n c e d by t h e presence o f h i g h p e r m e a b i l i t y zones. The h e t e r o g e n e i t y was t a k e n i n t o a c c o u n t i n a s i m p l e way, t h e t h i c k n e s s was d i v i d e d i n t o a good and a poor p e r m e a b i l i t y l a y e r . The r e s u l t s o f t h e h i s t o r y match can be seen i n F i g . 3 . The computed average p r e s s u r e s d i f f e r e d f r o m t h e measured ones by o n l y a b o u t 5

%.

A f t e r h a v i n g good r e s u l t s on t h e h i s t o r y match f o r S e c t i o n I I , t h e model was a p p l i e d t o t h e o t h e r 5 s e c t i o n s o f t h e area. 15-25 s i m u l a t i o n s were used t o reach t h e f i n a l r e s u l t s f o r each case. We had t o assume i n t h e m o d e l l i n g , t h a t no f l o w b o u n d a r i e s e x i s t e d between t h e s e c t i o n s though, as i s t o be expected, t h i s i s n o t t h e case. T h i s f a c t was proved by t h e c a l c u l a t i o n s . To some e x t e n t we had t o m o d i f y t h e i n j e c t e d gas t o g e t t h e good p r e s s u r e h i s t o r y match. However, t h e s e m o d i f i c a t i o n s were e q u a l i z e d f r o m t h e v i e w p o i n t o f t h e whole area, and a c a l c u l a t e d gas l o s s o f o n l y 6 % r e s u l t e d . The r e s u l t s o f h i s t o r y matching a r e summarized i n F i g . 4 . The c a l c u l a t i o n s were performed i n 1978. The f i g u r e shows p r e d i c t i o n s u n t i l 1983 t o g e t h e r w i t h t h e a c t u a l p r o d u c t i o n parameters o f t h e l a s t t h r e e y e a r s .

CONCLUSIONS A f t e r t h o r o u g h and e x t e n s i v e s t u d i e s economic f i e l d - w i d e t e r t i a r y displacement by carbon d i o x i d e c a r r i e d o u t i n Hungary. V o l u m e t r i c and phase behaviour o f t h e three-phase system can be modelled w i t h good a c c u r a r c y u s i n g t h e l a b o r a t o r y c o r r e l a t i o n s . The CO d i s p l a c e m e n t has proved t o be s u c c e s s f u l f o r 2 one-layer, r e l a t i v e l y homogeneous s e c t i o n s h a v i n g low w a t e r s a t u r a t i o n .

Budofo-West

unit

Sert;on

II.

309

FIGURE 3. Comparison of measured and cornouted data

b

c

/ /'

/

/

,

r01.r

-.mom\ .-

FIGURE L.

Comparison of measured a n d computed data Budafa-West unit

311 U t i l i z a t i o n o f t h e l o c a l p o t e n t i a l proved, i n t h i s case, t o be a s u b s t a n t i a l f a c t o r i n a c h i e v i n g economic a d d i t i o n a l o i l p r o d u c t i o n t h e r e b y overcoming t h e e f f e c t s o f unfavourable r e s e r v o i r conditions.

NOMENCLATURE

C

mass c o n c e n t r a t i o n

D

di f f usi v i t y

9

gravitational acceleration

-K

permeability tensor

k

r e l a t i v e permeability

P

pressure

9

mass s i n k p e r u n i t volume p e r u n i t t i m e

S

sa t u r a t i on

t

time depth viscosity density porosity

Subscripts

i

r e f e r s t o i t h component

j

r e f e r s t o j t h phase

REFERENCES

1. Ba'n, A.,

B a ' l i n t , V., D o l e s c h a l l , S., Zabrodin, P. I., Torok, J.: " P r i m e n e n i j e u g l e k i s l o v o gaza v d o b i c h e n e f t i " / " A p p l i c a t i o n o f carbon d i o x i d e i n o i l p r o d u c t i o n " / , Nedra Publ. Co., Moscow, 1977

2. B a ' l i n t , V., Paa'l, T.: "A n e d v e s i t 6 s i a ' l l a p o t 6s a z a'ramla'si jellemzo'k va'ltoza'sa CO d a l t e l i t e t t f l u i d u m - r e n d s z e r e k por6zus kozegben V a l 6 a'ramoltata'sakor~-/"Changes o f w e t t a b i I i t y c o n d i t i o n s and f l o w c h a r a c t e r i s t i c s f o r f l o w i n g c a r b o n d i o x i d e s a t u r a t e d f l u i d system i n porous media"/, KColaj 6s Foldga'z, Nov. 1979 3. Acs, G., D o I e s c h a I I , S., B i r 6 , Z., Farkas c . : "HBromfa'zisu, kompozici6s modell 6s alkalmaza'sa a Budafa-nyugat t e l e p sz6n-dioxidos muvel6s6nek l e ira'sa'ra" /"A three-phase, c o m p o s i t i o n a l model and i t s a p p l i c a t i o n f o r d e s c r i b i n g CO d i s p l a c e m e n t o f t h e Budafa-West r e s e r v o i r " / , P a r t I, Ko'olaj 6 s Folzga'z, Jan. i981; P a r t I I, Ko'olaj 6 s Foldga'z, Feb. 1981

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MISCIBLE GAS DISPLACEMENT

313

AN ITERATIVE METHOD FOR PHASE EQUILIBRIA CALCULATIONS WITH PARTICULAR APPLICATION TO MULTICOMPONENTMISCIBLE SYSTEMS NIKOS VAROTSIS, ADRIAN C. TODD, GEORGE STEWART Petroleum Engineering Department, Heriot- Watt University

ABSTRACT equation of state based method is used to establish phase behaviour and properties for mixtures of injection gases and reservoir fluids with specific application to multicomponent miscible systems including CO2' An

The modified Soave-Redlich-Kwong or the Peng-Robinson or a version of the The Redlich-Kwong equation of state can be selected to be used in the model. iteration method used requires a minimum number of variables for which simultaneous iteration is required and an algorithm based on the Broyden's modification of the full Newton step gives consistent phase properties and rapid convergence even near the very sensitive for a miscible displacement critical point area. The model has been tested against published data including simple binaries, ternaries and multicomponent mixtures of reservoir oil and C02 injection gases. Good agreement between the predicted and the experimental values has been found together with a minimum number of iterations required to solve each problem. The paper discusses briefly the specific use of the model in an experimental phase behaviour study for UK oil-C02 systems and as an integral part of a compositional reservoir simulator.

INTRODUCTION One of today's more promising oil recovery techniques is miscible C02 flooding. The use of CO to improve oil recovery is not a new idea since C02 has been investigated $or miscible displacement, for immiscible displacement of reservoir oil, for producing well stimulation and for carbonated water flooding. The current industry interest in co flooding is mainly concentrated on the mass transfer effect that takes place begween the injected CO2 phase and the reservoir oil inside the reservoir. The co extracts hydrocarbons from the oil phase and 2 at the same time co2 is absorbed into the liquid phase up to the moment that The study and prediction of oil recovery involving miscibility is achieved. injection of CO requires a knowledge of the vapour-liquid equilibria especially 2 . at the very sensitive critical point. A method is needed, first to calculate the saturation conditions for the mixtures of the injected gases and reservoir oils from which a prediction of the miscible pressure can be made and second to carry out the isothermal flash calculations for different pressures so that the phase behaviour of the system can be studied in detail. Such a model will be described which using any of the Peng-Robinson, modified Soave-Redlich-Kwong and

314 a version of the Redlich-Kwong equations of state can give predictions of the vapour-liquid equilibria of multicomponent mixtures and especially good and rapid convergence in the critical point region where most of the methods according to the literature fail to converge. extrapolation technique is used to improve the initial estimates for the consequative calculations of the saturation pressure of a reservoir oil-CO2 mixture across the phase envelope and up to the crLtica1 point. Although the model has been specifically applied to CO -oil systems is obviously applicable to 2 any injected gas or flowing system. An

MISCIBILITY MECHANISMS

-

DIFFERENT MODELLING APPROACHES

Two of the most important and promising gas injection enhanced oil recovery practices are C02 flooding and lean gas injection.

The major mechanisms to improve the oil recovery in a carbon dioxide flooding are vaporization and condensation. Mass transfer takes place between the C02 rich phase and the oil rich phase and the initially immiscible phases gradually become miscible as they are enriched in intermediate and even heavy hydrocarbons and C02 respectively. The extraction of hydrocarbons by CO and its condensation into 2 the reservoir fluid results finally in an one phase miscible fluid. The development of miscibility can be visualised conceptually with a ternary diagram (Figure 1 ) . This representation although not quantitative demonstrates how

F I G U R ~ 1. SCHEMATIC

TERNARY

DlAGRAM

315 important it is to be able to predict the critical point of a mixture for a The miscibility path passes throush the multiple contact miscible process. critical point and it is its relative position in respect of the point that represents the reservoir fluid composition that defines whether under certain conditions the mixture of the injected qas and the reservoir fluid can obtain miscibility (Figure 2). The requirement for the generation of a miscible displacement is that the reservoir fluid composition must lie either to the right of the extension of the tangent to the phase boundary curve at the critical point or above the critical point in the single phase region. The same remarks apply more or less for a lean gas injection flooding where the vaporization of the light hydrocarbons from the reservoir fluid to the gas phase controls the whole process. There are also some minor mechanisms to improve the enhanced oil recovery by injection of CO These are: oil swelling, reduction of oil viscosity, increase in oil density,2high solubility of CO in water which reduces the water density and therefore the overriding of the ca2-water mixture and the acidic effect on the rock which increases the permeability of the reservoir.

.

The theoretical studv of a miscible displacement experiment or of a miscible reservoir flooding requires accurate and reliable phase behaviour data. The phase envelope of the mixture at different conditions is required to determine the minimum miscibility pressure and the equilibrium lines (tie-lines) in order to study in detail the distribution of the different components in the two-phases.

CRITICAL POINT

TWO PHASE REGION

FIGURE 2. MISCIBILITY

CONDITIONS

A

3 16 Either an equation of state based method is used to establish phase behaviour and properties or equations are used which have been obtained by curve fitting experimentally derived data. Due to inconsistent phase properties near the critical point and the requirement for comprehensive experimental data for each oil composition of the latter, the equation of state based method is now widely preferred. Most of the current published equation of state based methods appear to suffer from requiring a great number of iterations or do not converge at all in the critical point area, the key area for any miscible displacement.

PHASE EQUILIBRIA MODEL FOR A MISCIBLE OIL RECOVERY PROJECT The technique being presented here for calculating vapour-liquid equilibria using an equation of state includes a system of non-linear equations and an iterative sequence to solve the equations. The system of equations consists of: (i) An overall material balance equation L + V = 1 (ii) Component material balance equations Lxi + vy = zi i = l,n i (iii) Restrictive equations on the phase compositions n c x i = l , i = l

n c y i = l i = l

(iv) Thermodynamic phase equilibria equations i = l,n

fiL = fiv

Three different equations of state can be used to provide values for the These are: compressibility factor of the vapour and liquid phase.

(1) The Peng-Robinson equation of state p=-RT v-b

v(v+b)

a (TI + b(v-b)

(P-Rl

or in terms of the compressibility factor: Z3

-

(1-B)Z

2

+

2 (A-3B -2B)Z

-

2 3 (AB-B -B )

= 0

where:

a(T) = 0.45724

J

R2Tc2 pC

RT

,A

b = 0.0778 pC

=

i+m(l-T:)

r2

-, B R T

,m = 0.37464

=

bP RT

+

1.542261

-

(for pure components)

2 026992W

317 (2) The modified Soave-Redlich-Kwong equation of state: p

-

RT v-b

(M-S-R-K)

v(v+b)

or in terms of the compressibility factor 3

Z -Z

2 2 +(A-B-B )Z-AB =

0

where: a(T) = 0.42727

J

RT b = 0.0867 2,A =

-,ap 2 2

B =

R T

pC

m = 0.48508

l+m(l-.,'),

R2T pC

-

bP RT

+

1.551711

-

0.15613W

(for pure components)

(3) Modified Redlich-Kwong Equation of State aT-4 v(v+~)

RT p=--v-b

(M-R-K)

or in terms of the compressibility factor

where: 2

a = R A

2.5

Tc t b

=

pc

S

RTC

&

~

h

bP

=

s

A

aP

bP RT

= 2- 2, B = -

R T

C

(pure components).

RA,nB are supposed to be functions of temperature and of the nature of each component. The values of these parameters are calculated from generalised correlations applicable over a wide range of temperature. In Table Ivalues of the parameters RA, RB calculated by our model are compared against those obtained bg Coats and Fussell for a ternary mixture of C - nC4 - nC at 160 F (344.3K). 10

RB

Ci nC4 nCIO

RA COATS

% COATS

A '

FUSS

% FUSS

0.4265

0.0862

0.42617

0.086173

0.4251

0.0859

0.4198

0.0794

0.419367

0.0794

0.4154

0.0759

0.4638

0.0734

0.451875

0,070452

0.46512

0.07259

2

318 For the same mixture and for composition (mole fraction) CH4

:

0.253

n-Butane

:

0.661

n-Decane

:

0.086

:

the K-values and the saturation pressure estimated using the Modified Redli' Kwonq Equation of State compared to the values predicted by Coats and to th, experimental ones are given in Table 11.

K-Val OUR MODEL

K-Val. COATS

K-Val. EXPER.

3.173

3.174

3 -174

nC 4

0.297

0.2969

0.297

nC

0.008

0.00806

0.013

972.7 psia

975.1 psia

1000 psia

10

Satur. Press.

For multicomponent mixtures the following mixing rules proposed by Soave are used: n a =

b =

n

C x x ai,. , aij

C

i=l

j=1

n C xibi i=l

,

0.5 a 0.5 (1-ki j

= ai

)

Kij = interaction parameter

The fugacity coefficients of component i in a mixture are calculated using the following equations For the liquid phase: (2 - 1 ) )

Px.exp{b fiL

-

(2 -B )

L

L

iL L B~ i' {1+ -} zL

1<-lSn

For the vapour phase: -

fiv -

Px .exp{b 1

iv

(Zv-l) 1 4 i S n

B i' (2 -B ){I+ ") v v zV

3 19 where:

U,

=

AL(2aiL-biL)/BL,

Wi = Av (2aiv-biv)/Bv

The equilibrium ratios K are defined as: i Ki = Yi/xi = (fiL/xiP)/(fiV/YiP) = $iL/$iv

DESCRIPTION OF THE PROGRAMME The programme is written in Fortran Iv language and is implemented as a conversational time-share package. The user is guided through the data input and calculation options by a question and answer sequence at the visual display unit

.

There are four modes of calculations. (i) Isothermal flash calculation (ii) Bubble or dew-point calculation (iii) K-values prediction (iv) Binary coefficient optimization The programme storesphysical properties for the pure components as molecular weights, critical temperatures and pressures and accentric factors. The results printed out by the programme comprise the following items: Liquid and vapour phase mole fractions, L and V, compressibilities and densities Composition of each phase by mole fractions x i, yi and k-values for each component Saturation pressure or temperature Liquid and vapour phase enthalpies and liquid yield Mass ratio of vapour to feed and volume ratio of vapour to feed Homogeneous mixture density Binary interaction coefficient (if requested)

SOLUTION TECHNIQUE Iteration Method minimum variable iteration method is used to reduce the size of the Correction The size reduction of the step by eliminating as many unknowns as possible. correction step is accomplished by dividing the unknown variables into two groups. The first group contains iteration (independent) variables which are The second grouv contains dependent variables the unknowns to be corrected. and there is an equal number of equations to define them. A

320 The iteration sequence is a four step process:

-

Use the defining equations to calculate the dependent variables

-

Use the error equations to calculate the error

-

Use a correction step to update the variables

Select the iteration variables and assume values for these variables

Initial Estimates of the Iteration Variables For the prediction of the saturation conditions a first estimation of the unknown phase composition has to be taken using the component K-values calculated by the empirical equation 1/Pri K = exp {5.37(1+Wi)(1- -)} T i ri

,

1

<- i

n

For the isothermal flash calculations the corresponding saturation conditions are used as initial estimates. Correction Step The correction step used is a modified full Newton step and it requires the calculation of an approximation to the Jacobian obtained by numerical differentation of the function f(G) for the first iteration and the Broyden’s updating technique to improve the matrix for the rest number of iterations. This technique avoids analytical differentation of very complex functions and requires only one numerical differentation of the function f(x) per calculation The value of the iteration variable x at the K + 1 iteration is given by: k+l

G

where:

-k k = x + A ( x )

Btk) is the Broyden’s approximation to the Jacobian.

x

The array contains n elements (the number of components present in the systein). For a saturation calculation these n iteration variables are n-1 compositions plus the saturation pressure or temperature. For an isothermal flash calculation are n-1 compositions plus the vapour of liquid phase fraction tv or L).

Error Equations The Euclidean norm of the residuals of the thermodynamic phase equilibria equation Mi

-

fiL

-

fiv, 1 c i

n

must be less than the error tolerance.

32 1 EXTRAPOLATION TECHNIQUE TO IMPROVE INITIAL ESTIMATES

There is an option available in the programme to calculate the whole phase envelope of a certain mixture of reservoir oil and injection gas starting from the saturation conditions of the reservoir fluid and ending at the critical point of the mixture where usually the injection gas composition is relatively high and the two fluids are becoming first contact miscible. The step for each successive calculation changes as the physical properties of the two phases are approaching each other. As the overall composition approaches the critical one, the step is being reduced to a minimum because in this region of the phase diagram very small changes in composition cause very significant and radical changes in the phase properties. Two different approaches have been tried to carry out this series of calculations. Either the estimated phase compositions and saturation conditions of the former step are used as initial estimates of the iteration variables in the next step or these values are extrapolated using a combination of quadratic and linear extrapolation to the new composition The second approach improved the method drastically by reducing more step. than 60% the rumber of iterations required to achieve convergence. Table I11 indicates the total number of iterations required for a complete bubble-point curve calculation. (At 18 different compositions of an eleven cmponents synthetic mixture ranging from 0% CO up to 81% CO which corresponds to the 2 2 critical composition). It also presents the number of iterations required for bubble point calculation for two different compositions of the synthetic oil-CO mixture. 2

TABLE I11

-

NUMBER OF ITERATIONS FOR A SYNTHETIC MIXTURE

No Extrapolation

Extrapolation

100

46

No. iterations for bubble-point 30% COP - 70% Oil

5

2

No. iterations for critical point 82% C02 - 18% oil

5

1

Total No. Iterations Bubble-point curve (18 points)

Using the extrapolation technique and the step by step approach to the critical region the final calculation forthe critical Doint itself usually requires only one or two iterations. Table IV gives the Euclidean norms for the same synthetic mixture with and without extrapolation. Table V demonstrates how close to the actual value, the extrapolated from the previous calculation initial estimates of the vapour phase CO2 compositions, are. The extrapolated values are also compared with those that would be the initial estimates if the extrapolation technique has not been applied.

322

There is also an option incorporated in the model to plot the pressure-composition data in an X - Y diagram. An attempt was made to calculate the matrix used for the iteration sequence only once in the beginning of each series of calculations and then to update it continuously all across the saturation curve avoiding the recalculation of the It has been found that approximation to the Jacobian at each composition step. this method can be applied only when the composition step is very small, smethirgthat seems to be time consuming and not practical at all.

TABLE IV

-

EUCLIDEAN NORMS FOR A SYNTHETIC MIXTURE

No. Iteration

No

Euclidean norms for bubble point 30% COP

Extrapolation

Extrapolation

0.4704

0.000502

0.04629

0.0000033

0.00697 0.000397 0.0000257

TABLE V

- EXTRAPOLATED INITIAL ESTIMATES I

Synthetic oil CO mixture calculation steps

30%C02-4O%CO2 40%C02-50%C02 50%C02-6O%CO

Extrap. initial estimates CO mole 2 fraction

Non extrap. initial estimates CO mole 2 fraction

Actual CO mole 2 fraction next step

0.5358

0.4176

0.5329

0.6393

0.5329

0.6356

0.7298

0.6356

0.7241

APPLICATIONS

-

DISCUSSION OF RESULTS

In order to test the accuracy of our computer model various calculations have been performed for hydrocarbon/CO mixtures for which the phase behaviour data 2 has been published. These tests include binaries, ternaries, synthetic oils and mixtures of injection gases and reservoir oils.

323 Isobutane

-

CO, system

The phase behaviour of this mixture has been measured by Besserer and Robinson and theoretical predictions reportedbypeng and-inson. The phase envelope was The fitting of the predicted calculated at 100°F and is illustrated in Figure 3 . A binary phase boundaries to the experimental data is almost perfect. coefficient of 0.105 was used in the modified Redlich-Kwong equation of state as the iteraction parameter for the mixture.

N-Butane-Decane-C02 system The experimental data for this ternary mixture has been published by Metcalfe and Yarborough. The phase envelopes were calculated for two different pressures 1700 psia and 1500 psia at 160°F (Figure 4).

Synthetic oil C02 system The composition of This mixture has been studied by Metcalfe and Yarborough. Figure 5 the synthetic oil and the phase envelope were calculated at 15OoF. and Figure 6 present the experimentally obtained pressure-composition data and the predicted data derived using the M-R-K and the M-S-R-K equations of state. The M-R-K equation of state seems to fit perfectly well the dew-point curve and the critical point. The maximum deviation between the predicted and the experimental points is 3.6%. The interaction coefficient used for CO 2 hydrocarbons is 0.1 and for methane -C6+ is 0.04-0.05.

Rangely field oil

-

injection gases 1

&

2

The calculated The experimental data has been published by Graue et al. bubble point curve using the Peng-Robinson equation of state is plotted in Figure 7. The maximum observed deviation between the predicted and the experimental points is 3.5% and occurs at the critical composition.

Reservoir oil-C02 mixture The C7+ cut has been divided into This oil has been studied by Simon et al. 0 three pseudo cdmponents and the bubble point curve was calculated at 255 F using the M-R-K equation of state (Figure 7). Once again in the near the critical point region the fitting of the predicted curve is almost perfect. The theoretical model described above, is a part of a research programme on dynamic contact CO miscible studies. The various calculations that have 2 already been performed are for U . S . oils and reservoir conditions. The next stage will be the generation of experimental phase behaviour data for CO2-oils for a whole range of North Sea crudes using a rig for multiple contact equilibrium experiments which has now already started to operate. The experimental results will be a test for our compositional simulator and A valid and reliable theoretical especially for the assumptions we used. model can decrease dramatically the cost of a miscible flooding because only a few experimental results, which are very expensive and time consuming, have to be obtained in order to establish a complete view of the phase behaviour of the reservoir fluids.

32 4

1.10.

I."-

+ PRED. POINTS

0 EXPER. POINTS

.90Q 6) Q

.80.

c

X

.70.60.50. 40.30.20.

@@ .OO " .OO

.I 0

.20

.30

.4a

.so

.m

.70

.80

.go

I .0a

MOLE FRACTION CARBON DIOXIDE FIGURE

3.PHASE ENVELOPE FOR C02- ISO-BUTANE MIXTURE TEMPERATURE=IBBF R-K EOS

50-50 '02-

50-50 FIGURE 4. PHASE

ENVELOPES

1500, 1700

FOR

THE

C O ~ - N C ~ - C ~ OTERNARY

PSIA TEMPERATURE

160O~

PRESSURE

COZ -

Nc4

325

MOLE FRACTION.CARBON D I O X I D E

FIGURE 5.

PHASE ENVELOPE FOR CO2-SYNTHETIC OIL MIXTURE TEMPERATURE=I50F R-K EOS

(0

a &! L

11

1.50-

2

1.40-

a

a

1.30-

I .20I . 10I .OO MOLE FRACTION CARBON D I O X I D E

FIGURE 6. PHASE ENVELOPE FOR'C02-SYNTHETIC OIL MIXTURE

TEMPERATURE=lSBF M0D.S-R-K

EOS

326

0 EXPER. POINTS

4.50 6)

GAS-2

< I E 3.00 3.50r

K l IJ

$

2w

2.50 2.001

.OO

GAS- I

J

. I0

.20

.30

.40

.50

.60

.70

.OO

.90

.OO

MOLE FRACTION CARBON D I O X I D E F I G W 7. BUBBLE POINT CURVE FOR RANGELY FIELD OIL-CM MIXTURES

TEMPERATURE=tGBF P-R EOS

2

: 2.00w I):

P

I .50. 1.00.50-

.OO MOLE FRACTION CARBON DIOXIDE

FIGURE 8. BUBBLE POINT CURVE FOR CU2-RESERVOIR OIL MIXTURE TEMPERATURE=255F R-K EOS

321

CONCLUSIONS robust computer programme for isothermal flash, bubble and dew point calculations using one of the Peng-Robinson, Soave-Redlich-Kwong,Modified RedlichKwong equation of state has been developed applicable to the severe reservoir conditions encountered in miscible gas flooding enhanced oil recovery schemes. A

The demonstrated examples show very good and rapid convergence at any point across the phase boundaries of the CO /hydrocarbon mixtures and particularly the 2 sensitive critical point region. A case has not yet been found where the proposed scheme does not converge although we have, however, found situations where the MSRK or PR equations of state converge to unrealistic solutions. Various tests indicated that the MSRK equation appears in some cases to give closer approximation to the experimental data than the PR equation. The MRK equation appears to fit better the dew point curve than the bubble point one. The treatment of the pseudo components in the oil mixtures is under more investigation. NOMENCLATURE a, b

f.

iL

fiv

=

Temperature, pressure and composition dependent parameters Fugacity of component i in liquid phase, psia Fugacity of component i in vapour phase, psia

K

Equilibrium ratio y./x i i

L

Mole fraction of liquid phase

P

Pressure

i

pc r'

Critical pressure Reduced pressure P/P

R

Gas constant

T

Temperature

TC

Tr

Critical temperature Reduced temperature T/T

V

Vapour phase mole fraction

V

Molar volume

X

i

Yi i'

Mole fraction of component i in liquid phase Mole fraction of component i in vapour phase Global mole fraction of component i

z

Compressibility factor of vapour phase

W

Accentric factor

L

328 REFERENCES 1.

McGLASHAN, R.S.; "A Compositional Phase Equilibrium Model Applied to Pressure Drop Prediction in North Sea Oil Wells", Ph.D Thesis, HeriotWatt University, 1980

2.

COATS, K.H.; 1980, p.363

3.

GARDNW, J.W., ORR, F.M., PATEL, P.D.; "The Effect of Phase Behaviour on CO Flood Displacement Efficiency", SPE 8367, 1979 2

4.

NGHIEM, L.X., AZIZ, K.; "A Robust Iterative Method for Flash Calculations using the Soave-Redlich-Kwong or the Peng-Robinson Equation of State", SPE 8285, 1979

5.

FUSSELL, D.D., YANOSIK, J . L . ; "An Iterative Sequence for Phase Equilibria Calculations Incorporating the Redlich=Kwong Equation of State". SPEJ, June 1978

6.

PENG, D.Y., ROBINSON, D.B.; "A New %-Constant Ind. Eng. Chem. Fundam. Vol. No. 1, 1976

7.

GRABOSKI, M., DAUBERT, T.; "A Modified Soave Equation of State for Phase Equilibrium Calculations", American Chemical Society Journal, 1978

8.

BESSERER, G., ROBINSON, D.; "Equilibrium Phase Properties of i-Butane-CO2 System", J. Chem. Eng. Data, Vol. 3, No. 3, 1973, p. 298

9.

OLDS, REAMER, SAGE, LACEY; "Phase Equilibria in Hydrocarbon Systems N-Butane CO System", Ind. & Eng. Chem., 1949, p. 475 2

"An Equation of State Compositional Model", SPEJ, October

Equation of State",

- Reservoir Oil

10.

SIMON, ROSMAN, ZANA; "Phase Behaviour Properties of CO2 Systems", SPEJ, Feb. 1978, p. 20

11.

GRAUE, D.J., ZANA, E.; "Study of a Possible C02 Flood in the Rangely Field, Colorado", SPE 7060, 1978

12.

METCALFE, R.S., YARBOROUGH, L.; "Effect of Phase Equilibria on the C02 Displacement Mechanism, SPE 7061. 1978

329

M I S C I B L E GAS DISPLACEMENT

PHASE EQUILIBRIUM CALCULATIONS IN THE NEAR-CRITICAL REGION RASMUS RISNES Norsk Agip AIS VILGEIR DALEN, JAN WAR JENSEN

Continen tal Shelf Institu te ABSTRACT The present paper addresses the problem of phase equilibrium calculations in the critical point region. The approach is based on an equation of state, and both the Soave-Redlich-Kwong and the Peng-Robinson equations are considered. An accelerated and stabilized successive substitution method is presented. A procedure for disappearing phases is included, making the method convergent also in the single phase region. The accelerated successive substitution method has been compared with Newton type methods like Powell's method. Maps of an error norm which measures the fugacity deviations, are presented to illustrate how the different solution techniques perform. The general conclusion is that the accelerated successive substitution method is faster and much more stable than the Newton type methods considered. INTRODUCTION During recent years, hydrocarbon phase equilibrium calculations based on cubic equations of state has received considerable attention, partly because of the demand for accurate and consistent phase predictions encountered in connection with enhanced oil recovery techniques like gas miscible flooding. Both the Soave-Redlich-Kwong (SFX) equation /1/ and the Peng-Robinson (PR) equation /2/ have been extensively used. They both perform well on hydrocarbon mixtures, the PR equation being slightly better in predicting liquid densities. The basic solution procedure for flash calculations is the successive substitution method (SSM). It has however been reported to show poor convergence, or even no convergence,'close to saturation pressures. To overcome the convergence problem, Fussel and Yanosik /3/ introduced Newton type iteration methods, and since then the trend has been towards such refined numerical solution techniques. Newton type methods are however dependent on good initial estimates. In a recent paper Nghiem and Aziz /4/ presented an algorithm using Powell's method which is a combination of a Newton method and the steepest decent method. They also presented a method to detect single-phase states. Their method was extended to three- and four-phase systems by Mehra 151. Also Mott / 6 / has presented a two-phase algorithm based on Powell's method. An important problem in equilibrium calculations is to avoid false trivial solutions where the vapor and the liquid phase are identical. This aspect has been discussed by Maddox and Erbar 111. The present work is part of a research project concerned with the development of numerical simulation models for enhanced oil recovery processes. It was

330 directed towards the development of a thermodynamic simulator capable of predicting the phase behaviour of mixtures of hydrocarbon reservoir fluids and possible injection gases. The resulting computer program is called COPEC. The program is based on an equation of state approach, and both the SRK and the PR equations are included. Several solution options are available including Powell's method, but the basic solution method is an accelerated and stabilized successive substitution method (ASSM). The method is designed to converge also in the single-phase region, and it contains a bring-back procedure that brings the solution back to the two phase region if it reaches the single-phase region too soon. The acceleration routine employs an Aitken type formula for correcting K-values. EQUILIBRIUM CONDITIONS If we consider N moles of mixture or feed of composition z . which separate into L moles of liquid of composition x. and V moles of vaior of composition y., we have an overall material balanceland a component balance equation for eich component: L + V = N

(1)

Lx. + vy. = Nz. As the compositions are given in mole fractions we have the following constraints: zz. =

L.= zy. =

1

(3)

Eqs. (l), (2) and one of the restricting equations ( 3 ) constitute a system of n+2 equations in the 2n+2 unknowns, L, V, xi, yi: n is the number of components. The remaining n equations needed are provided by the thermodynamic criterion stating that the fugacities in the liquid and the vapor phase must be equal:

These 2n+2 equations define the two-phase equilibrium problem. In an equation of state approach, the fugacities can be calculated from the equation of state. The fugacity will depend on temperature, pressure, composition and the type of phase considered, f. = f. (T, P, xi, type) 1

1

With cubic equations of state, the same equation is used both for the liquid and the vapor phase. A cubic equation may give 3 solutions in volume. The distinction between liquid and vapor phase is then made by choosing the smallest volume for the liquid phase and the greatest volume for the vapor phase. Formulas for the Soave-Redlich-Kwong (SRK) and the Peng-Robinson (PR) equations of state are given in Table l . BASIC SUCCESSIVE SUBSTITUTION METHOD The successive substitution method is based on the concept of equilibrium constants K defined by: i

K. = y./x. 1 1 1

(5)

331 Table 1

Suormary description of the Soave-Redlich-Kwong and Peng-Robinson equations of state.

Soave-Redlich-Kwong: =RT -

p

-

v-b

Peng-Robinson:

a

p=RT v-b

v(v+b)

- v(v+b)a + b(v-b)

RT

RT

b = 0.08664 2

b

= 0.07780 PC

pC

*

R ~ T a(T) = 0.42747

R a(T) = 0.45724

U pC

wom5 = 1 m

+

L Y ~ =’ ~1

= 0.480 + i.574~,- 0 . 1 7 6 ~ ~

(A-B-B2 )z

~

~

+ m(1

- Tro”)

2 = 0.37464 + 1.54226~ - 0.26992~

The cubic equation for the compressibility factor Z = Pv/RT is:

z3 - z2 +

T

pC

-)’*:T

m(l

~

-U

- AB = o

The cubic equation for the compressibility factor Z = Pv/RT is:

Z3 -(l-B)Z 2+(A-3B 2 -2B)Z-(AB-B2-B3) bP where A = - and B = RT

With mixing rules as given below, the fugacity coefficient of compoponent k is given by:

With mixing rules as given below, the fugacity coefficient of component h is given by:

=a

In Wk bk (Z-1) A

B (

’i

a

aik

-

ln(Z-B)

aP

= 0

aP and B = bP where A = RT R ~ T ~

.

R ~ T ~

-

In Vh = bk (Z-1)

- ln(Z-B) -

- a) bk ln(l+Z) B

The mixing rules employed for both equations are: b = 1 xi bi i a = I I xi x 8.. i j J 1J 8.. 1J

= (1

- ti..)

1J

.

0.5 .0.5 ai j

where tiij are binary interaction coefficients

332

where y. and x. are mole fractions in equilibrium. If values for the equilibrium chstanti are assumed, and the fugacity equations ( 4 ) are replaced by the Ki-equations (5), the resulting set of equations can easily be solved for the unknowns L, V, x. and y.. With these compositions improved K.-values can be obtained, and the'cycle ;epeated. Introducing the fugacity coefficients JI.

1'

the fugacities can be written

In equilibrium the fugacities are equal and hence the equilibrium constants are given by

Ki = JIiL1JIiV

(7)

This is an important relation as it allows the defin tion of K-values also outside the two-phase region. During the iteration process when the fugacities are not yet equal, the improved K-value estimates are obtained by

where j is the iteration number and R. is the fugacity ratio fiL/f.". The criterion for acceptance of a solutio; is based on the fugacity rakios. To comply with other solution methods the following error norm is used p

= I(Ri - 1)

2

<

E

When the equilibrium constants are given, the system of flash equations (11, (2), ( 3 ) and ( 5 ) can most conveniently be solved by introducing the g(V) function following Nghiem and Aziz 141. If we consider one mole of feed, N=l, eliminate L in Eq. (2), and then sum up all the equations we obtain 1Xi

The g(V)

+ m y i

-

Xi)

= 1

(10)

function is defined by (Ki-l)zi

g(V) = I(Yi -'x.) = 1

~

l+(Ki-l)V

(11)

From Eq. (10) we see.that V is determined as the root in the equation

P(V) = 0

(12)

This equation is readily solved by Newton's method. As the g(V) function always has a negative slope, there will only be one root of interest. When the value of V is determined, the compositions can be calculated in a straightforward manner. When the root of Eq. (12) gets outside the interval [0,1], this indicates a single-phase state. We then calculate the non-existing phase as if the system were at the saturation pressure:

333

K.x. 1 1 If VtO, then V is set equal to 0, xi = zi, yi = Z Ki xi

The normalization is necessary as this is not automatically assured outside the two-phase region. A common factor in the K-values has no effect on the composition of the nonexisting phase, and when the K-values are corrected according to the fugacity ratios, the compositions are corrected only to the extent that the fugacity ratios deviate from the average value. The system will converge to a definite composition, and the fugacity ratios will converge to a common constant value. This limiting value will be different from unity except if the system is at the saturation pressure. K-VALUE ESTIMATION The set of initial K-values is the starting point for the iteration procedure. There are 3 conditions these estimates should meet: 1.

The estimates should be as close as possible in order to obtain a rapid solution.

2.

The estimates should assure that the calculations start in the two-phase region in order to avoid false single-phase solutions.

3.

The estimates should have sufficient spread to avoid false solutions where all K-values become equal to one.

The often quoted empirical formula from Wilson /8/ 1 K. = exp [5.3727 (l+ui) (1 'ri

-

- 11 Tri

normally meets these requirements well. An alternative to the empirical formula can be based on the equation of state.

The basic idea is the following. The mixture or feed is assumed to be 1 quid at the temperature and pressure given, and the fugacities are calculate We then assume a gas phase to be formed by evaporation from this liquid. The evaporation rate for each component is assumed to be proportional to the fugacity of that component, the proportionality constant being the same for all components. The evaporation must be stopped before we run out of any component in the liquid phase, but if possible, the evaporation should proceed until only half of the liquid remains. From the resulting compositions, the fugacity coefficients are calculated, and from these we obtain the K-value estimates.

.

These fugacity based K-values work very well in the near critical region. The reason is probably that in addition to start with K-values consistent with the equation of state, we start in the middle of the two-phase region with both L and V equal to one half. The method also works well along the bubble point curve and in most of the two phase region. It may however break down along the lower dew point curve. There, a restriction of the liquid 2-factor to say ZL<0.3, may be needed in order to assure that the assumed liquid behaves liquid-like.

334

THE ACCELERATION PROCEDURE When the system is close to the critical point, the convergency may be very slow. A method similar to Aitken's accelerating formula can then be used to speed up the convergence rate. The equilibrium constants can be regarded as long products, starting with the initial estimate Ko and then multiplied by the fugacity ratios R. which approaches unity as the number of iterations increases. This can bi written

Taking the logarithm we obtain 1 log Ki = log KY + log R. + l o g : R + log : R

+

.... +

log : R

+

...

(17)

In the first part of an equilibrium calculation the fugacity ratios may change from values smaller than one to values greater than one, causing alternate signs in the series above. But after say 20 to 50 iterations, the situation is characterized by a monotone and steady approach towards the solution. The process can now be accelerated by replacing the remaining part of the series by a geometric series where k is the ratio between the terms

. log Ki = log Ki + l o g :R

(1 + k + k2 + . . ) = log KJ + 1

log : R ~

1-k

(18)

The quotient k is calculated as the ratio between the last two consecutive terms (omitting the subscript i)

and the resulting accelerating step is 1

K. = KJ 1

1

where l/(l-k)

'

R;

(l-k)

is exponent to the fugacity ratio.

When this acceleration step is used, it must always be tested that it leads to an improved solution in the way that it brings the fugacity ratios closer to unity. If not, it must be rejected and replaced by a single step. Between each accelerated step there must be a single step in order to determine the quotient k in the exponent in Eq. ( 2 0 ) .

A simplified approach is to assume a constant value for the exponent to the fugacity ratio. If we wait until the system is well on the right track, an exponent of 2 may normally safely be employed. We routinely apply this exponent after 10 iterations, also in conjunction with proper acceleration.

THE BRING-BACK PROCEDURE

When the system is in a single-phase state, the composition of the non-existing phase is calculated by formula (13) or (14). As a common factor in the set of equilibrium constants has no influence on the composition of the non-existing

335 phase, this gives the possibility to adjust the K-values to make the g(V)function zero, or in other words, to keep the non-existing phase at the edge of the two-phase region while we test for its existence. If we consider a single-phase liquid, V equals zero, and the multiplication factor y is determined from I(yKi

-

1 ) zi = 0

(21)

which gives a new set of equilibrium constants

= yK. = 1

Ki Z

(22)

Ki zi

on which we apply the normal correction factors (fiL/fiV). Physically this corresponds to creating a nucleus gas bubble and see if it will grow or disappear. A gas bubble will grow spontaneously if the fugacity is lower in the gas phase than in the liquid phase. This corresponds to having correction factors (f. /f. ) mostly greater than one. The K-values will then 1L kge system will return to the two phase state. If, be further increased and however, the fugacities are higher in the gas phase than in the liquid phase, the bubble will disappear spontaneously. When the correction factors (fi /f are mostly less than one, the K-factors are reduced bringing the system kacttv to the single-phase state. If the single phase is gas, we may reason in a similar way. As V equals one, the multiplication factor is in this case determined from Z(1

-)zi=o Y Ki NEWTON-TYPE METHODS

As a supplement to the acceleration procedure described above, we have also implemented the Newton-type method described by Powell / 9 / . This algorithm has been used by several other workers during recent times 1 4 , 5 , 6 / and is claimed to be a robust and efficient tool for the problem at hand. In summary, Powell's algorithm is based on the classical Newton method, but differs from that method in two important ways. First, the robustness is increased by combining the Newton method with the more stable steepest descent method. Secondly, inversion of matrices at each iteration step is avoided by using an approximate matrix-updating scheme directly on the inverse of the Jacobian.

Using Powell's method, the equilibrium problem is stated as a system of n nonlinear equations in n independent variables by

and the solution is accepted when the residual norm p of Eq. (9) gets below a selected tolerance as before. Independent variables are selected from the following options: =-iteration: LY-iteration: m-iteration: NV-iteration:

L and x . for all but the last component. V and yf for all but the last component. niL forla11 components. niV for all components.

336 n. and niv are liquid and vapor fractions per component, i.e. niL = Lxi and nii = vyi.

Following Nghiem and Aziz 141, the strategy adopted here is to start with successive substitutions and then switch to Powell's method if the convergence is slow. A switch after i iterations reauires all of the following conditions to be fulfilled: E~

< pj <

E~

0 < VJ < 1

and

--& > pJ-l

E~

1 VJ - VJ-ll <

and

Default valugs of E ~ E, ~ E, ~ cV , and 0.01 and 10 , respectively.

E

E

V of Eq. (

D - ~ , 0.5,

are set to

The flash equilibrium problem may also be formulated as a pure minimization problem, and some tests of this approach has been made utilizing the generalpurpose minimization routines E04JAF and EO4FDF contained within the NAG library /lo/. APPLICATIONS The above algorithms have been implemented into a computer program COPEC, and some applications on relatively simple fluid systems are discussed in the following. All cases are run in double precision on a VAX-11/780 computer. Relevant component properties are summarized in Appendix. Mixtures of Isobutane and Carbon Dioxide Tests with this binary system has been made with the PR version, and all results shown here are obtained for a temperature of 311 K (100'F). The phase behaviour of this system for a wide range of CO contents is depicted in 2 Fig. 1 and is in good agreement with previous calculations and experimental data 1 2 , 6 1 .

-CALCULATED 0

I

0

'A

!

"

0 ' 0

I I--\\

MEASURED

m

I

I 40

1

%a

I

'80

MOLE PERCENT CO2

Figure 1 Phase envelope for binary mixtures of isobutane and carbon dioxide at 311 K (100'F).

Y)

337

In most parts of the two-phase region of Fig. 1 , solutions are obtained easily even with pure successive substitutions, whereas the region indicated by a circle may pose more difficult problems. More detailed results in this region are given in Figs. 2 and 3 . With the refined successive substitution method presented here, we encountered no serious problems obtaining saturation points as indicated in Fig. 2. These points are obtained by repeated flash calculations and not by direct saturation point calculations, and they demonstrate thus the ability to perform flash calculations very close to a critical point. Details of the volumetric behaviour in this near-critical region are shown in Fig. 3 . A critical C02 content between 89.1 and 89.2% is predicted.

I

8

8

I

I

1

5

4

8

5

8

I

6

8

1

7

8

8

8

9

MOLE PERCENT CO,

Figure 2 Same system in the nearcritical region (calculated points are indicated bydots). 100

80

60

---T MOLE PERCENT

40

&'

/

20

0

m

970

980

geo

loo0

1010

1020

PRESSURE (PSIA)

Figure 3 Volumetric behaviour of I-C4 - C02 at 311 K (100'F) in the nearcritical region (calculated points are indicated by dots).

338 In Fig. 4, the predicted flash behaviour for a C02 content of 89 mole percent is considered in detail, and several observations can be made. First, it can be seen that a relatively high tolerance level on the8fugacity residuals ( E in E q . (9)) tends to widen the two-phase region. E = 10 also gives a smooth curve, but is obviously a too high tolerance this close to a critical point. If such a condition is suspected, the sensitivity of the solution with respect to the tolerance level should always be investigated. A more serious matter is the observation that for pressures above 6.977 MPa,

the Powell method converges to a false or, more precisely, trivial solution. Such solutions are characterized by all K-values approaching unity and may appear when the feed composition yields one and only one root in the cubic equation for the compressibility factor. The problem of avoiding such trivial solutions is probably the biggest problem encountered with flash calculations near to a critical point. The failure of Powell's method is investigated further in Figs. 5 and 6. These are plots of the fugacity residual norm p as function of the independent variables corresponding to a W-iteration and depict in detail the performance of the different solution alternatives. Contour values refer to the logarithm of p (log p ) . The vanishing norm for a I-C vapor mole fraction of 0.11 correspondsl?o the trivial solutions of K. = 4.0.

t o

0

90

ss.f ss. f = l1016 o16

0

ss.€=10-8

A

Powell. E = 10.16

80

c

t

0 K P Y

70 W -I

P P 2

9 -I

.60

50

40

30 6.94

Figure 4

6.95

6.96 6.97 PRESSURE (MPal

6.98

6.99

Flash behaviour of a I-C4 - CO mixture (89 mole percent C02) at 311 K (100'F) for different sofution alternatives.

339 Fig. 5 shows the solution space at a relatively large scale and depicts the performance of the first 15 pure successive substitutions. K-value estimates both by formula (15) and the fugacity approach are included. The fugacity approach starts off somewhat better, but in this case this makes very little difference when some 15 iterations hays been performed. After 15 iterations the residual norm is approximately 10 , and Fig. 6 depicts what happens if acceleration or Powell's method is started at this point. As may be seen, the accelerated successive substitution method proceeds in rather large steps towards a true solution whereas Powell's method rather quickly finds a trivial solution. The fi ure alsogshows what happens when Powell's method is employed at a norm of lo-' and 10 . In the former case, a trivial solution is rapidly found, while after 300 iterations in the latter case, the solution is stuck at what appears to be something like a saddle point. It should be noted gqso, that it takes 172 pure successive substitutions- reach a norm of 10 whereas the accelerated version reaches a norm of 10 in just 31 iterations.

''

Fig. 5 clearly shows that is not an appropriate tolerance level in the present case. A large region in the-fglution space satisfies this tolerance. Moreover, a maximum norm of only 10 separates the true solution from the trivial ones. It should be understood that the small-scale contour features in the lower left-hand parts of Fig. 6 are artifacts originating from that map (and all the other maps shown here) being contoured from a 101 by 101 network of points.

VAPOR MOLE F R A C T I O N

Figure 5 Residual norm plot for a 11% I-C4 T = 311 K).

-

89% C 0 2 mixture (P = 6.980 MPa,

340 VAPOR MOLE FRACTION

-

Figure 6 Residual norm plot for a 11% I-C4 89% CO mixture showing the 2 (P = 6.980 MPa, behaviour of different solution alternatives T = 311 K).

Fig. 7 shows similar fugacity residual norm plots for a decreasing pressure. P = 6.981 MPa corresponds to a single-phase liquid. The others show how the delineation between true two-phase solutions and trivial solutions is gradually improved as the pressure drops off from the bubble-point. The independent variables selected for the norm plots are probably not the natural ones for successive substitution. If anything, successive substitution must be considered as a process taking place in a space spanned by the K-values. It would be interesting to see the performance in such a space, and it might be an idea to employ the K-values as independent variables in Newton-type methods as well. A further illustration of the acceleration process is given in Fig. 8. Again the 89% C02 system is considered, and the iteration performance is plotted for two pressures in Fig. 4, namely P = 6 . 9 4 and 6.98 MPa. It is seen that the acceleration process improves the successive substitution method dramatically. AS we have seen, Powell's method does not give a true solution at all at 6 . 9 8 MPa. At 6 . 9 4 MPa a proper solution is obtained, but at approximately twice the no. of iterations required with acceleration. In addition, a Powell iteration generally takes more computer time than a successive substitution iteration.

341 0.10

a

f

zV -

U

z

0 V

9 w

0’I 0.11

P

P = 6.940 MPa

i

0.10

-

6.970 MPa

VAPOR M O L E F R A C T I O N

0.01

VAPOR MOLE F R A C T I O N

0.61

I

\

I a

p \

f

U

V

z

0 V

a lL

w

W

$

d5

I

0.11 P

0.01

-

VAPOR MOLE F R A C T I O N

VAPOR M O L E F R A C T I O N

6 9 7 9 MPa

.

0.51

\ a

P >

z-

0.11

P = 6.980 MPa

Figure 7 Residual norm plots for a 11% I-Cq

-

P - 6 . 9 8 1 MPa

89% COP mixture at 311 K.

342 0

I

I

OSS X SSwithur.

10-5

z

10-1(

P

I

K

::

I

5

I

I 10-l!

i

,

x

I

I

- __ __ __ 10-n

-

p 6.94 MPa p 8.98

1

1

I

l

l

l

,

,

50

l

,

loo

,

,

mh

,

0

NO. OF ITERATIONS

Figure 8

Iteration performance for a 11% I-CL

-

89% CO mixture at 311 K. 2

Another aspect of the refined successive substitution method presented here is illustrated in Fig. 9. It depicts the iteration performance for a step in a series of flash calculations where resulting K-values from one point is used as initial estimates for the next. A 89.3% CO mixture is considered and the pressure step in question is from 6.82 to 6.6% m a , corresponding to a decrease in liquid mole fraction from 9.01 to 0.46%. The solution escapes the two-phase region after 3 iterations, but with Eq. (14) defining a hypothetical liquid phase, the iteration is continued and brings the solution back into the twophase region before the tolerance level is met. The figure also shows the favourable effect of the multiplication factor y defined by Eq. (23). The solution is much more quickly returned to the two-phase region, and the no. of iterations required to achieve convergence is significantly reduced.

343 0.12

B

B

10-

1.10

10-

1.08

10-

10-

I

10-

\ Y

LO2

\

\ \ \

<

10-

10

1m .

7.0 NO. OF ITERATIONS

Figure 9

E f f e c t of bring-back procedure.

A Ternary Mixture

F i g s . 10 and 11 show some r e s u l t s obtained with a t e r n a r y mixture of 40% ethane, 40% propane and 20% n-butane. The SRK equation of s t a t e and t h e a c c e l e r a t e d successive s u b s t i t u t i o n method i s used throughout this example. This mixture has a l s o been s t u d i e d by Gundersen i l l / . Using a stepping procedure towards t h e c r i t i c a l region and a s p e c i a l treatment of 2 - f a c t o r s , he was a b l e t o perform f l a s h c a l c u l a t i o n s up t o some 0.02 MPa from the c r i t i c a l p o i n t . The p r e d i c t e d f l a s h behaviour a t some temperatures i n t h e v i c i n i t y of t h e c r i e had no d i f f i c u l t i e s obtaining cont i c a l temperature i s shown i n Fig. 10. W vergence even more c l o s e t o t h e c r i t i c a l p o i n t then i n d i c a t e d i n t h e f i g u r e .

344

4.8

4.8

6.0

6.1

5.2

PRESSURE (MR)

Figure 10 Flash behaviour of the ternary test mixture at different temperatures.

However, with a "normal" tolerance level of some of the isotherms were found to become irregular as the saturation pressure was approached. The previous example clearly shows that such irregularities are to be expected, and that the tolerance has to be gradually reduced to get accurate results as a critical point is approached. In most practical applications, consistency near a critical point is probably more important than to pursue solutions very close to this critical point. In Fig. 10 an attempt is made to define a critical point vicinity where a phase separation is not insisted on and the solution is interpreted as a single-phase "critical" mixture. Specifically, the calcula1) gets less than O281, and this criterion tions are terminated when 1 z.(K. is felt to be well adapted to'tht tolerance level of 10 Nghiem and Aziz 141 indicated a similar approach.

-

.

The effect on the isotherms is to create a discontinuity from two-phase to single-phase. In Fig. 10, all isotherms between 365.6 and 366.7 K experience this discontinuity (points beyond this discontinuity are not plotted), and the corresponding effect on the P-T phase diagram is to cut a top off the two-phase region as shown in Fig. 11.

Yarborough Mixture No. 8 The algorithms considered in this paper have been extensively tested also on systems consisting of a larger numbers of components, and some results obtained for a 6-component synthetic oil mixture commonly referred to as Yarborough mixture no. 8 1121 will be presented here. These results will concentrate on the solution performance. However, to set a background, the flash behaviour obtained at several temperatures is ploited in Fig. 12. Fair agreement with experimental results is obtained at 200 F, and the critical temperature is estimated to approximately 55'F.

345 I

I

I

!

I

I

/

/ I

I

TEMPERATURE I K I

Figure 11 Phase diagram of the ternary test mixture. The isotherm of 75'F is sufficiently close to the critical point to yield relatively hard flash equilibrium problems, and results of some testing of different solution alternatives for this temperature is given in Tables 2-4. Seven pressures are considered, and when converging, 514 the alternatives has been used in the yield essentially the same results. A tolerance of 10 present context,Resulting liquid mole fractions are included in Table 2 . Table 2

No. of iterations (and CPU-time) for different versions of SSM, Yarborough mixture no. 8 .

Pressure (psia)

Liquid mole fraction

2000 2500 2750 2875 3000 3050 3075

0.2621 0.3188 0.3537 0.3740 0.3953 0.3987 0.3878

NC

Pure

SSM with

SSM

overshoot

19 32 47 66 147 282

NC

(0.23) (0.35) (0.48) (0.67) (1.41) (2.71)

- Not converged within 300 iterations

13 20 28 37 224 293

NC

(0.16) (0.23) (0.31) (0.42) (2.45) (2.98)

SSM with acceleration 13 20 31 39 28 34 41

(0.16) (0.27) (0.37) (0.41) (0.34) (0.45) (0.48)

346

Table 2 compares different version of the successive substitution method. The pure version yield a prohibitively high no. of iterations for the higher pressure values. With overhoot the fugacity ratios are raised to the power of 2 in Eq. (8) after a fixed no. of iterations (10 in the present case). This may be seen to function well for the lower pressure values, but not so well more close to the saturation point. With the acceleration procedure, a maximum of 41 iterations is used for all the pressure values considered. The reason why the overshoot feature in some instances fails is probably that it is too uncritically employed, and the testing step included in the acceleration procedure should therefore be emphasized. The acceleration procedure proceeds in pairs of steps. First a simple iteration is done in order to determine k and the exponent of Eq. (20), and thereafter an accelerated step is made in accordance with Eq. (20). An important detail is, however, that the

Mole fractions c1

c2 c3 N-C5 c7 C10

0.8097 0.0566 0.0306 0.0457 0.0330 0.0244

0

PRESSURE IPSIA)

Figure 12 Volumetric behaviour of Yarborough mixture no. 8 at different temperatures.

347 a c c e l e r a t e d s t e p i s r e j e c t e d i f t h e f u g a c i t y r e s i d u a l norm f a i l s t o be decreased by t h i s s t e p . I n t h i s case j u s t t h e simple s t e p i s ' t a k e n and i s followed by a new p a i r of s t e p s . The a c c e l e r a t i o n performance recorded a t 3050 p s i a i l l u s t r a t e s t h i s point: Fugacity r a t i o exponent

I t e r a t i o n No.

17.764 -2.544 ( r e j e c t e d ) 27.007 0.940 ( r e j e c t e d ) 47.860 ( r e j e c t e d ) 27.125

22 24 26 28 30 32

I n essence w e have applied t h e same c r i t e r i o n f o r s t a r t of a c c e l e r a t i o n a s f o r switch t o Powell's method, see Eq. ( 2 5 ) . Table 3 compares d i f f e r e n t a l t e r n a t i v e s f o r t h e most important parameter i n t h i s c r i t e r i o n , namely &u, and ill u s t r a t e s t h a t some caution should be used when s e t t i n g t h i s parameter. If it i s too high, too many a c c e l e r a t i o n s t e p s a r e r e j e c t e d . I f it i s too low,-koo has many i t e r a t i o n s a r e made before a c c e l e r a t i o n i s attempted. A value of 10 been found t o be s u i t a b l e i n most cases and y i e l d s t y p i c a l l y some 15-30 i t e r a t i o n s before a c c e l e r a t i o n i s attempted. Comparisons with Powell's method a r e made i n Table 4 . Here, NL-iterations a r e somewhat more e f f i c i e n t than W - i t e r a t i o n s , b u t both a l t e r n a t i v e s a r e somewhat slower than t h e a c c e l e r a t e d successive s u b s t i t u t i o n method. Table 3

No. of i t e r a t i o n s a s f u n c t i o n of s t a r t of a c c e l e r a t i o n , Yarborough mixture no. 8

I

Residual norm a t s t a r t

Pressure (psis)

SSM with acceleration

SSM + Powell W-iteration

SSM + Powell NL-iteration

2000 2500 2750 2875 3000 3050 3075

13 20 31 39 28 34 41

13 20 23 32 17 21 23

13 20 23 32 17 21 23

(0.16) (0.21) (0.37) (0.41) (0.34) (0.45) (0.481

+ +

+ +

+

28 26 27 30 39

(0.16) (0.21) (0.70) (0.72) (0.58) (0.67) (0.83)

+ + + + +

17 18 19 26 30

(0.16) (0.21) (0.52) (0.59) (0.45) (0.59) (0.69)

348

We also did some tests with general-purpose, Newton-type minimization routines /lo/. Both the routines E04JAF and E04FDF were found to be less efficient than the other solution alternatives considered here, but one observation is worth mentioning. Working with the object function only, a more direct expression for Gibbs free energy is much better than a fugacity residual norm.

CONCLUSIONS

An accelerated and stabilized successive substitution method (ASSM) has been formulated for flash calculations of multi-component systems and has been especially designed for applications in the near-critical region. The method is made convergent also in the case of a disappearing phase,and will therefore detect single-phase solutions automatically. The acceleration procedure is based on an Aitken type formula for correcting the K-values, but acceleration steps are never taken unless they lead to improved solutions. In the examples presented, the ASSM method has been shown to be a highly stable and efficient method. As special saturation pressure calculations are not needed to delineate the two-phase region, the method is well adapted for incorporation in compositional simulators. Compared with Powell's method and other Newton type methods, the greatest advantage of the ASSM method is its stability close to saturation pressures. Generally, it is also faster than Newton type methods. The method presented is based on the Soave-Redlich-Kwong and the Peng-Robinson equation of state. However, it can easily be adapted to other equations of state.

NOMENCLATURE

k

K. L1 n N P R, Ri T V

V X

i ii

Zi Y E

P " i W

Equation of state coefficients Equation of state coefficients Liquid and vapor phase fugacities Gibbs free energy Acceleration parameter Equilibrium constants, K. = y./x. Liquid moles or liquid mile flacgion No. of components Total no. of moles Pressure Gas constant and fugacity ratios Temperature Molar volume Vapor moles or vapor mole fractions Mole fraction of component i in liquid Mole fraction of component i in vapor Mole fraction of component i in system Compressibility factor K-value multiplication factor Tolerance Fugacity residual norm Fugacity coefficients Acentric factor

349 Subscripts C

i, j j L r V

= = = = = =

Critical Component no. Iteration no. (as superscript) Liquid phase Reduced Vapor phase

ACKNOWLEDGEMENT This research is part of a joint project between Norsk Agip A/S and the Continental Shelf Institute (IKU). The project is fully financed by Norsk Agip A/S. The authors wish to thank Norsk Agip A/S for permission to publish this paper.

REFERENCES 1.

SOAVE, G.: "Equilibrium Constants from a Modified Redlich-Kwong Equation of State", Chem. Eng. Sci., Vol. 27 (1972), pp. 1197-1203.

2.

PENG, D.-Y. and ROBINSON, D.B.: "A New Two-Constant Equation of State", Ind. Eng. Chem. Fundam., Vol. 15, No. 1 (1976), pp. 59-64.

3.

FUSSEL, D.D. and YANOSIK, J.L.: "An Iterative Sequence for PhaseEquilibrium Calculations Incorporating the Redlich-Kwong Equation of State", Sac. Pet. Eng. J., Vol. 18, (June 1978), pp. 173-182.

4. NGHIEM, L.X. and AZIZ, K.: "A Robust Iterative Method for Flash Calculations Using the Soave-Redlich-Kwong or the Peng-Robinson Equation of State", SPE Paper 8285 presented at the 54th Annual Fall Meeting of SPE of AIME, Las Vegas (1979). 5. MEHRA, R.K. et el.: "Computation of Multiphase Equilibrium for CoIppositional Simulation", SPE Paper 9232 presented at the 55th Annual Fall Technical Conference and Exhibition of SPE of A W E , Dallas (1980).

6. MOTT, R.E.: "Development and Evaluation of a Method for Calculating the Phase Behaviour of Multi-Component Hydrocarbon Mixtures Using an Equation of State", AEE Winfrith Report 1331, Dorchester (1980). 7.

MADDOX, R.N. and ERBAR, J.H.: "Equilibrium Calculations by Equations of

State". Oil and Gas Journal, (Feb. 2, 198l), pp. 74-78. 8.

WILSON, G.: "A Modified Redlich-Kwong Equation of State, Application to General Physical Data Calculations", paper no. 15C presented at the AIChE 65th National Meeting, Cleveland, Ohio, May 4-7, 1969.

9. POWELL, M.J.D.: "A FORTRAN Subroutine for Solving Systems of Non-Linear Algebraic Equations", in RABINOWITZ, P. (ed.): "Numerical Methods for NonLinear Algebraic Equations", Gordon and Breach Science Publishers, London (1970). 10. NAG Library Manuals, Numerical Algorithms Group Ltd., Oxford (1978).

350 11.

GUNDERSEN, T.: "Numerical Aspects of the Implementation of Cubic Equations of State in Flash Calculation Routines", to appear in Comp 6r Chem. Eng .

12. YARBOROUGH, I,.: "Vapor-Liquid Equilibrium Data for Multicomponent Mixtures Containing Hydrocarbon and Nan-Hydrocarbon Components", J. Chem. Eng. Data, Vol. 17 (1972), pp. 129-133. 13. McCAIN, W.D.Jr.: Tulsa (1973).

"The Properties of Petroleum Fluids", Gulf Publ. Comp.,

APPENDIX

- COMPONENT DATA

The critical properties used in the computer program COPEC are taken from McCain /13/, and those used in the example calculations are given in Table 5. For the binary test system considered in this paper, the PR equation with a binary interaction coefficient of 0.13 has been used. For the tertiary test system, the SRK equation has been used with binary interaction coefficients as follows:

c2 c3

C2

- c3 - N-C4 - N-C4

: : :

0.001 0.009 0.012

For the six-component Yarborough mixture the PR equation is used with all binary interaction parameters equal to zero.

Table 5

Component properties

(ma)

Comp.

Hole weight

Pc

c02 c1 c2 c3 144 N-C4 N-C5 c7 c10

44.010 16.043 30.070 44.097 58.124 58.124 72.151 100.205 142.286

7.387 4.606 4.882 4.251 3.650 3.799 3.370 2.737 2.096

Tc (K)

Acentric factor

304.21 190.58 305.42 369.82 408.14 425.18 469.65 540.26 617.65

0.2250 0.0104 0.0986 0.1524 0.1848 0.2010 0.2539 0.3498 0.4885

351

MISCIBLE GAS DISPLACEMENT

THE EFFECT OF SIMULATED COZ FLOODING ON THE PERMEABILITY OF RESERVOIR ROCKS GRAHAM D. ROSS, ADRIAN C. TODD and J. ANDREW TWEEDIE

Department of Petroleum Engineering, Heriot-Watt University

Both formation damage and stimulation e f f e c t s have been experienced during "miscible" carbon dioxide f i e l d and laboratory tests i n the USA. While the stimulation e f f e c t s have been a t t r i b u t e d to d i s s o l u t i o n of t h e reservoir rock by carbon dioxide enriched flood water no work has been done t o i d e n t i f y and quantify t h i s phenomenon. Nor has any established theory f o r the formation damage been i d e n t i f i e d , although it seems l i k e l y t h a t i n some instances formation damage may be caused by formation f i n e s , released by d i s s o l u t i o n and subsequently migrating i n t o pore throats.

-

This paper describes a laboratory investigation i n t o the e f f e c t s of rock f l u i d i n t e r a c t i o n under s i m u l a t a r e s e r v o i r conditions, and i n p a r t i c u l a r t h e carbonated w a t e r carbonate mineral reaction in sandstones during a C02 enhanced recovery process. The design and operation of experimental equipment f o r flowing CO - w a t e r mixtures through l i n e a r rock cores are described, together w i t h $he a n a l y t i c a l methods used t o assess changes i n core c h a r a c t e r i s t i c s . The paper presents r e s u l t s from i n i t i a l tests on four d i f f e r e n t carbonate containing core materials.

-

(1)

General

Successful laboratory i n v e s t i g a t i o n s of miscible, carbon dioxide, flooding have been w e l l documented i n the literature. F i e l d experience, however, has only recently begun to accumulate. A l l the p r o j e c t s reported havebegunsince 1972 (mostly i n t h e United S t a t e s ) , thus, only limited empirical d a t a is currently available. Although encouraging, f i e l d r e s u l t s t o date have been s u f f i c i e n t to i d e n t i f y several major problems and opportunities with t h e carbon dioxide technique. One of the reservoirs due to the and carbon occurrence

problems is t h a t - o f reduced i n j e c t i v i t y experienced i n sane on i n j e c t i n g carbon dioxide. While many have reported t h i s to be depositfon of high molecular weight materials upon mixing of crude i n situ pluggiag tests have n o t proved the dioxide 2' of t h i s type of p r e c i p i t a t i o n Observed reductions i n

.

352 injectivity can probably therefore be attributed t o other mechanisms, one of which may be the disintegration of carbonate cements i n the reservoir rock, and movement of particulate matter i n t o the throats of i n t e r s t i t i a l pores. Conversely, increases in i n j e s t i v i t y have also been experienced i n the course of carbon dioxide f i e l d tests These were in t u r n attributed to dissolution of carbonate minerals i n carbon dioxide enriched floodwater (carbonated water), causing increased permeability.

.

I n view of the lack of data and uncertainty in the published r e s u l t s relating to carbonate dissolution on carbon dioxide flooding, a research programme has been i n i t i a t e d to study the phenanenon. The objectives of the programme are to evaluate the dissolution effects of carbonated water on formation carbonates, and to determine how formation permeability characteristics are likely to be altered during a carbon dioxide flood. This paperpresentsthe first phase of the study, the developpent and operation of apparatus for flowing C02-water mixtures through linear rock cores, together w i t h the results of experiments undertaken to establish the mechanism(s) of carbonate dissolution i n porous media. (2) Carbonate Dissolution i n Reservoir Rock

Many producing formations contain carbonates i n sme form. I n the case of limestone and dolomite reservoirs, carbonates constitute the bulk of the formation rock. I n sandstones, carbonates are cormnonly found as pore f i l l i n g and replacement cements consolidating the sand grains, although varying, but usually minor amounts of d e t r i t a l carbonate grains may also be present. Since the cementing material i n sandstone is located between sand grains adjacent to flaw channels, a relatively s m a l l change i n the pore framework due to carbonate dissolution may significantly a f f e c t the total permeability. Upon injection, carbon dioxide, mixing with either injection water or connate water, w i l l form carbonic acid. One characteristic of carbonic acid is t h a t a t very low carbon dioxide p a r t i a l pressure, the pH is reduced considerably. Thus, carbonated water w i l l retain its acid nature w i t h very l i t t l e C02 i n solution. The carbonates most conrmonly found i n reservoir rocks are those of calcium ( c a l c i t e ) , combinations of calcium and magnesium (dolomite) and iron ( s i d e r i t e ) . These minerals have a l o w solubility in pure water a t atmospheric conditions, but become increasingly soluble w i t h increasing water carbonation (or C02 concentration) and pressure. The carbonate form is converted to that of the soluble bicarbonate, the following equation representing the chemical reaction for calcium carbonate:

Similar chemical reactions take place w i t h the other carbonates. The solubility trends 6f calcium carbonate in carbonated water as a function of pressure and temperature are gresented i n Figure 1. Although no work has been carried out in the 0 to 100 C m f r a t u r e range a t pressures above 100 bars, indications from other studies are that c a l c i t e solubility: (1)

increases w i t h increasing temperature a t constant t o t a l pressure and COP concentration,

353 increases with t o t a l pressure a t constant temperature and CO concentratSon, and 2

increases up t o a maximum a t five weight per cent COP concentration before falling again a t higher CO concentrations a t constant temperature and tota9 pressure.

3 2

2 510 0[ 2(

CO* PRESSURE (bars) Figure 1

Solubility of c a l c i t e i n carbonated water

Carbonated water, formed upon injection of carbon dioxide i n t o a w e l l , w i l l react with the carbonate minerals i n the rock and transport the dissolved products through the reservoir. This dissolution effect w i l l be more pronounced i n the vicinity of the wellbore since the carbonated water solution w i l l approach t o t a l bicarbonate saturation as the water moves away from the well. However, whether the reaction effects a reduction i n permeability i n the reservoir by releasing particles which then migrate and plug flow channels, or an increase i n permeability, is not apparent from tests undertaken t o date. EXPERIMENTAL

A high pressure, high temperature penneameter was designed and constructed t o permit an examination of carbonated water dissolution effects. The apparatus, shown i n Plate 1 , i s capable of operation i n moderately corrosive liquid environments under controlled conditionerof temperature, pressure and flow rate. A process flow scheme of the core flooding apparatus is presented i n Figure 2.

354

Plate 1 A

Front view of experimental apparatus

d e t a i l e d description of the major e q u i p e n t components follows: (a)

Core Holder: The core holder c e l l was designed f o r high pressure core flooding i n corrosive l i q u i d environments. I t c o n s i s t s of a thick-walled s t a i n l e s s steel outer cylinder with removable l i d , f i t t e d i n t e r n a l l y with a sleeve core holding assembly. The sleeved core is secured between t h e c e l l l i d / i n l e t end p l a t e and the o u t l e t end p l a t e by three t i e rods. The end p l a t e s serve a s d i s t r i b u t o r and receptor respectively f o r the f l u i d flowing through the core. Both end p l a t e s a r e scored with l i n e s r a d i a t i n g from the c e n t r e and a l s o with concentric c i r c l e s about the centre. These l i n e s allow even f l u i d and pressure d i s t r i b u t i o n across the ends of a core, The o u t l e t end p l a t e can be p r e c i s e l y adjusted on the t i e rods t o enable s h o r t cores (down to 1.5 an long) to be f i t t e d i n the c e l l . The c y l i n d r i c a l s h e l l has four entry p o r t s o r taps, one i n the side-wall f o r t h e core sleeve confining pressure and the o t h e r s i n the l i d s one each f o r the core i n f l u e n t , the core e f f l u e n t and a thermocouple probe. The c e l l l i d is secured t o

1

Viscometer

Brine Preparation and vacuum System

Core Holder

P W

k==i Figure 2

Experimental F l o w

Apparatus

ul ul

356 t h e base by twenty high t e n s i l e b o l t s and sealed by Water from a hydraulic pump is used to an O-ring. supply t h e core sleeve confining pressure. The core holder has been t e s t e d and c e r t i f i e d f o r use up to a maximum working pressure of 6,000 p s i . (b) Viscosity Measurement System: Required d a t a on carbonated brine v i s c o s i t y are n o t reported i n the l i t e r a t u r e . Consequently an "in l i n e " c a p i l l a r y tube viscometer was incorporated i n t h e flow apparatus to enable l i q u i d v i s c o s i t y measurements t o be made under test conditions. The general arrangement of t h e v i s c m e t e r i s shown diagrauanatically i n Figure 2. The main elements ,are (1) a 20 QD length of 0.2 mm precision bore s t a i n l e s s steel tube (secured by epoxy r e s i n i n s i d e a length of support tubing) and (2) a d i f f e r e n t i a l pressure transducer. From the c a p i l l a r y tube dimensions and measurement of the

pressure drop across t h e tube a t known constant flow rate, t h e required v i s c o s i t i e s can be calculated from the HagenP o i s e u i l l e Equation.

(c) Transfer B a r r i e r : The t r a n s f e r barrier unit is a f l u i d pressure t r a n s f e r device, comprising an open-ended rubber bladder o r membrane enclosed i n a 5 l i t r e capacity c y l i n d r i c a l steel pressure vessel. I t serves as a mixing v e s s e l during carbonated water preparation and as a f l u i d separator i n which pressure and volume changes between the d r i v e f l u i d (hydraulic o i l ) and t h e core flooding f l u i d (brine o r carbonated brine) are tzansmitted through t h e f l e x i b l e rubber membrane. (d)

I n t e n s i f i e d C02 Supply: Carbon dioxide pressures g r e a t e r than cylinder pressure (830 p s i ) are obtained using a gas booster. I n t e n s i f i c a t i o n is obtained by a l a r g e area reciprocating p i s t o n pushing a s m a l l C02 compression p i s t o n with a r a t i o of 100 to 1 between t h e p i s t o n areas. A compressed a i r driven hydraulic pump d r i v e s t h e l a r g e area piston.

(e) Transfer Barrier Rocking Mechanism: To enable e f f i c i e n t and rapid preparation of equilibrium s o l u t i o n s of carbon dioxide i n w a t e r , a rocking mechanism was attached t o t h e t r a n s f e r b a r r i e r . The d r i v e f o r t h e mechanism is supplied by a Kopp v a r i a b l e speed motor, connected through a d r i v e arm and couplings to a steel c r a d l e holder bolted to the t r a n s f e r b a r r i e r . The d r i v e arm length is fixed to give a rocking angle of 30 degrees, and the rocking rate from 15 to 90 cycles per minute, i s controlled manually by a remotely controlled a d j u s t e r f r a a t h e v a r i a b l e speed motor. The f l u i d l i n e s to and from the t r a n s f i r barrier are s p i r a l l e d around the axis of rocking. The s p i r a l s help to maintain the i n t e g r i t y of various connections, by o f f e r i n g r e s i s t a n c e

to the j e r k s caused by the rocking mechanism.

(f)

Displacement System: The flow rate was determined i n a l l cases by employing an Eldex Precision Pump i n conjunction with t h e back pressure regulator. The Eldex p o s i t i v e displacement punp

357 delivers a steady flow t h a t can be varied from 0 to 4.5 cc per minute. The flow r a t e within this range is adjusted by a micrometer screw on the pump, which s e t s the length of stroke. The pump is capable of delivery pressures i n excess of 5000 psi. A

(9)

non-corrosive fluid (hydraulic o i l ) was used as a drive fluid t o displace the core flood liquid from the membrane i n the transfer barrier. The drive o i l was drawn fran a perspex reservoir by the Eldex pump and delivered a t constant volume to the base of the transfer barrier.

Pressure Measurement System: As shown i n Figure 2, the flow apparatus is equipped with four pressure gauges and two pressure transducers. The gauges are a s follows: (1) 0 t o -1.0 bar vacuum gauge, connected i n the l i n e to the vacuum pump used during i n i t i a l vessel and pipework evacuation.

-

(2)

0 to 10 bar gauge, connected i n the compressed to a i r supply l i n e to the gas booster monitor the a i r pressure to the gas booster

(3)

0 t o 600 bar gauge, connected to the core to monitor sleeve confining pressure l i n e

-

and hence the level of gas intensification.

-

core sleeve pressure. (4)

0 to 400 bar precision gauge with a stainless

s t e e l measuring element, connected immediately upstream of the back pressure regulator to monitor system back pressure.

-

Both pressure transducers a r e S.E. Labs. 21/V models: (1)

0 t o 5000 p s i absolute pressure transducer,

connected t o the transfer barrier to measure the system "upstream" pressure. It is e l e c t r i c a l l y connected to an Analogic d i g i t a l u n i t for visual observation. (2)

(h)

0

-

50 p s i d i f f e r e n t i a l pressure transducer, connected across the core holder and viscosity measurement capillary tube. I t is linked to a s t r i p chart recorder to provide a continuous record of the pressure d i f f e r e n t i a l data.

Temperature Control System: The temperature control System consists of three independent sub-systems: (1)

to heat khe contents of the transfer barrier,

(2)

to maintain the core and fluids entering the core a t the desired temperature level, and

(3)

to maintain the viscometer temperature.

Heat to the transfer barrier and core holder is supplied electricakly by close f i t t i n g mesh elements and controlled i n each case w i t h i n t 1 C ) by a thermostat/thermomuple controller. Xnmlatfon for the vessels is provided by 4 cm thick layers of rock wool encased in aluminised glass

358 cloth jackets. To ensure that a l l fluid entering the core is a t t e s t temperature, the f l u i d l i n e immediately upstream of the core holder is coiled tightly around the core c e l l lid. The capillary tube viscometer is enclosed i n a water bath where it i s maintained a t the desired temperature by hot water circulation. A s e r i e s of chromel-alumel thermocouples are used to monitor temperature

throughout the flow system. These are linked via a selector unit to a d i g i t a l thermometer for visual display and recording. (i) Effluent Collection and Measurement System: Core effluent, reduced to atmosuheric uressure on discharse from the back pressure regulator, enters the gas/liquid separator. The separator is a sealed perspex cylinder w i t h a capacity of 300 ccs. It has an i n l e t for the core effluent near the top and o u t l e t s i n the l i d and base for the separated gas and liquid respectively. The volume of carbon dioxide produced is measured by a wet-type volumetric meter connected directly to the gas o u t l e t fran the separator. The meter is a precision device provided with a 150 mm d i a l of 100 divisions and a s i x d i g i t revolution counter form of t o t a l i s e r . Liquid from the base of the separator flows via a five-way selector valve t o sealed glass collection vessels for measurement and analysis. (2)

Experimental Procedure

I n i t i a l testing consists of flowing base water (i.e. brine or d i s t i l l e d water) through the core t o establish the i n i t i a l or reference (stabilised) permeability. Subsequently brine, carbonated to the desired level inside the rubber membrane of the mixing vessel, is injected into the core a t constant r a t e by hydraulic o i l displacement. The carbonated water and core temperatures are carefully controlled to represent o i l reservoir conditions. A back pressure above the carbonation pressure is maintained throughout the t e s t t o ensure t h a t only liquid phase exists a t a l l p i n t s i n the flow system. The permeability of the core is measured as a function of time, and a l l core effluent is collected for chemical analysis. Following a core flood experiment a s e r i e s of analyses are performed on the core and effluent liquid. The effluent liquid is analysed for content of calcium and magnesium by EDTA t i t r a t i o n , and the core is divided i n t o a series of segments. The permeability, porosity, pore size distribution and overall dissolution e f f e c t i n each of the core segments is then assessed. (3)

Porous Media

To enable study of the carbonated water-carbonate mineral reaction i n sand-

stone without interference from other effects such a s clay or mica alteration, it was necessary to choose material w i t h a relatively simple mineralogical composition. Thus, a relatively pure quartz-carbonate sandstone, a calcareous g r i t , was chosen for the i n i t i a l stage of the study. The selection of this particular sandstone, fran a quarry i n the Yorkshire Jurassic, was also partly based on i t s high carbonate content. However, to gain a more complete understanding of the reaction e f f e c t of carbonated water on carbonate mineral i n reservoir rock, two other sandstones and a limestone were tested i n this i n i t i a l study. These materials are l i s t e d and described i n Table 1. The analytical procedures used i n the description of these materials, both before and a f t e r core flooding were:

TABLE I

Summarised descriptions of core materials

Formation

Rock Type

Description

Mineral Content

Physical Properties

Yorkshire Jurassic

Calcarenaceous Composed of subrounded detrital quartz grains Sandstone and detrital carbonate debris cemented by micritic calcite

Fife Carboniferous

Dololdtic Sandstone

Composed of angular to subrounded quartz grains partially cemented by secondary dolanite. The dolomite is evenly distributed, occurring as rho& shaped crystals and crystalline masses in the voids between sand grains

90% Permeability 20OmD Quartz Dolomite 10% Porosity 10% Felspar and Clay less than 1%

Rotliegende Sandstone

Calcitic Sandstone

Composed of subrounded to ro*mded quartz grains with patchy calcite pore fill and clay

Quartz 95% Calcite 2.5% Felspar and Clay 2%

Permeability 3 0 W Porosity 15%

Oxfordshire Jurassic

Oolitic Limestone

Composed of ooliths and shell fragments cemented by micritic calcite

Calcite Quartz

98% 2%

Permeability 6OmD Porosity 15%

Quartz 80% Ferroan Calcite 20%

Permeability 10OmD Porosity 16%

W

ul W

3 60 (1)

thin section petrographic analyses,

(2) differential dye staining for carbonate identification (3)

scanning electron microscope analyses,

(4)

porosity, pore size distribution and permeability measurements.

For each series of experiments a number of 2.5 cm diameter X 7.5 cm length cylindrical cores were drilled and trimmed from the same block of rock, so that variation in the properties would be kept to a minimum. As a precaution against collapse on dissolution, the cores were coated on the cylindrical surface with epoxy resin.

RESULTS (1) The initial series of experiments were carried out on the Yorkshire Jurassic calcitic sandstone. First tests with distilled water and brine (no carbonation) were aimed at establishing a stabilised or reference permeability, prior to any carbonated water flood. The results of two such tests, R7 and R9, are presented in Figure 3. Significant increases in permeability were obtained in the tests, with little apparent levelling off in the rate of permeability increase and attainment of a reference value, upon injection of up to 500 pore volumes. Chemical analysis of the core effluents for calcium showed the permeability increases to be attributable to the dissolution of calcite cement in the flood liquids.

a comparison with the base liquid experiments, a series of tests with carbonated brine were then undertaken. As shown in Figure 4 , much greater permeability increases were obtained, although again there was little indication of any fall in the rate of permeability increase. The results of the core effluent analysis as compared with those from a brine flood (R9) are presented in Figure 5 . As expected, the calcium concentrations in the effluent samples from the carbonated brine tests were far higher than in the brine test, although there was a significant difference between the results for carbonated brine tests R20 and R21. Examination of the flooded cores showed this was because in R20 a thin band was preferentially dissolved, whereas in R21 a more uniform dissolution took place (Plate 2). Presumably in R20, as the flood progressed, the main flow was through the thin permeability "streak", resulting in lower total dissolution than in R21.

As

To gain an understanding of the variation in local permeability, the cores from the various tests were retrieved after flooding and cut into three 2.5 cm long segments. The permeability of each segment was then measurod and plotted as a function of axial position in the core. The plots for R9 and R2O are presented in Figure 6. The profiles obtained show the permeability at the inlet end of the cores was increased considerably more than that at the outlet end. Also, the fact that the profiles have approximately the same shape, infers that the location of each profile is simply determined by the level of carbonation of the brine. Since constant flow rate was used in the experiments, this result implies that a zone of increasing permeability, which can be considered as a front, was moving through the cores. The velocity of the permeability front migration is in turn a function of the liquid flow rate through the core and carbonation level of the brine.

361

M0

2

/

R7 Calcitic Sandstone 3

R9 Calcitic Sandstone 3% Brine, 2Ooc, 1000 psi

1

: 200

100

300

400

PORE VOLUMES INJECTED Figure 3

Permeability changes during runs 7 and 9

22

19 16

13 10 7 4

1

i 00

200

300

PORE VOLUMES OF CARBONATED WATER INJECTED Figure 4

Permeability changes during runs 20 and 21,

500

362

0.12

-

0.08

-

0.04

R20

-

R21

- uniform

thin band preferentially dissolved

dissolution

-

-

R9

- brine w

W

600

flood A

W

1200

Q

w

1800

CORE FLOOD VOLUME (cc)

Figure 5

. ) .

Plate 2

Comparison of effluent calcium concentration profiles for runs 9, 20 and 21

.

Comparison of Yorkshire Jurassic sandstone cores before (left) and after (right, run 2 1 ) a carbonated water flood

363

600 ,

400

-

200

.

- - - INITIAL - -PERMEABILITY - - - - I

I

I

2.5

5.0

AXIAL

Figure 6

1 7.5

DISTANCE ALONG CORE (all)

Permeability profile for runs 9 and 20

The porosity and pore size distribution of each of the 2.5 an long segments from all the above tests were measured and compared to initial whole core values. Generally it was found that although large increases in the permeability had occurred, the porosity had changed little. This result illustrates that the main mechanism for the increase in permeability is probably not the uniform dissolution of carbonate cement, but rather the removal of constrictions in the larger pores. This is confirmed by the mercury porosimeter pore size distribution results, which show that it was primarily the diameters of the larger pores which were increased during the tests. (2) To further, and more realistically, test the permeability front migration phenomenon, a series of tests were initiated on material with a much lower carbonate concentration than the Yorkshire Jurassic sandstone. Difficulty in acquiring calcite cemented sandstone led to a dolomitic material from the Fife Carboniferous being used at this stage. It was hoped that it would be possible to dissolve out all the dolomite cement from this sandstone and thus eventually achieve constant permeability. However, the low reaction rate of dolomite in carbonated water, compared to that of calcite, effectively ruled out this possibility.

The permeability profiles of two tests, R22 and R23, on the dolomitic sandstone are presented in Figure 7. The very slow reaction rate of dolomite

under ambient temperature conditions meant virtually no dissolution effects were observed in R22, while in R23, although a fairly significant permeability increase was obtained, chemical analysis of the core effluent showed that only a small proportion of the dolomite cement was leached out. (3) Some tests were then carried out on a calcitic Rotliegende Sandstone from a Southern North Sea gas field, but a series of core collapses, caused by weakening on wetting, meant abandonning the use of this material and continuing the search for other sources of calcitic sandstone.

364

600

--

400

.

R23 Dolomitic Sandstone

-

200

R 2 2 Dolomitic Sandstone 1000 p s i Carbonation, ZOOC

"

-

0

v

200 400 PORE VGLUMES OF CARBONATED WATER INJECTED Figure 7

600

Permeability changes during runs 22 and 23

R26 O o l i t i c Limestone 1500 p s i Carbonation, 80°C

10

20

30

40

50

Pore Volumes of Carbonated Water Injected Figure 8

Permeability change during R26

( 4 ) A test w a s run on an o o l i t i c limestone from t h e Oxfordshire Jurassic, the permeability p r o f i l e of which is presented in Figure 8. A very rapid increase i n permeability was obtained, with the d i f f e r e n t i a l pressure across t h e core f a l l i n g t o almost zero a t maximum flow r a t e , a f t e r i n j e c t i o n of only 50 pore volumes. Examination of t h e flooded core shaved t h i s was because two 1.5 mm diameter "wormholes" of roughly c i r c u l a r cross section had formed over t h e length of t h e core.

365 Pore s i z e d i s t r i b u t i o n a n a l y s i s of the limestone i n d i c a t e d an extremely wide pore diameter d i s t r i b u t i o n and, as expected, it w a s the s e l e c t i v e enlargement of t h e l a r g e pores a t t h e upper extreme of t h e d i s t r i b u t i o n that c o n t r i b u t e d s i g n i f i c a n t l y to t h e i n c r e a s e i n p e r m e a b i l i t y i n this test.

CONCLUSIONS (1) The high p r e s s u r e , high temperature carbonated water permeameter c o n s t r u c t e d to i n v e s t i g a t e carbonate d i s s o l u t i o n e f f e c t s on carbon dioxide flooding i s providing new i n s i g h t i n t o the v a r i a b l e s that c o n t r o l t h e d i s s o l u t i o n process.

( 2 ) Only i n c r e a s e s i n c o r e p e r m e a b i l i t y from d i s s o l u t i o n of carbonate minerals were experienced. N o evidence f o r f i n e s migration o r p a r t i c l e plugging w a s obtained i n the experiments.

(3) The d i s s o l u t i o n of carbonate mineral from c o r e s produces a change i n local p e r m e a b i l i t y which t r a v e l s as a f r o n t through the c y l i n d r i c a l core. (4) The dramatic i n c r e a s e i n p e r m e a b i l i t y of a core d u r i n g a carbonated w a t e r f l o o d i s probably due t o removal of c o n s t r i c t i o n s and s e l e c t i v e d i s s o l u t i o n of t h e l a r g e r pores.

REFERENCES

1.

NEWTON, L. E. and McCLAY, R. A.; "Corrosion and Operation Problems, C02 P r o j e c t , SACROC Unit", Paper SPE 6391, presented a t t h e SPE-AIME Permian Basin O i l and G a s Recovery Conference, Midland, TX, March 10-11, 1977

2.

"North Cross U n i t C02 Flood WNTIOUS, S. B. and THAM, M. J.; Review of Flood Performance and Numerical Simulation Model", Paper SPE 6390, presented a t the SPE-AIME Permian Basin O i l and G a s Recovery Conference, Midland, TX, March 10-11, 1977

3.

HANSEN, P. W.; "A CO T e r t i a r y Recovery P i l o t , L i t t l e Creek F i e l d , Mississippi'!, Paper S8E presented a t the SPE-AIME 52nd Annual F a l l Technical Conference and Exhibition, Denver, O c t . 9-12, 1977

4.

DOSCHER, T. M. and KUUSKRAA, V. A.; "Carbon Dioxide f o r Enhanced Recovery o f Crude O i l " , paper presented a t t h e European Symposium on Enhanced O i l Recovery, Edinburgh, J u l y 5-7, 1978

5.

CAMERON, J. T.;

6.

MILLER, J. P.; "A P o r t i o n of t h e System CaC03-C0 0, with Geological Implications", Am. Jour. Sci. , (March 7953) 250,

-

6747,

-

"SACROC Carbon Dioxide I n j e c t i o n A Progress R e p o r t " , paper presented a t t h e API Production Department Annual Meeting, Los Angeles, A p r i l , 1976

161-203 7.

"The S o l u b i l i t y o f Calcite i n Carbon Dioxide SOlUtiOnS", ELLIS, A. J.; Am. Jour. Sci., (May 1959) 354-365

257,

366 8.

SEGNIT, E. R., HOLLAND, H. D. and BISCARDI, C. J.; "The Solubility of Calcite in Aqueiaus Solutions", Geochim. et Cosmochim. Act., (1962) 26, 1301-1331

9.

"The System CaO-C02-H20 in the Two Phase Region Calcite S H A R P , W. E.; and Aqueous Solution", PhD Thesis, Univ. of California, 1964

10.

"The System Ca0-C02-H20 in the Two S W , W. E. and KENNEDY, G. C.; Phase Region Calcite and Aqueous Solution", Jour. of Geol. (1965) 73, 391-403

-

NUMERICAL METHODS

367

COMPUTER MODELLING OF EOR PROCESSES KHALID AZIZ

Computer Modelling Group, 3512-33Street, N. W., Calgary,Alberta T2L 2A6, Canada

ABSTRACT This paper presents a rather personal view of recent developments, current problems and future prospects for the computer simulation of enhanced oil recovery schemes. While substantial progress has been made over the past twenty years o r so, some problems of significant practical importance remain unresolved. INTRODUCTION This paper is neither a comprehensive review of past work on reservoir simulation also referred to as reservoir modelling nor a complete catalogue of current activities in this field. Instead it presents the author's view of (a) the status of simulation technology, and (b) current and future problems. The paper is intended primarily for individuals interested in using models rather than those who are engaged in the development of models.

-

-

The contents of the paper are heavily influenced by work conducted by the author's students at the University of Calgary and his colleagues at the Computer Modelling Group (CMG). Important work underway at other institutions may not be mentioned here primarily because of the lack of up-to-date information available to the author. CMG is, however, a vehicle for cooperative research in reservoir simulation among universities, research organizations, government agencies and industry. Currently 34 such organizations are members of CMG and these organizations have a rather direct and significant influence on its work. Hopefully, because of this type of interaction, problems being investigated by CMG reflect current industry.needs. Modelling is an iterative process consisting of the following major stepsl: 1. 2.

3.

4. 5.

6. 7. 8.

Describe Reservoir Describe Recovery Mechanism Write Mathematical Model Develop Numerical Model Develop Computer Model (Program) Validate Model Match History Predict Future Performance

Often during steps 6, 7 and 8 it becomes necessary to go back to steps 1 , 2, 3 or 4 and alter some of the assumptions made earlier. Assumptions are necessary at various stages to (a) allow simulation of processes where recovery mechanisms are

368 n o t f u l l y understood, (b) make t h e problem tractable, and ( c ) reduce c o s t o f simulation. Obviously t h e need f o r t h e assumptions is c o n s t a n t l y changing with improved understanding o f t h e p h y s i c a l and chemical a s p e c t s o f t h e recovery processes, development of new numerical techniques, and hardware innovations. S t e p s 6 and 7 d e a l i n g with t h e v a l i d a t i o n and use o f models w i l l n o t be considered i n t h i s paper. CLASSIFICATION OF MODELS A large v a r i e t y o f models are i n c u r r e n t u s e and t h e number is c o n s t a n t l y i n creasing. New models are developed t o ( a ) s i m u l a t e new processes, ( b ) s i m u l a t e behaviour of r e s e r v o i r s with s p e c i a l c h a r a c t e r i s t i c s , (c) reduce c o s t , (d) i m -

prove accuracy, (el have access t o a s u i t a b l e model under a c c e p t a b l e c o n d i t i o n s , or ( f ) understand r e s e r v o i r simulation. Table 1 p r o v i d e s a c l a s s i f i c a t i o n based on Recovery Mechanisms, Reservoir/Well C h a r a c t e r i s t i c s , Numerical Approximations, FluidIRock P r o p e r t i e s , S o l u t i o n Techniques and Computer Type. Table 1

C l a s s i f i c a t i o n o f Models 1.

2.

3.

RECOVERY MECHANISMS 1.1

WATERFLOOD OR PRIMARY DEPLETION 1.1.1 Three component, t h r e e phase 1.1.2 Two component, two phase

1.2

GAS OR SOLVENT INJECTION 1.2.1 Multicomponent, s i n g l e phase 1.2.2 Multicomponent, multiphase

1.3

CHDfICAL FLOOD 1.3.1 Four component, two or t h r e e phase (polymer) 1.3.2 Multicomponent, multiphase ( s u r f a c t a n t , c a u s t i c )

1.4

THERMAL MODELS 1.4.1 Three component steam 1.4.2 Compositional steam 1.4.3 Steam w i t h a d d i t k v e s 1.4.4 I n s i t u combustion

RESERVOIR/WELL CHARACTERISTICS 2.1

RESERVOIR WELL COUPLING

2.2

FRACTURES 2.2.1 Static fracture 2.2.2 Dynamic f r a c t u r e 2.2.3 Uniformly d i s t r i b u t e d f r a c t u r e s

2.3

CONSOLIDATION OF RESERVOIR ROCK 2.3.1 Sand flow 2.3.2 Ground subsidance

NUMERICAL APPROXIMATIONS 3.1

PRIMARY VARIABLES 3.1.1 Selection of variables 3.1.2 Selection of equations 3.1.3 Alignment o f v a r i a b l e s and e q u a t i o n s

369 Table 1 (Cont'd)

3.2

LINEARIZATION

3.2.1 3.2.2 3.3

DECOUPLING

3.3.1 3.3.2 3.3.3 3.3.4 3.3.5 3.4

RELATIVE PERMEABILITY CALCULATION 4.1.1 Three phase model

4.1.2 4.1.3 4.1.4 4.2

6.

Standard f i n i t e - d i f f e r e n c e s Higher order f i n i t e - d i f f e r e n c e s Variational Semi-analytical Location of g r i d point i n a block Curvilinear g r i d Local g r i d refinement Moving g r i d

FLUID/ROCK PROPERTIES 4.1

5.

Single point upstream Two point upstream Harmonic average Centralized upstream Other interblock mobility c a l c u l a t i o n methods Nine-point schemes

TRUNCATION ERROR

3.5.1 3.5.2 3.5.3 3.5.4 3.5.5 3.5.6 3.5.7 3.5.8 4.

Fully i m p l i c i t Sequential I m p l i c i t Pressure E x p l i c i t Saturation (IMF'ES) Dynamic I m p l i c i t Band reducing techniques

INTERBLOCK FLOW

3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.4.6 3.5

Newton's method Other methods

Temperature effect model Composition e f f e c t model Hysteresis model

FLUID PROPERTIES 4.2.1 Empirical c o r r e l a t i o n s 4.2.2. Equation of s t a t e

SOLUTION TECHNIQUES 5.1

ORDERING OF EQUATIONS

5.2

GAUSSIAN ELIMINATION

5.3

ITERATIVE METHODS

COMPUTER TYPE 6.1

STANDARD

6.2

VECTOR PROCESSORS

6.3

INTERACTIVE DATA INPUT AND ANALYSIS OF RESULTS

3 70

This classification provides a suitable framework for comment on the status of some aspects of the technology. RECOVERY MECHANISMS The simplest models that can be used for primarily depletion and water or hydrocarbon gas injection studies are referred to as black-oil or models. Themodels of this type have been in use for over twenty years and are based on the assumption that the reservoir fluids can be assumed to consist of only three pseudocomponents oil, water and gas at standard conditions. This rather gross assumption works well for systems that remain far from the critical or the retrograde region during the recovery process and where the injected fluids consist of the same components as in the in situ fluids. Even in this relatively simple case different models can yield different results for the same problem2. Most of these differences may be attributed to the numerical aspects to be discussed later.

-

Compositional models allow for the representation of oil and gas by a mixture Of several m o m pseudo-components each. They can handle complex phase behaviour associated with, for example, the injection of C02. Chemical flood models are even more complicated compositional models with capabilities to handle important rock/fluid and fluid/fluid reactions. Each component or pseudo-component yields one conservation or mass balance equation to be solved for each grid point. Hence as the number of components increases, the number of equations to be solved increases in direct proportion. Thermal models can vary in complexity from the simple three component steam model to the complex in situ combustion model. In addition to the conservation of mass we must also add the conservation of energy to our system of equations to be solved. The problems in defining the recovery mechanism from the point-of-view of the modeller usually relate to the lack of experimental information for the selection of pseudo-components, to predict their physical and chemical properties, and to validate the assumptions of the mathematical model. Contrary to the belief held by some, reservoir simulation does not reduce or eliminate the need for experiments it allows us to get the most out of laboratory and field experiments we can afford to run.

-

Examples of the phenomena that can not be handled in a satisfactory fashion at this time are (a) formation and flow of emulsions, and (b) flow of more than two liquid phases. RESERVOIR/WELL CHARACTERISTICS The intimate interaction between the reservoir and the flow in the wellbore (tubing or annulus) of both injection and production wells must be recognized for realistic simulation. While it is relatively easy to do single phase well flow calculations to any desired accuracy, the same is not true when two or three phases exist in the wellbore. The transient nature of the flow causes further complications. Modellers often underestimate the importance of the wellbore/ reservoir coupling and overestimate the reliability of correlations for performing wellbore calculations. Errors of the order of 20% are possible even when "best" available methods are utilized. Since there are no clear schemes for the determination of what wellbore flow calculation method may be the best in each situation, even higher than 20% errors are possible. Simulation of the initiation, extension and closing of a fracture requires the coupling of rock and fluid mechanics. This important field has only recently started receiving attention. Much work is required before this technology can be used to improve the design of massive-hydraulic fractures now being conducted in tight formations4,5. These models are also required to predict fracture orienta-

371 tion and size in unconsolidated oil sands, where fracturing is used to provide initial communication between the injectors and the producers. Except for single well studies in cylindrical coordinates, economic constraints demand that blocks containing wells be orders of magnitude larger than the Size of the well. The problem then is to relate the calculated conditions at the grid point in a block to the well that may be located anywhere in that block. Analytical solutions based on single phase flow theory are used to relate the well pressure to the block pressure6. Detailed simulation of the zone near the well through the use of small blocks and cylindrical coordinates is necessary when saturation and/or thermal effects become important. The information generated from such a local study of the well vicinity is used in the form of pseudofunctions for the simulation of the reservoir. A better solution of this problem would be to have the capability to do local grid refinement without placing small blocks where they are not needed. The multi-grid approach may offer a solution to this problem7. Recently it has been possible to generalize the well treatment to handle vertical fractures that go through a number of grid pointsa. For single phase flow, where it is possible to compare numerical and analytical solutions, the agreement is excellent. For multiphase flow, in addition to the problems encountered for wells, we also have the unresolved problem of multiphase flow in the fracture. Reservoir rocks that are naturally fractured behave in a significantly different fashion from conventional reservoirs. They may be simulated through the concept of double-porous-media with separate equations for each system and appropriate transfer terms for interaction between the systemsg. Some of the problems with the practical use of this concept are (a) determination of the value of the transfer terms, and (b) experimental verification, particularly for multiphase flow. Some reservoirs are either unconsolidated or only partially consolidated. The flow of sand in such systems alters rock properties. In shallow reservoirs removal of fluids (and/or solids) may also cause ground subsidance. Little is known about these two mechanisms and their simulationlo. NUMERICAL APPROXIMATIONS The mathematical model of flow in a conventional reservoir consists of one partial differential equation for each pseudo-component. Furthermore, for thermal processes an additional partial differential equation for temperature is obtained from the conservation of energy. In addition several constraints and algebraic relations must also be satisfied. The equations of the mathematical model may be manipulated to obtain a set that is more amenable to numerical treatment. At this stage a set of primary variables, equal in number to the partial differential equations to be solved, is selected. Sometimes the selection is postponed until after the application of some technique to translate the partial differential equations to difference equations. For example in black oil simulation, the oil phase pressure, and gas and water saturations form a suitable set of primary variables. The selection of primary variables and the alignment of these variables with appropriate equations can have a substantial effect on the eventual performance of the model. Numerical difficulties can result due to the appearance and disappearance of a phase during simulation. This happens, for example, in thermal and in variable bubble point black oil problem simulation. This problem may be circumvented by variable substitution or b using a technique that does not allow the phase to disappear completely6,ll 9 1z~13. The same result is obtained by both techniques, however program complexity and computer time can differ substantially. With the use of variable substitution it is possible to solve for one less equation and

372

t h u s save computer time. However, s p e c i a l care is necessary f o r a smooth t r a n s i t i o n from one set o f v a r i a b l e s t o a n o t h e r s e t l 2 . Most r e s e r v o i r s i m u l a t o r s u t i l i z e three-point f i n i t e - d i f f e r e n c e approximation f o r second o r d e r space d e r i v a t i v e s a s s o c i a t e d w i t h t r a n s p o r t terms and two-point backward d i f f e r e n c e approximation f o r first o r d e r d e r i v a t i v e s a s s o c i a t e d w i t h t h e accumulation terms. The end r e s u l t of such a n e x e r c i s e is a set o f non-linear, coupled algebraic e q u a t i o n s of t h e form:

F(X) = 0

(1)

number Of where X is t h e v e c t o r o f unknowns ( = number o f primary v a r i a b l e s blocks) f o r a time s t e p . Such a set o f non-linear e q u a t i o n s can o n l y be solved by some i t e r a t i v e technique. Application o f Newton’s method y i e l d s : A(fi+1

- fi) =

(2)

-F(Xv)

where (v) is the l e v e l of i t e r a t i o n and A is t h e Jacobian w i t h elements a f i / a x j . These elements can be evaluated either numerically or a n a l y t i c a l l y , depending on the problem. The Jacobian matrix is s p a r s e w i t h t h e form shown i n F i g u r e 1. Each non-zero e n t r y i n t h e m a t r i x is a NEQxNEQ block element where NE4 is the number of primary v a r i a b l e s . 7

xx xxx xxx xx X x x x

x

x

X X

x

X X

xx x xxx x xxx x xx X xx X x xxx x xxx x xx

X X X X X X X X X X X

-

X

X X X

X X X X X X

xx x xxx x xxx x xx X xx x X x xxx x x xxx x x xx X X xx x xxx x xxx x xx

-

Figure 1 S t r u c t u r e of Matrix A f o r a 4 x 3 ~ 2Grid (Each X r e p r e s e n t s a NEQxNEQ block matrix) Each time s t e p u s u a l l y r e q u i r e s 2 t o 5 Newton i t e r a t i o n s f o r t h e s o l u t i o n of ( 1 ) . Hence f o r a t y p i c a l problem, equation ( 2 ) must be solved many hundreds of times. A s t h e number o f blocks i n c r e a s e s , t h e f r a c t i o n o f t o t a l computer time t h a t is spent on ( 2 ) also i n c r e a s e s . Recent research t o reduce t h i s e f f o r t w i l l be discussed i n the following s e c t i o n . The f u l l y i m p l i c i t method has u n l i m i t e d

373

stability, but Newton's method may not converge, or converge to an unreal solution if the initial guess (previous time step) is too far from the solution. Other variations of Newton's method like the semi-implicit or linearized implicit also work well for some problems. Non-linearities associated with the production/ injection terms can have a significant influence on the stability and time truncation error of the modell4. A problem of convergence to unreal solutions, which arises in the simulation of steam displacement with a non-condensable gas, has been eliminated through the addition of a "penalty source" term to the inert gas equationl2. The size of the matrix equation to be solved can be reduced by suitable approximations that partially or fully decouple the equations (SEQUENTIAL METHOD) and reduce the number of implicit equations to one (IMPES). In the I W E S method the pressure is solved for implicitly while the saturations are treated explicitly. This results in a limitation on stabilityl. The decoupling can take place at the Jacobian level of the partial differential equations, the difference equations, or the matrix. Approximations of this type do, in some cases, increase the number of iterations necessary for convergence over the time step or fail to converge. The reliability of such methods is questionable for difficult problems. The flow into and out of a block depends upon the permeability (kp,= k kr8)values at the block boundaries. The value of absolute permeability at the boundary is computed as the harmonic average of the two adjacent blocks. The rules for the computation of relative permeability are not well defined. The most comon approach is to use the relative permeability of the upstream block. Many different methods have been investigated with a view to reducing the grid orientation and truncation errorl5. KO et al.15 expressed transmissibilities for the two phase pressure and saturation equations as and

(3)

AT

fw AT respectively. They found that the centralized upstream for ,f fWIBB = 4 fWuu

- fWu

+

4 fwd

(4) (CUF): (5)

and harmonic total mobility (HTM):

worked best. Even this method failed when the shock mobility ratio, M,, exceeded 2. However their tests were for incompressible water flood problems. The behaviour of these schemes is different for compressible systems and when the saturation change is not monotonic. Another approach to reduce the grid orientation effect is to allow flow in directions that are both parallel and diagonal to the grid. This can be accomplished through a nine-point (as opposed to five-point ) scheme for two-dimensional problemsl3, l6 and a twenty-seven (as opposed to seven-point) scheme for threedimensional problems. Abou-Kasseml3 has observed significant reduction in grid orientation with the nine-point scheme for a steam displacement problem where five-point shows substantial effect of the orientation of the grid. Grid orientation is a major unresolved problem that raises some serious questions about the credibility of simulation for highly unfavourable mobility ratios. Although the nine-point formulation works, its use at this time is prohibitively expensive. For some situations ourvilinear grid can be used t o reduce both grid orientation and truncation error. However this approach is also not suitable for general applications.

374 Space and time t r u n c a t i o n e r r o r s can be maintained a t t o l e r a b l e l e v e l s f o r convent i o n a l simulation. However, t h e e f f e c t of space t r u n c a t i o n can mask t h e t r u e phenomena i n processes where block s i z e is t o o l a r g e t o d e f i n e e v e n t s i n t h e r e s e r v o i r . Examples o f t h i s s i t u a t i o n are ( a ) m i s c i b l e o r chemical s l u g s , and ( b ) combustion f r o n t . I n a m u l t i p l e c o n t a c t miscible d r i v e process, t h e r e s u l t s can be e s p e c i a l l y s e n s i t i v e t o t h e s i z e o f t h e blocks i n t h e zone where m i s c i b i l i t y i s being e s t a b l i s h e d . The accuracy of simulation could be improved by ( a ) a d a p t i v e g r i d refinement, ( b ) using higher o r d e r methods, o r ( c ) using a n o t h e r ( p o s s i b l y a n a l y t i c a l ) model w i t h i n t h e block t o provide t h e necessary d e t a i l . None of t h e s e approaches have f u l l y succeeded so far. FLUID/ROCK PROPERTIES R e a l i s t i c p r e d i c t i o n of f l u i d and rock p r o p e r t i e s f o r t h e changing c o n d i t i o n s during simulation is of c r u c i a l importance i n r e s e r v o i r simulation. However, t h i s a s p e c t of t h e problem is n o t t o t a l l y i n t h e c o n t r o l of t h e simulator developer. Often l a c k o f good experimental data and the need f o r answers w i t h i n t i g h t time c o n s t r a i n t s f o r c e s one t o make assumptions t h a t may o r may n o t be j u s t i f i e d . I n s i t u a t i o n s of t h i s type, i t is t h e r e s p o n s i b i l i t y of t h e modeller t o make t h e l i m i t a t i o n s of t h e r e s u l t s c l e a r t o t h e u s e r of t h e information derived from t h e simulation. Most of t h e p r o p e r t i e s required f o r t h e simulation of primary d e p l e t i o n o r water flooding i n crude o i l r e s e r v o i r s can e a s i l y be measured i n t h e l a b o r a t o r y , and are u s u a l l y a v a i l a b l e . One exception t o t h i s is data on t h r e e phase r e l a t i v e permea b i l i t y , and on the e f f e c t of temperature and i n t e r f a c i a l t e n s i o n on r e l a t i v e permeability, and c a p i l l a r y pressure. Models are o f t e n used t o p r e d i c t t h r e e phase r e l a t i v e permeability from two phase data, and t h e effects o f temperature, i n t e r f a c i a l tension and h y s t e r e s i s phenomenon. More data than what is c u r r e n t l y a v a i l a b l e are required t o v a l i d a t e and r e f i n e these models. R e l a t i v e l y simple equations of state when properly tuned and used o f f e r a powerful means of computing f l u i d p r o p e r t i e s i n an a c c u r a t e and c o n s i s t e n t fashionl7. These equations can be imbeded within a compositional model. Since compvtations with t h e equation of s t a t e a r e i t e r a t i v e , t h e modeller must ensure t h a t the scheme w i l l converge i n d i f f i c u l t s i t u a t i o n s with r e l a t i v e l y few i t e r a t i o n s l 7 , 1 8 . Several groups, including CMG appear t o be making s i g n i f i c a n t advances i n t h i s area. I n v e s t i g a t i o n s are a l s o underway on methods of s e l e c t i n g an optimum number of components t h a t can be used t o r e p r e s e n t t h e r e s e r v o i r and i n j e c t e d f l u i d s l g . There is a l s o concern t h a t , a t least f o r some processes l i k e t h e i n j e c t i o n of CO2 i n heavy o i l , t h e assumption of thermodynamic equilibrium between phases i n a block may not be valid. A s t h e processes become more complex t h e data requirements i n c r e a s e while the a v a i l a b i l i t y of data decrease. An example of t h i s is t h e k i n e t i c s of low tem-

p e r a t u r e oxidation f o r i n s i t u combustion processes. SOLUTION OF MATRIX EQUATIONS The heart o f a r e s e r v o i r simulator is a program f o r t h e s o l u t i o n o f a l a r g e set of l i n e a r equations t h a t may be expressed as

where A is a s p a r s e matrix with a well defined s t r u c t u r e , x*l is a vector r e p r e s e n t i n g change i n t h e primary v a r i a b l e s from v t o * l i t e r a t i o n , and r i s t h e r e s i d u a l vector. Equations of t h i s type may be solved d i r e c t l y by Gaussian e l i m i n a t i o n , o r by some i t e r a t i v e method which involves t h e repeated s o l u t i o n of s e v e r a l sets o f s m a l l e r matrix equations by Gaussian elimination. The work required f o r t h e d i r e c t s o l u t i o n of a system l i k e t h i s is given by

375 WD f I(NEQ J K ) 3 (8) where I, J , and K are the number of grid points in the three directions. To minimize work I is chosen to be the direction with the largest number of grid points. The coefficient f=l for standard ordering may be reduced to between .l9 and .5 for D4 orderingl. Work required for iterative methods is difficult to predict since the number of iterations required depends on the problem. Another problem with iterative methods is their reliability in difficult situations. In general iterative methods that work are cheaper than direct elimination for larger problems. The cross-over point depends upon the methods and the problem. Some rather powerful iterative methods have been developed recently. One such method, known as COMBINATIVE, has worked even for extremely difficult thermal problems20. This method became more economical than the direct elimination if (J*K*NEQ + NEQ-1) 2 50 (9) The combinative method involves the following steps: (a) decouple pressure equation by neglecting appropriate terms in (7), (b) solve the pressure equation by Gaussian elimination with D4 ordering and obtain initial estimate of pressure, (C) use this pressure estimate to form new residuals for (7), (d) do an LU factorization of the whole set and obtain an initial estimate of the remaining variables and an extra contribution to the initial pressure estimate obtained in step (a), and (e) apply ORTHOMIN20 acceleration. This procedure is repeated until convergence is achieved.

Other iterative methods based on the multi-grid21 approach now being developed show even greater promise. Iterative methods also require less storage than direct methods. In difficult problems it is necessary to treat the coupling between the well and the reservoir in a fully implicit fashion. If the well goes through more than one layer or block, additional terms are introduced. Unless properly handled, work required to solve the equations can increase substantially22. COMPUTER HARDWARE In addition to the computers becoming faster with larger and larger memory, there are two other developments that are beginning to have a profound influence on reservoir simulation. These are (a) the development of pipeline and parallel processors, and (b) the development of display and interactive techniques. The pipeline and parallel processors can perform a large number of operations (up to 5 x lo8 floating point operations per second) very quickly provided the software is designed to take full advantage of the hardware. The current compilers can only go partways in achieving high efficiency with such processors. Program structure and solution algorithms are being developed for this class of computers. One disadvantage of this approach is that as efficiency on one machine increases, the program becomes less and less portable. Interactive preparation of data and graphical display of results can make it much easier to run simulators and analyze results. This is particularly true of the new or infrequent users of a complex model. Within the next few years this is expected to become the normal procedure for conducting simulation studies. CONCLUSIONS The need for robust, economical, realistic and easy to use simulators is increasing as the oil recovery mechanisms being applied become more and more complex. Simulators are an essential tool for understanding and predicting reservoir performance. Their intelligent use can play a key role in optimizing oil recovery.

376 Along with the development of new numerical techniques, experimental studies must be continued to provide data and correlations for the prediction of fluid and rock properties. Model validation with carefully conducted experiments is also essential. Significant new developments in numerical techniques, process understanding and hardware have taken place over the last few years, but much more needs to be done and will be done over the next few years. ACKNOWLEDGEMENTS The Department of Energy and Natural Resources of the Province of Alberta and the Department of Energy, Mines and Resources of the Government of Canada, provide partial funding for the work of CMG through the AlbertaKanada Energy Resources Research Fund. Additional support is provided by Associate'Members of CMG through the membership fees. The work at the University of Calgary has been supported over the past sixteen years by the National Science and Engineering Research Council (previously National Research Council). The author is indebted to these organizations for financial support and to his students and colleagues for the generation of ideas and for their implementation in practical simulations. NOMENCLATURE

A

Jacobian matrix

I,J,K

Grid nodes along the three directions

k

absolute permeability

kr-9.

relative permeability of phase 9.

NE4

Number of equations per grid block ( = number of primary variables)

r

Residual vector

X

Vector of change in primary variables over an iteration

X

Vector of primary variables (unknowns)

Pa

viscosity of phase .9

SubscriDts

BB

Block boundary

d

1 point downstream of block face in question

U

1 point upstream of block face in question

uu

2 points upstream of block face in question

377 Superscript Iteration level

V

REFERENCES 1.

AZIZ, K. and SETTARI, A.; "Petroleum Reservoir Simulationf1,Applied Science Publishers, London (1979).

2.

ODEH, A.S.; "Comparison of Solutions to a Three-Dimensional Black Oil Reservoir Simulation Problem", J. Pet. Tech. (January 1981) 3,1, 13-25.

3.

FOGARASI, M., GREGORY, G.A. and AZIZ, K.; "Analysis of Vertical Two Phase Flow Calculations: Crude Oil - Gas Flow in Well Tubing", Cdn. J. Pet. Tech. (1980) 3, 1, 86-92.

4.

WADE, R. and AZIZ, K.; llStimulatingthe Triassic Carbonates in the Foothills Gas Trend of Northeast British Columbia", CIM 81-32-35, presented at the 32nd Annual Technical Meeting of the Petroleum Society of CIM, Calgary, Alberta (May 1981).

5.

SETTARI, A.; "Simulation of Hydraulic Fracturing Processes", Soc. Petrol. Eng. J. (December 1980) 20, 6, 487-500.

6.

AU, A., BEHIE, A., RUBIN, B. and VINSOME, K.; "Techniques for Fully Implicit Reservoir Simulation", SPE 9302, presented at the 55th Annual Fall Technical Conference and Exhibition of the SPE of AIME, Dallas, Texas (September 1980).

7.

BRANDT, A.; "Multi-Level Adaptive Solution to Boundary Value Problems", Math. Comp. (April 1977) 2,138, 333-390.

8.

NGHIEM, L.; llModellingInfinite-Conductivity Vertical Fractures Using Source or Sink Terms", CMG.Re.02, (February 1981).

9.

GESHELIN, B.M.;

10.

Ertekin, T. and Farouq Ali, S.M.; "Numerical Modelling of Reservoir Compaction and Associated Ground Subsidence under Non-Isothermal Two-Phase Flow Conditions", presented at the SIAM Fall Meeting, Houston, Texas (November 1980).

11.

CROOKSTON, R.B., CULHAM, W.E. and CHEN, W.H.; "A Numerical Simulation Model for Thermal Recovery Processes", Soc. Petrol. Eng. J. (February 1979) 9,1, 37-58.

12.

FORSYTH, P.A. Jr., RUBIN, B. and VINSOME, K.; "Elimination of the Constraint Equation and Modelling of Problems with a Non-Condensable Gas in Steam Simulation", CIM 81-32-50, presented at the 32nd Annual Technical Meeting of the Petroleum Society of CIM, Calgary, Alberta (May 1981).

13.

ABOU-KASSEM, J.H.; "Investigation of Grid Orientation in a Two-Dimensional, Compositional, Three-Phase Steam Model", Ph.D. Thesis, University of Calgary (1981).

14.

FONG, D.K.S. ; llTreatmentof Nonlinearities and Production Allocation in a Fully Implicit, Three-Phase Coning Model", M.Sc. Thesis, University of Calgary (1980).

15

-

Y3tatic Fracture Model", CMG.RB.01,

(January 1980).

KO, S.C.M., BUCHANAN, W.L. and VINSOME, K.; "A Critical Comparison of FiniteDifference Interblock Mobility Approximations in Numerical Reservoir Simulation", CIM 81-32-23, presented at the 32nd Annual Technical Meeting of the Petroleum Society of CIM, Calgary, Alberta (May 1981).

378

16.

KO, S.C.M. and AU, A.; **A Weighted Nine-Point F i n i t e - D i f f e r e n c e Scheme f o r Eliminating t h e Grid O r i e n t a t i o n E f f e c t i n Numerical Reservoir Simulation", SPE 8248, presented a t t h e 54th Annual F a l l Technical Conference and Exhibi t i o n of t h e SPE o f AIME, Las Vegas, Nevada (September 1979).

17.

N G H I D l , L. and A Z I Z , K.; "A Robust I t e r a t i v e Method f o r Flash C a l c u l a t i o n s Using t h e Soave-Redlich-Kwong o r t h e Peng-Robinson Equation o f Statell, SPE 8285, presented a t t h e 54th Annual F a l l Technical Conference and Exhibition of t h e SPE o f AIME, Las Vegas, Nevada (September 1979).

18.

MEHRA, R.K., HEIDEMA", R.A. and A Z I Z , K.; V a l c u l a t i o n of Multiphase Equilibrium f o r Compositional Simulationf1, SPE 9232, presented a t t h e 55th Annual F a l l Technical Conference and Exhibition of t h e SPE of AIME, Dallas, Texas (September 1980).

19.

LEE, S.T., JACOBY, R.H., T h e o r e t i c a l S t u d i e s on t h e mal Processest1, SPE 8293, f e r e n c e and Exhibition of 1979).

20.

BEHIE, G.A. and V I N S O M E , K.; "Block I t e r a t i v e Methods f o r F u l l y I m p l i c i t Res e r v o i r Simulation", SPE 9303, presented a t t h e 5 5 t h Annual F a l l Technical Conference and Exhibition of t h e SPE o f AIME, Dallas, Texas (September 1980).

21.

BEHIE, G.A. and FORSYTH, P.A. J r . ; "Multi-Grid S o l u t i o n o f t h e Pressure Equation i n Reservoir Simulationf1, CMG.Rl7.01 ( J u l y 1981).

22.

GEORGE, A.; "On Block Elimination f o r Sparse Linear Systems", SIAM J. Numer. Anal. (June 1974) 11, 2, 585-603.

CHEN, W.H. and CULHAM, W.E.; Wxperimental and F l u i d P r o p e r t i e s Required f o r Simulation o f Therpresented a t t h e 54th Annual F a l l Technical Cont h e SPE o f AIME, Las Vegas, Nevada (September

NUMERICAL METHODS

379

THREE-DIMENSIONAL NUMERICAL SIMULATION OF STEAM INJECTION P. LEMONNIER

Institut FranGais du Pktrole, Rueil Malmaison, France

ABSTRACT k three-dimensional thermal model has been developed for simulating both cyclic steam injection and steam drive. The numerical model !IWIST describes three-phase flow (oil, water and steam) heat flow in the reservoir a& heat conduction in the surrounding formations. Wellbore heat losses between the surface and the reservoir are taken into account. The various reservoir heterogeneities and temperature dependent parameters (including relative permeabilities) are considered. Distillation effects are approximated through the decreased residual oil saturation when steam is present. Mass conservation and energy equations are solved simultaneously to improve stability. A semi-implicit method is used for time formulation. The oil phase equstion is decoupled with a scheme of the type p-T-S /S This formulation enables this thermal simulator to be very efficient $n a k m s of coinputing time and stability

.

Numerical results are presented showing e steam stimulation history of five cycles and the influence of steam quality, initial reservoir pressure and steam injection rate on steamflood performance in a five-spot pattern.

INTRODUCTION TWIST (Tool When Injecting Steam) is a three-dimensional steamflood model, steam) and heat flow in the which describes.three-phaseflow (oil, water reservoir. Vertical heat losses to overlying and underlying strata and wellbore heat losses between the surface and the reservoir are taken into account. The literature on the simulation of steamflooding is extensive 1-7. The efforts have been concentrated on methods of solution. The equations are solved sequentklly or simultaneously and the formulation is explicit, weakly or highly implicit. We use a formulation which requires significantly less computing time per grid block-time step than the implicit scheme, and is nevertheless highly stable, owing to the fact that the water and gas flow equation and the energy equation are solved simultaneously with implicit treatment of the gas transmissibility. This formulation has been mentioned in the literature6 but not tested otherwise than in isothermal black-oil model.

380

iv'e encountered no difficulties in simulating field c a s e s rith TWIST. Our experience includes steam stimulation and steam drive for pilots o f various pattern shapes and various oil viscosities. Numerical results are present,ed shoving a steam stimlation history of five cycles and the influence of steam quality arid reservoir pressure on oil recovery in steam drive.

MODEL DESCRIPTION Simulator equations The model consists of four equations expressing (1) conservation of mass for water and steam, ( 2 ) conservation of mass for oil phase, ( 3 ) conservatioo of energy and ( 4 ) equilibrium constraints. The four unknowns are oil pressure, temperature, steam and water saturations. We have three additional equations for obtaining oil saturation, gas and water pressures : (5) saturations constraint, ( 6 ) and ( 7 ) capillary pressures.

s +s +s o

w

s

= 1

Po - Pw = PCW P,

- Po = Pcg The phase velocity 7: is defined as

The condensation term is eliminated by summing the water aad steam mass conservation equations 3 . The equilibrium constraints are expressed by one of the three equations ( 4 ) for the following cases : no steam, saturated steam, superheated steam.

381 Additional assumptions 1

- The model can operate in one, two or three dimensions with Cartesian or'radial grid.

4

-

5

- Reservoir can be anisotropic, homogeneous o r heterogeneous by layers

2

3

Reservoir dip and gra.vityare takeo into account. Reservoir rock and fluids areampressible. The model is not compositional. Distillation effects are approximated through decreased residual oil saturation in the presence of steam.

or by cells. 6

- Temperature dependency of the physical and thermal parameters is accounted for.

7

- Three-phase relative permeabilit'es i at each temperakure value are calculated using Stone's method

8

,

- Numerical simulations include steam drive and steam stimulation.

Heat loss to overburden and underburden Heat loss by conduction to the overlying and underlying strata is calculated from the numerical solution of the heat conduction equation. The equation is approximated by the standard finite -difference approximation. We assume negligible effects of heat conduction in the horizontal directions 3 . The heat conduction equation for the surrounding rock is not solved simultaneously with the reservoir equations. At,time step n+l the equation is solved using the reservoir boundary temperature at the previous time step. Well model The wells have the following specifications : 1

- Bottom-hole pressure

2

- Water or steam injection rate

3 4

5

- Liquid production rate - Oil production rate

- Shut in.

Each well can operate successively in injection and production modes (for huff and puff process for example). Wellbore heat losses in the injection wells are calculated. The injection pressure and the steam quality are s ecified at surface or reservoir conditions. We use the method o f Rameyl3, SatterP4 for wellbore heat losses computations 20. The basic assumptions o f the method are as follows:

-

Steam is injected at a constant rate, wellhead pressure, temperature and quality.

- Any variation in steam pressure with depth is negligible.

382 Fluid and rock properties The steam and water properties are expressed through correlations fron the steam tables. Oil and water enthalpies are expressed as polynomial functions of temperature. Steam enthalpy am2 all fluid densities are treated as functions of pressure and temperature. Water and steam viscosities are expressed as functions o f temperature. Oil \-iscosity is entered into the model as tabular function o f temperature with exponential interpolation between adjacent entries in the table. Residual oil and irreductible water saturations are represented as linear functions of temperature; the same assumption is made for the,relatire permeability end points. The influence of temperature on the relative permeability curves is described by shifting the curves wit.hout changing the curves shape5. The rock specific heat and thermal conductivity are represented as linear functions of temperature. User facilities User facilities have been developed in the simulator. Arrays are dimensioned automatically with appropriate values at the beginning of each run. All input cards are checked for validity and for inconsistencies. All errors encountered are listed at the end of the dataprocessing. Various print,ingoptions are allowed for input data and output rpsults. Array maps can be selected and printed with any orientation. Graphic plotting of input data (oil .) and well behaviour versus tine (presviscosity, relative permeabilities, sure, oil recovery, WOR, ...) are available, just as pressure, temperature or saturations contours or profiles,

..

SOLUTION METHOD

Discretization The three equations ( 1 ) ( 2 ) ( 3 ) are discretized into finite - difference form with upstream densities, mobilities and enthalpies in the flow terms. Semi-implicit .%pproximcttions9 are used for time discretization. Interblock transmissibilities o r flow terms are treated as follows. Explicit (i.e. time level n) dating is considered for fluid viscosities, fluid densities and f l u i d enthalpies, on account of the weak sensitivity to implicit versus explicit dating encountered in numerical simulations. Explicit dating is used f o r water and oil relative permeabilities end semi-implicit formulation is used for steam relative permeability. Capillary terms are expressed explicitly in saturation. The accumulation terms are written with implicit dating. formulation is then linearized as follows :

f (pn+', where

sn+l, Tn+') bX =

= f (p", Sn, Tn)

x"" - f

+

df df b~ b p +-6;5 b S

with X = p, S, T.

The resulting

df +z 6T

(9)

383 With these approximations the four equations ( 1 ) ( 2 ) ( 3 ) ( 4 ) are expressed in terms of the four unknowns bp, 6T, 6Ss andbs,. The first three equations can he represented by

The explicit treatment o f oil and water relative permeabilities allows the water saturation unknown 6 s to be eliminated in equations (10) and (12) by means of equation ( 1 1 ) . The"e1imination of 6 s W results in a system of two coupled equations ( 1 3 ) ( 1 4 ) :

A

I

..

= A , .

13

13

-,

A. l4

A24

-

X A

-

2j

A 14 .

I

F t i l = Fil

R . = R . --xR2 A24

A i4 A24

i = 1 et 3 ,

F21

j = 1,3

The equations ( 4 ) (13) (14) involving the three unknowns 6 p , bT, 8 S s are reduced to two equations in the two uknowns bp, 6X by use of the equilibrium constraints ( 4 ) . The unknown bX is equal t o b T o r 6Ss. The definition of 6 X can vary from one grid cell to an other and from one time step to an other according to the equilibrium condition in the grid cell at time step n+1. If no steam is present at time step n + l , for eliminating 6 S s . If steam is present at time step n+l, eliminating 6T

6X = 6 T and equation (4a) is used

6 X = 6 S S and equation (4b) is used for

If superheated steam is present at time step n+l, is used f o r eliminating 6 S s .

6 X =6T and equation (4c)

Explicit dating of saturation-dependent production terms can give saturation oscillations in grid cells near the wellbore. A semi-implicit formulation for production terms similar to that described by Spivak and Coatsto is used for increasing computational stability. Resolution Procedure The procedure of solution of the equations for the time step n+l is as follows :

-

1 Solve the two equations ( 1 3 ) (14)for bp and 6 X using Gaussian direct solution with I) 4 ordering 1 1 . The substitution of the unknowns 6s or bT is made with the equilibrium conditions at time step n.

384

-

2 Check the validit,y of the solution for each grid cell. If not, choose an other equilibrium condition and solve again the two equations for 6 p and 6X. 3

-

Solve equation ( 1 1 ) for

6 sW using the values dp, 6T and 6 s s .

EXAX’LES OF API‘LICATIOXS

k’e used the model for simulating a number of field cases. Numerical simulation studies of a steam drive pilot12 were made with a two-disensional grid. Simulations of the whole seven-spot pattern are now pursued with a three dimensional grid (12 x 9 X 5). Two example cases are presented to illustrate the use of the model in the case of well stimulation and steam drive.

Well stimula.tion The first application of the model consisted in simulating the production history of a well submitted to five successive steam stimulation cycles. The data are given in Table 1. The top of the reservoir is located at a depth o f 228 m (748 ft). Oil viscosity at initial temperature of 26OC (790F) is 4270 mPa.s (cP). Other values are given in Table 2. The run were made in a two-dimensional radial configuration (r, z) with a 12 x 6 grid. TABU 1

- DATA FOR W L L STIMULATION PROBLEM

Zone thickness Exterior radius Porosity Horizontal permeability Anisotropy kh/kv Irreductible water saturation Residual oil saturation to water Residual oil saturation to steam Rock compressibility Initial temperature Initial pressure Initial water saturation TABLE 2 Temperature 200’2 ( 680F) 5OoC (1220F) 1 oooc (2120F) 150OC (3020F) 2OOOC (3920F) 26OOC ( 5000F)

24 m (78.74 ft) 200 m (656.16 ft) from 0.1 to 0.25 from 0.8 to 2 p 2 (800 to 2,000 nd) 10

0.2 0.43 at 26OC and 0.19 at 22OOC 0.1 5.10-5 Ha-’ (3.4 1C-4 psi-1\ 26OC (790F) 2800 kPa (406 psia) 0.2

- OIL PRASE VISCOSITT

Well stimulation problem 8924 mPa.s (cP) 545 I’ 36 ’’ 8.3 I’ 4.1 2.5 It

Steam drive problem 5159 nif‘a.S (CP) II 180 II 19 5.5 2.6 1.27

We specified a steam injection rate of 1 0 0 metric tomes per day (629 B/D cold water equivalent) into the six layers. The steam quality was 100% at surface conditions and the injection temperature was 264OC (5070F). Wellbore heat losses computed by the model give at the end of injection a quality of 90% at the bottom of the well.

385

We simulated five cycles. One cycle involves 25 injection days, 5 soaking days and a producing period with a totai fluid production rate of 20m3/ day (126 BID). A new cycle is initiated when the oil rate has decreased to 5m3/da.y (31 BID). According to this criterion the durazions of the successive production cycles have been 152, 9 9 , 136, 130 and 133 days. The variations of oil rate and water cut with time for the successive cycles are shown in Fig. 1 and Fig. 2. The well bottom-hole pressure evolution is shown in Fig.3 16

I

T I M E , DAYS

Fig. 1

-

Oil production rate for five successive steam stimulation cycles

1.

0.8

-

Cycle 1

.)

P

. \ )

S 0.6I-

3 0

-

I

a

?

g 0.4-

f

o ! 0

Fig. 2

I

I

200

400 T I M E , DAYS

- Water-cut versus

600

time for five stimulation cycles

t 0

386 during the 800 days of history. The history includes 125 days of injection, 25 days o f soaking and 650 days of production. The total oil recovery was 3,570m? (24,346 STB) for a total steam injection of 12,500 tomes (78,616 STB cold water equivalent) and a total water production o f 8 ,1271113 (51,113 STB) The values of the oil/steam ratio for each of the five cycles are the Dollowing: 0.64, 0.18, 0.31, 0.23 and 0.19. The criterion chosen for the end of the production phase leads to a greater length, L higher depletion and a better performance for the first cycle and to a relatively poor per%ormance forthe second cycle (Fig. 1).

.

Cycle 2

Cycle 1

Cycle 3

Cycle 4

.

Cycle 5

END OF INJECTION

60 START OF PRODUCTION

0

a

240 0

u

t 5

v)

3t 20

0

I

1

200

400

I

600

8 0

T I M E , DAYS

Fig. 3

- Well bottom-hole pressure versus time for five stimulation cycles

An other simulation performed with predefined values for the length of the five successive production phases leads to the following values of the oil/steam ratio: 0.4 after 90 producing days o f the first cycle, 0.24 after 90 producing days of the second cycle, 0.32 after 120 producing days of the third cycle, 0.29 after 150 producing days o f the fourth cycle and 0.27 after 180 production days of the last cycle. The total oil recovery was the same. The fair values of the oil/st,eam ratio may be essentially attributed to the relatively low porosity of the reservoir and to the high viscosity of the oil.

387 Steam-drive Many studies have been devoted to the evaluation of the performance of steam flooding technique .l 5-18. However the influence of some operating parame-cershas not yet been clarified. The effects of steam quality and reservoir pressure on steamflood performance were investigated in a five-spot pattern with the simulator. One eighth of a five-spot pattern was represented by a 6 X 3 X 5 grid (Fig.4) with A x =Ay = 14.14m (46.4 ft) and Az = 4m (13.12 ft) Table 3 summarizes the data for this problem and Table 2 shows the oil viscosity versus temperature. The relative permeabilities were temperatwe dependent. The water-oil relative permeability curves are shorn in Fig. 5 for two temperature

.

3

U

I

1

INJECTOR

Fig. 4

Fig. 5

2

3

- Simulation grid for

- Water-oil relative permeclbility curves

4

5

6

PRODUCER

one--eighth of five spot pattern

Fig. 6

- Gas-oil relative permeability curves

388 TABLE 3

-

DATA FOR STEAM-DRIVE PROBIXM

Area (5-spot) Reservoir thickness Porosity Horizontal permeability Vertical permeability Formation compressibility Specific heat of formation Specific heat of overburden and underburden Thermal conductivity of formation Thermal conductivity of overburden and underburden Oil compressibility Thermal expansion coefficient of oil Specific heat of oil Stock-tank oil density Irreductible water saturation Residual oil saturation to water Residual cil saturation to steam Initial temperature Initial water saturation Initial pressure Injection rate for full pattern (WE) Production bottomhole pressure

values 09 25OC (77OF) and 2OO0C (3920F). curves are shown in Fig. 6.

2 10,000 m (2.5 acres) 20 m (65.6 ft) 0.35 2 . 5 p2 (2500 md) I. 1

p2 (1000 md) 1 (6.8 psi- ) OC ( 3 5 Btu/cu.ft -OF)

2.35 J/cm3 3 2 . 5 J/cm

2.3 W/m

-

2 . 3 Wim

-

6.4 6.5

-

-

O C

(37 Btu/cu.ft -OF)

OC

( 3 2 Btu/ft

OC

(32 Btu/ft

- day - day -

OF) OF)

kPa-’ ( 4 . 4 10-6 psiA’) OC-’ (3.6 OF-l) 2.1 J/e O C ( 0 . 5 Btu/lb OF) 0.95 g/cm3 (60 lb/cu. ft) 0.25 at 25°C and 0.4 at 175OC 0 . 4 at 25°C and 0.2 at 17joC 0.1 25°C (77OF)

-

-

0.4 500 kPa (72.5 psia) and 4000 lil’a

(580 psia) 50 m3/day (314 B/D) 300 kEa (43.5 psia) and 3800 kPa ( 5 5 1 psia)

The gas-oil relative permeability

We studied the effects of varying bottom-hole steam quality from 0 to 1 for t w o values o f initial reservoir pressure, 500 kPa (72.5 psia) and 4000 kPa (580 psia) respectively. Specified injection rate for both set of cases was 50 tonnes/day (314 B/D cold water equivalent) for the full pattern; steam is injected only into the two bottom layers. Well injectivity and productivity indices as calculated according to Peaceman l 9 were multiplied by two. Production wells produce from the five layers at deliverability against a bottom-hole pressure of 300 kPa (43.5 psia) and 3800 kF’a ( 5 5 1 psia), for both cases respectively. Fig. 7 shows the effect of steam quality on injection pressure. The high increase of injection pressure results from the formation of a high viscosity oil bank downstream from the condensation front. Injection pressure starts to decrease when the oil bank becomes mobile.

As shown in Fig. 8 the oil recovery for a given heat input is little sensitive to steam quality when quality is above 6%. The heat input is equal to the cumulative enthalpy o f steam at sand face referred to initial reservoir temperature. Fig. 9 shows earlier steam breakthrough when steam quality increases and initial pressure decreases.

389

-

60

2 -r

w

4

45-

----- I

2 4

Lu & 3 v,

y 30a

si=

22 15-

-

INITIAL

-O--

I

Fig. 7

0

Fig. 8

0.2

- Effect

-

-----------

2 3 T I M E ,YEARS

1

0

P R E S S U R E = 500 k P o

- Effect

of steam quality and initial reservoir pressure on injection pressure

0.4 0.6 STEAM OUALITY

0.8

of steam quality and initial reservoir pressure on oil recovery after 30 TJ heat input.

1 S T E A M OUALITY

Fig. 9

- Effect

of steam quality and initial reservoir pressure on steam breakthrough.

390

Vertical heat losses to overlying and underlying strata are relatively independent of time after steam breakthrough. Heat losses after 6 Sears of steam injection are presented in Fig. 10; less heat losses are achieved for the lower initial pressure when quality is above 3@, due to lower steam t,emperature and faster heating of the reservoir. For a steam quality of 6% and an initiai reservoir firessure of 500 kPa (72 psia) the vertical heat loss is 31% of hea.t input. The heat injection rate for this case is 460 kJD-m3 reservoir and t,he reservoir thickness 50 m.. For these two values the vertical heat l o s s curves of Gomaal7 obtained with an initial pressure of 414 kPa give the same Talue of 31%. The results in Fig. 10 show that the curves are also reservoir pressure dependent. For a pressure of 4000 kPa (580 psia) the heat injection rate is 505 kJ/D-m3 res. and the heat loss is 38.5% of heat input, instead of 29% in the low-pressure case considered by Gomaa. Low heat, loss to overburden strata and early breakthrough result in a high amount of heat produced by the wells when operating at low initial reservoir pressure (Fig. 1 1 ) .

a 6o -

2

--

-

I

I N l T l P L PRESSURE

500 k P o ( 72 p i 1 0 I 4000kPo~580p8is)

50-

z

0

Fig. 10

0.2

0.4 0.6 STEAM OUALlTY

- Effect of

0.8

steam quality and initial reservoir pressure on vertical heat loss after 6 years

0

0.2

0.4

0.6

0.6

1

STEAM O U A L l T r

Fig. 11

- Effect of steam quality and initial reservoir pressure on heat produced

The cumulative oil/steam ratio is plotted in Fig. 12 versus steam quality and initial reservoir pressure, after 6 years of injection. It appears that the oil/steam ratio is improved when steam quality increases and initial reservoir pressure decreases. The oil/steam ratio does not take into account the variation of heat input due to the variation of steam quality. Hence we introduce an adimensional parameter, the energy yield EY, f o r comparing the performances of the tests. The energy yield is defined as the ratio between the calorific value of the cumulative oil produced and the heat input previously defined. The value of EY is equal to one when the energy content of the steam at sand face is equal to the calorific value of the produced oil (calorific valae of oil = 38 GJ/m3). Fig. 13 shows the effect o f steam quality and initial reservoir pressure on the energy yield. An optimum steam quality value can be determined in Fig. 1 3 , depending on initial reservoir pressure and on the duration of steam injection.

39 1 T n e selisitilTitY t o steam qualitj- is much stronger at l o w pressure than 2 t high pressure. This is relared t o t h e higher amount of heat transported by the produced fluids in the case of lokT pressure tests (Fig. 11). The same reason may explain the shift o f the optimum sream quality towards lower values when t,ime increases. As 2 matter of fact the heat produced after 6 years of injectiori is about tvice the value obtained after 3 years.

02

0

Fig. 12

0:4 0:6 STEAM OUALlTY

- Effect of

0.8

1

steam quality and initial reservoir pressure on cumulative oil/steam ratio after 6 years

Fig. 13

-

Effect of steam quality and initial reservoir pressure on energy yield.

The optimum volumetric injection rate, after the project had reached a peak oil-production rate, was determined at Kern River from field results16. We made a similar study with the simulator in the case of 6% bottomhole steam quality and 500 kPa (72.5 psia) initial reservoir pressure.Fig. 14, as a result optimizes the rate o f t e instantaneous oil/steam ratio. An optimum steam in. jection rate of 2.5 10 m3/day/m3 o f reservoir volume (1.94 B/D A-ft) was found (1.5 B/D -A-ft for Kern-River16). The curve in Fig. 14 has the same shape as the curve developed for Kern-River. The dispersion o f the data is less than in the case of Kern-River since the simulations were carried out on a uique pattern whereas the correlation f o r Kern-River had been obtained from the field results o f several pilot tests. This optimum steam rate corresponds to the value of 50 m3/day (314 B/D ) used in the sensitivity study for the full fivespot pattern.

-5

-

Model running time The formulation described above is very efficient in terms of computing time. A three-dimensional run with a 25 x 8 x 4 grid (800 cells) requires 0.002 seconds per grid block-time step on the CDC 7600 computer. The simulation of the steam drive pilot12 with a three-dimensional grid 9 X 12 x 5 (405 active cells) requires 0.0018 seconds per grid block-time step. The case presented here of a three-dimensional steam-drive with a 6 X 3 x 5 grid ( 6 0 active cells) requires 0.0008 seconds per grid block-time step. The computation time f o r simulating a 9-year steam drive (582 time steps) with 4000 kPa initial pressure

392 BOTTOM-HOLE STEAM CUALITY

0

0.25

0.50

= 6041~

Oj5

1.60

1.25

PRODUCTION 1 6 4 d / L J A Y - M 3 OFRESERVOIR VCUJME

Fig. 14

-

Optimum injection rate

and 6% downhole steam quality has been 28 seconds on the CDC 7630 computer. The ratio between computing times on a CDC 7600 and a vector computer CUP 1 has been 5.5 f o r a 12 X 12 X 4 grid (576 cells). CONCLUSIONS

-

1 The semi-implicit formulation of the.solution method used for the three-phase three-dimensional model TWIST enables the simulator to be very efficient in terms of computing time and stability. The model may be used for simulating a wide variety of thermal problems.

-

2 Five successive steam injection cycles in a low porosity reservoir have been simulated to evaluate the decline of the oil/steam ratio from cycle to cycle.

-

3 The influence of steam quality and initial reservoir pressure on steamflood performance has been investigated. It appears that these parameters affect the heat loss to the surrounding formations, the heat transported by the produced fluids and the performance of the process. Better performances and higher sensitivity to steam quality are observed at lower pressures.

-

4 The analysis of the steamflood performances obtained for various steam injection rates at givenquality and pressure indicates the existence of an optimum injection rate.

ACKNOWLEDGEMENTS

The author wishes to thank Institut Franqais du PCtrole for permission to publish this paper. He also expresses his appreciation to Mr. J.G. BURGER of Institut Francais du PBtrole f o r his helpful and constructive discussions. Partial financial support for the realfzation of the simulator used in this study was provided by Soci6t6 Nationale Elf-Aquitaine (Production).

393

NOMEXCLATURE = = = = =

= = =

qL S t T TS

U

= =

= =

= =

= = = = = = =

enthalpy (J/g) absolute permeability (m2) relative permeability thermal conductivity (W/m OC) pressure (kPaj capillary pressure (pa) mass injection or production rate (Ton/day) enthalpy production rate (J/day) heat loss rate (J/day) saturation time temperature ("C) temperature of saturated steam (OC) internal energy (J/g) phase velocity depth, measured vertically downward (m) specific weight (kPa/m) time difference operator, e.g., 6~ = Xn+l viscosity (Pa.s) porosity density (g/cm3 )

-

- X"

Subscripts and superscripts = steam = time level = oil = rock

= steam = water

RGFERENCES

- Shutler, N.C.: "Numerical, Three-Phase Model of the Two-Dimensional Steamflood Process", SOC. Pet. Eag. J., (Dec, 1970) 405-417. 2 - Weinstein, H.G., Wheeler, J.A., Woods, E.G.: "Numerical Model for Thermal Processes", SOC. Pet. Eng. J, (Feb, 1977) 65-78. 3 - Coats, K.H, George, W.D., Chu, Chieh, Marcum, B.E.: "Three-Dimensional Simulation of S';eamflooding", SOC. Pet. Eng. J. (Dec, 1974) 573-592. 4 - Ferrer, J. Farouq Ali, S.M.: "A Three-Phase, Two-Dimensional, Compositional Thermal Simulator for Steam Injection Precesses" - Paper 7613 presented at 1

5

-

6

-

7

-

8

-

27th Annual Technical Meeting of the Petroleum Society of CIM, Calgary, June 7-11 1936. Coats, K.H.: "Simulation of Steamflooding with Distillation and Solution Gas", SOC. Pet. Eng. J. (Oct. 1976) 235-247. Coats, K.B.: "A Highly Implicit Steamflood Model", SOC. Pet. Eng. J (Oct. 1978) 369-383. Grabowski, J.W., Vinsome, P.K., Lin, R.C., Behie, A. and Rubin, B.: "A fully Implicit General Purpose Finite-Difference Thermal Model for In-SLtu Combustion and Steam?, paper SPE 8396, presented at SPE 54th Annual Fall Meeting, Las Vegas, W, Sept. 23-26, 1979. Stone, H.L.; "Estimation of Three-Phase Relative Permeability and Residual Oil Data", J. Can. Petr. Tech., V. 1 2 , no 4 , (Oct. 1973).

394

9

-

Lolen, J.S, Berry, D.W. : "Tests o f the Stability an2 Time-Step Sensitivity of Semi-Implicit Reservoir Simulation Techniques", SOC. Pet,. Eng. J (June 1972) 253-266.

11

- Spivak, d . , Coats, K.H. : "Kumerical Simulation of Coning Using 1mpli.cit Production Terms", SOC. Pet. Eng. J. (Sep. 1970) 257-267. - Price, H.S., Coats, K.H. : "Direct Methods in Reservoir Simulation", SOC.

12

-

10

Pet. Eng.J. (June 1974) 295-308. Sahuquet, E.C, Ferrier, J.J. : "Steam Drive Pilot in a Fractured Carbonated Reservoir Lacq SupCrieur Field, "paper SPE 9453, presented at SPE 55th Annual Fall Meeting, Dallas, Texas, Sept. 21-24, 1980. Ramey, H.J, JR. : "Wellbore Heat Transmission", J. Pet. Tech. (Apri1,1962)

427-435. 14 - Satter, A. :"Heat Losses During Flow of Steam Down a Wellbore", J. Pet. Tech. (July, 1965) 845-851. 1 5 - Chu, C., Trimble, A.E. :"Numerical Simulation of Steam Displacement Field Performance Applications", J. Pet. Tech. (June, 1975) 765-776. 16 - Bursell, C.G., Pithan, G.M. : "Performance of Steam Displacement in the Kern River Field", J. Pet. Tech. (August, 1975) 997-1004. 17 - Gomaa, E.E. :"Correlations for Predicting Oil Recovery by Steamflood", J. Pet. Tech. (Feb. 1980) 325-332. 18 - Nolan, J.B., Ehrlich, R., Crookston, R.B. Applicability of S t e m 13

:I1

20 -

19

flooding for Carbonate Reservoirs*!,paper SPE 8821, presented at the First Joint SPE/DOE Symposium of Enhanced Oil Recovery, Tulsa, Oklahoma, April 20-23, 1980. Peaceman, D.W., : I 1 Interpretation of Yell-Block Pressures in Numerical Reservoir Simulationt9,SOC. Pet. Eng. J. (June, 1978) 183-194. Burger, J., Sourieau, P. :"Thermal Methods of Oil Recovery: Chapter 4 . To be published by Editions Technip, Paris.

39 5

NUMERICAL METHODS

SPECIAL TECHNIQUES FOR FULLY-IMPLICIT SIMULATORS J. R. APPLEYARD, I. M. CHESHIRE and R. K. POLLARD

Atomic Energy Research Establishment, Hawell, Oxfordshire, England

ABSTRACT This paper addresses some problems which arise when a fully-implicit black oil simulator is allowed to take large time steps. It is shown that, by using a new form of time averaged relative permeability, it is possible to reduce time truncation errors to a very low level. The application of this technique also reduces the non-linearities in the mass conservation equations which are solved at each time step. The solution of the linearised equations using iterative techniques becomes more difficult as the time step is increased. A new 'nested factorisation' algorithm for solution of these equations is described. The new method is shown to be more efficient than existing techniques on a set of 2D test problems. Experience with large 3D problems arising from North Sea applications has been most encouraging.

INTRODUCTION The use of fully-implicit numerical methods in reservoir simulators is becoming This shift away from IMPES and semi-implicit increasingly wide~pread('*~'~). methods I s motivated principally by the much greater stability and robustness of fully-implicit methods when applied to problems involving strong gravity segregation, high permeability contrasts, coning, bubble point crossing, etc. As a direct result of this improved robustness, reservoir engineers are freed from the need to consider the internal working of their simulator, and can concentrate on more important issues. The wide applicability of fully-implicit methods also reduces the need for special purpose simulators designed for particular applications (e.g. coning). It is often thought that fully-implicit simulators are less efficient in their use of computer time than IMPES and semi-implicit alternatives. In our experiencecl), this need not be the case, as the strong stability of the method allows the simulator to take much longer time steps than would otherwise be possible. Indeed, for many problems, a fully-implicit simulator is the most efficient, as well as the most robust alternative. However, this gain in efficiency is realised only if the special problems associated with long time steps can be overcome. Of these problems, the most obvious is the increased numerical dispersion arising from time truncation errors (as distinct from space truncation errors) resulting in additional smearing of flood fronts. The convergence of the non-linear equations which are solved at each time step can also present difficulties for long time steps, particularly if the relative permeability curves are highly non-linear. Finally,

396 s o l u t i o n o f t h e l i n e a r e q u a t i o n s u s i n g i t e r a t i v e t e c h n i q u e s becomes more d i f f i c u l t as t h e t i m e s t e p i s i n c r e a s e d . T h i s p a p e r a d d r e s s e s each o f t h e s e problems i n t u r n . F i r s t l y , w e show t h a t i t is p o s s i b l e t o reduce t i m e t r u n c a t i o n errors s i g n i f i c a n t l y u s i n g a new t e c h n i q u e f o r computing t i m e averaged flows. The a p p l i c a t i o n o f t h i s t e c h n i q u e a l s o reduces t h e s e v e r i t y o f n o n - l i n e a r convergence problems. F i n a l l y , w e i n t r o d u c e a new and h i g h l y e f f i c i e n t t e c h n i q u e f o r i t e r a t i v e s o l u t i o n o f t h e l i n e a r e q u a t i o n s , and p r e s e n t comparisons w i t h o t h e r widely used methods.

T I W TRUNCATION ERRORS The s p a c e d i s c r e t i s e d f i n i t e d i f f e r e n c e e q u a t i o n s governing t h e flow o f o i l , water and g a s c a n be summarised i n t h e form -dM = dt

.............................

F

(1)

where M and F are v e c t o r s . Elements o f Y r e p r e s e n t t h e mass of a phase i n a c e l l , and e l e m e n t s o f F t h e sum o f flows from n e i g h b o u r i n g c e l l s and w e l l s . I n t e g r a t i n g (1) o v e r a t i m e s t e p A t g i v e s AM = I n the s t a n d a r d f u l l y - i m p l i c i t approximated by

I

t+At F
.........................

(2)

method t h e r i g h t - h a n d s i d e of e q u a t i o n ( 2 ) is

rAt FCt')dt'

.....................

= F(t+At) . A t

(3)

and t h e t i m e d i s c r e t i s e d e q u i v a l e n t o f t h e d i f f e r e n t i a l e q u a t i o n (1) i s

t:

-=

F(t+At)

..........................

(4)

Equation (4) is s t r o n g l y s t a b l e which m a k e s i t p o s s i b l e t o a c h i e v e h i g h computing e f f i c i e n c y by t a k i n g l a r g e t i m e s t e p s . However, i n p r a c t i c e , i t i s o f t e n n e c e s s a r y t o l i m i t t h e t i m e s t e p i n o r d e r t o p r e v e n t t h e growth o f t i m e t r u n c a t i o n errors. An estimate o f t h e s e errors can b e o b t a i n e d by comparing flow and w e l l terms a t t h e b e g i n n i n g and end o f each t i m e s t e p .

E = F(t+At)

-

F(t)

.......................

(5)

Using e q u a t i o n ( 5 ) i t i s p o s s i b l e t o p l o t g r i d maps o f t h e t i m e t r u n c a t i o n e r r o r and, as one might e x p e c t , t h e main t i m e t r u n c a t i o n errors o c c u r i n t h o s e c e l l s where s a t u r a t i o n s are changing r a p i d l y . T h i s s u g g e s t s t h a t i t may b e p o s s i b l e t o reduce t i m e t r u n c a t i o n e r r o r s s i g n i f i c a n t l y by performing a c a r e f u l t i m e i n t e g r a t i o n i n which s p e c i a l a t t e n t i o n i s g i v e n t o t h e n o n - l i n e a r r e l a t i v e p e r m e a b i l i t y terms. Time T r u n c a t i o n C o r r e c t i o n The s t a n d a r d f u l l y - i m p l i c i t

flow i n t e g r a l can b e w r i t t e n a s

F(t')dt'=

X(t+At)kr(t+At)At

..................

(6)

397 where kr(t+At) is t h e value of t h e r e l a t i v e permeability a t t h e end of t h e t i m e s t e p . To o b t a i n a more a c c u r a t e approximation w e wish t o r e p l a c e t h e r e l a t i v e permeability by i t s t i m e averaged value

t+At kr(t')dt'

- =-LA t

kr

........................

R e l a t i v e p e r m e a b i l i t i e s a r e f u n c t i o n s of s a t u r a t i o n , and necessary t o transform t h e t i m e i n t e g r a t i o n i n ( 7 ) t o an i n t e g r a l . An approximate transformation can be obtained (a) t h e flow is l o c a l l y incompressible (b) c a p i l l a r y forces a r e negligible (c) t h e flow o u t of a c e l l depends only on the average so t h a t

_ ds dt - 0(6-f(s))

(7)

it is t h e r e f o r e equivalent saturation by assuming t h a t

saturation i n the c e l l

.........................

(8)

where 0 is a c o n s t a n t , and f(s) is t h e f r a c t i o n a l flow curve f o r t h e phase under consideration. The c o n s t a n t , 6 , is set t o 1 f o r an invading phase and zero for a d i s p l a c e d phase t o ensure t h a t

-ds- dt

0

.............................

(9)

as t h e s a t u r a t i o n approaches i t s l i m i t i n g value. Equation ( 8 ) can now be used t o transform t h e t i m e i n t e g r a t i o n i n ( 7 ) t o an equivalent s a t u r a t i o n i n t e g r a l giving krds

.........................

(10)

Equation (10) forms t h e b a s i s of a p r a c t i c a l technique for computing average r e l a t i v e p e r m e a b i l i t i e s during l a r g e t i m e s t e p s . If t h e r e l a t i v e permeability curves a r e approximated by piecewise l i n e a r f u n c t i o n s , t h e i n t e g r g l s i n

2

equation (10) can b e performed a n a l y t i c a l l y , so t h a t both ir and can be computed e x a c t l y a t modest o v e r a l l c o s t . Because t h e c a l c u l a t i o n takes d e t a i l e d account of t h e shape of t h e r e l a t i v e permeability curve, r a t h e r than focusing a t t e n t i o n a t one or two p o i n t values, i t is p o s s i b l e t o take l a r g e t i m e s t e p s without l o s i n g accuracy. I t may b e shown t h a t t h e t i m e averaged r e l a t i v e permeability is c l o s e t o t h e time-centred value, &(kr(t+At) + k r ( t ) ) , if t h e s a t u r a t i o n change is small, but approaches t h e i m p l i c i t value, k r ( t + A t ) , a s t h e s a t u r a t i o n change increased.

The d i s c r e t i s e d equivalent of (1) may now be w r i t t e n a s

_ AM - P ............................. At

(11)

where is obtained by r e p l a c i n g r e l a t i v e p e r m e a b i l i t i e s by t h e i r t i m e averaged values, k,. A l l o t h e r terms a r e evaluated a t t h e end of t h e t i m e s t e p . The coupled non-linear equations (11) are solved for p r e s s u r e and s a t u r a t i o n i n each g r i d block by Newtonian i t e r a t i o n :

-

[---Z]AZ=EA t az ax E

....................

(12)

398 where t h e s o l u t i o n v a r i a b l e s ( p r e s s u r e and s a t u r a t i o n changes) are r e p r e s e n t e d by x.

(1*ax - 2] ax ,

AM

and r e s i d u a l v e c t o r , At At e v a l u a t e d a t t h e c u r r e n t b e s t estimate of t h e s o l u t i o n , x. The J a c o b i a n m a t r i x ,

-

-

F, are

I n some c a s e s , t h i s i t e r a t i o n converges v e r y slowly. F o r example, when s t u d y i n g t h e e f f e c t s o f water i n j e c t i o n , e n g i n e e r s f r e q u e n t l y u s e r e l a t i v e p e r m e a b i l i t y c u r v e s f o r t h e i n j e c t e d phase which a r e s e t t o z e r o below t h e Buckley-Leverett s a t u r a t i o n . T h i s t e c h n i q u e h e l p s t o reduce numerical d i s p e r s i o n , b u t i t a l s o i n t r o d u c e s a d i s c o n t i n u i t y i n t o t h e f u l l y - i m p l i c i t e q u a t i o n ( 4 ) , which makes t h e s o l u t i o n much more d i f f i c u l t t o f i n d . These problems are much reduced i f t i m e averaged r e l a t i v e p e r m e a b i l i t i e s are used. T h i s is because Er i s e v a l u a t e d as a n i n t e g r a l o v e r t h e t i m e s t e p , and as such v a r i e s c o n t i n u o u s l y i n t i m e , even i f k r ( t + A t ) does n o t . A s a r e s u l t t h e r e i s no d i s c o n t i n u i t y i n t h e t i m e averaged e q u a t i o n (11) Numerical Examples o f T i m e T r u n c a t i o n C o r r e c t i o n The e f f e c t o f t h e T i m e T r u n c a t i o n C o r r e c t i o n (TTC) is i l l u s t r a t e d u s i n g l D , 2D and 3D examples. The f i r s t i s a s t a n d a r d Buckley-Leverett problem w i t h e q u a l o i l and w a t e r viscosities. The f r a c t i o n a l flow o f water used i s

f

=

km

+

2

=

kl-w

kro

......me

s2

+ (I-s)

........ (13)

F i g u r e 1 shows water s a t u r a t i o n d i s t r i b u t i o n s a f t e r twelve c e l l p o r e volumes have been i n j e c t e d . A l l t h e r e s u l t s show c o n s i d e r a b l e numerical d i s p e r s i o n due t o s p a c e t r u n c a t i o n errors, b u t o u r concern h e r e i s s o l e l y w i t h t i m e t r u n c a t i o n e r r o r s . R e s u l t s are d i s p l a y e d f o r one p o i n t upstream w e i g h t i n g u s i n g 32 t i m e s t e p s b o t h w i t h and w i t h o u t t h e t i m e t r u n c a t i o n error c o r r e c t i o n . A series of runs showed t h a t t h e t i m e t r u n c a t i o n error i s h a l v e d as t h e number of t i m e s t e p s i s doubled and t h a t t h e s t a n d a r d f u l l y - i m p l i c i t method e v e n t u a l l y converges t o the TTC r e s u l t as t h e t i m e s t e p is r e f i n e d . The convergence rate i s shown .in Table 1 f o r c e l l number 12. TABLE 1 THE WATER SATURATION I N G R I D BLOCK 12. RESULTS OBTAINED USING SINGLE POINT UPSTREAM WEIGHTING Number o f t i m e s t e p s

16

32

64

128

256

512

Standard r e s u l t

-659

.677

.687

.692

-695

.697

TTC r e s u l t

.700

.698

.698

.698

.698

.698

F i g u r e 1 a l s o shows r e s u l t s u s i n g t w o p o i n t upstream ~ e i g h t i n g ' ~ ) . The e f f e c t of t h e t i m e t r u n c a t i o n e r r o r c o r r e c t i o n is similar t o t h a t observed w i t h s i n g l e p o i n t upstream w e i g h t i n g . The a n a l y t i c Buckley-Leverett r e s u l t i s also shown f o r comparison. F i n a l l y , w e n o t e t h a t i f t h e r e l a t i v e p e r m e a b i l i t y o f water is 1 then the fully-implicit set t o z e r o below t h e Buckley-Leverett s a t u r a t i o n (--)

Jz

two p o i n t upstream w e i g h t i n g r e s u l t i s v i r t u a l l y i d e n t i c a l t o t h e a n a l y t i c result

399

h

,Analytic Solution

c 0 .c 0

L

3

c

0

ln

-.-.

2 P T Upstream ITTCI 2 P T Upstream .......... 1 PT Upstream ITTCI 1 PT UDstream

J1

Cell Number FIG.l.SATURATION PROFILES FOR O N E DIMENSIONAL TEST OF TIME TRUNCATION CORRECTIONS

Problems 2 and 3 were run on PORES, a fully-implicit black oil simulator described in reference 1. Time stepping in PORES is not controlled by maximum permitted saturation and pressure changes as in most other simulators. Instead, the estimate of time truncation error (equation 5) is converted to a local material balance error by scaling with cell pore volumes and formation volume factors. The time stepping algorithm attempts to keep the root mean square of this local material balance error within specified bounds. Thus time stepping is tied directly to the best available estimate of time truncation error. Case 2 is a 38 x 8 cross section with a water injector in column 1 and an oil producer in column 38. Both wells are completed in layers 1, 3-5 and 7-8. The second layer is inactive and the reservoir is therefore in two sections which communicate only through the wells. Further details of this problem are given in reference 1. Figure 2 shows the water cut as a function of time for Case 2 using (a) PORES default TTE controls (z ASmax = 0.3) (b) PORES default TTE controls/lOO ( z ASmax = 0 - 0 5 ) (c) PORES default TTE controls with time averaged relative permeahilities. The results indicate that the time averaging technique virtually eliminates time truncation errors. The results Case 3 is a 3 dimensional gas/oil problem described by Odeh(5). shown in figure 3 again illustrate that time truncation errors are dramatically reduced using time averaged relative permeabilities.

-

0.7

0.6-

0.5-

-P

0.4-

L

a

0.3-

0.2-

.-...,.......

Standard TTE Controls

Standard TTE Controls 1100 --- Standard TTE Controls + T T C I

I h Y S

F I G . 2 . W A T E R CUT AGAINST T I M E FOR TWO D I M E N S I O N A L I X S E C T I O N 1 TEST OF T I M E TRUNCATION CORRECTION

I

:

.”

.........

,

Standard TTE Contrds

---- Standard TTE Contrds 1100 - Standard.TTE Controls t T T C I

I

Years F I G 3 . G O R AGAINST T I M E F O R T H R E E D I M E N S I O N A L T E S T OF T I M E T R U N C A T I O N C O R R E C T I O N

I

401 LARGE TIME STEPS AND THE SOLUTION OF THE LINEAR EQUATIONS

A t each Newton i t e r a t i o n , i t i s necessary t o s o l v e t h e l i n e a r i s e d equations (121, t o o b t a i n an updated e s t i m a t e of t h e s o l u t i o n t o t h e non-linear equations (11). For small problems, t h e s e equations may be solved by Gaussian e l i m i n a t i o n . Howe v e r t h i s i s not p r a c t i c a b l e f o r l a r g e 3 dimensional s t u d i e s , a s s t o r a g e and computing t i m e i n c r e a s e very r a p i d l y with t h e problem s i z e . I n such c a s e s , some form of i t e r a t i v e s o l u t i o n method must be used. The e f f i c i e n c y and robustness of t h e r e s u l t i n g procedure depend c r i t i c a l l y on t h e e f f e c t i v e n e s s of t h e s o l u t i o n method adopted. This observation i s p a r t i c u l a r l y t r u e of f u l l y - i m p l i c i t s i m u l a t i o n s with long t i m e s t e p s , a s t h e mass accumulation t e r m i n t h e Jacobian matrix (equation (12)) which makes it d i a g o n a l l y dominant (and t h e r e f o r e non-singular) i s i n v e r s e l y As a r e s u l t , t h e l i n e a r equations a r e proportional t o the t i m e s t e p length, A t . more d i f f i c u l t t o s o l v e i f long time s t e p s a r e taken. This e f f e c t i s i l l u s t r a t e d i n Table 2 , which shows how t h e number of l i n e a r i t e r a t i o n s r e q u i r e d f o r each Newton i t e r a t i o n i n c r e a s e s with t h e t i m e s t e p s i z e , for a f a i r l y e v e n t f u l period i n a t y p i c a l simulation.

Time S t e p s for Tot a1 Simulation Period

T o t a l Number of Newton I t e r a t i o n s

T o t a l Number of Linear I t e r a t i o n s

Linear I t e r a t i o n s Per Newton Iteration

12

67

366

5.46

18

55

237

4.31

23

64

226

3.53

48

116

273

2.35

Because t h e l i n e a r equations a r e more d i f f i c u l t t o s o l v e with l a r g e t i m e s t e p s i t is important t o devise powerful i t e r a t i v e methods t o make f u l l y - i m p l i c i t codes e f f i c i e n t . I n t h e following s e c t i o n w e d e s c r i b e t h e method used i n PORES. Nested F a c t o r i s a t i o n A l l i t e r a t i v e methods f o r t h e s o l u t i o n of t h e l i n e a r equations Ar = b

.............................

(14)

depend on t h e e x i s t e n c e of an approximation, B , t o t h e c o e f f i c i e n t matrix A such t h a t B-'8 i s e a s i l y c a l c u l a t e d f o r any v e c t o r 8. The r a t e of convergence of t h e i t e r a t i o n depends p r i m a r i l y on how w e l l B approximates t o A. The b e s t choice of B w i l l , i n g e n e r a l , depend on t h e s t r u c t u r e of A. Five p o i n t f i n i t e d i f f e r e n c e methods g i v e rise t o t h e n e s t e d block t r i d i a g o n a l s t r u c t u r e shown i n Fig. 4. A = d

+

1

+

U1

+ E2 +

U2

+ E3 +

U3

............... (15)

I n t h i s paper, w e p r e s e n t a way of approximating such a matrix by n e s t e d f a c t o r i s a t i o n . Because t h e algorithm e x p l o i t s t h e s t r u c t u r e of t h e matrix t o t h e f u l l , i t i s not e a s i l y adapted t o d e a l with g e n e r a l s p a r s e matrices.

402

I, .u1 Bands connect Cells in X Direction 1 2 , u2 Bands connect Cells in Y Direction 1 3 , u 3 Bonds connect Cells in Z Direction

FIG.L.THE STRUCTURE OF THE COEFFICIENT MATRIX FOR A F I V E POINT F I N I T E DIFFERENCE SIMULATION

The n e s t e d f a c t o r i s a t i o n approximation for a 3D system may be summarised a s

............................... (16) ............................... (17) a = (8 + E2)6-1(8 + uz) ............................... (18) 8 = (y + E1)y -1 ( y + U1) ........... (19) Y d - Ely -1 u1 - colsum(E 2 8 -1u 2 + E.a-lu3) 3

B = (a + E3)a-l(a + u 31

Here,colsum(X) is the diagonal matrix formed by summing t h e elements of X i n COlUmaS.

403 By combining equations 16-19, we obtain the following expression for B

B = A + (E28-1u2

+

E3a -1u 3 )

-

colsum(.E2B -1u2 + E 3a -1u,)

D o . . a

(20)

For two dimensional systems, E3 = u3 = 0, and the outermost layer of the factorisation (equation (16)) may be omitted, leaving

B = ( B + E,)B = A

-1

( B + u,)

+ E2B -1U 2 -

colsum(!L2B -1U2)

...........

(21)

The method reduces to an exact Cholesky decomposition for one dimensional problems -1

(.Y

B = (Y +

ul)

......................................

= A

(22)

In PORES, this approximation is used as a preconditioning matrix for a truncated For conjugate gradient algorithm of the type described by Vinsome(6). applications which give rise to a symmetric coefficient matrix, it would be more appropriate to use it as preconditioning for a symmetric conjugate gradient algorithm as described by Meijerink and Van der Vorst('). The procedure for evaluating B-l8 is hierarchical. At the outermost level, we solve block triangular matrix equations of the form (a

+

E3)p = B

..........................

(23)

Because the matrix a is block diagonal, these equations can be solved a plane at a time, using

u

= a

-1 (8

-

P.9)

........................

(24)

This is not recursive, as E3p involves the solution from the previous plane. Within each plane, the equations are solved a line at a time using = B-'(B

-

E2p)

........................

(25)

where once again, only known solution variables appear on the right-hand side. Similar considerations apply to the evaluation of y, which must be done before the iteration begins. The calculation proceeds a plane at a time and, within each plane, a line at a time. At each stage,,the calculation involves elements of y from the previous cell in the current line, the previous line in the current plane, and from the previous plane. The evaluation of ~olsum(E~B-~u + 2P.3a-lu3) which is required in the calculation of y, is achieved by multiplying a column vector whose elements are all unity by the transpose of (E26-1~2+ k3a-1243). The result vector contains the diagonal elements of cols~m(I126-~u~ + E3a-12.43). It will be noted from equation ( 2 0 ) that y has been set in such a way that the column sum of the error matrix, B-A,is zero. The object of this choice of y is to force the sum of the residuals, which in a reservoir simulator corresponds to a total material balance error, to zero. I f the iteration is started from the

404 initial solution 5

..... ~.~.. ..*.

= B ' b

o .

9 . .

... .

a

-

(26)

then the initial residual ro is given by r

= b - A x

and the sum of the components of ro is zero if colsum(B - A) = 0. It is easily shown that this condition, once established, remains valid throughout the iteration('). Moreover, it may be seen that because the error matrix is block diagonal, the residuals sum to zero independently within each plane (or, for 2D systems. within each line) and that this condition also holds throughout the i terat ion ~

It is well known that in most iterative methods for solving linear equations, it is low frequency eigenvectors which are most persistent, and which ultimately determine the rate of convergence. Indeed, it was this observation which prompted the additive correction methods of Watts(') and of Settari and Azi~'~), and which led to the recent upsurge of interest in other multi-grid methods(''). The method described above avoids the worst of these problems by eliminating the lowest frequency eigenvectors (those with a non-zero residual sum) from the outset. Algorithms displaying similar properties have been described by Gustafsson(ll) and Cheshire et a l ( ' ) although only the latter noted the importance of starting the iteration from an initial solution with zero residual sum (equation 26). The fact that residuals sum to zero within each plane may also be used as a test on the correctness of the program.

An important consideration in the implementation of this algorithm is the orientation of lines (cells connected by the &1 and u1 bands) and planes (lines The best strategy, deduced from a series of connected by the 11, and u2 bands). numerical experiments, appears to be to align the axes so that the largest offdiagonal elements are on the 111 and u1 bands, the next largest on the E2 and 7.42 bands. and the smallest on the 113 and 7.43 bands. In the PORES implementation, this choice is made automatically. Whilst it is convenient when describing the algorithm to view it as a series of nested LDU factorisations (equations 16-18) a significantly more efficient implementation is achieved by combining the D and U factors.

where

B = (a + E3) (I

+

a-' u3)

+

+

f3

a = (B

i2) (I

-1 u,)

...-

D . e s D . . . . O . . . D . O

Oe.D.O.OO.....eD....

(28) (29)

Given this form of the algorithm, the evaluation of B-'8 for an arbitrary nvector 8 requires about 22n floating multiplications for 3D problems (10n for 2D problems). The total for each preconditioned conjugate gradient iteration is 33n(19n) if A is symmetric, or somewhat more for a Vinsome type truncated conjugate gradient algorithm. The figure for 2D problems can be reduced to 16n by combining the calculation of B-% with that of AB-10.

An important feature of the nested factorisation algorithm is its very modest requires storage for only one diagonal storage requirements. Evaluation of B-'8

405 Some s t o r a g e is a l s o

matrix ( i n general y - l ) i n a d d i t i o n t o t h e elements of A. required by t h e conjugate g r a d i e n t algorithm. Numerical T e s t s of t h e Nested F a c t o r i s a t i o n Algorithm

The n e s t e d f a c t o r i s a t i o n algorithm was t e s t e d on a series of s i n g l e phase 2D test problems described by S e t t a r i and Aziz('). Because t h e s e problems give rise t o symmetric c o e f f i c i e n t m a t r i c e s , w e have used a symmetric conjugate g r a d i e n t algorithm t o a c c e l e r a t e convergence. The r e s u l t s a r e shown i n Table 3 , t o g e t h e r with r e s u l t s obtained on t h e same problem using SlP(12), I C C d 7 ) , a v a r i a n t of ICCGO i n which t h e column sum of t h e e r r o r matrix i s forced t o zerocl), and ICCG3(7). In each c a s e , w e have shown t h e computational work required t o reduce t h e l a r g e s t normalised r e s i d u a l t o The u n i t of work is taken a s a SIP i t e r a t i o n (about 22n f l o a t i n g p o i n t m u l t i p l i c a t i o n s ) . The corresponding f i g u r e s for t h e o t h e r methods a r e 16n f o r ICCGO and ICCGO with colsum, 22n for ICCC3 and 19n f o r n e s t e d f a c t o r i s a t i o n , ( i t would be p o s s i b l e t o reduce t h i s f i g u r e t o 16n on t h e s e problems). TABLE 3

COMPARISON OF NESTED FACTORISATION WITH OTHER ITERATIVE METHODS

COMPUTATIONAL WORK (SIP ITERATIONS) Problem Number

SIP*

ICCGO

I CCGO (WITH COLSUM)

1

28

32

19

20

13

20

29

6

2

20

26

ICCG3

NESTED FACTORISATION

3

38

36

22

22

13

4

28

31

20

20

16

5

> 50

34

21

21

12

6

50

27

17

15

11

The r e s u l t s show t h e nested f a c t o r i s a t i o n method t o be f a s t e s t of t h e methods t e s t e d on a l l t h e problems. Perhaps t h e m o s t s i g n i f i c a n t r e s u l t is t h a t on problem number 2,which is t h e only one which e x h i b i t s t h e s t r o n g d i r e c t i o n a l i t y On t h i s problem c h a r a c t e r i s t i c of c r o s s s e c t i o n and 3D r e s e r v o i r simulations. t h e n e s t e d f a c t o r i s a t i o n algorithm i s f a s t e s t by a f a c t o r of t h r e e .

The importance of f o r c i n g t h e sum of t h e r e s i d u a l s t o zero by choosing B i n such a way t h a t colsum(B-A) is zero is shown by t h e r e s u l t s from ICCGO and ICCGO (with colsum). The l a t t e r converges s i g n i f i c a n t l y f a s t e r i n every case, and competes e f f e c t i v e l y with ICCG3 which i s more complex and r e q u i r e s more s t o r a g e . The 2D r e s u l t s discussed above correspond only t o a s i n g l e n e s t i n g (B = a ) and

do not demonstrate t h e f u l l p o t e n t i a l of t h e technique a r i s i n g from t h e second n e s t i n g for 3D problems. The algorithm is implemented i n PORES for 1, 2 and 3 phase simultaneous problems and o u r experience t o d a t e on l a r g e complex 3 D s i m u l a t i o n s a r i s i n g from p r a c t i c a l North Sea s t u d i e s h a s been very encouraging.

406 CONCLUSIONS 1.

A new technique has been developed t o c o n t r o l t i m e t r u n c a t i o n e r r o r s i n r e s e r v o i r simulation.

2.

The method can be incorporated i n t o e x i s t i n g s i m u l a t o r s with r e l a t i v e e a s e and has been demonstrated on one, two and t h r e e dimensional t e s t problems.

3.

I t i s shown t h a t , a s l a r g e r time s t e p s a r e taken, t h e l i n e a r i s e d equations become more d i f f i c u l t t o s o l v e by i t e r a t i v e methods.

4.

A new n e s t e d f a c t o r i s a t i o n method i s described f o r t h e s o l u t i o n of t h e

l i n e a r i s e d f i n i t e d i f f e r e n c e equations. 5.

Because t h e nested f a c t o r i s a t i o n method i s highly r e c u r s i v e i t makes minimal a d d i t i o n a l demands on computer s t o r a g e .

6.

By comparison with e x i s t i n g published r e s u l t s i t is shown t h a t t h e n e s t e d f a c t o r i s a t i o n method i s highly e f f i c i e n t f o r simple two dimensional problems.

7.

The nested f a c t o r i s a t i o n method has been incorporated i n PORES and our experience t o d a t e i n d i c a t e s t h a t t h e f u l l power of t h e method i s most apparent on l a r g e d i f f i c u l t t h r e e dimensional s t u d i e s a r i s i n g i n North Sea applications NOMENCLATURE

A

= Jacobian matrix a r i s i n g i n f i n i t e d i f f e r e n c e c a l c u l a t i o n s

B

= an approximation t o t h e Jacobian m a t r i x A

Colsum = diagonal matrix formed by summing t h e elements of a matrix i n columns b

= right-hand s i d e of t h e l i n e a r equatian

d

= diagonal elements of A , each element of d is a 3x3 matrix i n simultaneous 3 phase s i m u l a t i o n s

E

= e s t i m a t e of t i m e t r u n c a t i o n e r r o r v e c t o r

F

= flow v e c t o r , each element r e p r e s e n t s t h e sum of flows i n t o a c e l l from neighbouring c e l l s and wells

-

F

= flow v e c t o r obtained by r e p l a c i n g a l l r e l a t i v e p e r m e a b i l i t i e s a t t h e

f

= f r a c t i o n a l flow of o i l , water or gas

end of a t i m e s t e p by t i m e averaged r e l a t i v e p e r m e a b i l i t i e s

fW

kr kr krw kro II

= f r a c t i o n a l flow of water = r e l a t i v e permeability ( o i l , water o r gas) = average r e l a t i v e permeability over a t i m e s t e p = r e l a t i v e permeability of water = r e l a t i v e permeability of o i l

= lower band of t h e Jacobian matrix

M

= mass accumulation v e c t o r , each element of M r e p r e s e n t s t h e mass of a phase i n a c e l l

Ah!

= change i n M over a timestep A t

n

= number of elements i n d

r

= residual vector

407 = saturation

S

As

= change in saturation during a time step

t

= time

At

= duration of a simulation time step

TTC

= time truncation correction

U

= upper band of the Jacobian matrix

X

= solution of a linear equation, state vector

Ax

= change of state vector during a Newton iteration

a

= matrix for two dimensional systems

B

= matrix for one dimensional systems

Y

= diagonal matrix

6

= 0 or 1 corresponding to an invading or displacing phase

0

= constant

x

= pressure dependent component of the flow vector

Q

= right-hand side of a linear equation

U

= solution of a linear equation

ACKNOWLEDGEhlENTS The authors wish to thank the United Kingdom Department of Energy, the British National Oil Corporation and the British Gas Corporation for permission to publish this work. REFERENCES 1.

CHESHIRE, I.M., APPLEYARD, J.R., BANKS, D., CROZIER, R.J., and HOLMES, J.A.; "An Efficient Fully Implicit Simulator", paper EUR 179 presented at the European Offshore Petroleum Conference and Exhibition, London, England, (Oct. 1980), 325-336.

2.

BANSAL, P.P., HARPER, J.L., McDONALD, A.E., MORELAND, E.E. and ODEH, A.S.; "A Strongly Coupled, Fully Implicit, Three Dimensional, Three Phase Reservoir Simulator", paper SPE 8329 presented at the SPE-AIME 54th Annual Fall Meeting of the SPE, Las Vegas, Nev. (Sept. 1979).

3.

AU, A.D.K., BEHIE,,A., RUBIN, B., and VINSOME, P.K.W.; "Techniques for Fully Implicit Reservoir Simulation", paper SPE 9302 presented at the SPE-AIME 55th Annual Fall Meeting of the SPE, Dallas, Texas (Sept. 1980).

4.

TODD, M . R . , O'DELL, P.M. and HIRASAKI, G.J.; "Methods for Increasing Accuracy in Numerical Reservoir Simulators", Soc.Pet.Eng.J. (Dec. 1972), 515-530 ~

5.

ODEH, A.S.; "Comparison of Solutions to a Three-Dimensional Black-Oil Reservoir Simulation Problem", J.Pet.Tech. (Jan. 1981) 33, 13-25.

6.

VINSOME, P.K.W-; "Orthomin, an Iterative Method for Solving Sparse Banded Sets of Simultaneous Linear Equations", paper SPE 5729 presented at the SPE-AIME Fourth Symposium on Numerical Simulation of Reservoir Performance, Los Angeles, Ca. (Feb. 1976).

7.

MEIJERINK, J.A. and VAN DER VORST, H.A.; "An Iterative Solution Method for Linear Systems of which the Coefficient Matrix is a Symmetric MMatrix",Mathematics of Computation (Jan. 1977) 2,148-162,

8.

WATTS, J.W.; "An Iterative Matrix Solution Method Suitable for Anisotropic Problems", S0c.Pet.Eng.J. (March 1971) 11,47-51.

9.

SETTARI, A. and AZIZ, K O ; "A Generalisation of the Additive Correction Methods for the Iterative Solution of Matrix Equations", SIAM J.Numer.Ana1. (June 1973) 2,506-521.

10.

BRANDT, A.; "Multi-Level Adaptive Solutions to Boundary-Value Problems", Mathematics of Computation (April 1977) 3l, 333-390.

11.

GUSTAFSSON, I.; "A Class of First Order Factorisation Methods", BIT (April 1978) 18, 142-156.

12.

STONE, H.L.; "Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations", SIAM J.Numer.Ana1. (Sept. 1968) 5 , 530-558.

409

NUMERICAL METHODS

SOME CONSIDERATIONS CONCERNING THE EFFICIENCY OF CHEMICAL FLOOD SIMULATIONS R. W.S. FOULSER

AEE Winfn’th,Dorchester, Dorset, DT2 8DH

ABSTMCT This paper discusses some aspects of improving computational efficiency and accuracy in surfactant flood calculations. The use of curvilinear grids in chemical flooding simulation can reduce grid orientation effects and speed up the calculations. For the low tension, low concentration surfactant processes being considered, the work of Martin and Wagner supports the application of conformal grids. The development at Winfrith of the PASL code, which applies the results of potential theory, has enabled suitable grid patterns to be generated for use in the CFTE code. This mesh generation code has also proved useful in visualising flow patterns and consequent mesh requirements for studying possible pilot applications of surfactant flood under real reservoir conditions. A further improvement in the efficiency with which the CFTE code can be applied has been achieved by incorporating a line successive overrelaxation iterative solver (LSOR) into the code, as an alternative to the direct inversion method. Initially written for a scalar machine, its application on the CRAY vector machine has led to the development of alternative LSOR codes using different grid block orderings. These LSOR options run about twice as quickly as the direct inversion on the IBM scalar machine and, when vectorised on the CRAY, they run up to 6 5 times faster than the original code on the IBM. Thus the vectorised LSOR approach has proved to be very powerful.

INTRODUCTION The Chemical Flood Ternary Equilibrium Simulator (CFTE Ref I ) is one of several EOR codes being used at AEE Winfrith. During the period for which CFTE has been available, a number of assessments studies have been performed, one of which has been reported elsewhere by Fayers et a1 (Ref 2). As more difficult assessment calculations have been undertaken, it has become necessary to develop supplementary programs to aid the generation of input for the studies. Computational time is also becoming a significant factor in the use of the CFTE code in large assessment calculations. This paper briefly presents some of the experience associated with the use of a special mesh generation code, PASL, that has been written as one of the support programs, and also the steps that have been taken to improve the efficiency of CFTE when used on the CRAY vector processor.

4 10

The PASL mesh generation code has been used as a tool in preliminary studies to determine broad characteristics of flow patterns within possible pilot areas of an oil field. This has been especially useful in examining alternative well patterns in a pilot flood and also as a means of studying pattern confinement strategies. The preliminary flood pattern studies provide a basis for identifying computing mesh requirements in subsequent CFTE calculations. The PASL code may also be used to generate curvilinear co-ordinate systems for use in CFTE. The use of curvilinear co-ordinates in surfactant flood calculations allows a considerable improvement to be obtained in calculation efficiency as well as a reduction in the errors caused by grid These improvements are quantified by comparing the results orientation effects. using parallel and diagonal Cartesian grids with curvilinear grids. The CFTE code uses the IMPES formulation, and the resulting implicit pressure matrix problem was originally solved by direct methods. With about 400 grid blocks in three-dimensional calculations, the matrix inversion time begins to dominate the total execution time. Because of this, it was decided to incorporate an iterative solver into the code. The recent availability of a CRAY-I vector processor in association with the IBM 3033 at Harwell, where the computing for this project is undertaken, emphasised the need to choose a method which could be readily vectorised. The LSOR method was chosen, partly because of its robustness and its relatively simple form for progranrming, but also because this iterative method is more readily vectorised than some of the more complicated strategies, such as SIP. The second part of this paper is concerned with an investigation of the performance of the LSOR method in chemical flooding calculations and also with the aspects of vectorisation of this particular method. THE DETERMINATION AND USE OF CURVILINEAR GRIDS IN SURFACTANT FLOODING STUDIES The generation of curvilinear grids and the study of flow fields for arbitrary arrangements of injection and production wells has been implemented in the PASL code. No-flow boundaries associated with linear fault lines have also been included in the formulation which uses the basic results of potential theory. The faults are dealt with by applying conformal transformations.to obtain a continuous line fault and the method of images is then used to provide an equivalent system of wells in an infinite domain. The solution method then uses the classical equations for representing a distribution of wells in infinite space (Ref 3). For a system of wells the velocity potential and stream function are given by:

where mi is the strength of well i. Once the streamlines and equipotentials have been computed, inverse conformal transformations are used to map the results back to the original co-ordinate system. The code provides output of curvilinear mesh dimensions in a format suitable for direct input to CFTE. One of the first examples studied using a grid generated bv PASL, was Concerned with the problem of mesh orientation effects during the calculation of a simple surfactant flood in a 5 s p o t geometry with a uniform residual oil saturation. The CFTE code was used to model a low concentration surfactant flood in a 1/8 th symmetry sector of the 5-spot pattern. Sone investigations of this type of surfactant flood for North Sea applications have been discussed in Ref 2. The basic

411 d a t a adopted a r e s i m i l a r t o those described i n t h a t reference. A v a r i a t i o n of r e l a t i v e permeability w i t h c a p i l l a r y number similar t o t h a t used by Todd and Chase (Ref 1) has been assumed where, i n t h i s case, t h e r e l a t i v e permeability of t h e o i l and water phases move progressively from t h e i r i n i t i a l o i l - w a t e r to their limiting straight l i n e forms a t low c a p i l l a r y numbers (26 x forms as the c a p i l l a r y number i n c r e a s e s t o 2 x The r e s u l t s of the c a l c u l a t i o n s a r e shown i n Figure 1 where the +spot region has been covered by 90 g r i d blocks f o r t h e p a r a l l e l and c u r v i l i n e a r g r i d systems and 91 blocks f o r t h e diagonal g r i d system. These diagrams show t h e o i l d i s t r i b u t i o n a f t e r 0.5 PV of s u r f a c t a n t s o l u t i o n i n j e c t i o n which i s not long a f t e r breakthrough of the o i l bank. A l l t h r e e c a l c u l a t i o n s show low concentrations around t h e i n j e c t i o n w e l l w i t h a f a i r l y s t e e p rise i n o i l s a t u r a t i o n i n t o t h e o i l bank where t h e o i l s a t u r a t i o n reaches about 40%. A l l t h r e e c a l c u l a t i o n s a l s o show t h e o i l bank pinching o f f a small region where t h e s a t u r a t i o n has not y e t r i s e n above t h a t l e f t a f t e r waterflooding. A s would be expected, t h e p a r a l l e l g r i d shows a p r e f e r e n t i a l flow along t h e d i r e c t path between t h e w e l l s , while t h e diagonal g r i d allows t h e less a c c e s s i b l e corner region t o be swept more e a s i l y . The p r e d i c t i o n of t h e c u r v i l i n e a r g r i d s i m u l a t i o n l i e s between t h e s e two r e c t a n g u l a r g r i d r e s u l t s . The cumulative o i l production curves, n o t Shawn, a l s o i n d i c a t e s t h a t t h e c u r v i l i n e a f g r i d gives r e s u l t s i n t e r m e d i a t e t o t h e C a r t e s i a n mesh arrangements. From a computational p o i n t of view, t h e c u r v i l i n e a r c a l c u l a t i o n was by f a r t h e most e f f i c i e n t , running some 5 times f a s t e r than t h e o t h e r s . This occurred because the connections with t h e wells i n t h e c u r v i l i n e a r c a l c u l a t i o n s was v i a 5 f a i r l y l a r g e g r i d b l o c k s , r a t h e r than v i a t h e s i n g l e smaller g r i d block i n t h e Cartesian systems. It i s these connecting g r i d blocks which tend t o c o n t r o l t h e timestep s i z e t h a t can be taken i n the e x p l i c i t s o l u t i o n of t h e c o n c e n t r a t i o n and s a t u r a t i o n equations.

(4b)

I n t h e p a r t i c u l a r example s t u d i e d the water + f r o n of t h e o i l bank h a s a m o b i l i t y of 1.25 mD/cp, t h e t o t a l m o b i l i t y + i n t h e o i l bank i s 1 .OS and behind t h e bank t h e m o b i l i t y of t h e s u r f a c t a n t s o l u t i o n i s somewhat g r e a t e r than 5. Thus t h e e q u a l l y mobile two phase mixture i n t h e o i l bank and the watered o u t zone ahead are being d i s p l a c e d by a much more mobile f l u i d . This i s , t h e r e f o r e , a n example of t h e unfavourable mobility r a t i o e f f e c t s i n s u r f a c t a n t flooding. Martin and Wagner (Ref 4) suggest t h a t t h i s type of problem i s amenable t o f i x e d stream tube methods, thus supporting use o f c u r v i l i n e a r two-dimensional g r i d s i n CFTE c a l c u l a t i o n s with t h i s type of system. The s u i t a b i l i t y of c u r v i l i n e a r g r i d methods f o r more g e n e r a l a p p l i c a t i o n i s a l s o being s t u d i e d . Figure 2 shows flow p a t t e r n s generated from t h e PASL code, when a p p l i e d t o an i n v e r t e d 5-spot operated i n i s o l a t i o n , b u t i n t h e v i c i n i t y of two i n t e r s e c t i n g impermeable f a u l t s . Note t h a t t h e f a u l t s a r e s t r e a m l i n e s of t h e flow p a t t e r n and t h a t t h e e q u i p o t e n t i a l s c r o s s t h e steamlines perpendicularly. The i n t e r s e c t i o n of s t r e a m l i n e s and e q u i p o t e n t i a l s have been used i n CFTE c a l c u l a t i o n s as t h e g r i d block c o r n e r s of a conformal c u r v i l i n e a r co-ordinate system. For maximum e f f i c i e n c y i n t h e CFTE code t h e e q u i p o t e n t i a l s are u s u a l l y chosen t o produce equal volume g r i d blocks along t h e s h o r t e s t stream tube. The shaded region i n t h e Western s e c t o r of t h i s f i g u r e has been used i n t h i s way t o generate co-ordinate s y s t e m f o r t h e problem on which CFTE performance estimates are reported i n t h e second h a l f of t h i s paper. This i s an example of a f i e l d problem f o r which s e l e c t i o n of a s a t i s f a c t o r y Cartesian mesh would have been very d i f f i c u l t . A t t h i s s t a g e , i t has only been p o s s i b l e t o study problems f o r s p e c i a l l y chosen s e c t o r s , because of l i m i t a t i o n s i n t h e c o n n e c t i v i t y of mesh which can be handled by t h e CFTE code. G e n e r a l i s a t i o n of t h e mesh c o n n e c t i v i t y arrangements w i l l be s t u d i e d i n t h e f u t u r e i n connection w i t h t h e LSOR method discussed i n t h e next s e c t i o n .

4 12

PARALLEL GRID

,-

-1

--

DIAMNAL GRID

FIG.I COMPARISON OF LW TENSION SURFACTANT FLOOO COMPUTED aL MSTRlBUTlONS AFTER 0.5 PV OF FLUB INJECTION.

4 13 quipatmtid

rrtnomlir

lnpcrmeoblc foul1

FIG.2

EXAMPLE OF APPLICATION OF POTENTIAL FLOW THEORY TO ROW FAlYDN VISUALISATION IN AN INVERTED 5-SPOT CONFINED BY INTERSECTING FWLTS.

THE PERFORMANCE OF SCALAR AND VECTOR VERSIONS OF THE LSOR METHOD IN CHEMICAL FLOOD CALCULATIONS In view of the need to speed up the inversion process for large problems with curvilinear meshes, and the practical difficulties imposed by generalised connectivities between meshes introduced by such schemes, it was decided to investigate the application of the LSOR iterative procedures as analternative to the existing direct inversion method in the CFTE code. The robustness of the convergence behaviour of LSOR, its ease of programning, and its simplicity for vectorisation on a CRAY were further reasons for choosing this method. Outline of LSOR In block successiveaver relaxation the system of equations to be solved can be written in the form:

-

...,

C h i y = q k I, K (3) i where xi is an n-tuple of variables (the block sire) and Aki and Q are the correspodding sub-matrix of co-efficient8 and the n-tuple right-hand side. In line successive over relaxation, the blocks are chosen to correspond to lines of grid blocks. An iterative sequence of vectors sf: may then be defined

where

B is a relaxation factor.

This may be w r i t t e n i n matrix form:

The convergence of the i t e r a t i v e scheme describe- by equation (5) depends on the s p e c t r a l r a d i u s w of t h e i t e r a t i o n m a t r i x E-’F (Ref 5 ) . For a seven p o i n t approximation t o the three-dimensional Laplacian o p e r a t o r i t can be s h m n t h a t , provided the blocks hi are ordered c o n s i s t e n t l y , t h e n w i s r e l a t e d t o the s p e c t r a l r a d i u s !J of the matrix (Aii)A-I by:

Since the matrix (&d)A-I i s dependent only on t h e o r i g i n a l matrix and on the block s e l e c t i o n ( i e t h e d i r e c t i o n of the l i n e s i n LSOR), !J depends only on the block arrangement of t h e matrix and on t h e r e l a x a t i o n f a c t o r 6. As i n p o i n t successive r e l a x a t i o n t h e optimal r e l a x a t i o n f a c t o r B can b e shown t o be given by:

By p u t t i n g BPI i n equation ( 6 ) , i t may be seen t h a t p2 = w.1 so t h a t equation (7) may be r e w r i t t e n as:

This shows t h a t the optimum r e l a x a t i o n f a c t o r can be determined by powering the i t e r a t i o n m a t r i x E-’F assuming B = 1 . w l i s t h e asymptotic r a t i o of successive i t e r a t e s of t h e eigenvector elements (p287 Ref 6 ) . The s p e c t r a l r a d i u s of t h e i t e r a t i o n matrix with t h e optimal r e l a x a t i o n f a c t o r can be shown t o be w = 6-1 and t h i s g i v e s a value f o r the asymptotic r a t e of convergence of:

I L=

-log

(;I

The e s s e n t i a l p o i n t s of LSOR a r e thus: (i)

To choose t h e d i r e c t i o n of t h e l i n e s ( i e the Akk) 80 a s t o maximke the rate of convergence given by equation (9). In r e s e r v o i r s i t u a t i o n s t h i s almost i n v a r i a b l y means choosing the v e r t i c a l d i r ect i o n f o r the l i n e s.

415 (ii)

(iii)

(i v )

To choose an o r d e r f o r r e v i s i n g the a t h a t i s c o n s i s t e n t . A necessary and s u f f i c i e n t condition f o r an o r d e r i n g t o b e c o n s i s t e n t i s given on page 245 of Ref 7. To power t h e m a t r i x E-lF with f b 1 so a s t o determine w and then use equation (8) t o determine t h e optimum r e l a x a t i o n f a c t o r . To use equation (5) t o i t e r a t e on the unknown v e c t o r zn+lu n t i l convergence i s achieved.

The convergence t e s t f o r the p r e s s u r e d i s t r i b u t i o n t h a t has been used i n t h i s application is:

(10)

and E has been taken t o be 0.001. This t e s t ensures t h a t successive i t e r a t e s must be more t i g h t l y converged when t h e convergence i s slow, i e w i s close t o u n i t y . Checks of the m a t e r i a l balance i n chemical flooding c a l c u l a t i o n s have shown t h i s t o be an adequate test.

S c a l a r Code E i t h e r t h e x, y o r z d i r e c t i o n may be chosen f o r the l i n e d i r e c t i o n i n a l l t h r e e v a r i a n t s of t h e LSOR code discussed i n t h i s paper. However, f o r convenience i t i s r e f e r r e d t o as t h e v e r t i c a l d i r e c t i o n . I n the s c a l a r version of t h e code, t h e l i n e s of g r i d blocks are ordered i n a n a t u r a l o r d e r i n the h o r i z o n t a l plane, s t a r t i n g i n one c o m e r of t h e a r e a modelled and working up t o t h e o p p o s i t e corner. A n o r d e r i n g of a 7 x 7 arrangement of g r i d block l i n e s i s shown i n Figure 3. This ordering i s c o n s i s t e n t . Although the g r i d block arrangement i s displayed a s a square, t h i s i n f a c t r e p r e s e n t s t h e c u r v i l i n e a r co-ordinate system f o r t h e c u r v i l i n e a r s t r u c t u r e shown i n Figure 2, where t h e wells a r e connected t o the g r i d blocks along the l e f t a n d r i g h t e d g e s . I n o r d e r t o determine the i t e r a t i o n matrix eigenvalue the matrix i s powered. This involves t h e i d e n t i f i c a t i o n of the eigenvector corresponding t o the maximum eigenvalue of t h e i t e r a t i o n matrix. This s t e p i n the procedure can be q u i t e c o s t l y unless a l l t h e eigenvector i s s t o r e d f o r use as a n i n i t i a l guess a t subsequent t i m e s t e p s . Usually the eigenvector changes r e l a t i v e l y slowly d u r i n g a displacement c a l c u l a t i o n and only a few a d d i t i o n a l i t e r a t i o n s are needed a t each timestep. The eigenvector a r r a y r e p r e s e n t s about h a l f t h e s c r a t c h s t o r a g e requirement. The o t h e r h a l f of t h e s c r a t c h s t o r a g e i s used t o s t o r e t h e previous eigenvector i t e r a t e during the s p e c t r a l norm c a l c u l a t i o n , and a f t e r t h i s t h e previous i t e r a t e of t h e pressure d i s t r i b u t i o n i s s t b r e d during the pressure solution. The p r e s s u r e d i s t r i b u t i o n i s found using equations (5) and ( 8 ) and the convergence c r i t e r i o n i n equation (10). The t o t a l s c r a t c h s t o r a g e space needed by the s c a l a r LSOR code i s compared i n Figure 4 with t h e s t o r a g e r e q u i r e d by t h e D4 d i r e c t e l i m i n a t i o n code o r i g i n a l l y i n CFTE. The advantage of i t e r a t i v e schemes i n t h i s r e s p e c t i s w e l l known.

1

7

43

l

Tt;t; 11

12 13

1 "

2 "

3 "

4

5

6

I

M 2

3

4

5

6

7

2

1

1

2

1

NOLEN'S RED-BLAtK OROERNG USED FOR VECTOR PROGRAM

DIAGONAL GRoupHt USB) FOR VBCTOR PROGRAM PRINCIPLE OF ORMRlNG SHOW ABOVE HAS VETOR LENCTH OF 7 DEVELOPMENT S E W HAS VECTOR LENGTH OF 21

FIG.3 GRID BLOCK ORDERIN6 SCHEMES USED TO INVESTIGATE LSOR PERFORMANCE.

Words

10

/

Oirrt lmtnion D,

1C

FIG.4

Ordwig

LSOR

I

I

1

S

lo

6

J-Dimcnrion

COMPARISON OF SCRATCH STORAGE REQUIREHENT FOR LsoA MATRIX INVERSKW STRATEGIES J x J x 5 PROBLEM.

A number of t e s t s have been made using t h i s version of the code. The n m b e r of g r i d blocks varying from 7 x 7 ~ 5(245 g r i d blocks), 10~10x5(500 g r i d blocks) and 14x14~5(980 g r i d blocks). The same s u r f a c t a n t system as described i n the s e c t i o n on c u r v i l i n e a r g r i d s has been used,and t o introduce some a x i a l v a r i a t i o n s , the p e r m e a b i l i t i e s of t h e 5 + e r t i c a l l a y e r s have been varied with values of 10,3,10,3,10 mD r e s p e c t i v e l y . Pressure constrained w e l l models were assumed i n which 15% of the t o t a l pressure drop a t t h e i n i t i a l conditions was l o s t i n t h e w e l l completion f a c t o r . This influences t h e s p e c t r a l norm of the i t e r a t i o n matrix.

The canputing time taken t o i n v e r t t h e pressure matrix using LSOR v a r i e s with time according t o t h e d i f f i c u l t y of the problem ( i e i n i t i a l guess and the matrix s p e c t r a l r a d i u s ) . Figure 5 shows t h e t i m e taken f o r the f i r s t 150 timesteps of the sample problem. Also shown f o r comparison purposes is t h e time taken by the d i r e c t E4 m a t r i x , i n v e r s i o n r o u t i n e a v a i l a b l e i n the CFTE

4 18

0.2

.-:& -. .-.. -*.-.

*

6

Gaussian etiminatim

ordering .- .- .-. -.with 01, ...- . -. --. - ....- .

c-

. :a

I

.

..-

.r.,

7 x 7 x 5 GRIDBLOCKS

..#

lOxlDx5 G R D W C K S

Y t r l C x S GRIDBWCKS

RG.5

EXAMPLES OF TIME SPENT IN MATRIX INVERSION USING SCALAR VERSION OF LSOR Co[E AND CURVILINEAR GRlO BUXK REPRESENTATION OF WESTERN QUADRANT OF INVERTED 5-SPOT SHOWN IN FIG.2

4 19 code. The o v e r a l l p a t t e r n of behaviour i n these c a l c u l a t i o n s , most c l e a r l y seen i n t h e l a r g e s t problem, i s t h a t of a decrease i n i n v e r s i o n t i m e from the i n i t i a l conditions, followed by an i n c r e a s e a t about 0.2 PV of f l u i d i n j e c t i o n and then a gradual decrease. Over t h e timescales represented, LSOR i s more e f f i c i e n t than the d i r e c t method, even f o r the smallest problem (245 g r i d blocks). A t long timescales the c a l c u l a t i o n a l time i n LSOR becomes i n s i g n i f i c a n t as the pressure d i s t r i b u t i o n changes very l i t t l e during t h e timesteps. The i n c r e a s e i n i n v e r s i o n t i m e a t 0.2 PV co-incides with t h e breakthrough of the o i l bank a t t h e producer w e l l . This occurs because of t h e r e l a t i v e l y rapid pressure changes t h a t occurred making the eigenvector and pressure d i s t r i b u t i o n s a t t h e previous timestep less good as i n i t i a l guesses. In micellarfpolymer floods t h e most pronounced peaking has been noted when a highly viscous micro-emulsion breaks through i n t o the producerwell. It i s of i n t e r e s t t o compare t h e achieved convergence rates with the asymptotic rates given by equation (9). This i s summarised i n Table I be low :

TABLE 1 COMPARISON OF THEORETICAL AND CALCULATIONAL CONVERGENCE RATES

Mesh s i z e

7X7X5

IOxlOx5

I t e r a t i o n matrix s p e c t r a l r a d i u s

0.674

0 796

0.854

Asymptotic convergence rate

(9)

0.39

0.23

0.16

Typical average convergence rate

0.30

0. I8

0.12

14X14X5

A s may be seen, t h e average convergence r a t e achieved i s somewhat slower than t h e asymptotic rate, as would be expected. The i n c r e a s e i n i t e r a t i o n matrix s p e c t r a l r a d i u s , and thus t h e decrease i n convergence rates, with i n c r e a s i n g problem s i z e i s w e l l known; however, a l s o of i n t e r e s t i s the f a c t t h a t t h e w e l l f a c t o r s can considerably i n f l u e n c e t h e convergence p r o p e r t i e s of t h e i t e r a t i o n scheme. Making t h e w e l l f a c t o r s very l a r g e , and thus i n c r e a s i n g t h e coupling between t h e c a l c u l a t i o n a l mesh and the f i x e d well bore pressures, speeded up convergence by 20% i n t h e examples discussed above.

V e c t o r i s a t i o n of LSOR f o r CRAY

- Algorithm

Performance

The s c a l a r v e r s i o n of LSOR described i n t h e previous s e c t i o n w a s t r a n s f e r r e d t o t h e CRAY without modification and some m a t r i x i n v e r s i o n timings were made t o compare the CRAY and IBM performance. The CRAY c a l c u l a t i o n s without v e c t o r i s a t i o n were about twice as f a s t as the IM c a l c u l a t i o n s . This i s less than the f a c t o r of four expected equivalent B on t h e b a s i s of the r e l a t i v e clock times of t h e machines. I t i s believed t h a t t h i s r e s u l t s from t h e optimising c a p a b i l i t y of t h e IBM compiler used, which more than halved t h e running t i m e r e l a t i v e t o code generated by a non-op t imi sing compiler

.

420

It should also be noted that very little of the original LSOR coding could be vectorised automatically. This was due to three causes: (i)

the use of conditional testing to eliminate inactive grid blocks.

(ii)

the recursive nature of the Thomas' algorithm which is the kernel sub-program in the LSOR method.

(iii)

the extensive use of indirect addressing to reference neighbouring grid blocks.

Most of the conditional testing and indirect addressing could be removed by suppressing the elimination of inactive grid blocks. For Cartesian grid approximations to flow patterns in repeated patterns, the removal of this facility incurs a significant work penalty since unnecessary matrix solutions are undertaken for grid blocks which are isolated from the active region by imposing zero transmissibilities. However, for the preferred curvilinear co-ordinate method the inactive grid block facility would not normally be required. Each line of grid blocks gives rise to a tridiagonal system of operations which cannot be vectorised by the CRAY due to the recursions that occur in performing the forward eliminations and back substitutions. Following Buzbee et a1 (Ref 8) the method employed to overcome this has been to solve for a number of lines simultaneously. The choice of lines which are solved simultaneously is important for two reasons. Firstly, the ordering of the grid blocks must not degrade the basic solution strategy of the algorithm. Killough has described an attempt to vectorise the SIP algorithm (Ref 9); unfortunately the vectorisation method degraded the convergence of the algorithm so as to outweigh the gain in speed due to vectorisation. Secondly, the choice must lead to a grid block referencing systemwhichallows the gridblocks in a line, and thegridblocks in neighbouring lines, to be easily referenced. The attraction of the LSOR method is that the lines for simultaneous solution can be chosen so that the asymptotic convergence behaviour is preserved. The required condition is that any chosen ordering must be consistent. Nolen (Ref 8) has identified one possible ordering scheme in which the lines are ordered with a chequer board arrangement, the red lines are solved first and then the black lines. The concept has been generalised slightly fromthat reported by Nolen to allow an odd number of grid block lines to be used, as well as even. An example of the line ordering is shown in Figure 3. The vector length for the simultaneous tridiagonal solver is NX.NY/2 for problems with an even number of grid blocks, and (NX.NY+I)/Z and (NX.NY-I)/2 for the red and black groups respectively, when there is an odd number of lines. The generalisation to an odd number of grid block lines in the plane makes the arithmetic expressions for referencing neighbouring grid blocks more complicated than in the less general situation. An alternative to the red-black ordering scheme has also been investigated. This was prompted by the observation that the red-black scheme resembles a two-step line over relaxed Jacobi scheme for the initial iterations, and therefore the average convergence properties might be less than for other possible ordering schemes. The alternative scheme devised corresponds to

421 grouping the lines in diagonals so as to obtain a number of line problems that can be solved simultaneously. Each diagonal is considered in turn until all the grid block eigenvector elements or pressures have been revised. The basic arrangement is illustrated in the top middle diagram of Figure 3. This scheme allows neighbouring grid blocks to be referenced by simple arithmetic expressions. To understand the possible differences in initial convergence behaviour further, it is necessary only to consider curvilinear calculations with a symmetric arrangement of NxN grid blocks in the horizontal plane. With the diagonal grouping, the influence of the well connected to the left hand edge of the grid pattern is transmitted in the first iteration to the lower triangular zone of 0.5 (N2+N) mesh points, but only the line of 1.0N grid points along the right boundary are directly coupled to the well on the right in this iteration. In the red-black arrangement, 0.5N grid points are coupled to wells on each side in the red sweep (for N even), and I.ONgrid points in the black sweep. Thus the diagonal arrangement can on average transmit boundary effects across the area faster, but is asymmetric in its behaviour. Symmetry could be introduced in the diagonal scheme by reversing the sweep order on successive iterations, but this has not been investigated. The asymptotic convergence rates of the two schemes must be identical with the standard ordering, since all three are consistently ordered. Thus for slowly convergent problems the schemes should behave identically. On the CRAY the vector performance becomes awre advantageous the longer the vector length, subject to the limitation of filling the 64 element registers. The diagonal grouping leads to vector lengths of NY for the tridiagonal solver, which for small problems may not be sufficient to take full advantage of the vector machine. Thus, for small problems, the diagonals have been combined to increase the vector length. The lower diagram in Figure 3 indicates one of these combinations, and the order in which the grid block line problems are solved in this strategy. The ordering remains consistent despite these combinations. In the particular case shown each pass of the program revised each line three times, so one pass is equivalent to three iterations. The calculations already reported for the scalar code have been repeated using code modifications employing the red-black and diagonal grouping ordering. These calculations correspond to the initial steps in a chemical flood simulation and as such represent the calculation of an almost symmetric problem. The average rates of convergence achieved by the alternative strategies are s h a m in Table 2:

TABLE 2 COMPARISON OF CONVERGENCE RATES WITH VARIOUS ORDERINGS

7X7X5

1 ox 10x5

14X14X5

Standard ordering

0.30

0.18

0.12

Red-black ordering

0.38

0.22

I).16

Diagonal line ordering

0.37

0.22

0.14

Mesh size

422

For some small problems, such as the 10x10~5calculation, the red-black and diagonal group orderings cu-kcidedue to the combining of groups to increase the vector length, and thus the convergence rates are identical. The diagonal grouping in the 7 x 7 ~ 5problem leads to a slight asymmetry in the initial revision pattern, so the convergence in this case is slightly slower. In the 14x14~5case, four diagonals are grouped together, and the asymmetric propagation is more marked, thus the reduced convergence compared with the red-black scheme. In all cases the standard ordering leads to an initial asymmetric behaviour even more pronounced than the diagonal grouping, and this explains why this scheme has the poorest average convergence rate. Vectorisation of LSOR for CRAY

-

Coding Performance

While the overall strategy in the vectorised scheme is the same as in the original code, the implementation of the two alternative ordering schemes entailed completely rewriting the routines concerned with powering of the iteration matrix, and iterating the pressure distribution. Initial attempts to vectorise the above algorithms involved the extensive use of additional scratch storage associated with use of the CRAY SCILIB routines GATHER and SCATTER (Ref 10). However, program refinements eliminated the need for these routines and the additional scratch storage, with the resulting storage requirements shown in Figure 4. Conditional testing, an inefficient computing task, has also been completely eliminated from the routines, except when testing for convergence. Most of the execution time is expended in the iterating routines. Table 3 indicates the vector lengths achieved in the major sections of these routines when applied to the 14x14~5sample problem. TABLE 3 EXAMPLE VECTOR-LENGTHS ACHIEVED WITH DIFFERENT ORDERING SCHEMES

Operation

Red-Black Ordering

Diagonal Grouping

980

980

5

70

490

70

98

56

Updating solution (relaxation step)

490

70

Convergence test

980

980

Updating previous iterate Setting up right-hand sides for Thomas' algorithm Setting up left-hand sides Thomas' Algorithm

Table 4 gives the CRAY cpu time required by the various vectorised options to perform one iteration in either the eigenvalue calculation or the calculation of the pressure distribution.

423

TABLE 4 CRAY CPU TIME IN MILLI-SECONDS TO EXECUTE ONE ITERATION

Eigenvalue calculation

Pressure distribution

Mesh size 7 x 7 ~ 5 10x10~5 14x14~5 7x7~5 10x10~5 14~14x5 Standard ordering

3.67

-

Red-Black ordering

0.73

Diagonal grouping

0.34

11.04

3.69

-

14.78

I .47

2.85

0.77

1.49

2.88

0.51

0.89

0.35

0.51

0.90

As may be seen the red-black coding is 4 or 5 times faster than the original code and the diagonal grouping is 10 to 16 times faster. The difference between the last two options is almost certainly due to the slightly more complex arithmetic needed in the red-black code to identify the neighbouring grid blocks, and also the shorter vector length associated with setting up the right-hand side column vector. By reverting to the restricted case where the number of grid blocks in the plane is known to be even, it may be possible to make the two vectorised options comparable. A small part of the gains achieved above are associated with simply reducing the generality of the inversion programming and the generation of better fortran coding. This has been demonstrated by using the same inversion routines on the IBM machine, where enhancements by factors of 1.2 and 1 .3 were observed. CONCLUSIONS This paper has discussed advantages which can be derived in utilising curvilinear mesh co-ordinate systems in surfactant flood calculations. This allows a computational geometry to be adopted broadly consistent with the anticipated flow patterns of a problem. Implementation of flow stream geometry utilising the code PASL has been illustrated for a generalised field problem with sealing fault lines. The curvilinear geometry gives advantages in choice of mesh blocks adjacent to wells, which in turn gives a superior time step capability in an IMPES formulation, such as that adopted in the CFTE code for simulation of surfactant floods. The reduction in mesh orientation errors resulting fromthe use of curvilinear co-ordinates has been demonstrated for a 5-spot pattern with surfactant flooding. Direct inversion employed in the solution of the implicit formulation of the pressure equation in the CFTE program leads to computer speed limitations for large curvilinear mesh problems. To overcome this, the LSOR method has been programed and tested using the standard ordering, as well as a red-black and a diagonal line consistent ordering. The last two arrangements have been shown to be amenable to selection of long vector lengths on a CRAY computer so that diagonal line formulation in the revised code runs up to 19 times faster than the standard ordering in LSOR. Relative to D4-direct inversion on the IBM 3033

424

machine, LSOR diagonal line inversion runs some 65 times faster on the CRAY. The total code performance is dependent on problem size and for the largest example discussed here of 980 mesh blocks, direct inversion required about 60% of the overall running time. Much larger problems are needed for real field studies where the inversion aspect becomes completely dominant. Thus these improvements have placed field computation closer to practical realisation in terms of computer costs. Consideration of further generalisation of the LSOR method to curvilinear meshes with a wider range of connectivities, and with consequent difficult patterns of off-diagonal non-zero elements, needs to be considered in the future .

ACKNOWLEDGEMENT The work reported i n t h i s paper has been funded by the UK Department of Energy.

REFERENCES 1

TODD M.R. and CHASE C.A., "A Numerical Simulator for Predicting Chemical Flood Performance". Paper SPE 7689, presented at the Fifth Symposium on Reservoir Simulation, Denver 1979.

2

FArdRS P . J . , HAWES R.I. and MATTHEWS J . D . , "Some Aspects of the Potential Application of EOR Processes in North Sea Reservoirs". Paper EUR 194, presented at the European Offshore Petroleum Conference and Annual Exhibition, 1980. MUSKAT M., "Flow of Homogeneous Fluids Through Porous Media", McGraw Hill, 1937. W T I N J.C. and WAGNER R.E., "Numerical Solution of Multiphase TwoDimensional Incompressible Flow Using Stream Tube Relationships". SOC. Pet. Eng. J. (October 1979) pp313-323.

5

PEACEMAN D.W., "Fundamentals of Numerical Reservoir Simulation", Elsevier, 1977.

6

VARGA R . S . , "Matrix Iterative Analysis", Prentice Hall, 1962.

7

FORSYTHE G.E. and IiASOW W . R . , "Finite Difference Methods for Partial Differential Equations". John Wiley, 1960.

8

BUZBEE B.L., BOLEY D. and PARTERS.V., "Applications of Block Relaxation" Paper SPE 7672, presented a& the Fifth Symposium on Reservoir Simulation, Denver 1979.

9

KILLOUGH J.E., "The Use of Vector Processors in Reservoir Simulation". Paper SPE 7673, presented at the Fifth Symposium on Reservoir Simulation, Denver 1979.

10

CRAY-I Library Reference Manual.

SR-0014.

NUMERICAL METHODS

425

CONTROL OF NUMERICAL DISPERSION IN COMPOSITIONAL SIMULATION D. C. WILSON, T. C. TAN, P.C. CASINADER Deparmzent of Mineral Resources Engineering, Imperial allege, London SW 7 2BP

ABSTRACT T h i s p a p e r p r e s e n t s a technique, s u i t a b l e f o r multidimensional a p p l i c a t i o n , f o r reducing numerical d i s p e r s i o n on f u l l y i m p l i c i t compositional simulators. S i m p l e g e o m e t r i c a l a n a l y s i s of curve prof i l e s and r e e x a m i n a t i o n of v a r i o u s weighting schemes l e a d t o t h e development of a dynamic w e i g h t i n g t e c h n i q u e t h a t e x p l o i t s t h e optimum f e a t u r e s o f 1 - p o i n t , 2 - p o i n t and m i d - p o i n t weighting schemes. T h i s weighting scheme l a g e n e r a l i n i t s a p p l i c a t i o n i n f i n i t e d i f f e r e n c e models f o r r e d u c i n g d i s p e r s i o n i n convective parameters We show how t h i s scheme c a n b e s u c h a s s a t u r a t i o n and c o n c e n t r a t i o n . i m p l e m e n t e d on a n i m p l i c i t , e q u a t i o n o f s t a t e , c o m p o s i t i o n a l model. Numerical examples i n c l u d i n g m u l t i p l e c o n t a c t (MCM) and n e a r m i s c i b l e (NM) p r o b l e m are used t o compare i t s performance w i t h two published compositional s i m u l a t o r s which u t i l i s e f u l l u p s t r e a m w e i g h t i n g . Our r e s u l t s show a s i g n i f i c a n t r e d u c t i o n i n t h e number of g r i d b l o c k s r e q u i r e d t o achieve t h e same numerical accuracy.

1.0 INTRODUCTION The f i r s t compositional s i m u l a t o r s appeared i n t h e l a t e 1960's. Since then, tremendous p r o g r e s s h a s been achieved i n t h e t r e a t m e n t of f l u i d p r o p e r t i e s , s o l u t i o n t e c h n i q u e s and model g e n e r a l i t y . In common w i t h B-simulators, numerical d i s p e r s i o n r e m a i n s a m a j o r problem. The most d o m i n a n t a s p e c t of n u m e r i c a l e r r o r s o c c u r i n t h e composltfonal f i e l d . As i n B-models, a l b e i t i n a l e s s o b v i o u s m a n n e r , s a t u r a t i o n d i s p e r s i o n and e r r o r s i n t h e p r e s s u r e f i e l d remain. Various t e c h n i q u e s have been reviewed and are d i s c u s s e d below. McFarlane e t a1 (1) used smaller cells i n t h e r e g i o n of m a x i m u m compositional change, w i t h l a r g e r c e l l s e l s e w h e r e . T h i s technique is n o t even robust enough f o r 1-D problems. P r i c e e t a1 (2) proposed t h e u s e of time and space d i s c r e t i s a t i o n i n 1-D, such t h a t t h e n u m e r i c a l d i f f u e i v i t y i s of t h e same order as t h e physical d i f f u s i v i t y . This i s too expensive f o r practical application. The works o f Peaceman ( 3 ) and L a n t z ( 4 ) on s t a b i l i t y and t r u n c a t i o n e r r o r a n a l y s i s l a i d down t h e foundation f o r many subsequent works, i n c l u d i n g t h e p r e s e n t one. It i s t h u s p o s s i b l e t o u s e a n a r t i f i c i a l d i f f u s i o n term t o c a n c e l o u t t h e numerical d i f f u s i v i t y i n e x p l i c i t backward (Chaudhari (S)), and i m p l i c i t backward (Van Quy ( 6 ) ) d i f f e r e n c e e q u a t i o n s . They r e q u i r e s e v e r e t i m e s t e p , g r i d s i z e l i m i t a t i o n s a n d are p r i m a r i l y

426 s u i t a b l e f o r miscible d i s p l a c e m e n t . Laumbach ( 7 ) d e v e l o p e d a t r u n c a t i o n c a n c e l l a t i o n procedure which removed t h e time s t e p and g r i d s i z e l i m i t a t i o n s by c a n c e l l i n g a p o r t i o n of t h e e r r o r i n t h e convection term w i t h t h a t i n t h e a c c u m u l a t i o n term. I t is a p p l i c a b l e f o r m i s c i b l e , incompressible systems, where c o m p o s i t i o n s a r e t h e o n l y v a r i a b l e s s o l v e d . Field application, however, r e q u i r e s both p r e s s u r e and c o n c e n t r a t i o n s o l u t i o n s . It appears t h a t t h e e a r l y work of Gardner e t a1 ( 8 ) using t h e method of c h a r a c t e r i s t i c s is of g r e a t e r u t i l i t y i n m i s c i b l e flooding. However, t h e compositional f i e l d is decoupled from t h e c o n s e r v a t i o n e q u a t i o n used f o r s o l v i n g t h e p r e s s u r e , and so d o e s n o t s t r i c t l y o b s e r v e t h e c o n s e r v a t i o n p r i n c i p l e . The e x p l i c i t 2 - p o i n t u p s t r e a m w e i g h t i n g scheme is t h e most w i d e l y q u o t e d d i s p e r s i o n c o n t r o l t e c h n i q u e (Todd e t a 1 ( 9 ) ) . It h a s r e c e n t l y been improved (Banks e t a1 ( L O ) ) , and extended f o r i m p l i c i t t r e a t m e n t (Wheatley (11)). Nghtem e t a 1 ( 1 2 ) , r e p o r t e d t h e u s e o f 2 - p o i n t u p s t r e a m weighting scheme f o r a n IMPES compositional s i m u l a t o r . T h i s p a p e r g i v e s some simple a n a l y s i s of v a r i o u s r e p r e s e n t a t i v e p r o f i l e s o f convective parameters i n t h e l i g h t of e x i s t i n g s t a b i l i t y and t r u n c a t i o n e r r o r analysis. T h i s l e a d s t o t h e i d e n t i f i c a t i o n of s e v e r a l weaknesses i n t h e 2 - p o i n t u p s t r e a m w e i g h t i n g scheme, and t h e b e s t m e t h o d o f e x p l o i t i n g mid-point weighting. A v a r i a b l e time l e v e l , v a r i a b l e d i s t a n c e weighting scheme h a s been developed which o p t i m i s e s t h e b e s t f e a t u r e s o f t h e 1 - p o i n t , 2 - p o i n t and t h e h i t h e r t o unused m i d - p o i n t schemes. The d e v e l o p m e n t is e m p i r i c a l , i n n a t u r e , b u t is w i t h i n t h e c o n s t r a i n t s of n u m e r i c a l S t a b i l i t y , e report and is g u i d e d by t h e a v a i l a b l e knowledge on t r u n c a t i o n e r r o r s . W s u c c e s s f u l a p p l i c a t i o n s on d i f f i c u l t numerical problems.

2.0

THEORETICAL DEVELOPMENT

The following s e c t i o n s d i s c u s s t h e t h e o r e t i c a l b a s i s f o r our model. 2.1 I n t e r p o l a t i o n Methods C o n s i d e r a c o n v e c t i v e p a r a m t e r C, which is assumed t o be c o n t i n u o u s and l i n e a r i n space and t i m e (Fig. 1).

I

n+I

L-l

i

.4

i+I

For i n t e r b l o c k f l o w a t i+3, t h e p a r a m e t e r C f o r t h e f i n i t e d i f f e r e n c e e q u a t i o n must be e v a l u a t e d a t I+&. An o b s e r v e r a t I+* w o u l d n o t i c e a continuous change in t h e value of C from Cn I+$ a t t h e start of a t i m e s t e p , to a t t h e end of t h e time s t e p . The i n t e g r a l average of C i+Qover t h e This analysis time s t e p is t h e arittnoetic mean of CM1 I+% and Chr I+& a g r e e s w i t h t h e l i n e a r i s e d t r u n c a t i o n e r r o r a n a l y s i s f o r t h e convection equation in which mid-point weightings in space and t i m e are found t o b e t h e most a c c u r a t e (Appendix A l ) . In p r a c t i c e , however, C v a r i e s non-lineazly, and may become d i s c o n t i n u o u s . C o n s e q u e n t l y , t h e i n t e r - b l o c k v a l u e Ci+k is n o t a simple a r i t h m e t i c mean between tn and tn*'; i n s t e a d , i t must be found by a time-integration over t h i s range.

Cyit

.

427 S i n c e t h e p a r a m e t e r C p r o p a g a t e s w i t h time, i t f o l l o w s t h a t t h e a b o v e i n t e g r a l must be equal t o a d i s t a n c e i n t e g r a l between x I+$ and some upstream X p o i n t X Thus:-

-

C ( % t 7 dx]

c;+r =,,[ Mean Value Theorem, Ci++

/(x-

"'+&I

,

(2

1

and.~- by t h e must correspond t o some point i n t h e i n t e r v a l (xi++, X). T h i s shows t h a t n e i t h e r s i n g l e p o i n t u p s t r e a m n o r midstream w e i g h t i n g i s t o t a l l y c o r r e c t f o r t h e non-linear problem, and that some i n t e r m e d i a t e weighting f a c t o r must be determined. A d e s c r i p t i o n of our proposed theory now follows. rr+l Consider t h e general l i n e a r i n t e r p o l a t i o n formula:tn4t b t

*

*

(3 )

cx = e [ ~ c ~ + ~ + ~ ~ - w ~ c ~ ~ ' ~ + ~ ~ - Xei &~X "[ Xwi + ,c >~ + ~ ~ - w ~ c where 8 and W are t h e t i m e and d i s t a n c e weighting f a c t o r s , w i t h values between 0 and 1. W o c o n d i t i o n s must be s a t i s f i e d f o r l i n e a r i n t e r p o l a t i o n t o b e valid. (1) A continuous l i n e a r ( o r near l i n e a r ) curve between t h e p i v o t a l points. (2) The p i v o t a l p o i n t s must be "mobile". By t h i s we mean t h a t C should be For i n t h e mobile range bounded by t h e maximum and minimum p o s s i b l e v a l u e s . example, t h e mobile range of water s a t u r a t i o n i s between Swc and (1-Sor),but does not include t h e s e a c t u a l values. Our a i m i s t o u s e e q u a t i o n ( 3 ) t o p r e d i c t t h e v a l u e of an i n t e r b l o c k c o n v e c t i v e p a r a m e t e r such t h a t i t l i e s c l o g e t o t h e t r u e t i m e - i n t e g r a l a v e r a g e v a l u e of C on t h e h i s t o r y curve a t L*. Before doing t h i s , i t i s necessary t o examine t h e r e p r e s e n t a t i v e curves which a r e t o be i n t e r p o l a t e d . 2.2 Curve Anal sis C o n s i d e r 4 arYbitrary p r o f i l e s a t a f i x e d t i m e l e v e l ( F i g . 2 ) . following d e s c r i p t i o n , equal g r i d spacing is assumed.

-c

Figure2a

PROFILE

1

I

In the

1FigureZb

r

igure 2d

I

I

I I

1

Figure (2a) Curve (2b) Curve ( 2 c ) Curve (2d) Curve

1 2 3

4

: increasing : increasing : decreasing : decreasing

J

I

gradient, gradient, gradient, gradient,

concave convex convex concave

We a r e i n t e r e s t e d i n a p p r o x i m a t i n g t h e value of C at I*. Both upstream e x t r a p o l a t i o n from 1-1 and 1, and i n t e r p o l a t i o n b e t w e e n i a n d i + l , a r e possible. On Curves 1 and 2 , t h e e x t r a p o l a t e d values can be found on t h e upstream p o r t i o n of t h e c u r v e s , w h i l e t h e i n t e r p o l a t e d v a l u e s l i e o n t h e downstream p a r t of t h e curves with r e f e r e n c e t o I+$. This implies that t h e use of upstream e x t r a p o l a t i o n i s e f f e c t i v e l y upstream weighted ( f c w < l ) , a n d

428 hence s t a b l e . The use of i n t e r p o l a t i o n i s e f f e c t i v e l y downstream weighted (o< W < i ) , and h e n c e u n s t a b l e . T h i s s i t u a t i o n occurs j u s t behind an immiscible Thus Curve 1 c a n displacement,where a shock i s p r e s e n t , o r i s b u i l d i n g up. r e p r e s e n t t h e o i l s a t u r a t i o n , and Curve 2 can r e p r e s e n t t h e water S a t u r a t i o n . It i s w e l l known that t h e u s e of mid-point weighting c r e a t e s o v e r s h o o t u n d e r such circumstances,while full upstream weighting r e s u l t s i n a n undershoot o f t h e d i s p l a c i n g phase ( s a t u r a t i o n d i s p e r s i o n ) . The u s e of u p s t r e a m On C u r v e s 3 a n d 4, t h e r e v e r s e c o n d i t i o n s o c c u r . e x t r a p o l a t i o n is e f f e c t i v e l y downstream weighted. Thus on Curve 3 , u p s t r e a m e x t r a p o l a t i o n c r e a t e s u n d e r s h o o t , a n d on C u r v e 4, i t c r e a t e s o v e r s h o o t . F u r t h e r a n a l y s i s of upstream e x t r a p o l a t i o n and m i d - p o i n t I n t e r p o l a t i o n i s given i n t h e Appendix A2. S u f f i c e i t t o s a y h e r e t h a t both e x t r a p o l a t i o n and i n t e r p o l a t i o n have t h e i r advantages and l i m i t a t i o n s . They are camplementary i n t h e i r f u n c t i o n s . When e x t r a p o l a t i o n i s u n s t a b l e , i n t e r p o l a t i o n i s s t a b l e , and v i c e v e r s a . Under c e r t a i n c o n d i t i o n s t h e y a r e b o t h m i s t a b l e . This o c c u r s when t h e p i o v o t ( s ) become "immobile". In s u c h s i t u a t i o n s upstream weighting i s t h e b e s t s t a b l e approximation. e The same a n a l y s i s can be extended t o t h e h i s t o r y c u r v e s a t a f i x e d point. W are i n t e r e s t e d i n t h e h i s t o r y curve a t 1% o v e r t h e time s t e p . Due t o t h e c o n v e c t i v e n a t u r e of C, a h i s t o r y curve a t a f i x e d p o i n t over a t i m e s t e p i s r e l a t e d t o t h e p o r t i o n of t h e d i s t a n c e p r o f i l e i m m e d i a t e l y u p s t r e a m of t h e f i x e d p o i n t a t t h e beginning of t h e t i m e s t e p . 2.3 A Dynamic Weighting Scheme The p u r p o s e o f t h i s d e v e l o p m e n t i s t o f i n d a method of e v a l u a t i n g e x p l i c i t l o c a l weighting f a c t o r s , such t h a t t h e l i n e a r i n t e r p o l a t i o n formula, e q u a t i o n ( 3 ) . c a n be incorporated i n t o an i m p l i c i t simulator t o s u b s t i t u t e f o r i n t e r b l o c k convective parameters o r t h e i r dependent f u n c t i o n s . The 4 b a s i c c u r v e t y p e s ( F i g 2.) can be subdivided i n t o 2 groups. Group 1 (curves 1 and 2 ) h a s i n c r e a s i n g g r a d i e n t s i n t h e flow d i r e c t i o n , a n d Group 2 ( c u r v e s 3 a n d 4 ) h a s d e c r e a s i n g g r a d i e n t s . E i t h e r Group 1 or Group 2 are p r e s e n t l o c a l l y a t a f i x e d t i m e . I d e n t i f i c a t i o n is p o s s i b l e through g r a d i e n t testing.

[\Gi\-~GIL-,\]

> < =

0

.=$

crouP

'

0 4 Group 2},

0

S)

&-car

[

G i = q+l-c;

- xi - ci xi - xiXk,

(4)

ci-l

I The b,ssic assumptions are:Group 1 curves do n o t evolve i n t o Group 2 c u r v e s over a time s t e p . The (1) same d i s t a n c e weighting f a c t o r s can be used a t two f i x e d t i m e l e v e l s , n and n+l, i n t h e l i n e a r i n t e r p o l a t i o n equation. (2) The h i s t o r y curve a t t h e block i n t e r f a c e over t h e t i m e s t e p i s i n t h e same c u r v e g r o u p as t h e immediate upstream p r o f i l e a t t i m e l e v e l n (see next s e c t i o n ) . Therefore, t h e i n t e r p o l a t i o n f a c t o r on t h e h i s t o r y p r o f i l e , 8 , i s assumed t o be e q u a l t o t h e d i s t a n c e i n t e r p o l a t i o n f a c t o r , W. Based on t h e previous curve a n a l y s i s , t h e following s t r a t e g y i s adopted. When a Group 1 c u r v e i s d e t e c t e d , a n upstream e x t r a p o l a t i o n i s r e q u i r e d t o provide low numerical d i s p e r s i o n , w h i l e maintaining numerical s t a b i l i t y . T h i s c a n b e i n v o k e d on t h e l i n e a r i n t e r p o l a t i o n f o r m u l a by choosing weighting Simple g e o m e t r i c a l f a c t o r s between 0 . 5 and 1.0 ( e q u a l g r i d s p a c i n g ) . c o n s t r u c t i o n s show how t h i s can b e done. (Pigs. 3a, b).

ie

F i q r e 3.3

2 - p i n t upstream extraplation. D can be foundon t h e chord BF.

Firmre 3b

/lE

t

429 BF is a downstream chord. It is required t o f i n d t h e e x t r a p o l a t e d p o i n t D on BF. This point is D’. The necessary weighting f a c t o r f o r t h e i n t e r p o l a t i o n formula, W, is derived below.

A B is an upstream chord.

= ai + (I- a L ) ( x - x , ) / x .

(54)

s u b s t i t u t i n g equation (5c) i n t o equation (5b) g i v e s (54 w b = I (ai-i)/Q The w e i g h t i n g When a Group 2 curve is d e t e c t e d , i n t e r p o l a t i o n is s u p e r i o r . I f t h e g r i d spacing is miform, t h i s f a c t o r s are c a l c u l a t e d by s e t t i n g R i l l . g i v e s Wi-ai-0.5.

+

S c r e e n i n g must be a p p l i e d t o e x c l u d e t h e use of t h e i n t e r p o l a t i o n formula under 2 i n v a l i d conditions:(1) Gradient r e v e r s a l (R i is n e g a t i v e ) (2) E i t h e r , o r both,of t h e p i v o t s (%, c ) are ”immobile” Once t h e s e c o n d i t i o n s are d e t e c t e d , f u l f upstream weighting a f f o r d s t h e best s t a b l e a l t e r n a t i v e available. The i n t e r p o l a t i o n scheme proposed is t h e r e f o r e dynamic i n nature. E f f e c t i v e f u l l upstream, 2-point upstream e x t r a p o l a t i o n , o r mid-stream i n t e r p o l a t i o n w i t h v a r y i n g d e g r e e of i m p l i c i t n e s s c a n be invoked l o c a l l y via t h e same l i n e a r i n t e r p o l a t i o n formula. 2.4

R e l a t i o n s h i p Between Time Weighting and Distance Weighting

Figure 4a

Figure 4b

Figure 4c

F i g u r e 4a shows t h e p r o f i l e of a t y p i c a l parameter C a t t i m c t“ , CI being i t s value a t t h e i n t e r f a c e between b l o c k s i and i+l. F i g u r e 4 b shows t h e same p r o f i l e w i t h r e s p e c t t o X , t h e d i s t a n c e measured upstream from t h e i n t e r f a c e . Assuming that t h e p r o f i l e X(C) and t h e v e l o c i t y of p r o p a g a t i o n V ( C ) a r e known, i t is required t o determine t h e shape of t h e h i s t o r y curve, t ( c ) (Figure 4 c ) , a t t h e i n t e r f a c e , which is given by:-

-

-

Case 1 V(C) constant v T h i s assumption is approximately v a l i d i f t h e t i m e s t e p is smal1,so that t h e band of v a l u e s ( c l , c2),which c r o s s e s t h e i n t e r f a c e o v e r t h e t i m e - s t e p , i s narrow. For such a case, t(c)

-,

= x(4 V

-

and hence t ”(C) X “(C)/V. S i n c e V is p o s i t i v e , t ” has t h e same sign a s X”, and hence t (C) belongs t o t h e same group of curves as X (C).

4 30 Case 2 V(C) i s v a r i a b l e . D i f f e r e n t i a t i n g ( 6 ) w.r.t.

t J= (vx'-

C, we o b t a i n :

xv')/v2,

a n d , d i f f e r e n t i a t i n g y e t a g a i n , we have

tJ'= [v(vx"-

xv'/) - ~ V / ( V X ' - X V ' ) ] / V 3

Now, s i n c e X ' and V' have o p p o s i t e s i g n s , i t follows t h a t t h e second term of X V ' ) ] i s always p o s i t i v e . Furthermore, i f t h e above e x p r e s s i o n [ - 2 v - (VX' X '*70, t h e n V Y 0, and t h e e n t i r e e x p r e s s i o n w i l l be p o s i t i v e , and so X" and t " w i l l have t h e same s i g n , and t h e c u r v e s w i l l b e l o n g t o t h e same g r o u p ( 1 . e . Group 1). I f , however, X Z O (1.e. Group 2 ) , t h e n , due t o t h e second be c e r t a i n w h e t h e r or n o t t " w i l l c h a n g e term being p o s i t i v e , we cannot sign. N e v e r t h e l e s s , f o r p r a c t i c a l purposes, we s h a l l assume that, f o r a l l c a s e s , X and t belong t o t h e same group.

-

3.0

OVERALL APPLICATION TO AN IMPLICIT COMPOSITIONAL SIMULATOR

There is a unique dependence of t h e o v e r a l l component f r a c t i o n a l flows on t h e o v e r a l l composition. For p r o p a g a t i o n a l s t a b i l i t y , c o n c e n t r a t i o n v e l o c i t i e s a t a f i x e d p o i n t i n s p a c e and t i m e a r e e q u a l ( H e l f f e r i c h (13)). It i s t h e r e f o r e a p p r o p r i a t e t o f i n d t h e dynamic w e i g h t i n g f a c t o r s b a s e d o n t h e l o c a l overal concentration profiles. W e f u r t h e r assume t h e l o c a l e x i s t e n c e of e i t h e r t h e Group 1 c u r v e s , o r t h e Group 2 c u r v e s . The c o n c e n t r a t i o n p r o f i l e o f t h e most " s e n s i t i v e " component i s u t i l i s e d t o e v a l u a t e t h e weighting f a c t o r s . They a r e used f o r a l l components i n b o t h h y d r o c a r b o n p h a s e s , i f 2 phases e x i s t . S e l e c t i o n of t h e most " s e n s i t i v e " component i s important t o a v o i d t h e need t o c h o o s e t h e most s t a b l e w e i g h t i n g f a c t o r s evaluated f r a n a l l t h e c o n c e n t r a t i o n p r o f i l e s . The "immobile" c o n d i t i o n s f o r t h e s e l e c t e d canponents must a l s o be d e f i n e d . These i d e a s are i l l u s t r a t e d i n t h e n u m e r i c a l examples. To account f o r phase d i s c o n t i n u i t y , f u l l upstream weighting i s used i f t h e upstream and downstream blocks do not have t h e same number of hydrocarbon phases. C o n s t r u c t i o n of t h e Model The c o m p o s i t i o n a l model used i n t h i s s t u d y i s based on a n e q u a t i o n of s t a t e , a n d f o l l o w s t h e i m p l i c i t f o r m u l a t i o n p r e s e n t e d by C o a t s (14). We w i l l , t h e r e f o r e , o n l y d i s c u s s t h e model where i t h a s b e e n modified t o take i n t o account t h e preceding d i s c u s s i o n .

3.1

3.1.1

Temporal and S p a t i a l Weightin

Figure 5

A t any p o i n t i n t h e system, t h e v a l u e of a v a r i a b l e u, a t t i m e t*(where tnS t% tn+' 1, can be r e l a t e d t o i t s v a l u e s a t tn and tn+' by:-

*

u =

n+I

eK

+(I-e)Z =

kn+

eSu""

(10%)

Of,

2'-

U"

= SU*

= e Sun+'-

00 4)

431 so, f o r each i t e r a t i o n , t h i s implies:-

st$ - 8 sLn+l 4

(4

U

C+l

c+:

-

%

u. ) denote t h e change i n u over t h e The symbols %AI' (=cC K ) and SK (=V i t e r a t i o n 1, and t h e cumulative change, r e s p e c t i v e l y . I f , however, i n a d d i t i o n t o t h i s intermediate time-level, u i s also evaluated a t a p o i n t o t h e r than t h e b l o c k - c e n t r e s , t h e n i t h a s t o be r e l a t e d t o t h e block-centre values by means of t h e d i s t a n c e weighting formula. Thus:-

* u" = wu;* +(l-w)uL+l

;

s u b s t i t u t i o n then l e a d s to: 4 n+l

?'S

-!n+( = ewsKL; + e(i-w)Sai+,.

3.1.2 Expansion of t h e "Flow" term The f l o w between two n e i g h b o u r i n g b l o c k s i a n d i + i can be expressed i n t h e form:-

T+(C,-) : P .

I n c r e m e n t s i n t h e t r a n s m i s s i b i l i t y term T are c a l c u l a t e d by means of partial derivatives w.r.t. t h e complete set of v a r i a b l e s (U, , Un).

.....

and, f i n a l l y , using equations ( ~ O C ) ,( l l b ) and (12a), we o b t a i n t h e expansion of t h e flaw term, as follows:-

4.0

DISCUSSION OF RESULTS

T h r e e d i f f e r e n t d i s p l a c e m e n t p r o b l e m were chosen, i n o r d e r t o demonstrate t h e a p p l i c a t i o n of t h e above theory i n a v a r i e t y of s i t u a t i o n s . The d a t a f o r t h e s e r u n s were t a k e n from Coats (14). Leach and Y e l l i g ( 1 5 ) , and Smith and Yarborough ( 1 6 ) , r e s p e c t i v e l y . 4.1 Displacement 1 (Coats (14)). T h i s i s a n MCM problem, involving components: C1,n-C4 and n-C 10. The system e x i s t s i n i t i a l l y as a n undersaturated l i q u i d , and i s displaced by a r i c h gas. I n t h e s i m u l a t i o n , t h r e e zones can be i d e n t i f i e d : a downstream zone containing undersaturated o i l , a middle zone comprising two p h a s e s whose c o a p o s i t i o n s c o n v e r g e i n t h e u p s t r e a m d i r e c t i o n , and f i n a l l y an upstream miscible zone containing a s i n g l e dense f l u i d whose composition changes from t h e c r i t i c a l composition t o t h a t of t h e i n j e c t i o n gas. The boundary between t h e f i r s t two zones w i l l be r e f e r r e d t o a s t h e g a s f r o n t , while t h a t between t h e latter two w i l l be c a l l e d t h e miscible f r o n t . In MCM problems, t h e use of s i n g l e p o i n t upstream weighting l e a d s t o s e v e r e c o m p o s i t i o n a l d i s p e r s i o n which causes s u b s t a n t i a l delay i n t h e attainment of miscibility. T h i s r e t a r d a t i o n of t h e m i s c i b l e f r o n t i s c o n s p i c u o u s in C o a t s ' r e s u l t s , where t h e u s e of 20, 4 O m d 80 b l o c k s show a p r o g r e s s i v e

432 8.2-

,

,

,

,

,

,

,

.

COAT S I - D M C M P R O B L E M 1.0'

TIME=210 DAYS

20 BLKS

COAT S I - D M C M P R O B L E M

D l M A X = 7 . 5 DAYS

z

0 L 200

-NO c o u r m

DINAMC WEICIIIWC

TIME.DAYS

0

0.5

COAT S I - D M C M PROBLEM TlMEn2lO D A Y S 20 BLKS OlMAX=T.S DAYS

U

.

+

-"0 CO"TI10L

a

COAT S I - D M C M PROBLEM 6 1 . 0 U

4

W U

I-

m 3 0.1

.

@z

0.2.

_I

0

-

Figure 6 D i s p l a c e m e n t 1 (MCH) : 1-D c o m p a r i s o n o f d y n a m i c weighting with f u l l upstream weighting. (a) Sg p r o f i l e . ( b ) Advance of m i s c i b l e f r o n t . c o n c e n t r a t i o n p r o f i l e ( d ) o i l recovery and GOR vs time.

(c)

C4

i n c r e a s e i n i t s speed of p r o p a g a t i o n . I n t h e a b s e n c e of a n a n a l y t i c ' a l s o l u t i o n , i t is j u s t i f i a b l e t o assume t h a t t h e 80-block s o l u t i o n is t h e nearest t o real i t y. The i n t r o d u c t i o n of t h e dynamic w e i g h t i n g scheme described i n t h i s paper produces a marked improvement, and has enabled u s t o o b t a i n , w i t h 2 0 b l o c k s , a n s w e r s w h i c h a r e of c o m p a r a b l e a c c u r a c y t o C o a t s ' 40-block s o l u t i o n . Figures 6a, b, c , d show a comparison between t h e use of t h i s t e c h n i q u e and s i n g l e - p o i n t u p s t r e a m weighting. The use of t h e proposed technique c l e a r l y results In a f a s t e r advance of t h e m i s c i b l e f r o n t , which is confirmed by t h e e a r l y and s t e e p rise i n GOR, following i t s breakthrough t o t h e producer. The scheme has a l s o been t e s t e d i n 2D, using a C a r t e s i a n g r i d of 9x9 b l o c k s , w i t h t h e i n j e c t i o n and p r o d u c t i o n w e l l s l o c a t e d i n two diagonally-opposite Once a g a i n , a n improvement i n t h e c o r n e r blocks. ( F i g u r e s 7a, b, c, d ) . s i z e of t h e miscible zone can be observed, using our technique. 4.2 Displacement 2 (Smith and Yarborough (16)). The system used i n t h i s displacement was a binary mixture of C 1 and nC5,being displaced by d r y g a s (Cl). I n t h i s case, e v a l u a t i o n of weighting f a c t o r s can be c a r r i e d out on e i t h e r component. Thus C 1 was a r b i t r a r i l y chosen f o r t h i s purpose. Tbo runs were perfomed on t h i s system, t h e f d r s t of t h e s e b e i n g d e s i g n e d t o s i m u l a t e FCN d i s p l a c e m e n t . T h i s was achieved by assuming a n i n i t i a l composition of 50% C 1 and 50% n-CS,and simulating t h e displacement i n t h e s u p e r c r i t i c a l region ( a t 3000 psi). Since t h i s is a p e r f e c t piston-type displacement, t h e a n a l y t i c a l s o l u t i o n c o n s i s t s of a s t e p change i n c o m p o s i t i o n from t h e i n j e c t i o n c o m p o s i t i o n t o t h e i n i t i a l c o m p o s i t i o n .

-

433

''''

T I VF I 0 1.240 PV INJ ~0.637

0

OIL R E C ~ 0 . 5 6 4

\

v.

?\

c 7 d)

A

Figure 7

- Displacement 1 (MCM)

: 2-D

o 1-240 INJ -0.637 = O .564

T IVEI PV

\

\

I

0

\

comparisons.

( a ) Gas s a t u r a t i o n map, dynamic weighting. ( b ) C4 c o n c e n t r a t i o n map, dynamic weighting. ( c ) Gas s a t u r a t i o n map, f u l l u p s t r e a m weighting. ( d ) C4 c o n c e n t r a t i o n map, f u l l upstream weighting. F i g u r e s 8a and 8 b show t h e C 1 p r o f i l e a t 210 days, and the n-C5 concentration i n t h e e f f l u e n t a s a f u n c t i o n of time. The weighting technique shove better r e s u l t s than t h e "full u p s t r e a m " case, a l t h o u g h b o t h show a n a p p r e c i a b l e compositional d i s p e r s i o n r e l a t i v e t o t h e a n a l y t i c a l s o l u t i o n . I n t h e second run, a n i n i t i a l c o m p o s i t i o n of 87.5% C 1 and 12.5% n-C5 was c h o s e n , so a s t o y i e l d an i n i t i a l condensate l i q u i d of 7% s a t u r a t i o n a t 1525 p s i , which was a l s o t h e p r e s s u r e a t which t h e s i m u l a t i o n was c o n d u c t e d . Agein, C 1 was i n j e c t e d , and t h e problem was run i n t h e 2-phase mode, with t h e l i q u i d assumed t o be immobile. The purpose of t h i s r u n was t o d e m o n s t r a t e t h a t , f o r some problems ( s u c h a s of t h i s type) t h e amount of compositional dispersion i s negligible. T h i s p o s t u l a t e d a b s e n c e of c o m p o s i t i o n a l d i s p e r s i o n i s v e r i f i e d by t h e numerical results shown i n Figures 8 c and Ed, i n both of which t h e results of u s i n g s i n g l e p o i n t upstream weighting are v i r t u a l l y i d e n t i c a l t o t h o s e obtained with t h e p r e s e n t technique.

434

':

DRY GAS DISPLACING RICH GAS ' ' ' ' ' ' ''' ' '''' 1.1

=

0

i4

'

'

'

'

'

'

.385 PV INJECTED

DRY GAS DISPLACING RlCH G A S

210 D A Y S ( 3 4 S T E P S ) .

l=W=DYN

50

100

150

200

,

250

DISTANCE ,FEET CONOENSATE REVAPORIZATION

PV CH4 INJECTED CONDENSATE REVAPORIZATION I

Q+IO-

0.08--

0.06--

0.04.-

0.02--

DISTANCE ,FEET PV METHANE INJECTED Figure 8 Displacement 2 : 1-D c o m p a r i s o n of dynamic w e i g h t i n g with f u l l upstream weighting. ( a ) C1 c o n c e n t r a t i o n p r o f i l e (FCN). ( b ) C5 c o n c e n t r a t i o n i n e f f l u e n t v s t i m e (FCN). ( c ) C1 and o i l s a t u r a t i o n p r o f i l e s (re-vaporieation). (d) C5 c o n c e n t r a t i o n i n e f f l u e n t , and advance of "dry f r o n t " v s t i m e (re-vaporization).

-

4.3 Displacement 3 (Leach and Y e l l i g ( 1 5 ) ) . This m e a study of t h e mechanisms involved i n t h e displacement, by CO2, of a s y n t h e t i c crude o i l . Leach e t a1 (15) presented l a b o r a t o r y results c o v e r i n g t h e various displacement t y p e s (PCM, MCM and NM), and aleo simulated t h e s e on t h e i r compositional model, using 100 blocks. To t e s t our technique, two rune were chosen: an MCM d r i v e (Run 61, and a n NM d r i v e (Run 7). The component which we s e l e c t e d f o r " g r a d i e n t t e s t i n g " was namely C6. The rJeighting t h e one which had t h e least i n i t i a l c o n c e n t r a t i o n technique h a s enabled u s t o match t h e l a b o r a t o r y results t o a good a c c u r a c y , with merely 20 blocks. C o n s i d e r i n g t h e MCM r e s u l t s f i r s t , F i g u r e 9 a demonstrates t h e f a s t e r advance of t h e m i s c i b l e f r o n t , and t h e s t e e p e r C02 p r o f i l e r e s u l t i n g f r a n t h e use of t h i s technique. Figures 9b and 9c f u r t h e r support our d i s p e r s i o n c o n t r o l method, by showing t h e delayed breakthrough of C02, and t h e s t e e p change i n t h e GOR and t h e e f f l u e n t composition. The above f e a t u r e s have a l s o been v e r i f i e d i n t h e NM r u n , p e r h a p s t o a g r e a t e r e x t e n t , a s c a n be s e e n , f o r example, i n t h e s i g n i f i c a n t sharpening

-

435 LEACH ETAL DATA 20 BLK DT=.I

0.

0.2

.-0.4

RUN 6

DAY

, 0.6

0.8

A. .

I

1.0

...

1

1.2

.

1

1

HCPV COZ INJECTED

(b)

LEACH ETAL DATA ( R U N 6 ) DINAMC

wuGnnNG

NO CONfRCX

I '

, -.-...,. . . , .... LEACH ETAL DATA RUN 7

. . -. , . . . . , . . . . ,

I.?

. 4 HCPV C02 INJECTED

-

20 ELKS wmcnn"

OVNAHC

.I-

u . a .(I

3

I

a

. L

0.6-

[L

-

,

'

J

'O.O0

(d)

TIME ( D A Y S )

l!o' (C)

''

bj2:

bi4'

O

~

l

i

O

'I'

HCPV C 0 2 INJECTCD

'

DISTANCE FROM INJECTION END ( F E E T

,!.

Fig.9

(a)-(d). Capuon overleaf.

)

436 15.-

Q

I.4

13.5-

20 ELK

D

DT=.I

-

-

12.

C -L

p 10.5

0

c

m

z u LI

\

W

L

u

9.

-

7.5

m

=

W

-a

0

> w

I I

c

a

6.

>

( I

0

='

0

V 4.5

W

I I

\

L

n

;

a

0 3 .o--

=I

0

I .5

"8 . 0

(el

0.2

0.4

HCPV

0.6

0.8

1.0

C02 INJECTED

1.2

1.4

'O.Q0

-

Figure 9 Dirplacement 3 : 1-D comparison of dynamic VOightlng vlth full uprtrerm Wlghting. (a) Sg and COZ concentration (b) Normalized concentration of 032, rod CZ-C6 in profller (MCM). ( c ) COR and o i l recovery vs HCPV effluent vr HCPV injected (MCW). injected (ncn). (d) Sg and COZ concentration profilea (Nn). (e) Norullred concentrrtlon of CO2 and C 1 i n effluent v. HCPV injected (f) COR and 011 recovery va HCPV injected (NH). (Nn).

which o c c u r s i n t h e Sg and C02 p r o f i l e s , due t o t h e weighting scheme ( F i g u r e 9d). The p r o d u c t i o n h i s t o r y ( F i g u r e 9 e ) and t h e e f f l u e n t C 1 and C02 c o n c e n t r a t i o n s ( F i g u r e 9 f ) confirm t h e delayed a r r i v a l of t h e 2-phase z o n e , and t h e consequent h i g h e r recovery r e s u l t i n g from t h e u s e of t h i s technique. It needs t o be mentioned, however, t h a t a c r i t i c a l g a s s a t u r a t i o n o f 1 5 % had t o be i n t r o d u c e d t o t h e r e l a t i v e p e r m e a b i l i t y t a b l e , b e f o r e t h e r e s u l t s o f Leach e t a1 ( 1 5 ) could be s u c c e s s f u l l y reproduced.

-

5.0

-

CONCLUSIONS

The work d e s c r i b e d i n t h i s p a p e r l e a d s u s t o t h e f o l l o w i n g main conclusions : (1) The u s e of single-point upstream weighting c a u s e s s e v e r e c o m p o s i t i o n a l d i s p e r s i o n , p a r t i c u l a r l y when s i m u l a t i n g FCM, MCM and NM displacements. (2) A dynamic w e i g h t i n g scheme h a s b e e n d e v e l o p e d , which u t i l i s e s t h e p r o f i l e of t h e v a r i a b l e concerned, t o determine t h e optimum weighting f a c t o r s i n t i m e and space. I t e x p l o i t s t h e c l a s s i c a l f e a t u r e s of mid-stream, t w o - p o i n t u p s t r e a m , and s i n g l e - p o i n t u p s t r e a m s c h e m e s , b a s e d o n t h e p r o p e r t i e s of t h e p r o f i l e . (3) The t e c h n i q u e h a s been s u c c e s s f u l l y t e s t e d o n M C M , FCM a n d NM d i s p l a c e m e n t s , a n d y i e l d s r e s u l t s which, i f t h e i r a c c u r a c y i s t o be reproduced on a " f u l l y upstream" model, would r e q u i r e s e v e r a l times a s many g r i d blocks. (4) The method i s supported by g e o m e t r i c a l arguments, and can beimplemented e a s i l y i n multi-dimensional s i m u l a t o r s .

-

437 ACKNOWLEDGEMENTS The a u t h o r s would l i k e t o t h a n k t h e UK D e p a r t m e n t of Energy and Imperial College of S c i e n c e and Technology f o r s u p p o r t i n g t h i s r e s e a r c h , P r o f e s s o r C.G. Wall, D r . R.A. Dam f o r t h e i r c o n t i n u i n g i n t e r e s t , a n d Hiss M. Green o f ERC f o r h e r p a t i e n c e i n typing t h e v a r i o u s d r a f t s of t h i s paper.

REFERENCES

1. MCFARWE, R.C., MUELLER, T.D., MILLER, F.G.; " U n s t e a d y - S t a t e D i s t r i b u t i o n s o f F l u i d C o m p o s i t i o n s i n Two-Phase O i l R e s e r v o i r s U n d e r g o i n g Gas I n j e c t i o n " , S o c i e t y o f Petroleum Engineers J. (March, 1967), 1, 61-74. 2. PRICJ3,H.S. and DONOHUE, D.A.T., "Isothermal Displacement P r o c e s s e s w i t h I n t e r p h a s e Mass Transfer", Society of J. (June 1967) 1, 115-130. PetroleumEngineers 3. P E A C W , D.W. "Fundamentals of Numerical R e s e r v o i r Simulation", E l s e v i e t , Amsterdam, ( 1 9 7 7 ) 65-82 4. LANTZ, R.B. " Q u a n t i t a t i v e Evaluation of Numerical D i f f u s i o n (Truncation Error)", s o c i e t y of PetroleumEngineers J. (1971), 11, 315-320; Trans. AIME, 251 5 . CHAUDHARI, N.M. "An Improved N u m e r i c a l T e c h n i q u e f o r S o l v i n g M u l t i - D i m e n s i o n a l M i s c i b l e D i s p l a c e m e n t E q u a t i o n s " , S o c i e t y o f P e t r o l e u m E n g i n e e r s J. ( 1 9 7 7 ) , 2, 277-284; Trans., AIME, 251 6. VAN QUY, N., SIMANWUX, P. and CORTEVILLE, J . ; "A Numerical Study of Diphasic Multicomponent Flow", S o c i e t y o f P e t r o l e u m Engineers J. ( A p r i l 1972), 12, 171-184; Trans., AIME 253 7. LAUMBACH, D.D.; "A H i g h A c c u r a c y , F i n i t e D i f f e r e n c e T e c h n i q u e f o r T r e a t i n g t h e Convection-Diffusion Equation", S o c i e t y o f P e t r o l e u m E n g i n e e r s J . , ( 1 9 7 5 ) -1,5 517-531 8. GARDNER, A.O. and P E A C W , D.W. and POZZI, A.I.; "Numerical C a l c u l a t i o n o f M u l t i d i m e n s i o n a l M i s c i b l e D i s p l a c e m e n t by t h e Method of C h a r a c t e r i s t i c s " , S o c i e t y o f P e t r o l e u m E n g i n e e r s J . (19641, 26-36 9. TODD, M.R., ODELL, P.M., and HIRASAKI, G.J.; "Methods f o r I n c r e a s e d Accuracy i n Numerical R e s e r v o i r Simulators", S o c i e t y of Petroleum Engineers J. (1972), l.2, 515-530 10. BANKS, D., 'CHESHIRE, I.M., and POLLARD, R.K.; "A Technique f o r C o n t r o l l i n g Numerical D i s p e r s i o n i n F i n i t e - D i f f e r e n c e O i l R e s e r v o i r S i m u l a t i o n " , P r o c e e d i n g s of BAIL Conference, Dublin (June 1980). 99-203 11. WHEATLEY, M.J.; "A Version of Tvo P o i n t U p s t r e a m W e i g h t i n g For Use i n I m p l i c i t N u m e r i c a l R e s e r v o i r Simulators", paper presented a t S o c i e t y of Petroleum Engineers 5 t h Symp. On R e s e r v o i r Simulation, Denver, 1979; SPE Paper No. 7677 12. NGHIEM, L.X., FONG, D.K., and AZIZ, K.; "Compositional Modelling w i t h An E q u a t i o n o f S t a t e " , SPE P a p e r 9306, SPE Annual F a l l Meeting, Dallas, Texas (September 1980) 13. HELFFERICH, F.G.; " G e n e r a l Theory of Multicomponent, Multiphase Displacement I n Porous Media", Trans., AIME, 261 S o c i e t y of Petroleum Engineers J. (February 1981), 14. COATS, K.H.; "An Equation of S t a t e Compositional Model", S o c i e t y of Petroleum Engineere J. (October 1980). 20, 363-377

A,

z,

438 LEACH, M.P. and YELLIG, W.F.; "Compositional Model S t u d i e s : Co2 O i l Displacement Mechanisms", SPE P a p e r 8368, SPE Annual F a l l Meeting, Las Vagas, Nevada (September 1979) 16. SMITH, L.R. and YARBOROUGH, L.; " E q u i l i b r i u m R e v a p o r i z a t i o n of Retrograde Condensate by Dry Gas I n j e c t i o n , " 87-94 Trans. AIM, (1968), 17. P E A C W , D.W.; "A Nonlinear S t a b i l i t y A n a l y s i s f o r D i f f e r e n c e Equations Using S e m i - I m p l i c i t Mobility", S o c i e t y of P e t r o l e u m E n g i n e e r s J. ( F e b r u a r y 1 9 7 7 ) . 79-91; Trans., AIME 259 15.

-

243

17,

APPENDICES Al.

S t a b i l i t y , T r u n c a t i o n Errors and Numerical D i s p e r s i o n

The n o n l i n e a r c o n v e c t i o n e q u a t i o n is:

ax

2.

(A\.\)

T r u n c a t i o n e r r o r a n a l y s i s o n t h e f i n i t e d i f f e r e n c e a p p r o x i m a t i o n of t h e l i n e a r i s e d equation

(A I . 2 ) shows a l e a d i n g t r u n c a t i o n e r r o r term of t h e form:

ank*a+ 2% DalLm =

1

(A I .3) V / A ~ [w-+) vd+g(e--:)]. W and 8 a r e t h e d i s t a n c e and time weightinn f a c t o r s f o r C i n t h e d i f f e r e n c e equation. By s o l v i n g t h e d i f f e r e n c e e q u a t i o n of e q u a t i o n A1.2, w e are, i n convection e q u a t i o n of t h e form: e f f e c t , solving a d i f f u s i o n

+

-

-

a%"f';: ac. %&* ax+ at

(A 1 . 4 ) .

This c r e a t e s a r t i f i c i a l d i f f u s i o n of C,and is terned numerical d i s p e r s i o n . L i n e a r i s e d s t a b i l i t y a n a l y s i s shove that t h e numerical s o l u t i o n s a r e s t a b l e i f t h e w e i g h t i n g f a c t o r s l i e i n t h e r a n g e 0.5 t o 1 (Equal g r i d s p a c i n g ) . Peaceman ( 1 7 ) showed t h a t a n o n l i n e a r s t a b i l i t y a n a l y s i s g a v e t h e same p r a c t i c a l c r i t e r i a for a f u l l upstream d i f f e r e n c e scheme (W-1). The r e s u l t s of t h e l i n e a r i z e d s t a b i l i t y a n a l y s i s a r e summarised i n t h e diagram shown below. The a p p r o x i m a t e s t a b i l i t y subdomain i n which t h e dynamic weighting scheme is o p e r a t i n g is more r e s t r i c t i v e t h a n t h a t permitted by t h e l i n e a r i z e d S t a b i l i t y analysis.

A Schematic I l l u s t r a t i o n of The Numerical S t a b i l i t y Domains

S t a b i l i t y Domain Domain i n whichdynamic weighting schemeoperates

0

w-

I

Conditional S t a b i l i t y Domain

la

I n c r e a s i n g Numerical S t a b i l i t y and Truncation Errors

0

439

A.2 A d d i t i o n a l Notes on 2-Point Upstream Weighting and Mid-Point Schemes

Weighting

The p r e v i o u s c u r v e a n a l y s i s shows t h a t 2-point upstream weighting cannot be a p p l i e d on Group 2 curves. Todd e t a 1 ( 9 ) showed 2 c a s e s which,according t o our p r e s e n t a n a l y s i s , b e l o n g t o t h e Group 2 curves category. Case 1: Todd e t a 1 showed a n example of u n i t m o b i l i t y , m i s c i b l e d i s p l a c e m e n t It i s p o s s i b l e t o c a l c u l a t e o i l r e l a t i v e permeability o f o i l by s o l v e n t . which is g r e a t e r t h a n 1 by 2-point upstream eXtraFQlatiOn,aS shown. T o d d e t a1 recommended s e t t i n g t h e s p u r i o u s e x t r a p o l a t e d value t o t h e maximum of t h e 2 bounding v a l u e s . Our c u r v e a n a l y s i s i n d i c a t e s t h a t t h i s i s e f f e c t i v e l y downstream weighting and could create a n undershoot of t h e o i l phase i f i t i s approaching zero s a t u r a t i o n . A m i d s t r e a m i n t e r p o l a t i o n is t h e b e s t alternative. I t i s e f f e c t i v e l y upstream,but not f u l l y upstream weighted on t h e a c t u a l curve p r o f i l e . Case 2: Todd showed t h a t a s p u r i o u s e x t r a p o l a t i o n e r r o r would o c c u r n e a r a s h a r p WOC or GOC. T h i s i s a Group 2 curve s i t u a t i o n c r e a t e d by t h e use o f r e l a t i v e p e r m e a b i l i t y (Kr) e x t r a p o l a t i o n , w h i c h i s l e s s c o n s i s t e n t t h a n s a t u r a t i o n e x t r a p o l a t i o n on t h e following grounds:(1) S a t u r a t i o n s a t t h e block interface d i c t a t e t h e i n t e r b l o c k flow. However, t h e e x t r a p o l a t e d r e l a t i v e p e r m e a b i l i t i e s w i l l not correspond t o a t o t a l s a t u r a t i o n of 1. (2) I t c r e a t e s , o r a c c e n t u a t e s t h e c r e a t i o n o f , a Group 2 p r o f i l e (which i s n o t amenable t o l i n e a r e x t r a p o l a t i o n ) . I n t h i s example, a Group 1 s a t u r a t i o n p r o f i l e exists. Had s a t u r a t i o n e x t r a p o l a t i o n been used, Krw a t 1124 would be 0.7 i n s t e a d of t h e s p u r i o u s n e g a t i v e value. (3) T y p i c a l l y , f o r a water f l o o d i n g problem, Group 2 s a t u r a t i o n p r o f i l e s e x i s t above t h e shock f r o n t s a t u r a t i o n value. The corresponding K r w p r o f i l e s

1.1

.

.

.

,

.

.

.

LANGSRUD DA TA

-

F i g u r e LO Comparison of w a t e r s a t u r a t i o n p r o f i l e s f o r v a r i o u s m o b i l i t y e v a l u a t i o n schemes ( b l a c k o i l model). (a) Spivak d a t a (SPEJ, February 1977). ( b ) Langsrud d a t a (Nolen and Berry, SPEJ June 1972).

.

.

44 0

have s t r o n g e r Group 2 c h a r a c t e r i s t i c s . The f a c t that e x p l i c i t 2-point Kr e x t r a p o l a t i o n d o e s n o t c a u s e i n s t a b i l i t y is p r o b a b l y d u e t o t h e non-sharpening n a t u r e of t h i s s a t u r a t i o n range. On t h e o t h e r hand, Group 1 curves (which are not amenable t o i n t e r p o l a t i o n ) a r e p r e s e n t around t h e flood front. The s a t u r a t i o n r a n g e b e l o w t h e s h o c k f r o n t s a t u r a t i o n i s self-sharpening, thereby a g g r a v a t i n g t h e weakness of i n t e r p o l a t i o n . This supports t h e evidence that mid-point weighting i s unstable. Figure 1Oa i l l u s t r a t e s some ueaknesees of u s i n g Kr e x t r a p o l a t i o n , n o r m a l l y n o t o b s e r v a b l e without imposing f r o n t a l c o n t r o l . An e x p l i c i t v e r s i o n of t h e dynamic weighting scheme, using 2 - p o i n t s a t u r a t i o n e x t r a p o l a t i o n a t t h e c o n t r o l l e d f r o n t and m i d s t r e a m weighting everywhere else, i s i l l u s t r a t e d i n Figure lob.

441

NUMERICAL METHODS

INTERPHASE MASS TRANSFER EFFECTS IN IMPLICIT BLACK OIL SIMULATORS D.BANKS and D.K.PONTING Atomic Energy Research Establishment, Hanuell, Oxfordshire,Enghnd

ABSTRACT

Mass t r a n s f e r may be described i n black o i l s i m u l a t o r s by allowing o i l and gas t o e x i s t i n both l i q u i d and vapour phases. A n q f f i c i e n t f u l l y implicit method of simultaneously modelling bubble and dew p o i n t is described. A s u b t r a c t e d t o t a l gaa formulation is found t o combine t h e advantages of t h e free and total gas approaches. A partial re-solution algorithm o p t i o n is d e s c r i b e d which I n t e r p o l a t e s bettween total- and no- re-solution logic. The d l s p r e i o n o f di88olved gaa and vapourlsed o i l is discussed.

B l a c k o i l s i m u l a t o r s , c h a r a c t e r i s e d by the treatment of j u s t two hydrocarbon

components, have t r a d i t i o n a l l y been more concerned w i t h d i 8 p l a c e m n t mechanisms t h a t the PVT dominated processes of EOR 8 t u d i e s . C-sltional effects are modelled simply by mass t r a n a f e r between l i q u i d and vapour phases. I n t h i s paper we d i s c u s s a n u m b e r o f v p e c t s ofma8stransferinblackoilsimulator8, mainly f r o m t h e s t a n d p o i n t of a f u l l y implicit formulation. Black o i l models g e n e r a l l y d e s c r i b e the c o n c e n t r a t i o n o f d i s s o l v e d gaa i n the reservoir l i q u i d by t h e bubble p o i n t p r e s s u r e , Pb, or the rrolution g a a - o i l ratio, R The q u a n t i t y o f o i l i n t h e vapour is described by t h e dew p o i n t p r e s s u r e , Pa, or t t e vapour oil-gaa ratio r or R ,[1,23. The vapour oil-gru ratio is g e n e r a l l y preferable, aa it enabfes thx vapour t o be described i n r e g l o n s o f low p r e s s u r e and re, for which no dew p o i n t exists. The ‘ o i l ’ and ‘gaa’ M y be any two groups of

.

hydrocarbon components, or t r u e stock tank o i l and gaa. I n a g e n e r a l b l a c k o i l model t h e r e are therefore f i v e independent v a r i a b l e s per cell: , Pb or Re, Pd or re, Sw, S The equation6 determining P and r8 would involve d f f f u s i o n , convection and &EI transfer rates. A t p r e s e n t , t h e extra c a p l t a t i o n a l effort r e q u i r e d t o s o l v e the f o u r t h and f i f t h e q u a t i o n s is p r o h i b i t i v e . The three equation p i c t u r e may be r e s t o r e d by employing bubble and dew p o i n t models, d i n g two o f t h e v a r i a b l e s dependent on t h e primary ones. A v a r i a b l e s u b s t i t u t i o n method for simultaneouslymodellingofp and rs v a r i a t i o n s i n an implicit b l a c k s i m u l a t o r is d e s c r i b e d i n S e c t i o n 2. mil%thi8 cannot y i e l d the d e t a i l e d d a c r i p t l o n obtrined from a t r u e multi-coaponent compositional s i m u l a t o r , the greater computational

P

.

442

e f f i c i e n c y enables detailed f u l l f i e l d s t u d i e s t o be performed. F a c i l i t i e s such as f a u l t connections and d i r e c t i o n a l r e l a t i v e permeabilities are t h e n a v a i l a b l e for s t u d i e s involving m i l d l y v o l a t i l e o i l s or dew p o i n t t r a n s i t i o n s , and numerical d i s p e r s i o n may be limited by the use of amall g r i d blocks. I n o u r experience v a r i a b l e s u b s t i t u t i o n is t h e o n l y method of modelling mass t r a n s f e r which does not l i m i t the a b i l i t y of the s i m u l a t o r t o t a k e l a r g e time steps, although other methodg are possible i f t h e time step l e n g t h is restricted. The q u a n t i t y o f g a s e x i s t i n g i n s o l u t i o n may be t y p i c a l l y 50-1000 times g r e a t e r t h a n t h a t e x i s t i n g i n t h e vapour phaae. The q u e s t i o n arises aa t o whether t h e maas conservation equation for g a s should involve a l l t h e g a s , or j u s t the f r e e component. O r i g i n a l l y a free g a s formulation w a a used i n PORES [lo]. I n s o l v i n g t h e material

c o n a e r v a t i o n e q u a t i o n s , however, a c o l u m n s u m c o n d i t i o n i s i m p o s e d w h i c h a t t e m p t s t o z e r o the sum of errors on d i a g o n a l p l a n e s of cells w i t h i n the reservoir model. T h i s is p a r t i c u l a r l y important i n the s e q u e n t i a l method of s o l v i n g t h e l i n e a r matrix equations. For a free g a s formulation, t h e column sum c o n d i t i o n r e p r e s e n t s an attempt t o c o n s e n e free gas, a conservation c o n d i t i o n v i o l a t e d when i n t e r p h a s e maas t r a n s f e r occurs. A t o t a l gaa formulation avoids t h i s , b u t , due t o the l a r g e d i s s o l v e d g a s c o n t r i b u t i o n , leaas t o p o o r l y conditioned e q u a t i o n s which t h e s e q u e n t i a l method f r e q u e n t l y fails t o s o l v e . A subtracted t o t a l gaa method which overcomes t h i s is described i n S e c t i o n 3. Such methods may be important f o r compositional s i m u l a t o r s aa the i n c r e a s i n g number of e q u a t i o n s r e n d e r s f u l l y simultaneous s o l u t i o n methods i m p r a c t i c a l l y expensive. Gas must come o u t o f s o l u t i o n when the o i l p r e s s u r e crosses the bubble p o i n t , b u t the re-solutionof gasdepends on t h e p r e s e n c e o f g a s i n c o n t a c t w i t h l i q u i d o i l , and the rate at which s o l u t i o n o c c u r s . Experiment [7] i n d i c a t e s that, where an i n t i m a t e gas-oil c o n t a c t e x i s t s , e q u i l i b r i u m is established on a timescale short compared t o those t y p i c a l l y involved i n reservoir engineering. The determining factor i n g a s s o l u t i o n is the rate a t which g a s d i f f u s e s through l i q u i d o i l . I n PORES, and other black o i l s i m u l a t o r s , t w o a l t e r n a t i v e s are a v a i l a b l e f o r the t r e a t m e n t o f g a s s o l u t i o n . Those are the no- r e - s o l u t i o n and total- r e - s o l u t i o n o p t i o n s . No- res o l u t i o n assumes that d i s s o l v e d gaa does not d i f f u s e through o i l , so that a layer of s a t u r a t e d o i l w i l l immediately b u i l d up at a gas-oil i n t e r f a c e and p r e v e n t f u r t h e r solution. While t h i s o p t i o n is l o g i c a l l y c o n s i s t e n t , it is u n r e a l i s t i c f o r r e s i d u a l o i l droplets, and w i l l o v e r e s t i m a t e g a s cap sizes. Using typical d i f f u s i o n c o e f f i c i e n t s , it can e a s i l y be shown t h a t a Inm d r o p l e t w i l l reach 991 of its u l t i m a t e d i s s o l v e d g a s c o n c e n t r a t i o n i n less than 24 hours. Total re-solution l o g i c assumes that i n t e r p h a s e e q u i l i b r i u m always exists i n each cell, so that free g a s may o n l y exist w i t h s a t u r a t e d o i l . T h i s aSSumptiOn of instantaneous e q u i l i b r i u m is u s u a l l y also made i n compositional s i m u l a t o r s . and e s s e n t i a l l y implies i n s t a n t a n e o u s flow of d i s s o l v e d gaa through o i l . I n practice, however, vapour invading o i l is l i k e l y t o f i n g e r or channel, r e s u l t i n g i n the gas bypassing some of the o i l . Free g a s may t h e n pass through a cell without Coqpletely s a t u r a t i n g the o i l . I n S e c t i o n 4 we d e s c r i b e a partial re-solution o p t i o n which enables the engineer t o set a r e - s o l u t i o n or e q u i l i b r i u m f r a c t i o n for each cell, the f r a c t i o n o f the l i q u i d hydrocarbon i n a cell i n c o n t a c t w i t h the vapour. This can s t i l l be f u l l y expanded i n a three v a r i a b l e formulation, and is similar t o the

t r a p p i n g f r a c t i o n approach. Simulators which permit g a s s o l u t i o n have d i f f i c u l t i e s w i t h the d i s p e r s i o n of d i s s o l v e d g a s and cell size dependence. These problem8 are, i f anything, more s e v e r e for vapourised o i l . This is due t o the non-specification of the d e t e d n i n g d i f f u s i o n rates, so that changes i n R and r are M i a t e l y p r o m a t e d across cells. I n a sense, t h e artificial'cell k u n d a r i e s introduced by t h e s i m u l a t o r prevent d i s p e r s i o n f r o m b e i n g t o t a l , rather than c a u s i n g it. NO r e - s o l u t i o n logic has an e q u i v a l e n t problem i n t h a t g a s is evolved from undersaturated o i l when flow

443

o c c u r s across an R g r a d i e n t . It is possible t o c o n t r o l t h i s d i s p e r s i o n for t h e simple case of fret g a s invading o i l by o n l y allowing R t o rise due t o c o n t a c t w i t h f r e e vapour. However, such methods run i n t o t r o u b l e &en a d r y vapour or d i s s o l v e d g a s s l u g is propogated, as t h e y modify the s l u g shape by sharpening t h e l e a d i n g edge.

MODELLING BUBBLE AND DEW POINT VARIATIONS

Two main approaches e x i s t t o modelling mass t r a n s f e r i n black o i l s i m u l a t o r s : the v a r i a b l e s u b s t i t u t i o n method [ 4 , 5 ] , and one cell methods i n which cell properties are modified t o be c o n s i s t e n t w i t h t h e s o l u t i o n i n terms of a f i x e d set of v a r i a b l e s [3]. These correspond t o s a t u r a t i o n p r e s s u r e and flash technique8 i n compositional s i m u l a t i o n [ 5 , 6 ] . Both methods have been used i n PORES, and v a r i a b l e s u b s t i t u t i o n has proved s u p e r i o r , although it i n v o l v e s o r g a n i s a t i o n a l d i f f i c u l t i e s i n keeping trackof whether t h e t h i r d s o l u t i o n v a r i a b l e is S P o r r The cell by cell b 8' technique r e t a i n s Po, Sw and S as s o l u t i o n varia%;es, and a d j u s t s R (Pb) t o s a t i s f y phase e q u i l i b r i u m . If g a s i a e c t i o n o c c u r s i n t o u n d e r s a t u r a t e d 011.for example, R;I is i n c r e a s e d , as i n the pseudo s o l u t i o n gas method. Unless t h i s is done e x a c t l y , a n e g a t i v e gas s a t u r a t i o n is o b t a i n e d on t h e subsequent i t e r a t i o n and g e n e r a l l y c a u s e s m a t e r i a l b a l a n c e errors. This can be overcome by u s i n g a one cell Newtonian i t e r a t i o n toexact m a t e r i a l b a l a n c e t o f i x t h e Rs change p r e c i s e l y . This y i e l d s a working scheme, b u t r u n s i n t o convergence problem on l o n g t i m e steps, as t h e p r e s s u r e changes which occur when free gas goes i n t o s o l u t i o n d i s t u r b the i n t e r b l o c k flows i n a manner n o t i n c o r p o r a t e d i n t o the Jacobian of the newtonian i t e r a t i o n . I n t h e u n d e r s a t u r a t e d o i l case t h e gas e q u a t i o n is b e i n g converged t o a known s o l u t i o n , S 0 ; more p r e c i s e l y , the bubble p o i n t is implicit, b u t n o t f u l l y expanded. 9

-

V a r i a b l e s u b s t i t u t i o n does n o t attempt t o r e t a i n gas S a t u r a t i o n as the t h i r d

v a r i a b l e a t a l l times.

Depending on the c o n d i t i o n s i n a cell, gas 8 a t u r a t i o n ,

bubble p o i n t or vapour oil-gas ratio, r , may be the primary s o l u t i o n v a r i a b l e . I n each case it is c r u c i a l that the f u n c t f o n a l dependence o f the secondary variables, ( s u c h as Pb and r i n a cell i n which S is the primary v a r i a b l e ) , and of f u n c t i o n s of t h e s e secondary bariables, is knoun 8nd included i n the Jacobian. The omission of a p p a r e n t l y minor terme from the Jacobian can l i m i t convergence of t h e non l i n e a r e q u a t i o n s unacceptably. However, t h e exact c a l c u l a t i o n of i n t e r b l o c k and w e l l flows a t the advanced time level, which is o b t a i n e d w i t h i n c r e a s i n g accuracy as the Newtonian i t e r a t i o n converges, p r e v e n t s i n s t a b i l i t i e s which can occur using first order approximations t o the implicit flows [ll].

Assuminginterphase e q u i l i b r i u m , there areonlythreepossibilities f o r t h e state of a cell:-

(i) Vapouronly. Po, Swandr a r e s o l u t i o n v a r i a b l e s , w i t h S -1-S andPb-Po s o w S and S are Solution ( ii ) Liquid and vapour hydrocarbon A t e s e n t . P g variables, w i t h Pb-Po, rs-rs ( Po+Pcq?kg fi (iii) Liquid only. S -0

g

Po,

s and

and rS-r

sat

s

P are s o l u t i o n v a r i a b l e s , w i t h b

(Po+Pcog( 0 ) )

.........................

(1)

r sat( P ) is t h e curve d e s c r i b i n g the oil-gas ratio for vagour in e q u i l i b r i u m w i t h

lfquid

811.

444

The maas conservation equations take the form

Rj

j-l,..,N

-

1 TAT -[m. AT J

-

mT] j

-

TAT

qJ

-

T+AT

& fnj n

I

............

(2)

, N the number of c e l l s .

Elements of the residual, R, mass terms, w e l l term and flows have a three vector formr-

-

Rj

qj W + R s

qO j w1

............... where fo Law

fw

i n t%' us&

(3)

and fg are the free o i l , water and free gaa flows given by Darcy's way, "Ad g,w are the corresponding w e l l terms.

The equatioagiven by R ( X w A T a are solved by Newtonian iteration, derivatives being taken w i t h respect t o the primary solution variables for each c e l l . Transitions may occur between t h e three states of (l), on the -is of the c u r r e n t approximation t o

the advanced time step solution, as follows:-

From s t a t e

(i), if rs)rss a t (Po+P (1-5 ) ) . S e t rs-r s a t , S -6, cog w 0 9 . c h a n g e t o (ii) sat

Prom s t a t e

(ii), i f So
From s t a t e

(ii), i f S < O . S e t S -O,Pb-Po-c, 9 g

(Po+P

From s t a t e (iii), i f Pb)Po. S e t Pb-PO,Sg-~,

( S ))-c,Sg-l-Sw, cog g c h a n g e t o (i)

change t o ( i i l )

change t o ( l i )

...................... This is essentially a combination of the methods proposed by Cook et a1 [ 2 ] and Spivak and Dixon [l], The extra cost of aodelling r variation is s m a l l , aa c e l l s i n which r

is the Solution variable would o t h e h s e be repeatedly solved for a constane gas saturation of zero. When re is not the prirary variable, the effeck is merely t o add extra terme t o the Jacobian. This enable. effects such as the vapourisation of residual o i l into re-injected gas, an EOR type process expected t o some extent i n most reservoirs with gaa injection, t o be followed, aa w e l l as gaa solution and a primary recovery waterflood.

(4)

445

TBE SUBTRACTED 'IDTAL GAS PO-TION The r e s i d u a l i n ( 3 ) i n c l u d e s t e for t o t a l o i l , water and total gaa. The corresponding free gaa r e s i d u a l is?'-R "-R R A free gaa f o m l a t i o n was o r i g i n a l l y used i n PORES. Both it.&$ l l n e a r solver and s e q u e n t i a l method

'.

thd

u s e column sum methods to preserve zero r e s i d u a l s u r - s f f e c t i v e l y material balance on d i a g o n a l planes of cells. This c o n s t r a i n t , which g e n e r a l l y speeds convergence, haa l i t t l e v a l u e i f a free gas f o r m u l a t i o n is used, as free gaa r e s i d u a l s w does not correspond t o material b a l a n c e i f s a t u r a t e d o i l is p r e s e n t . It is possible n o t t o d i f f e r e n t i a t e t h e R t e r m i n the r e s i d u a l , l e a d i n g t o a eet of e q u a t i o n s , which, i f s o l v e d exactly, a r e e t q u i v a l e n t t o those o b t a i n e d from a total gaa r e s i d u a l . The J a c o b i a n is t h e n n o t t h e derivative of the r e s i d u a l , and acme of the convergence properties of the f u l l Newton method are lost. The a l t e r n a t i v e is t o u s e a s t r a i g h t f o r w a r d total gas formulation. This is p o s n i b l e for simultaneous s o l u t i o n methods, b u t t h e s e q u e n t i a l method fails completely. The dissolved gaa c o n t r i b u t i o n swampa the free component i n t h e e q u a t i o n determining t h e

gaa s a t u r a t i o n .

The S e q u e n t i a l method of s o l v i n g t h e linear eqUatiOM, i n the simple case of a noncondensate gaa o i l system, i n v o l v e s t h e matrix d e c o l p o s i t i o n r -

IJgrp

J 0,p

J 019

Jg,gl

-I

JolP-DJglp

1

J

llJg,p

O

-

J

X - R - R t g

9,g 9

9

x

9

9

.................................

where

Rtg X is approximate, g i v e n by: R

I f a free gas f o r m u l a t i o n is used, X

9

(5)

and D is a d i a g o n a l m a t r i x , such that i t e r a t i o n i 8 X -6( As ), dofinad by

S R The elements of Re are g i v e n by ( R ) The change i n ASg ov&iaN&Anfat; 9.9-Jo.g.

Ix3

........... O I 919

-

J

( Jo

(6)

,p-DJg,p)-bo-D(Rf
is g i v e n b~

Zr or8 arise i n t h e e v a l u a t i o n of t h e right-hand aide of (b). I n t h e free gaa cam R f g c o n s i s t s f a n approxisate m a t r i x a c t i n g o n R -D R , w h i l e i n a total g u &-lation R is g i v e n by a approrirate m a t r i x %tini%n Ro-D( Rf +R R ) If2the ersors i n t h e l i q u i d and vapour flaw are camQarab1e. Rxg I R8R ,k tR 8 O( 10 10 ). The right-hand s i d e of t h e e q u a t i o n d e f i n i n g gaa s a t u r a 6 o M cowk8, i n the t o t a l gaa caae, of two large c a n c e l l i n g term, one of which i 8 agproriute, and the r e s u l t i n g v a l u e s of As are less a c c u r a t e than i n the f n e QMC a m

.

"

.Y

9

-

446

Errors i n S are fed back i n t o the o i l r e s i d u a l v i a o f t e n diveqges.

So-

1-s -S w

g'

and

the

iteration

The advantages of both f o r m u l a t i o n s may be combined i n a subtracted t o t a l g a s formulation, i n which the g a s e q u a t i o n r e s i d u a l is

Rs t g

-

-

Rg

R'"~sR

..*.....................*.......( 8 )

0

The choice o f R sub is rather critical, and s e v e r a l a l t e r n a t i v e s have been t r i e d . The best eema 80 be$, updated by the predictor a t t h e start of each tim step. The An USC d R rather t h a n z s can i n c r e a s e run times by 50%. The continuous updating of sub

R~ a d seem e s s e n t i a l .

Anadvantage o f t h i s m e t h o d i s t h a t i s o l a t e d d i s s o l v e d gaa changes, s u c h a s those due t o gaa i n j e c t i o n , s t a n d o u t o v e r the R s u b t r a c t i o n , c a u s i n g r e s i d u a l s which the s i m u l a t o r converges o u t a c c u r a t e l y . that is r e m v e d is the b u l k of the i n i t i a l d i s s o l v e d g a s which otherwise c a u s e s the gaa e q u a t i o n t o be a n e a r m u l t i p l e of the o i l equation. The s e q u e n t i a l method can s t i l l f a i l when a l a r g e i n i t i a l R gradient exists across t h e reeerpoir, i n which case a f u l l y simultaneous s o l u t i o n k t h o d must be used.

all

THE S O u l T I O N OF GAS I N O I L Black o i l s i m u l a t o rs h a v e tended n o t t o p r o v i d e the e n g i n e e r w i t h v e r y comprehensive facilities for i n v e s t i g a t i n g gaa S o l u t i o n effects. P a r t l y , t h i s is due t o a lack of knowledge concerning the processes involved. It seem clear that r e s i d u a l o i l droplets w i l l e q u i l i b r a t e q u i c k l y , b u t a l metre diameter area of o i l w i l l take over a Y e a r t o s a t u r a t e i f f r e e gaa channels past it. Providing no- and total- r e - s o l u t i o n o p t i o n s e n a b l e s t h e s e n s i t i v i t y of t h e problem t o g a s s o l u t i o n effects t o be e s t a b l i s h e d . If t h i s is a major effect, however, as i n t h e Odeh test problem [9], there are no facilities for h i s t o r y matching. I n p a r t i c u l a r , the degree of e q u i l i b r i u m between phases w i l l be d i f f e r e n t for r e s i d u a l o i l i n a g a s cap from that

a t t a i n e d i n t h e case o f g a s i n j e c t i o n i n t o u n d e r s a t u r a t e d o i l , and these processes may occur i n t h e same s t u d y . The PORES partial r e - s o l u t i o n o p t i o n a l l o w s t h e u s e r t o d e f i n e a r e - s o l u t i o n or e q u i l i b r i u m f r a c t i o n , f , o f the o i l i n a c e l l which is i n close c o n t a c t w i t h vapour. For a time step from T t o *AT, t h e partial r e - s o l u t i o n o p t i o n r a y be sunmurised as;-

Undersaturated o i l , Pb is s o l u t i o n v a r i a b l e I f PT

<

T+AT

Pb

T+AT then


bmin If

sT+ATIOl

pT+AT_pT

bmin

g

then

Saturated o i l , S

g

T+ATIO

S

9

T+ATlpT+AT

I P

bmin

b

is s o l u t i o n v a r i a b l e

T+AT T+AT T+ATIMin I f S >O t h e n Pb -P ,P 9 0

T

bmin

447

B u b b l e p o i n t t r a n s i t i o n , gas appearing

I f Pb

9

s e t t o E,PT+AT-P TtAT ,PT+AT_Min b 0 bmin

T

................. ( 9 ) i s t h e minimum bubble p o i n t a t t a i n e d by t h e c e l l d u r i n g the s i m u l a t i o n . The q u a n t i t y of d i s s o l v e d g a s i n t h e cell and i n t e r b l o c k flows is o b t a i n e d as a weighted average u s i n g Pban

a c t i n g as bubble p o i n t for the 'trapped' or non-equilibrium o i l f r a c t i o n . This model y i e l d s t o t a l and no-resolution as the limits of f-1 and 0 r e s p e c t i v e l y . The r v a l u e can be followedfir t h e vapour as described i n S e c t i o n 2 . A l l function& d e r i v a t i v e s can be expanded i n t h e JaCobianInlkrms of t h e prvariables. There are s e v e r a l respects i n which t h i s partial r e - s o l u t i o n scheme is less t h a n ideal I ( i ) I f p r e s s u r e drops through the bubble p o i n t of t h e by-passed o i l , and gas comes o u t of s o l u t i o n a t less t h a n m o b i l e s a t u r a t i o n , t h e n it w i l l not r e - d i s s o l v e i n t h e non-equilibrium f r a c t i o n or r e - p r e s e u r i s a t i o n . This c o u l d be allowed, b u t it seem u n r e a l i s t i c t o ascribe d i f f e r e n t behaviours t o gas at j u s t under and over c r i t i c a l s a t u r a t i o n . I n a d d i t i o n , d i s c o n t i n u o u s changes i n the f u n c t i o n a l form of t h e r e s i d u a l can s l o w convergence. (ii) When f i n g e r i n g or c h a n n e l l i n g occurs, it would be expected that t r a n s v e r s e s a t u r a t i o n would o c c u r behind the f r o n t . This does n o t o c c u r i n t h i s model. O t h e r possibilities exist for partial r e - s o l u t i o n o p t i o n s , such as re-solution i n r e s i d u a l o i l . However. when gaa displacement is stable, due t o g r a v i t y segr e g a t i o n , t h i s is e q u i v a l e n t t o t o t a l r e - s o l u t i o n . For gas i n j e c t i o n , r e s i d u a l o i l s a t u r a t i o n is r a r e l y a t t a i n e d . There is also t h e d i f f i c u l t y of i d e n t i f y i n g t h e r e s i d u a l o i l i f the cell is subsequently f l u s h e d w i t h mobile o i l . I t would be possible t o have a similar o p t i o n f o r o i l v a p o u r i s a t i o n . I n most condensate s t u d i e s , however, o i l s a t u r a t i o n s remain less t h a n critical, so t h a t e q u i l i b r i u m is a r e a s o n a b l e assumption. The e q u i v a l e n t of g u i n j e c t i o n r a r e l y arises.

DISPERSION PROBLElls I N MASS TRANSPER

V a r i a t i o n s i n Rs and Is, due t o convection and maas t r a n s f e r u s u a l l y show d i s p e r s i o n effects. When, for example, the bubble p o i n t rises i n a cell due t o gas s o l u t i o n t h i s rise is assumed t o o c c u r evenly throughout the e n t i r e cell, and is c o m u n i c a t e d t o its neighbours by o i l flows. The r e s u l t i n g rise i n R for the neighbouring cell s is t h e n passed, i n t h e same time step, t o t h e next cell. I n cases of h i g h throughput ratio, a c o n s i d e r a b l e f r a c t i o n of t h e reservoir r a y need t o be s a t u r a t e d before free g a s appears i n the i n j e c t i o n cell. This problem might be expected t o be r a t h e r less s e v e r e i n IHPES type s i m u l a t o r s , which e f f e c t i v e l y impose an upper l i m i t of AX/AT on t h e speed a t which d i s s o l v e d g a s or vapourised o i l may propopate, as d i f f u s i o n is limited t o one block per time etep. However, such a s i m u l a t o r i e l i k e l y t o t a k e more steps than a f u l l y implicit one t o s o l v e a given problem, o f f - s e t t i n g t h e advantage of lover d i s p e r s i o n per time step.

448 For simple g a s i n j e c t i o n i n t o undersaturated o i l , it is f a i r l y e a s y t o p r e v e n t t h i s d i s p e r s i o n by assuming t h a t g a s p a s s i n g i n t o a cell s a t u r a t e o i l o n l y as it o v e r r i d e s it, so t h a t a n i n c r e a s e d R v a l u e w i l l not appear a t the downstream i n t e r f a c e u n t i l the cell is s a t u r a t a . The result. of such a technique on the c a m 2 odeh problem are shown i n f i g . 1. However, t h i s method of d i s p e r s i o n c o n t r o l r u n s i n t o problems when the convection of s l u g s is considered. P a r t i c u l a r l y i n the came

of condensate reservoirs, where g a s i n j e c t i o n may be c o n t r o l l e d by production rates and s a l e a c o n t r a c t s , the r e s u l t i n g r d i s t r i b u t i o n s may not have simple shapes. Front sharpening methods w i l l t e n d to d i s t o r t such s l u g s by sharpening the l e a d i n g edge. I n t e r b l o c k flow schemes other t h a n upstreamlng w i l l y i e l d unphysical r e s u l t s i f f l o w o c c u r s fromacellof zero re t o o n e o f f i n i t e r b u t upatreaming c a u s e s 8' unacceptable a r t i f i c i a l d i f f u 8 i o n .

CASE 2,

GOR VS T I M E

cy 0 U

0 0

1

3

2

T I M E I N YEARS Figure 1.

4

5

6

7

8

9

10

449 W e can p r e s e n t no simple s o l u t i o n t o the d i s p e r s i o n problem, and it may be t h a t it is i n h e r e n t i n the concept of u s i n g a dew or bubble p o i n t model r a t h e r t h a n a separate e q u a t i o n . The b a s i c a l l y c o n v e c t i v e n a t u r e of r and R transport s u g g e s t s a p o i n t

following algorithm, although those s u g g e s t e d t o date are n o t f u l l y implicit. It may be cheaper, however, to add an extra t r a n s p o r t - t y p e e q u a t i o n t o t h e t r a d i t i o n a l black o i l p i c t u r e t h a n t o go t o t h e number o f cells r e q u i r e d t o reduce d i s p e r s i o n t o an acceptable l e v e l . CONCLUSIONS ( i ) It is possible t o model g a s condensate and bubble p o i n t e f f e c t s simult a n e o u s l y i n an e f f i c i e n t g e n e r a l purpose black o i l s i m u l a t o r . Minor o i l vapouris a t i o n and condensate effects w i l l occur i n many s t u d i e s , and these can be included a t l i t t l e extra cost. ( i i ) There is a need t o p r o v i d e e n g i n e e r s w i t h a more flexible method of matching g a s s o l u t i o n e f f e c t s . A r e - s o l u t i o n f r a c t i o n approach e n a b l e s o i l by- pass and c h a n n e l l i n g e f f e c t s t o be included, and has a simple f u n c t i o n a l form which is p a r t i c u l a r l y s u i t a b l e for i m p l i c i t s i m u l a t o r s . No- and total- r e - s o l u t i o n o p t i o n s are o b t a i n e d as l i m i t i n g caees.

For s e q u e n t i a l methods, a c o n t i n u o u s l y modified subtracted total gas formulation is preferable t o either total or f r e e g a s formulationn.

(iii)

( i v ) A l l bubble and dew p o i n t models are a poor excuse f o r s o l v i n g a d i s s o l v e d gas or vapourised o i l e q u a t i o n . I n p a r t i c u l a r , numerical d i s p e r s i o n o f vaporised o i l and d i s s o l v e d g a s can be s i g n i f i c a n t . This can be c o n t r o l l e d i n Simple cases, such as d r y gaa invading u n d e r s a t u r a t e d o i l , b u t d i s p e r s i o n c o n t r o l methods may d i s t o r t t h e shape of convected s l u g s . This may be p a r t i c u l a r l y important for g a s i n j e c t i o n i n t o condensate reservoirs.

b

Ir

p

P

b

Pr

'

f

~ a ~ e ~ ~ ~ r f O ~ u ~ ~ factor ~ e V o for l u phase m e p, d e f i n e d aa

/P

P I

I

nj to

p

I

P

: The

P Pj

I

S

: The

P qjw R j

P

:

rock

cell

P

Pj

p is f l u i d d e n s i t y

The flow rate, measured i n terms o f s u r f a c e volume, of phase p, from cell n

: The

dj

, where

b xb.

N bj

P

j

numbsr of a c t i v e cells i n the reservoir

The bubble p o i n t p r e s s u r e of cell j

dew p o i n t p r e s r u r e o f cell j

The p r e s s u r e of phase p i n cell j

s a t u r a t i o n o f phase p i n cell j

The rate of flow, measured i n term of s u r f a c e volume, from w e l l w t o cell j

: The

r e s i d u a l of the maas convervation e q u a t i o n for cell j , phase p

4 50 J 'j : The element of the Jacobian, P,V

x

Pj

s

: The pth p r i m a r y

solution v a r i a b l e for cell j

:The minimum Re v a l u e i n the reservoir model : The

Rs

a
mean Rs value i n the reservoir model

REFERENCES 1. SPIVAII. A. and DIXON, T.N.; " s i m u l a t i o n of g a s condensate reseervoirs", SPE4271, P r o c . 3rd symp. on Numerical S i m u l a t i o n o f Reservoir Performance, Houston, 1973. 2.

COOIC, R.E., JACOBI, R.H. and RAWZSH, A.B.

J

"A

beta-type reservoir S i m u l a t o r for

approximating compositional e f f e c t s d u r i n g g a s i n j e c t i o n " , Soc.Pet.Eng.J., (06. 1974), 471-481

EERIE, A, RUBIN, 8 . and VINSOM!, K. ; T e c h n i q u e s for f u l l y -licit resemoir s i m u l a t i o n " , P r o c . 5 5 t h Ann. P a l l Conf. and E x h i b i t i o n of SPE,

3. AU, A.D.K.,

milas, 4.

5.

6.

1980.

BANSAL, P.P. et al; "A s t r o n g l y coupled, f u l l y implicit, t h r e e d i m e n s i o n a l , t h r e e p h a s e reservoir s i m u l a t o r , SPE8329, Proc. 5 4 t h Ann. F a l l Conf. and E x h i b i t i o n o f sPE, Las Vegas, 1974.

COATS, K.H.; "An e q u a t i o n of state c o m p o s i t i o n a l Podel", Soc.Pet.Eng.J., 1980 ), 363-376

(Oct.

NGEEIU, L.X., PONG, D.K. and AZIZ, K.; "Compositional modelling w i t h an e q u a t i o n of state", SPE9306, P r o c . 55th Ann. P a l l Conf. and E x h i b i t i o n o f SPE, milas, 1980.

NO=, J.S.; "Numerical simulation of compositional phenomena i n petroleum reservoirs", SPE R e p r i n t S e r i e s , No. 11, (1973). 269. 7.

RAIIIOM)I, P. and mRCAS0, U.A.; "naes transfer between phases i n a medium: A s t u d y of equilibrium", Soc.Pet.Eng.J. (March 1965), 51-59, AIM! 234

porous Trans.

8,

SAWDRu, R. and NIELSEN, R.; " ~ y n d c sof petroleum reservoir. i n j e c t i o n " , Gulf Pub.Co., 1974

9.

ODEE, A; "Comparison o f solutions t o a three d i m e n s i o n a l black-oil reservoir s i m u l a t i o n problem", J.Pet.Tech., (Jan. 1 9 8 l ) , 13-25

10.

under g a s

CBESHIRC, 1.14. e t al; " ~ n efficient f u l l y implicit simulator", -79. Proc. European O f f s h o r e Conference and E x h i b i t i o n , London, 1980, 325

11. COATS, K.H.; "Reservoir simulation: A g e n e r a l model f o r m u l a t i o n and associated p h y s i c a l / n u m s r i c a l sources o f i n s t a b i l i t y " , Proc. BAILl Conf., Dublin, June 1980. 62-76, ed. Uiller, J.J.H., Bode P r e s s .

EXPERIMENTAL TECHNIQUES

451

A NOVEL DEVICE FOR CO, CORE FLOODING VOLKER MEYN

Institut f i r Tiefbohrkunde und Erdolgewinnung der TU clmrsthal

ABSTRACT A newly d e v e l o p e d core f l o o d i n g a p p a r a t u s i s described. The appa-

r a t u s p e r m i t s t h e c o n d u c t i n g of f l o o d e x p e r i m e n t s w i t h l i v i n g o i l w i t h i n a p r e s s u r e r a n g e b e t w e e n 1 and 600 bar a t f l o o d i n g r a t e s from 1 t o 50 cm3.h-l.

During t h e e x p e r i m e n t , t h e mass f l o w of C02

a t t h e i n p u t i s h e l d c o n s t a n t . The f o l l o w i n g d a t a a r e t h e r e b y meas u r ed : o i l p r o d u c t i o n , water c u t p r o d u c e d , number of moles of g a s p r o d u c e d , g a s c h r o m a t o g r a p h i c a l g a s a n a l y s i s u p t o . C 7 , a n a l y s i s of s t o c k t a n k o i l up t o C26, p r e s s u r e d i f f e r e n c e . B e c a u s e t h e p e r f o m a n c e of core f l o o d i n g e x p e r i m e n t s i s f e a s i b l e onl y w i t h i n a c e r t a i n l e n g t h l i m i t , w h e r e a s t h e d e v e l o p m e n t of t h e t r a n s i t i o n z o n e n e a r t h e m i n i m a l miscibility

pressure requires a

f l o o d d i s t a n c e of a t l e a s t 1 m , a new e x p e r i m e n t a l s e t - u p h a s been

tested. The f l o o d i n g e x p e r i m e n t s are t o be c o n d u c t e d w i t h t h e t r a n s i t i o n zon e s p r e v i o u s l y e s t a b l i s h e d . T h i s d e s i g n i s based on a p u b l i c a t i o n by WATKINS. The e s t a b l i s h m e n t of t h e t r a n s i t i o n z o n e d u r i n g the f l o o d p r o c e s s i s s i m u l a t e d i n a t h r e e - s t a g e m i x i n g d e v i c e , which cons i s t s of i n c l i n e d p i p e s w i t h a t o t a l l e n g t h o f a b o u t 6 m . The m i x e r was tested w i t h o i l from German o i l r e s e r v o i r . The c o n c e n t r a t i o n s of t h e components C 0 2 ,

a s w e l l a s C1

t o C Z 6 , were recorded gas-chroma-

t o g r a p h i c a l l y a t t h e o u t p u t of t h e m i x i n g d e v i c e . With t h e h e l p of t h e s e e x p e r i m e n t s , i t c a n be d e m o n s t r a t e d t h a t s u c h a mixer i s cap a b l e of p r e p a r i n g a p h a s e whose c o m p o s i t i o n s i m u l a t e s t h a t i n t h e r e a l t r a n s i t i o n z o n e , e v e n i n t h e v i c i n i t y of t h e minimal miscib i l i t y pressure.

452

INTRODUCTION L a b o r a t o r y i n v e s t i g a t i o n s a r e b e i n g p e r f o r m e d i n t h e c o u r s e of a p r o j e c t /1/ c o n c e r n i n g t h e p o s s i b i l i t i e s of C 0 2 f l o o d i n g i n West Germany. For t h e f l o o d e x p e r i m e n t s , a d e v i c e which s h o u l d be s u i t e d f o r b o t h s l i m t u b e tests and c o r e f l o o d e x p e r i m e n t s

h a s b e e n d e v e l o p e d . A main o b j e c t i v e i s t o p r o v i d e e x p e r i m e n t a l d a t a f o r a simulation study. A r e q u i r e m e n t f o r t h e u s e of

black o i l s i m u l a t o r s i s t h a t t h e t r a n -

s i t i o n z o n e i s r e s t r i c t e d t o a s i n g l e c e l l . For t h i s r e a s o n t h e t r a n s i t i o n z o n e must be s h o r t . Such a r e q u i r e m e n t c a n n o t be s a t i s f i e d i n t h e c a s e of c o r e f l o o d e x p e r i m e n t s w i t h p u r e C 0 2 , s i n c e t h e c o n s t r u c t i o n of t h e t r a n s i t i o n z o n e r e q u i r e s . a length of a t least 1 m /2/.

WATKINS / 3 / h a s d e m o n s t r a t e d t h a t t h e r e s i d u a l o i l s a t u r a t i o n c a n be s u b s t a n t i a l l y r e d u c e d , e v e n i n " s h o r t " r e s e r v o i r models, by t h e u s e of a p r e m i x i n g v e s s e l . C o n s e q u e n t l y , o n l y a s h o r t l e n g t h is n e c e s s a r y f o r c o n s t r u c t i n g t h e t r a n s i t i o n zone i n t h i s c a s e . F o l l o w i n g t h i s c o n c e p t , t h e u s e of a p r e m i x e r s h o u l d p e r m i t d i s p l a c e m e n t by a medium whose c o m p o s i t i o n i s s i m i l a r t o t h a t of t h e t r a n s i t i o n z o n e . I n order t o d e m o n s t r a t e s u c h a p o s s i -

b i l i t y , m i x e r tests and c o m p a r a b l e s l i m t u b e e x p e r i m e n t s h a v e been conducted. I n order t o a l l o w a measurement of t h e u n i t d i s p l a c e m e n t e f f i c i e n c y , s l i m cores a r e b e i n g employed d u r i n g a n i n i t i a l p h a s e . However, t h e embedding, e s p e c i a l l y of s l i m c o r e s , i m p o s e s d i f f i c u l t i e s b e c a u s e of t h e h i g h - p r e s s u r e C 0 2 and t h e t e m p e r a t u r e s u p

t o 12OoC. I n g e n e r a l , o r g a n i c s e a l i n g m a t e r i a l s t e n d t o s w e l l and b l i s t e r u n d e r t h e s e c o n d i t i o n s . A f u r t h e r d i f f i c u l t y a r i s e s from t h e i n v a s i o n of t h e core by t h e

a d h e s i v e . F o r t h i s r e a s o n a c e l l of t h e Hassler t y p e c o n s i s t i n g o n l y of T e f l o n (PTFE) and s t a i n l e s s s t e e l h a s b e e n d e v e l o p e d .

EXPERIMENTAL SET-UP The s e t - u p i s d e s i g n e d f o r a p r e s s u r e u p t o 6 0 0 bar and a t e m p e r a t u r e u p t o 150OC. It c o m p r i s e s a pumping u n i t f o r i n j e c t i n g t h e C 0 2 , t h e f l o o d t u b e , and t h e a n a l y t i c a l e q u i p m e n t .

453

8

mesitylene

F i g . 1: Set up of t h e f l o o d d e v i c e : 1 , 2 back p r e s s u r e r e g u l a t o r ; 3 m i x e r tank; 4 f l o o d t u b e ; 5 C02-sto.rage v e s s e l ; 6 d i s p l a c e m e n t pumps The set-up

( f i g . 1) is d e s i g n e d such t h a t t h e C 0 2 mass f l o w a t t h e i n l e t i s m a i n t a i n e d c o n s t a n t . For t h i s p u r p o s e , C 0 2 is d i s p l a c e d by mercury a t a c o n s t a n t f l o w r a t e from a s t o r a g e vessel ( 5 ) , i n which t h e p r e s s u r e and t e m p e r a t u r e a r e m a i n t a i n e d con-

stant. T h e s t o r a g e v e s s e l is t h e r m o s t a t e d a t a t e m p e r a t u r e below t h e c r i t i c a l v a l u e , i n o r d e r t o keep t h e c o m p r e s s i b i l i t y low. The p r e s s u r e i n t h e s t o r a g e vessel i s h e l d c o n s t a n t by means of t h e . b a c k - p r e s s u r e r e g u l a t o r ( 1 ) .T h e pumping r a t e c a n be v a r i e d 3

w i t h i n a r a n g e from 0.4 t o 5 0 cm / h . I n t h e c a s e of t h e s l i m t u b e t e s t s , t h e f l o o d t u b e ( 4 ) c o n s i s t s of s t r a i g h t t u b e s e c t i o n s 2 m i n l e n g t h connected by elbows. For a n a l y t i c a l r e a s o n s a c o m p a r a t i v e l y l a r g e d i a m e t e r of 0 . 8 7 5 c m was chosen f o r t h e t u b i n g . The f l o o d t u b e i s immersed i n a t h e r m o s t a t i c o i l b a t h which c a n accomodate a t o t a l l e n g t h of 30 m . I n o r d e r t o f a c i l i t a t e t h e packing of t h e f l o o d t u b e , tee f i t t i n g s were i n s t a l l e d a f t e r e v e r y 4 m of l e n g t h . The t u b e bundles can be e a s i l y emptied and t h e r e f o r e r e u s e d o f t e n . For t h e c o r e f l o o d e x p e r i m e n t s of t h e f i r s t p h a s e , a d i a m e t e r of a b o u t 11 mm was s e l e c t e d . The aim is t o a c h i e v e a t o t a l l e n g t h of 2 m . According t o p r e v i o u s e x p e r i e n c e , c o r e s up t o

454

200 mm i n l e n g t h and w i t h a d i a m e t e r of 11 mm c a n be d r i l l e d w i t h o u t d i f f i c u l t y . The d r i l l i n g of l o n g e r c o r e s p r e s e n t s d i f f i c u l t i e s w i t h t h e s a n d s t o n e u s e d h e r e . The c o r e s e c t i o n s a r e i n s e r t e d i n t o a Teflon sleeve. This s l e e v e is i n s t a l l e d i n t h e s t a i n l e s s s t e e l body by means of p a c k e r s ( f i g . 2). S i n c e a s i n g -

l e p a c k e r s e a l s a t two p o s i t i o n s , i t i s p o s s i b l e t o d r i l l a h o l e t h r o u g h t h e p a c k e r down t o t h e core a f t e r t h e a s s e m b l y , i n order t o attach a pressure transducer.

F i g . 2: Packer assembly: 1 c o r e ; 2 PTFE s l e e v e ; 3 p a c k e r

I n order t o p r e v e n t l e a k a g e d u e t o t h e f l o w of t h e T e f l o n a t e l e v a t e d t e m p e r a t u r e s , t h e packer is d e s i g n e d as an a u t o m a t i c g a s k e t . To s i m p l i f y t h e a s s e m b l y , t h e t u b e c o n s i s t s of f o u r p a r t s . Each f l a n g e i n c l u d e s a p o r t f o r c o n n e c t i n g a p r e s s u r e transducer. A n a l y t i c a l equipment The a n a l y t i c a l e q u i p m e n t ( f i g . 3 ) i s i n t e n d e d t o c o l l e c t s u c h d a t a a s o i l p r o d u c t i o n , b r i n e p r o d u c t i o n and g a s p r o d u c t i o n ,

a s w e l l a s c o m p o s i t i o n of t h e g a s u p t o C, o i l up to C26.

and of s t o c k t a n k

O i l / b r i n e i s s e p a r a t e d from t h e g a s i n a s m a l l p a c k e d column (1): t h e gas i s s u b s e q u e n t l y withdrawn i n t o e v a c u a t e d v e s s e l s . The number of moles of g a s i s d e t e r m i n e d by means of a p r e s s u r e

455

F i g . 3: A n a l y t i c a l e q u i p m e n t : 1 g a s / o i l s e p a r a t o r ; 2 b r i n e l o i l s e p a r a t o r ; 3 sample

valve; 4 evacuated v e s s e l s measurement.

I n order t o m a i n t a i n t h e p r e s s u r e i n t h e s e p a r a t o r

c o n s t a n t , a back-pressure

r e g u l a t o r h a s been

i n s t a l l e d . The

a d v a n t a g e o f s u c h a s e t - u p i s t h e f a c t t h a t t h e measurement is l a r g e l y i n d e p e n d e n t of t h e p r o d u c t i o n r a t e and t h a t t h e method o f measurement is c u m u l a t i v e . A bypass w i t h a sample v a l v e ( 3 ) t o a g a s chromatograph ( P e r k i n

E l m e r Sigma 1) i s i n c l u d e d .

I n p r e l i m i n a r y t e s t s i t became e v i d e n t t h a t e m u l s i o n s c a n be p r o d u c e d w i t h t h e o i l employed. An e l e c t r o s t a t i c o i l / b r i n e s e p a r a -

t o r w a s t h e r e f o r e i n s t a l l e d ( f i g . 4 ) . T h i s s e p a r a t o r h a s been milled from P l e x i g l a s . The c h a n n e l s a r e p r e d o m i n a n t l y 5 x 5 mm

i n s i z e . The v o l t a g e of 60 V o v e r t h e p l a t e s i s s u f f i c i e n t for s e p a r a t i o n . The water c o n t e n t i n t h e s t o c k t a n k o i l produced w a s less t h a n 0 . 1 p e r c e n t a f t e r t h e s e p a r a t i o n .

Gor

-

.GOS

F i g . 4 : S k e t c h of t h e o i l / b r i n e s e p a r a t o r 0 o i l / w e i r ; B b r i n e / w e i r , A l o c a t i o n of t h e b r i n e /

water c o n t a c t

456 The q u a n t i t i e s of o i l and b r i n e i n t h e s e p a r a t o r a r e g o v e r n e d by t h e d i f f e r e n c e i n h e i g h t s o f t h e w e i r s 0 and B , r e s p e c t i v e l y . I n order t o a c h i e v e s u f f i c i e n t a c c u r a c y , t h e q u a n t i t i e s of b r i n e and o i l i n t h e s e p a r a t o r must be k e p t c o n s t a n t w i t h i n L 0 . 1 cm

3

.

T h a t i s , t h e h e i g h t of t h e o i l / b r i n e c o n t a c t a t A must be h e l d c o n s t a n t w i t h i n 5 0.2 cm. T h i s is n o t f e a s i b l e f o r a c o n s t a n t s e t t i n g of t h e weirs, s i n c e t h e bond stress b e t w e e n t h e media and t h e w a l l m a t e r i a l c a n c h a n g e , f o r e x a m p l e . T h e r e f o r e t h e s e p a r a t o r i s a u t o m a t i c a l l y t i l t e d when t h e o i l b r i n e c o n t a c t a t A d e v i a t e s from t h e s e t p o i n t . The p o s i t i o n i s d e t e r m i n e d by

means of t h e c h a n g e i n c o n d u c t i v i t y when t h e o i l / b r i n e c o n t a c t p a s s e s an electrode. I n order t o c i r c u m v e n t t h e r e m a i n i n g p r o blems w i t h t h e bond stress ( c r e e p i n g of o i l , f o r m i n g of a hemis-

p h e r e a t t h e water w e i r ) a V i t o n i n s e r t was u s e d a s o i l weir, and t h e e d g e of t h e b r i n e w e i r was p r o v i d e d w i t h a c e l l u l o s e rider. The s e p a r a t o r s a r e t h e r m o s t a t e d a t a t e m p e r a t u r e of 2OoC. The o i l and b r i n e which emerge from t h e s e p a r a t o r a r e weighed i n c o l l e c t i n g bottles. I n order t o d e t e r m i n e t h e o v e r a l l c o n c e n t r a t i o n of t h e i n d i v i d u a l o i l components, e s p e c i a l l y i n t h e t r a n s i t i o n zone, g a s chrom a t o g r a p h i c a l a n a l y s e s a r e p e r f o r m e d on b o t h t h e g a s and t h e o i l . The s a m p l e s of s t o c k - t a n k the gas-oil

o i l a r e w i t h d r a w n from t h e bottom of

s e p a r a t o r by means of a s y r i n g e . S a m p l i n g b e h i n d t h e

o i l - b r i n e s e p a r a t o r i s n o t f e a s i b l e b e c a u s e of t h e l a r g e dead volume and o f t h e r e s u l t i n g r e m i x i n g .

G a s and o i l a n a l y s e s a r e

c a r r i e d o u t s i m u l t a n e o u s l y i n t h e g a s c h r o m a t o g r a p h . For t h e g a s p h a s e , a P o r a p a c k Q/S-packed 1 / 8 " column 6 m i n l e n g t h is e m p l o y e d ; t h e o i l i s a n a l y s e d i n a s i l i c o n e r u b b e r c a p i l l a r y column 40 m i n l e n g t h . T h i s p r o c e d u r e i m p l i e s t h a t a compromise must be r e a c h e d b e t w e e n t h e a n a l y t i c a l r e q u i r e m e n t s imposed by t h e c a p i l l a r y column and t h e packed column. The s i m u l t a n e o u s e x e c u t i o n of b o t h a n a l y s e s i s n e c e s s i t a t e d by t h e l o n g d u r a t i o n o f 2 h. The sample s t o r a g e r e q u i r e d f o r a v o i d i n g such a procedure a p p e a r s impractical

.

ANALYTICAL PROCEDURE A

c a l c u l a t i o n of t h e l o c a l c o n c e n t r a t i o n u n d e r r e s e r v o i r con-

d i t i o n s from t h e measured d a t a is p o s s i b l e o n l y i f t h e o i l anal y s i s is c o m p l e t e . However, t h e a n a l y s i s e x t e n d s o n l y u p t o C26.

457

F u r t h e r m o r e , t h e a c c u r a c y of i n j e c t i o n does n o t s u f f i c e f o r calc u l a t i n g t h e m o l a r f l u x of t h e components.

Hence, a t a g g i n g com-

pound, i n t h i s c a s e m e s i t y l e n e , i s a d d e d t o t h e o u t f l o w a t cons t a n t r a t e b e f o r e t h e p r e s s u r e r e d u c t i o n . Thus i t i s p o s s i b l e

t o c a l c u l a t e t h e m o l a r f l u x of a l l d e t e c t e d components from t h e g a s chromatograms. From t h e known f l o w r a t e i n t h e r e s e r v o i r model, t h e c o n c e n t r a t i o n

i s o b t a i n e d d i r e c t l y from t h e m o l a r f l u x . A c c o r d i n g t o t h e f o l l o wing e q u a t i o n , t h e f l o w r a t e c a n be c a l c u l a t e d from t h e known C02-mass f l u x and t h e measured p r e s s u r e v a l u e s :

-d-V dt

-

The main p u r p o s e of t h i s p r o c e d u r e i s t o correct f o r i n t e r f e r e n c e d u e t o i n s u f f i c i e n c i e s i n t h e p e r f o r m a n c e of t h e b a c k - p r e s sure regulator a t the outlet. SLIM TUBE EXPERIMENTS The s l i m t u b e e x p e r i m e n t s were p e r f o r m e d p r i m a r i l y f o r o b t a i n i n g a n estimate of t h e minimal m i s c i b i l i t y p r e s s u r e . I n order t o determine t h e r e s i d u a l o i l , t h e flood tube w a s flushed with a solv e n t , f o r example t o l u e n e . The f l u s h i n g p r o c e s s w a s c h e c k e d f o r t h o r o u g h n e s s by means of p r e l i m i n a r y tests. For t h i s p u r p o s e s a n d from t h e i n l e t and o u t l e t was a n a l y s e d f o r t o t a l c a r b o n . For t h e

o i l s u s e d h e r e , a mass c o n t e n t of c a r b o n l e s s t h a n

0 , l per cent

was o b t a i n e d a f t e r f l u s h i n g , and d r y i n g by low p r e s s u r e C 0 2 . I n order t o d e t e r m i n e t h e amount of r e s i d u a l o i l i n t h e e f f l u e n t , t h e major p a r t o f t h e s o l v e n t was d i s t i l l e d o f f , and t h e d i s t i l l a t e w a s analysed gas-chromatographically.

Of c o u r s e , o n l y a small

q u a n t i t y of o i l is p r e s e n t i n t h e d i s t i l l a t e . S i n c e t h e major s h a r e of t h e r e s i d u a l o i l l i e s beyond C Z 6 and t h e r e f o r e c a n n o t be analysed gas-chromatographically,

n-hexane is added t o t h e resi-

d u e a t a r a t i o o f 1 : .1. From t h e g a s chromatogram,

t h e mass r a -

t i o of n-hexane t o s o l v e n t i s d e t e r m i n e d , and t h u s t h e r e s i d u a l

o i l mass c a n be c a l c u l a t e d w i t h good a c c u r a c y . MIXER TANK

WATKINS / 3 / h a s u s e d premixed media f o r d i s p l a c e m e n t e x p e r i m e n t s . H e allowed C 0 2 t o b u b b l e t h r o u g h t h e o i l from below i n a n a u t o -

458

c l a v e . With t h e u s e of s u c h a p r o c e d u r e , a good m i x i n g p e r f o r m a n -

ce c a n n o t be e x p e c t e d , b e c a u s e o f t h e u n f a v o u r a b l e d i a m e t e r - t o l e n g t h r a t i o . Hence a d i f f e r e n t method was u s e d . C 0 2 i s i n j e c t e d i n t o an o i l - f i l l e d m i x e r t a n k c o n s i s t i n g of s l i g h t l y i n c l i n e d tubes ( f i g . 5 ) .

filter p l a t e 1

F i g . 5 : S k e t c h of t h e m i x e r t a n k The t u b e s h a v e an i n n e r diameter o f 0.9 cm and a l e n g t h of 2 m . The v e r t i c a l t u b e s e c t i o n s , i n which t h e d e n s e r l i q u i d p h a s e i s d i s p l a c e d by a g a s p h a s e , s u b d i v i d e t h e m i x e r i n t o t h r e e s t a g e s . Within t h e i n d i v i d u a l stages, t h e d e n s i t y d i f f e r e n c e between C02r i c h and C02-poor o i l p r o v i d e s f o r a d e q u a t e c i r c u l a t i o n , whereby t h e d i f f u s i o n p a t h s a r e s h o r t b e c a u s e o f t h e s m a l l diameter-tolength ratio. The f l o o d i n g of t h e t a n k ( f i g . 1 0 ) shows t h a t o n l y p u r e o i l f l o w s o u t a t f i r s t . I f t h e amount of o i l d i s p l a c e d p u r e l y by s w e l l i n g

i s c a l c u l a t e d from t h e PVT d a t a f o r C 0 2 - o i l

mixtures, a value

of 1 7 0 c m 3 is o b t a i n e d . The q u a n t i t y which was p r o d u c e d p r i o r 3 t o t h e C 0 2 b r e a k - t h r o u g h was 1 3 7 cm A f t e r 1 6 1 cm3 had b e e n p r o -

.

d u c e d , t h e s t o c k - t a n k o i l was o n l y s l i g h t l y c o l o u r e d . From t h e s e

two f i n d i n g s i t c a n be c o n c l u d e d t h a t t h e e q u i l i b r a t i o n i s r a t h e r good i n t h e i n d i v i d u a l s t a g e s . RESULTS AND DISCUSSION E x c l u s i v e l y recombined o i l s were u s e d f o r t h e i n v e s t i g a t i o n .

For b o t h s l i m - t u b e e x p e r i m e n t s described h e r e , o i l w i t h a v i s c o s i t y of 6 mPa.s

( u n d e r r e s e r v o i r c o n d i t i o n s ) was employed.

For t h e f i r s t s l i m t u b e t e s t shown i n f i g . 6 a s a n d p a c k w i t h a p e r m e a b i l i t y of 3.08 D was u s e d .

For p r e p a r i n g t h e s a n d pack f o r t h e second t e s t ( f i g . 8 and 9 ) a 1 : 1 m i x t u r e of s a n d and silca p d e r was used (permeability: 3.03 D ) . The f i r s t e x p e r i m e n t ( f i g . 6 and 7 ) was p e r f o r m e d a t a mean p r e s s u r e of 219 b a r and a C 0 2 - m a s s l e n g t h of 6 . 3 m ,

f l u x of 4.77 g / h , w i t h f l o o d

r e s u l t i n g i n a v e l o c i t y of 5 . 3 m / d .

459 Curve I shows t h e measured p r e s s u r e d i f f e r e n c e o v e r t h e e n t i r e l e n g t h , c u r v e I1 shows t h e amount of s t o c k - t a n k

o i l produced,

and c u r v e I11 shows t h e q u a n t i t y of g a s p r o d u c e d ( f i g . 6 ) . 1 I

111

.

lrngth

AF n bar

6.3 m L.11 g/h 219 bar

C02-moss flux mean prrssurc

"9

nsol

2.1 0.

1.'

1.3

1.2 a' I

m

m m

. I

.

31

0

F i g . 6 : S l i m t u b e experimeh't a t 219 bar:

PV

D e a d o i l mass mo p r o d u c e d , p r e s s u r e d i f f e r e n c e Ap,

moles& g a s p r o d u c e d n i n j e c t e d PV

9

p l o t t e d v e r s u s p o r e volumes

dmO

From t h e p r o d u c e d mass and t h e f l o w r a t e , t h e ' $ e n s i t $ ' of t h e oilu n d e r r e s e r v o i r c o n d i t i o n s c a n be c a l c u l a t e d . The c a l c u l a t e d val u e s a r e shown by c u r v e I ( f i g . 7 ) . The m e a n 8 e n s i t y " b e f o r e C02 break-through

amounts t o 0 . 1 7 5 g/cm3. The e x p e c t e d v a l u e i s 0.805.

T h i s d e v i a t i o n c o r r e s p o n d s t o a volume e f f e c t d u e t o t h e d i s s o l u t i o n of C 0 2 i n t h e o i l . If i t is assumed t h a t t h e volume e f f e c t d u e t o d i s s o l u t i o n d u r i n g t h e f l o o d p r o c e s s is comparable w i t h t h e

e f f e c t o b s e r v e d i n s i n g l e - c o n t a c t PVT m e a s u r e m e n t s , and i f t h e tot a l volume s h r i n k a g e is e s t i m a t e d from t h e l e n g t h of t h e t r a n s i t i o n z o n e , t h e f o l l o w i n g v a i u e is o b t a i n e d f o r t h e " d e n s i t y " : dm = dV 0

0 . 7 8 g/cm 3

The d e c l i n e of d m o / d V

( f i g . 7 and 8 ) a f t e r t h e C 0 2 b r e a k - t h r o u g h

r e m a i n s l i n e a r o v e r a c e r t a i n r a n g e . Hence i t a p p e a r s p l a u s i b l e

4 60

in

I

II

bP

-

dm0

length COjmass flux mean pressure

dV m 9/cm3

! ! ! x)2!lx dV

6.3 m L.77 g/h 219 bar

n mi c i 3 I

1.0

I \

0.5

--_._.-.-. k& ......-.-.-.-.--. 111

. . . . a .

0,l

0.3

0.2

F i g . 7: S l i m t u b e

'' Dens i t y flow

0.1

23

0.5

0.6

0.7

08

3.1

.--.-.-. 0.9

1.0

PV

x p e r i m e n t a t 219 b a r :

dn LdV O , g a s concentration + , r e s i s t a n c e 3 p l o t t e d v e r s u s pore volumes at 'I

i n j e c t e d P\

to d e f i n e t h e l e n g t h of t h e t r a n s i t i o n z o n e by means of t h e i n t e r c e p t s of t h e s t r a i g h t l i n e w i t h t h e a b s c i s s a and w i t h t h e h o r i z o n -

t a l p o r t i o n of t h e c u r v e . F i g u r e s 8 and 9 show a s e l e c t e d i n t e r v a l of an e x p e r i m e n t a t 1 8 9 bar and a C 0 2 mass f l u x of 1 . 9 8 g / h . I n f i g u r e 9 t h e o v e r a l l c o n c e n t r a t i o n d n i / d v of C1, C 2 , i - C 4 and n-C4 u n d e r r e s e r v o i r c o n d i t i o n s are p l o t t e d . T h e s e v a l u e s h a v e b e e n c a l c u l a t e d from t h e gas p r o d u c t i o n d n / a t , t h e f l o w r a t e dV/dt, and t h e gas-chrog m a t o g r a p h i c a l l y measured c o n c e n t r a t i o n . It c a n be s e e n t h a t v e r y pronounced c o n c e n t r a t i o n maxima o c c u r f o r t h e lower a l k a n e s . Moreover, t h e maxima a r e a l l s i t u a t e d a t t h e same p o s i t i o n . The maximum of t h e n o r m a l i z e d C1-gas-concentration

cc

i n t h e e f f l u e n t amounts to 1 . 0 6 o n l y .

The p r g s s u r e i s a p p r o x i m a t e l y e q u a l to t h e MMP. A c c o r d i n g to t h e l i t e r a t u r e /2,4,5,6/ t h e b e h a v i o u r of m e t h a n e s h o u l d d i f f e r from t h a t o f t h e o t h e r l i g h t a l k a n e s . N o s u c h d i f f e r e n c e is r e c o g n i z a b l e h e r e . Methane d o e s n o t show a l e a d , and t h e i n c r e a s e i n m e -

461

-

om0

1

dV

in gcm3

Iength

10.8 m 1.98 g/h 189 bar

COZ-moss flux mean pressure

P

.. F i g . 8 : P a r t of a s l i m t u b e e x p e r i m e n t a t 1 8 9 bar: dn p l o t t e d versus pore D e n s i t y dmo , g a s c o n c e n t r a t i o n 9

dV

volumes i n j e c t e d PV

dV

t h a n e c o n c e n t r a t i o n i s of t h e same order of m a g n i t u d e as t h a t f o r t h e o t h e r components shown. F i g . 1 0 shows t h e c a l c u l a t e d C 0 2 and C1 c o n c e n t r a t i o n u n d e r res e r v o i r - c . o n d i t i o n s . I t c a n be s e e n t h a t t h e s t a r t of c o n c e n t r a t i o n i n c r e a s e i s a t t h e same p o s i t i o n f o r m e t h a n e and c a r b o n dioxide. To d e m o n s t r a t e t h e s i m i l a r i t y b e t w e e n t h e f l o o d i n g r e s u l t s obt a i n e d w i t h t h e m i x e r and w i t h t h e s l i m t u b e , t h e c o n c e n t r a t i o n c a l c u l a t e d i n t h e same manner from t h e m i x e r o u t f l o w is p l o t t e d aga i n st i n j e c t e d PV i n f i g u r e 11. T h i s e x p e r i m e n t was cond u c t e d a t a C 0 2 mass f l u x of 9 . 9 1 g / h and a p r e s s u r e of 202 bar. The s c a l e i s so c h o s e n t h a t 1 PV c o r r e s p o n d s t o t h e m i x e r volume 3 of 424 cm The o b s e r v a t i o n t h a t t h e c o n c e n t r a t i o n maxima f o r C1, C 2 , i - C 4 and n-C4 o c c u r a t t h e same time for t h e m i x e r test t o o is e s p e -

.

cially striking.

462

Fig. 9:Part of a slim tube experiment at 189 bar: dn Concentration -d Vi of C1, C2, i-C4, n-C4 under reservoir- conditions plotted versus pore volumes PV injected

The maximal concentrations for the slim tube and mixer tests are presented in the following table. Table: Maximal concentrations in mol/cm 3 c1 Slim tube

1.03

Mixer

1.38

.

-

c2 2.60 3.42

. .

i-C4 1.14

n-C4 3.28

1.61

5.13

. .

. .

In view of the fact that the maximal value of the concentration is given only by one gas chromatogram, the agreement between the values is remarkably good. Furthermore, it must be taken into consideration that the relative change in flow rate due to dissolution of C02 in the oil is certainly different for the slim tube and mixer tests. For both tests it should be emphasized that increase in concentration by a factor of about 5 occurs for the lower alkanes considered here.

463 length CO2-mass flux mean pressure

c1 5,103 dV in md mi3

10.8 m 1.98 g/h 189 bar

10

1.0.

0.5

,

C1 -./-a\./-

0.8 0.9 1.o 0.7 W n F i g . 10: Part of a s l i m tube experiment a t 189 bar: conConcentration d n . of C1 and C 0 2 under r e s e r v o iirr conditions p l o t t e d versus pore volumes PV i n j e c t e d

1 1 10

In 9

Mixer- test C02- 1110)s flux mean pressure

11 9,91 202

g/h bar

I

...*.

*:.

......... - * . . 'n9

'inmd

45

m.

.3.0

100.

11

.

'

.l.S

50

. .--02. . . . *.... 0.b

Fig. 11: Mixer test

0.6

0.8

1.o

1.2

PV

'

Dead o i l mass produced mo, moles of gas produced n plotted 9' Versus pore volumes PV i n j e c t e d

Mixer- test C O y m s r flux mean pressure

9.91 g/h 202 bar

1.0

0.5

0.5

1.0

1.5

W

Fig. 12: Mixer test dn. 1 Concentration of C1, C2, i-C4, n-C4 under reservoir conditions plotted v ersus pore volumes injected

Conclusions On the basis of the results obtained so far, the apparatus developed appears to be suited for C02 core flooding experiments. In particular, it allows conclusions concerning the composition under reservoir conditions. The use of the three-stage mixer tank for core flooding experiments appears promising. By means of this device, cores can be flooded with media corresponding to a transition zone. Nomenclature P P(p) k V

= inlet pressure = C02-density = C02-mass flux = volume under reservoir conditions

465 v2 vO

-y0

= volume filled by C02 = volume filled by oil

= compressibility of oil

X1 m 0 n g

= compressibility of C02

t

=

C

= gas-concentration of methane in the effluent

=

mass of stock tank oil

= moles of gas

time

Acknowledgements The autor is grateful to the Federal Ministry of Research and Technology (BMFT) for financial support of the project as well as to Prof. G . Pusch, the project leader, for his advice and support.

References 1.

V. Meyn G. Pusch

2.

J.J.

3.

Laboruntersuchungen zum KohlendioxidFluten (PVT-Verhalten und Flutversuche) ET 3048 A

F. J. Stalkup R. C. Hassing

A Laboratory Investigation of Miscible Displacement by Carbon Dioxide SPE 3483 (1971)

R. W. Watkins

A

Rathmell

Technique for the Laboratory Measure-

ment of Carbondioxide Unit Displacement Efficiency in Reservoir Rock SPE 7474 (1978) 4.

R.S. Metcalfe L. Yarborough

The Effect of Phase Equilibria on the C02 Displacement Mechanism SOC. Pet. Eng. J. (1979) p. 242

5.

L.X. D.h

Compositional Modelling with a Equation of State SPE 9306 (1980)

Nghiem Fong

K. Aziz 6.

M.P. W.F.

Leach Yelling

-

Compositional Model Studies C02 OilDisplacement SOC. Pet. Eng. J. (Feb. 19811,~. 89

This Page Intentionally Left Blank

467

EXPERIMENTAL TECHNIQUES

THE USE OF SLIM TUBE DISPLACEMENTEXPERIMENTS IN THE ASSESSMENT OF MISCIBLE GAS PROJECTS BERNARD J. SKILLERNE DE BRISTOWE British Petroleum Company Limited ABSTRACT Slim tube displacemeht experiments can b e employed t o optimise dynamic m i s c i b l e displacement p r o j e c t s with r e s p e c t t o both p r e s s u r e and composition. By analogy w i t h t h e minimum dynamic m i s c i b i l i t y p r e s s u r e concept a minimum dynamic m i s c i b i l i t y composition may be defined which may be used t o a s s e s s t h e s u i t a b i l i t y o f a l t e r n a t i v e i n j e c t i o n gasses. D e t a i l s are given of t h e way i n which t h e s l i m tube displacement experiments are performed and a r e operated with automated data a c q u i s i t i o n . Examples are provided of t h e phenomena observed d u r i n g t h e course of t h e experiments which may be used t o a s s e s s t h e n a t u r e of t h e displacement process. The r e s u l t s are discussed i n r e l a t i o n t o s u p e r c r i t i c a l e x t r a c t i o n phenomena which provides an e x p l a n a t i o n f o r t h e r e s i d u a l o i l phase l e f t behind i n t h e s l i m tube a t t h e end of the experiment.

INTRODUCTION During t h e l a s t decade a p r o f u s i o n of d a t a has been generated i l l u s t r a t i n g t h e phenomena a s s o c i a t e d w i t h dynamic m i s c i b l e displacement A s h o r t p e r u s a l of t h e l i t e r a t u r e quickly shows t h a t t h e displacement gas used i s almost always carbon dioxide and t h a t most o f t e n the o i l i s a West Texas, Permian Basin Crude. Despite t h i s r e s t r i c t i o n i n comp o s i t i o n l i t t l e consensus of opinion has been reached as t o what s u i t e of l a b o r a t o r y experiments must be performed i n o r d e r t o e v a l u a t e a given f i e l d p r o j e c t (1) except t h a t they w i l l be e x t e n s i v e , time consuming and consequently extremely expensive t o perform. For an o p e r a t o r whose i n t e r e s t s l i e f a r from West Texas and who needs t o e v a l u a t e many p o t e n t i a l p r o s p e c t s i t i s imperative t h a t the maximum amount o f information i s generated i n t h e most economical way p o s s i b l e . To do t h i s , t h e experiments performed should be designed i n such a way t h a t they w i l l form a r a t i o n a l b a s i s f o r investment d e c i s i o n s . Of the many experiments proposed, t h e s l i m tube displacement experiment o f f e r s t h e c l o s e s t analogue t o t h e processes t h a t occur w i t h i n ' the r e s e r v o i r while a t the same t i m e i t can be performed s u f f i c i e n t l y r a p i d l y for repeated experiments t o be performed under varying o p e r a t i n g c o n d i t i o n s . I n using t h e method the assumption is made t h a t t h e p r o c e s s e s which r e s u l t i n dynamic m i s c i b l e displacements a r e independent of t h e n a t u r e of the h o s t porous m a t r i x and depend e x c l u s i v e l y on t h e composition and p h y s i c a l p r o p e r t i e s of t h e f l u i d s involved and on t h e temperature and p r e s s u r e a t which t h e displacement takes place. The displacement i s confined w i t h i n t h e w a l l s of a

468 narrow tube so t h a t the flow i s e s s e n t i a l l y one dimensional. I t can thus provide no information regarding t h e gross f l u i d movements w i t h i n a r e s e r v o i r which a r e s u b j e c t t o hydrodynamic i n s t a b i l i t i e s s u c h as viscous f i n g e r i n g and g r a v i t y s e g r e g a t i o n . I t s major use t h e r e f o r e i s i n t h e i n i t i a l assessment o f a given p r o j e c t where the compatability of the i n j e c t e d gas with t h e r e s e r v o i r o i l i s sought. N e v e r t b e l e s s , s i n c e a v a r i e t y of evidence now e x i s t s t o suggest t h a t the p e t r o p h y s i c a l p r o p e r t i e s of t h e rock a r e of secondary importance i n determining the displacement e f f i c i e n c y (2) i t may be used t o provide valuable q u a l i t a t i v e information about t h e elementary displacement mechanism. The key t o t h i s i s i n i d e n t i f y i n g when t h e dynamic m i s c i b l e displacement process i s o p e r a t i n g . The purpose of t h i s paper i s t o show t h a t once t h i s can be done t h e process can be optimised with r e s p e c t t o e i t h e r the p r e s s u r e o r t h e composition of the i n j e c t e d gas.

THE

SLIM

TUBE

DISPLACEMENT

EXPERIMENT

I n o r d e r t o improve the e f f i c i e n c y with which t h e s l i m tube experiments can be performed while making t h e b e s t use of t h e information a v a i l a b l e t h e d a t a g a t h e r i n g p a r t of the experiment h a s been automated. The g e n e r a l experimental arrangement i s shown schematically i n Figure 1 and a block diagram of t h e computer c o n t r o l l e d d a t a a c q u i s i t i o n system i n Figure 2.

+VENT

,-* __----

I

I L

------

KLY 1. YOTORISED MERCURY P U M P

1. C O ~ I C , R E F I L L CYLINDER

L

KLROSINP CYLINDCR

1. O I L CYL!NOEI

% CO1IC~CYLINDCR

& PRESSURE 1RANSOUCCI

7, S L I Y - I U O E

L

VISUAL CELL

1 01611AL O E N S l l Y Y E I E I

?

VENT

I0 DACK - P l E S S U I 1 E I L G U L A I O I 1l.LIDUIO S A Y ? L E V A L V E 1 1 . S C P A R A l O R A N 0 BALANCE 1 l . C A S S A Y P L e VALVE

PLOW IS.VALVE I~.VALVC IL.hA5

Figure 1.

utim

Schematic Diagram of the Slim Tube Apparatus.

469

TRANSDUCERS

Figure 2.

Microcomputer Control of Slim Tube Experiments.

Many d i f f e r e n t designs f o r s l i m tube apparatus have been reported i n t h e l i t e r a t u r e . These have been r e c e n t l y reviewed by O r r e t a1 ( 1 ) . The p r e s e n t a p p a r a t u s c o n s i s t s o f a motorised Ruska pump which can d i s p l a c e mercury i n t o one o r o t h e r of two sample veerel's (4) and ( 5 ) . The s i n g l e phase f l u i d s contained i n t h e s e v e s s e l s then pass sequent i a l l y through t h e s l i m tube ( 7 ) . the windowed viewing cell (8) and t h e d i g i t a l d e n s i t y meter (9) t o a back p r e s s u r e r e g u l a t o r (10). The r e g u l a t o r maintains t h e o u t l e t p r e s s u r e a t a predetermined v a l u e s e t by a gas r e s e r v o i r v e s s e l c o n t a i n i n g n i t r o g e n . As t h e e f f l u e n t f l u i d s p a s s through t h e back p r e s s u r e r e g u l a t o r , they are s e p a r a t e d i n t o a gas and l i q u i d phase. The l i q u i d i s c o l l e c t e d i n a perspex v e s s e l p l a c e d on t h e pan of a d i g i t a l e l e c t r o n i c balance (12). The volume of l i q u i d i n t h i s s e p a r a t o r can be determined independently by observing t h e h e i g h t of o i l i n t h e s e p a r a t o r using a cathetometer. Although t h e d e n s i t y of t h e o i l changes a f t e r gas breakthrough the l i q u i d production f a l l s o f f r a p i d l y so t h a t t h e assumption t h a t t h e d e n s i t y remains c o n s t a n t only i n t r o d u c e s a small e r r o r i n t o t h e volume of o i l recovered. The gas phase p a s s e s o u t of the s e p a r a t o r , through a gas sample v a l v e (13) and a d i g i t a l w e t gas meter (14) and i s vented t o atmosphere. The s l i m tube i s c o n s t r u c t e d from API Schedule 40 s t a i n l e s s s t e e l t u b i n g and a f t e r packing was c o i l e d t o form a square' s e c t i o n h e l i x and i s mounted h o r i z o n t a l l y . The p r o p e r t i e s of the s l i m tube are summarized i n Table 1. The packing is h e l d i n p l a c e by s t a i n l e s s s t e e l s i n t e r s pressed i n t o t h e ends of the tube. S p e c i a l l y designed s h u t o f f valves which a r e shown i n Figure 3 are f i t t e d t o each end of t h e tube. These are equipped with b l e e d valves which f a c i l i t a t e c l e a n i n g and allow t h e pore volume of the tube t o be determined by weighing t h e column b e f o r e and a f t e r i t had been f i l l e d w i t h d i s t i l l e d w a t e r a t the temperature and p r e s s u r e a t which t h e experiments a r e t o be c a r r i e d o u t . Thus

4 70

where

i s t h e equation of s t a t e f o r water of K e l l and Whalley ( 3 and 4). I n t h i s way allowance can be made f o r t h e d i l a t a t i o n of the tube and the compression of t h e packing.

Table 1.

P r o p e r t i e s of t h e Slim Tube

I n t e r n a l Diameter Length Pore Volume (25OC. O.1MPa) Absolute Permeability Packing Porosity Diameter range of packing

9.25 m

12.19m 290.4cm3 9.6 (urn) Lead Glass spheres 36% e a 80%pass 0.115mm t o 0.18Omm

The p r e s s u r e drop a c r o s s t h e s l i m tube was measured by measuring the. i n l e t and e x i t p r e s s u r e s u s i n g B e l l and H o w e l l s c a l e d r e f e r e n c e s t r a i n gauge p r e s s u r e transducers. These were connected u s i n g t h e s p e c i a l f i t t i n g s shown i n Figure 4,

TRANSDUCER

IN

Figure 3.

S p e c i a l Valves

-

Figure 4.

-SMALL SWEPT DEAD VOLUME

-our

Transducer f i t t i n g s

471 which minimise the dead volume while allowing i t t o be swept by t h e flowing stream. This'arrangement was adopted because t h e d i f f e r e n t i a l p r e s s u r e transducers a v a i l a b l e on t h e market have l a r g e unswept dead volumes which may vary w i t h p r e s s u r e . Furthermore, d i f f u s i o n of t h e i n j e c t i o n gas i n t o t h e transducer can l e a d t o s p u r i o u s mixing and m o b i l i s a t i o n of dead volume o i l which cannot b e accounted f o r and complicates subsequent i n t e r p r e t a t i o n . Prevention of t h i s can only be achieved a t the expense of s e n s i v i t y and the t r a n s d u c e r s must b e very c a r e f u l l y c a l i b r a t e d w i t h r e s p e c t t o t h e e x c i t a t i o n v o l t a g e and temperature a s w e l l as t h e response of t h e diaphragm. The p r e s s u r e a t which t h e displacement is performed, t h a t i s t h e p r e s s u r e a t the displacement f r o n t , i s b e s t approximated by t h e i n l e t p r e s s u r e t o t h e tube. The p r e s s u r e i s c o n t r o l l e d , however, a t t h e o u t l e t by t h e back p r e s s u r e r e g u l a t o r . The flow r a t e must t h e r e f o r e be k e p t low i f a s u b s t a n t i a l p r e s s u r e change a t t h e displacement f r o n t i s n o t to take p l a c e d u r i n g the d i s placement. This change may be regarded a s an u n c e r t a i n t y i n the displacement p r e s s u r e . The c o n t r o l of the gas dome-loaded back p r e s s u r e r e g u l a t o r depends upon t h e p r e s s u r e i n the n i t r o g e n v e s s e l . Since 9 thermostating the pressure reference P T e f f e c t i v e l y e l i m i n a t e s d r i f t s . I n t h i s way t h e o u t l e t p r e s s u r e i n t h e tube can r e a d i l y be k e p t w i t h i n f50kPa of the s e t p o i n t . On e x i t from t h e s l i m tube t h e f l u i d s flow through a windowed c e l l which is d e p i c t e d i n Figure 5. I t c o n s i s t s o f two s a p p h i r e windows h e l d w i t h i n a s t a i n l e s s steel body. The windows a r e h e l d c a 0.lm a p a r t by two PTFE "D" shaped i n s e r t s which reduce the swept volume. This arrangement produces a l a r g e area f l a t f i e l d which is photographed by a pulsed c i n e camera m u n t e d o u t s i d e t h e oven. Time l a p s e photographs are taken a t c a 0.001 i n j e c t e d pore volume i n t e r v a l s so t h a t a complete record i s k e p t of the phases flowing d u r i n g t h e experiment. The u t i l i t y of t h i s when t h e d a t a i s analysed a f t e r t h e experiment i s over cannot be exaggerated.

1 OUT

Figure 5.

Windowed C e l l .

472 From the windowed c e l l the f l u i d s pass t o an Anton Paar high p r e s s u r e d i g i t a l d e n s i t y meter which i s housed i n an a u x i l l a r y a i r thermostat b a t h . This instrument allows a continuous record t o be k e p t of the d e n s i t y of t h e f l u i d s flowing through i t . I t is thus a very s e n s i t i v e i n d i c a t o r of changes i n composition and of t h e appearance of a low d e n s i t y '*gas**phase w i t h i n t h e o i l and can thus be used t o d e t e c t breakthrough. The most important o f the experimental parameters a r e t h e volume of gas i n j e c t e d and t h e volume of o i l recovered. These a r e both normalised w i t h r e s p e c t t o t h e pore volume of t h e s l i m tube. So t h a t the displacement may be used as an i n d i c a t i o n of the process t a k i n g p l a c e w i t h i n t h e r e s e r v o i r , both of these measurements are r e f e r r e d t o t h e i n l e t and e x i t f a c e s of t h e s l i m tube under r e s e r v o i r c o n d i t i o n s . The volume of f l u i d e n t e r i n g t h e s l i m tube i s o b t a i n e d , i f the flaw rate from t h e pump i s assumed t o be c o n s t a n t , by

c qHg

(Pin, Tamb) pkg (Pin, Tamb) At

-

6Vin

@Ig (Pin, TOV)

Vi(t) =

vp (Pin, TOV) where GVin i s t h e dead volume on t h e and the s l i m tube. This is arranged The s u m a t i o n i s taken from t h e time changed from crude o i l t o d i s p l a c i n g

i n l e t s i d e between v a l v e (15) t o be as small as p o s s i b l e . t = O a t which the flow i s gas.

The volume of o i l recovered a t t i m e t a t t h e o u t l e t from the s l i m tube i s given by

V,(t)

=

The f i n a l term i n the dividend makes allowance f o r t h e dead volume between t h e o u t l e t of t h e s l i m tube and the s e p a r a t o r . Up t o t h e time of gas breakthrough t h i s s e c t i o n of tubing i s completely f i l l e d w i t h o i l b e f o r e and a f t e r a time i n c r e m e n t i n t h e flow and consequently does n o t a f f e c t t h e measured recovery. From t h e time of gas breakthrough onwards t h e o i l o r i g i n a l l y i n the o u t l e t dead volume i s p r o g r e s s i v e l y drained and replaced by gas. This p r o g r e s s i v e drainage can b e allowed f o r i f t h e f r a c t i o n a l flow of gas i s known. Before breakthrough F g ( t ) = 0 and a t the end of the run when no l i q u i d i s b e i n g recovered F g ( t ) = 1. A t i n t e r m e d i a t e times F g ( t ) i s experimentally i n a c c e s s i b l e . In p r i n c i p l e i t could be obtained from a f l a s h c a l c u l a t i o n i f t h e composition and d e n s i t i e s of the flowing stream were adequately known. However, i f o n l y u l t i m a t e r e c o v e r i e s a r e r e q u i r e d t h i s complicatibn i s unnecessary. The procedure f o r performing t h e displacement experiments i s as follows. O i l i n t h e sample v e s s e l i s made s i n g l e phase and t h e apparatus i s h e a t e d t o t h e displacement temperature. O i l i s pumped through t h e s l i m tube a t a high r a t e , c a Z O o ~ r n ~ h t- ~ o miscibly d i s p l a c e t h e k e r o s i n e l e f t i n the tube a f t e r cleaning. A f t e r about

473 one pore volume has been i n j e c t e d the r a t e i s reduced t o t h a t a t which t h e displacement i s t o be performed and i n j e c t i o n i s continued u n t i l t h e p r e s s u r e drop and t h e GOR a r e both c o n s t a n t . During t h i s p e r i o d t h e base of t h e gas c y l i n d e r i s connected t o t h a t of the o i l c y l i n d e r so t h a t they come t o t h e same p r e s s u r e . When a l l i s steady, the o i l c y l i n d e r i s closed and t h e gas c y l i n d e r i s opened t o the tube. A s i g n a l is fed t o t h e microcomputer t h a t t h e displacement h a s commenced. A l l of t h e transducers a r e f e d v i a s u i t a b l e i n t e r f a c e s t o t h e microcomputer which scans a l l o f t h e i n p u t channels a t pre-arranged t i m e i n t e r v a l s . Simple c a l c u l a t i o n s such as converting t h e m i l l i v o l t t r a n s d u c e r i n p u t s t o p r e s s u r e s and temperatures and time averaging n o i s y s i g n a l s a r e performed i n r e a l t i m e . 'Ihis i s most r e a d i l y performed i f a 280 microprocessor i s used which h a s a programmable i n t e r r u p t . A l l of the computed d a t a i s s t o r e d on a floppy d i s c and a l l o f t h e sequences of t h e measurement and c o n t r o l a r e s y n c h r o n i s e d by a real-time clock. A summary r e p o r t showing the v a r i a t i o n i n t h e major v a r i a b l e s a s a f u n c t i o n o f the i n j e c t e d pore volume i s l i s t e d on t h e l i n e p r i n t e r as t h e experiment progresses. A t t h e end of t h e experiment any f u r t h e r computations a r e performed. and t h e r e s u l t s a r e t a b u l a t e d and output t o a d i g i t a l X-Y p l o t t e r . The tube i s then cleaned by f l u s h i n g w i t h s o l v e n t s and f i n a l l y w i t h k e r o s i n e i n p r e p a r a t i o n f o r t h e next experiment. PHENOMENA

OBSERVED DURING

SLIM

TUBE

DISPLACEMENTS

Displacement experiments may be perfonued w i t h e i t h e r composition o r p r e s s u r e as t h e independant v a r i a b l e depending upon which parameter may most r e a d i l y be optimised w i t h i n a given p r o j e c t . 'Ihese two approaches a r e i l l u s t r a t e d with r e f e r e n c e t o the t w o . o i l s whose p r o p e r t i e s are l i s t e d i n Table 2. O i l A i s from t h e Egmanton Table 2.

Composi t i on (massfractions)

N2 a 2

c1

Oil A

Oil B

0.0001

0.0000

0.0012

0.0305

0.0061

0.0535

c2

0.0028

0.0080

c3

0.0079

0.0079

nC4

0.0100

0.0066

i C4

0.0033

0.0022

"C5

0.0094

0.0055

i C5

0.0067

0.0040

c6

0.0187

0.0107

c7

0.0342

0.0217

C8

0.0466

0.0294

cg cg+

0.0355

0.0308

0.8180

0.7892

3.27MPa a t 43.3OC

23.54MPa a t 93.3OC 0.377 m l kg-'

Bubble p o i n t p r e s s u r e

<M>

P r o p e r t i e s of the o i l s s t u d i e d .

474 r e s e r v o i r and was s t u d i e d i n t h e e a r l y p a r t of BP's East Midlands Additional O i l P r o j e c t where a number of s m a l l , h i g h l y d e p l e t e d r e s e r v o i r s were e v a l u a t e d a s EOR candidates (5). This r e s e r v o i r was over-pressured by w a t e r i n j e c t i o n and i t was of i n t e r e s t t o know the e x t e n t t o which i t could be depressured while allowing t h e process t o o p e r a t e . The only source of gas a v a i l a b l e was pure COq formed as a b i p r o d u c t of annnonia production. O i l B i s from a p a r t i a l l y depleted r e s e r v o i r c l o s e t o a source of a s s o c i a t e d gas c o n t a i n i n g a s u b s t a n t i a l q u a n t i t y of C02. I t was t h e r e f o r e of i n t e r e s t t o determine what enrichment of the C02 by t h e i n t e r m e d i a t e hydrocarbons might be required f o r a dynamic m i s c i b l e displacement process t o o p e r a t e . For o i l A a s e r i e s o f displacement experiments were c a r r i e d o u t a t d i f f e r e n t displacement p r e s s u r e s . Two sets of experiments were performed with and without formation water being p r e s e n t a t connate s a t u r a t i o n w i t h i n t h e s l i m tube. The r e s u l t s f o r these a r e shown i n Figs. 6 and 7 where curve ( a ) i s t h e r e s u l t obtained when connate water was p r e s e n t i n each case. In Figure 6 t h e u l t i m a t e recovery, approximated by t h e recovery when 1.2 pure volumes had been i n j e c t e d i s p l o t t e d , whereas i n Figure 7 the recovery i s t h a t obtained a t gas breakthrough. Ihe curves a r e

100

A T = ! =

--. ~5

6

Figure 6.

b

-0-

---7

--7

8

--

1 -

0

10

P M P4

11

12

Ultimate recovery a s a f u n c t i o n of p r e s s u r e f o r o i l A.

0

S

6

7

Figure 7.

8

B

lo

-

P UP0

II

Recovery a t breakthrough f o r o i l A

'I2

475 t y p i c a l l y sigmoid and t h e r e i s seen t o be a s l i g h t l y b e t t e r recovery when connate w a t e r i s p r e s e n t than i n i t s absence. This i s thought to be due t o the o i l b e i n g a non-wetting phase when w a t e r i s p r e s e n t b u t t h e w e t t i n g phase when i t i s absent. 'Ihe p r e s s u r e a t which the sudden i n c r e a s e i n recovery i s observed i s independent o f the p o i n t on t h e recovery curve a t which measurements a r e made. However, i t i s g e n e r a l l y more convenient t o use t h e value a t ca V i = 1.2 s i n c e dVr : 0 dVi

The p o i n t of gas breakthrough was determined i n these experiments by o b s e r v i n g t h e change i n t h e GOR and by monitoring the pH of a small f l a s k c o n t a i n i n g d i s t i l l e d water through which t h e e f f l u e n t gas was passed. As t h e a s s o c i a t e d gas c o n t a i n s no GO2 o r H2S a sudden decrease i n pH i s observed as Cog f i r s t emerges from t h e tube as shown i n Fig. 8.

0.50.

0

02

O&

0.6

1.0

0.8

11

V.

Figure 8.

Recovery and pH v a r i a t i o n d u r i n g a s l i m tube displacement o f o i l A.

The sequence of events observed i n t h e v i s u a l c e l l was s i m i l a r t o t h a t described by Henry and Metcalf ( 6 ) with t h e exception t h a t a heavy phase was never observed. A t p r e s s u r e s below 8MPa breakthrough was accompanied by t h e appearance of a c o l o u r l e s s CO2 r i c h phase a s bubbles w i t h i n t h e o i l r i c h phase. A t 8.5 MPa a p r o g r e s s i v e sequence of l i g h t e n i n g i n t h e colour of t h e o i l r i c h phase w a s observed b u t w i t h t h e presence of a c o l o u r l e s s C02 r i c h phase. Bubbles o f t h i s c o l o u r l e s s phase were s e e n t o accompany t h e o i l up t o c a 10.5 ma. I n o r d e r t o determine t h e e f f e c t of the o p e r a t i o n a l v a r i a b l e s on t h e r e c o v e r i e s observed a series of measurements were perfonned a t 12MPa, where dVr is small, i n which t h e displacement rate was varied. dP No d i f f e r e n c e w a s observed w i t h i n experimental e r r o r as shown i n Fig. 9. Recently, we have been a b l e t o compare the r e c o v e r i e s with those o b t a i n e d using a v e r t i c a l 2m longcolumn 2.5cm i n diameter used by IFP who are now p a r t i c i p a t i n g i n t h e Egmanton CO2 p r o j e c t . A t p r e s s u r e s above ca 9MPa very good agreement e x i s t s between t h e r e s u l t s o b t a i n e d from t h e two p i e c e s of apparatus. The break i n s l o p e and minimum dynamic m i s c i b i l i t y p r e s s u r e s are l i k e w i s e i n good agreement. However, a t p r e s s u r e s below 8MPa where an immiscible gas displacement i s t a k i n g p l a c e t h e v e r t i c a l column c o n s i s t a n t l y gives h i g h e r

476 lQ0 0

Q

0

'c 0.50

P; 12 cpo

0

50

100

oco

2

Figure 9 .

Dependance of Recovery on Flow Rate a t 12MPa.

r e c o v e r i e s than thoseobtained from t h e h o r i z o n t a l l y c o i l e d tube. As t h e displacement i n t h e v e r t i c a l column i s g r a v i t y s t a b i l i s e d t h i s i s taken t o i n d i c a t e t h a t hydrodynamic i n s t a b i l i t i e s may be p r e s e n t i n the flow i n the s l i m tube even though i t i s of small diameter. For o i l B, t h e e f f e c t of p r o g r e s s i v e l y i n c r e a s i n g the mole f r a c t i o n of propane i n t h e displacement gas (mixtures of CO2 w i t h propane) i s shown i n Fig. 10.

1.2

0

Figure 10.

0 25

0.5

Recovery a s a f u n c t i o n of g a s composition f o r O i l B

0 . 2 t h e displacements show a l l of t h e c h a r a c t e r i s t i c s With Xc3 r e f e r r e d t o previously which are observed when a dynamic m i s c i b l e process i s t a k i n g place. With Xc3 < 0 . 2 t h e displacements are t y p i c a l l y i n m i s c i b l e i n c h a r a c t e r . The diagram shows a break i n s l o p e a t 0 . 2 which is similar t o t h a t seen on t h e Vr(p) diagrams. This Xc3 p o i n t i s r e f e r r e d t o as t h e minimum dynamic m i s c i b i l i t y composition by analogy with t h e minimum dynamic m i s c i b i l i t y pressure.

477 I t h a s been observed t h a t when t h e dynamic m i s c i b l e process i s o p e r a t i n g u l t i m a t e recovery i s reached by V i = 1 . 2 . To i l l u s t r a t e this is p l o t t e d as a f u n c t i o n of X3 i n Figure 11. dVi

dVr

XC

Figure 11.

3

The v a r i a t i o n of % w i t h dVi

composition

Since O i l B contains an a p p r e c i a b l e amount of C02, gas breakthrough could not be d e t e c t e d by monitoring the pH as with O i l A. Figures 12 and 13 show t h e v a r i a t i o n observed i n t h e t o t a l stream d e n s i t y and t h e gas-oil r a t i o during an experiment. I t w a s found t h a t t h e d e n s i t y measurement gave a much more s e n s i t i v e i n d i c a t i o n of t h e f i r s t change i n compq8ition than d i d t h e COR. Furthermore i f gas bubbles of low d e n s i t y a r e e n t r a i n e d w i t h i n t h e o i l t h e recorded d e n s i t y becomes very erratic. When a dynamic m i s c i b l e process is o p e r a t i n g t h e d e n s i t y v a r i e s f a i r l y smoothly a s shown i n Figure 12 This a l s o s e r v e s t o show t h a t t h e composition of t h e t r a n s i t i o n zone may b e more complex than i s u s u a l l y depicted.

.

-

1.0

"I-

0.5'

0 0

0'5

I

.o

V.

Figure 12.

Recovery and d e n s i t y as f u n c t i o n s of V i a t Xc3

12

-

0.5

478 1.0

vr

0'5

0

0

05

Figure 13.

V.

PO

k2

Recovery and GOR as f u n c t i o n s of V i a t Xc3 = 0 . 5

DISCUSSION The break i n s l o p e of t h e Vr(p) and Vr(x) f u n c t i o n s i s now known t o be a f u n c t i o n of t h e composition of t h e d i s p l a c i n g f l u i d , the composition of t h e o i l and t h e displacement temperature ( 7 ) . Recently, Johnson and P o l l i n (8) have shown t h a t t h e minimum dynamic m i s c i b i l i t y p r e s s u r e f o r C02 d i s p l a c i n g a s e r i e s of pure n-alkanes i s almost e x a c t l y given by the c r i t i c a l p r e s s u r e of t h e b i n a r y mixture a t t h e temperature a t which the displacement i s c a r r i e d out. I f e q u i l i b r i u m e x i s t s w i t h i n t h e displacement tube t h e sudden i n c r e a s e i n recovery which i s observed m u s t b e l a r g e l y a r e s u l t df t h e increased s o l v e n t powers of t h e displacement gas w i t h i n t h e c r i t i c a l region. The increased s o l u b i l i t y i s a r e s u l t of t h e l a r g e d e v i a t i o n s from i d e a l i t y which occur w i t h i n t h e c r i t i c a l region. A s c r i t i c a l i t y i s reached l a r g e changes a r e observed t o occur i n many p h y s i c a l p r o p e r t i e s as shown i n Figure 14 f o r pure C02. The Vr(p) curve f o r O i l A has been superimposed upon t h i s . A t t h e same t i m e as t h e s o l u b i l i t y i n c r e a s e s

- 4.0

1000

P

,

L lo

*

*

1.00

D"P

vI-

&Om-' 5 00

0

Figure 14.

-2.0

10

The v a r i a t i o n i n t h e p h y s i c a l p r o p e r t i e s of C02 i n t h e c r i t i c a l region.

0 50

0

479 w i t h i n t h e c r i t i c a l region o t h e r physical p r o p e r t i e s change i n such a way a s t o favour the displacement. Thus the d e n s i t y and v i s c o s i t y both i n c r e a s e while t h e product of t h e d e n s i t y and s e l f - d i f f u s i o n c o e f f i c i e n t decreases i n agreement with k i n e t i c theory. Although t h e s e l f d i f f u s i o n c o e f f i c i e n t decreases i t s value s t i l l remains considerably h i g h e r than t h a t found i n normal l i q u i d s enabling trapped o i l t o be more r e a d i l y contacted. I t i s not known a t t h e p r e s e n t time whether these changes i n p h y s i c a l p r o p e r t i e s w i l l e f f e c t convective d i s p e r s i o n o t h e r than through the mutual d i f f u s i o n c o e f f i c i e n t which appears t o follow t h e behaviour of t h e s e l f d i f f u s i o n c o e f f i c i e n t i n t h e c r i t i c a l region. The s o l u b i l i t y of a given compound depends upon t h e n a t u r e of t h e i n t e r m o l e c u l a r i n t e r a c t i o n s between i t and the s o l v e n t a s i s r e f l e c t e d i n the phase diagram. A t the p r e s e n t time phase diagrams have been determined f o r mixtures of C02 with a range of n-alkanes and a few simple cycloalkane and aromatic hydrocarbons ( 9 ) . p(T) s e c t i o n s f o r t h e n-alkanes are shown i n Figure 15. I t can be seen from t h i s diagram t h a t f o r t h e lower homologues the c r i t i c a l l i n e i s s e p a r a t e d i n t o two branches, one of V-L c r i t i c a l p o i n t connecting t h e c r i t i c a l p o i n t s of t h e pure end members and t h e o t h e r of L-L c r i t i c a l p o i n t s which terminates a t a c r i t i c a l end p o i n t . For t h e

LO

J

vapov' p-csrure c u r v e of

Figure 15.

co2

t

/'c

C r i t i c a l Lines f o r CO2 + n-alkane mixtures.

h i g h e r homologues the c r i t i c a l l i n e i s continuous b u t may f o l d back upon i t s e l f r e s u l t i n g i n gas-gas i m m i s c i b i l i t y of the f i r s t kind. The c r i t i c a l p r e s s u r e i n c r e a s e s with t h e carbon number a t a given temperature. Thus f o r e x t r a c t i o n a t a given temperature and p r e s s u r e some of t h e homologues w i l l have t h e i r c r i t i c a l regions w i t h i n t h e range of p r e s s u r e s considered, while o t h e r s w i l l r e q u i r e a much h i g h e r p r e s s u r e and y e t o t h e r s , i f t h e temperature i s s u f f i c i e n t l y low,can never be brought i n t o t h e c r i t i c a l r e g i o n by i n c r e a s e i n p r e s s u r e alone. This w i l l account a t l e a s t i n p a r t f o r a r e s i d u a l 'heavy" o i l b e i n g l e f t behind a f t e r t h e displacement and f o r t h e small b u t p e r s i s t a n t i n c r e a s e i n recovery t h a t i s observed a f t e r t h e minimum dynamic m i s c i b i l i t y p r e s s u r e h a s been reached. A

4 80 s i m i l a r s u i t e of curves e x i s t f o r t h e aromatic and naphthenic compounds. "he displacement of t h e s e curves from one another suggests a degree of s e l e c t i v i t y i n t h e e x t r a c t i o n process and i t is i n t e r e s t i n g t o s p e c u l a t e t h a t t h e p a r a f f i n , naphthene, aromatic d i s t r i b u t i o n w i t h i n t h e o i l s recovered may change a s t h e p r e s s u r e changes. Although t h e minimum dynamic m i s c i b i l i t y p r e s s u r e appears t o be l a r g e l y governed by t h e . e q u i l i b r i u m thermodynamic p r o p e r t i e s of t h e f l u i d s the a b s o l u t e recovery w i l l depend both on t h e proportion of u n e x t r a c t a b l e components i n t h e o i l and on t h e hydrodynamics of t h e displacement. I t does not seem reasonable t h e r e f o r e t o quote a f i x e d recovery which m u s t be reached b e f o r e i t can be coficluded t h a t t h e m u l t i p l e c o n t a c t mass t r a n s f e r mechanism is o p e r a t i n g . Deduction of t h e process mechanism m u s t thus b e made on t h e b a s i s of many d i f f e r e n t observations r a t h e r than a s i n g l e one. An attempt t o summarise t h e more g e n e r a l characteristics of t h e d i f f e r e n t process types i s given i n t a b l e 3.

TABLE 3

KEY

TO

PROCESS

IDENTIFICATION

Process 5 p e PROPERTY [miscible Recovery a t V i = 1.2

dVf a t dVi

vi

= 1.2

lOW

Low IFT

intermediate

large

Breakthrough

early

First Contact

high

high

zero

zero

none

none

intermediate

late

late

high

Rate Dependance

Mu1 t i p l e Contact

small

Density Change a t breakthrough

Becomes very erratic

erratic a t times

smooth

smooth

S i g h t Glass Observations a t breakthrough

colooties! bubbles i n dark o i1

Colourless bubbles i n lighter coloured o i l

Dark t o light colour change i n o i l with occasional colourless bubbles

Progressive lightening i n colour of the o i l w i t h o u t gas bubbles

I f a series of displacements are c a r r i e d o u t a t d i f f e r i n g compositions o r p r e s s u r e s a s i n t h e example given above s e v e r a l o f t h e s e mechanisms w i l l be observed t o o p e r a t e . Considerable refinement of t h i s scheme i s r e q u i r e d p a r t i c u l a r l y i n r e l a t i o n t o t h e d i f f e r e n t types of displacement which may take p l a c e i n t h e L-L and L-V r e g i o n s .

481 CONCLUSIONS

I t has been s h a m above t h a t s l i m tube displacement experiments may be used t o optimise i n d i v i d u a l p r o j e c t s with r e s p e c t t o both p r e s s u r e and composition. A considerable amount of information may be gathered i n the course of t h e s t u d i e s upon which t h e dominent mechanism which o p e r a t e s i n a given p r e s s u r e o r composition may be deduced.

ACKNOlrTLEDGEMENT The author wishes t o thank G . J . J . Williams. A . G . Steven, A. Booth, C.G. Osborne, D . J . Thomas, S . Takhar. S . Bahal and C. Liang from whose work t h e contents of t h i s paper have been drawn. NOMENCLATURE

Bo

Flash formation volume f a c t o r of o i l

Fg

Volume f r a c t i o n of gas phase

COR

Gas o i l r a t i o

i , j, k

I n d i c e s i n equation of s t a t e

ml

Mass of evacuated s l i m tube

m2

Mass of water f i l l e d s l i m tube


Number average molar mass Pressure

P

e

Standard p r e s s u r e (101.325 kPa)

P

qng.

cop

Volumetric flow r a t e of mercury o r CO2

Vi

I n j e c t e d pore volume

VP

Pore volume of s l i m tube

Vr

Recovered pore volume

6Vin

I n l e t dead volume

6Vout

O u t l e t dead volume

xc3

Mole f r a c t i o n of propane i n mixtures

T

Temper a t u r e

6T

Temperature movement

At

T i m e movement

a ij

c o e f f i c i e n t i n equation of s t a t e

p r e s s u r e movement density of o i l density o f water d e n s i t y o f mercury

REFERENCES

1.

Orr, F.M., J n r . and Taber, J.J. "Displacement o f - O i l by Carbon Dioxide" F i n a l Report WE/ET/12082-9, 1980.

2.

Y e l l i g , W.F. "Carbon Dioxide Displacement o f a West Texas R e s e r v o i r O i l " SPE/DOE9785, 1981.

3.

K e l l , G.S. " P r e c i s e R e p r e s e n t a t i o n of t h e Volume P r o p e r t i e s o f Water a t One Atmosphere" J . Chem. Eng. Data 12, 1, 66-69

4.

K e l l , G.S. and Whalley, E. "The pVT p r o p e r t i e s of Water" P h i l Trans Roy SOC (Lond)

565

(1965)

5.

Gair, D . J . , Grist, D.M., and M i t c h e l l , R.W. "The E a s t Midlands A d d i t i o n a l O i l P r o j e c t " SPE 195 P r e s e n t e d a t t h e 1980 European Offshore Petroleum Conference and E x h i b i t i o n .

6.

Henry, R.L., and M e t c a l f e , R.S. "Multiple Phase Generation During COP Flooding" SPE 8812, p r e s e n t e d a t t h e F i r s t J o i n t SPE/DOE Symposium i n Enhanced O i l Recovery, Tulsa, A p r i l 20-23 (1980).

7.

Holm, L.W., and J o s e n d a l , V.A. " E f f e c t o f O i l Composition on Miscible-Type Displacement by Carbon Dioxide". SPE 8814, p r e s e n t e d a t t h e f i r s t j o i n t SPE/DOE Symposium i n Enhanced O i l Recovery a t T u l s a , A p r i l 20-23, 1980.

8.

Johnson, J.P., and P o l l i n , J.S. "Measurement and C o r r e l l a t i o n of C02 M i s c i b i l i t y P r e s s u r e s " SPE/DOE 9790, p r e s e n t e d a t t h e 1981 SPE/DOE j o i n t Symposium i n Enhanced O i l Recovery, T u l s a , A p r i l 5-8.'.

9.

S c h n e i d e r , G.M. "Physicochemical P r i n c i p l e s of E x t r a c t i o n w i t h S u p e r c r i t i c a l Gases". Angew. Chem. I n t . Ed. Engl. 11 716-727 (1978)

EXPERIMENTAL TECHNIQUES

483

NUCLEAR MEASUREMENTS OF FLUID SATURATION IN EOR FLOOD EXPERIMENTS N. A. BAILEY, P. R. ROWLAND, D. P. ROBINSON

AEE Winfrith.Dorchester, Dorset DT2 8BH

ABSTRACT This paper describes the nuclear measurement methods which have been selected for the determination of fluid saturation distributions within the cores of high pressure flood experiments to be carried out at Winfrith in a study of enhanced oil recovery processes. Such methods should be capable of producing the accurate measurements of saturations, including their spatial and temporal variations, which are required to obtain a better understanding of the EOR process occurring within cores. It is intended that such measurements will provide a wider range of information for the validation of computer programs. These EOR codes are to be used for the assessment of the feasibility of EOR processes in North Sea Fields. A range of possible measurement techniques has been studied and the basis of the selection of the preferred nucleonic methods is described. The methods selected are based on the use of deuterium to determine water saturations or hydrocarbon gas componentsutilising a g a m a neutron reaction, and the introduction of radioactive ferrocene as an additive to oil to measure oil saturation from gaama emission. The development work carried out to establish these nucleonic techniques is discussed in some detail, showing their clear potential, and the methods of application to high pressure core fluids are discussed. These techniques are currently being used in ongoing flood experiments.

INTRODUCTION

A programme of EOR studies is being carried out at AEE Winfrith under contract to the UK Department of Energy and an important element of this programme is the experimental programne. The experimental programme, whose objectives are the testing of EOR processes under relevant conditions and the validation of codes, is centred around a number of high pressure flood rigs, the first of which is currently being constructed. These rigs have been designed to allow experiments to be carried out at reservoir pressure, temperature and flow rate using reconstituted reservoir oils, correct salinity brines and a variety of EOR fluids including Cog and surfactants. The displacement process itself will take place in sandstone cores up to 5m long. Key measurements which are required of such a rig are the analysis of the fluids produced from the outlet end of the core and the determination of fluid saturations within the core as a function of axial position along the core and time. The selection, development and application of methods for such measurements of fluid saturation is the subject of this paper. A number of techniques have been used in the past for such measurements, and these are discussed below, but most

are not applicable to high pressure core floods where the core has to be surrounded by a thick-walled steel pressure vessel. Various nuclear measurement techniques have, therefore, been considered as they are less influenced by the presence of the pressure vessel and considerable experience with them already existed at Winfrith. It has been concluded that at least two phases need to be marked within an EOR displacement test in which three phases can occur. Two preferred techniques have, therefore, been selected for the measurement of oil and water phases which have been subjected to detailed development, supported by theoretical assessments, to determine their performance under representative conditions. These tests have shown that very satisfactory measurements can be made of fluid saturations within sandstone cores, and work has continued to consider in detail the application of these techniques to the High Pressure Flood Rigs. One of the problems considered is the need to avoid any partition of the radioactive tracer from the phase which is being marked. In parallel with these high pressure flood experiments, some low pressure studies have started at Winfrith, including a prograrane of waterflood displacement of oil, and these nuclear techniques are being used in these experiments where some comparisons are possible with other measurement methods. SELECTION OF MEASUREMENT TECHNIQUES FOR FLUID SATURATIONS WITHIN CORES The measurement of fluid saturation within cores is a difficult task and a review of the published literature suggests that it has only been attempted infrequently. Such measurements can, however, contribute substantially to the development of the understanding of EOR processes and their quantitative evaluation. Various techniques have been proposed for the present programme for such measurements and these have been cbnsidered for use in high pressure floods. Physical sampling of fluids along the length of a core has some attractions, but capillary effects lead to the extraction of samples which are unrepresentative of local saturations. The low flow rates which would occur in the sample lines if the core were operated at reservoir velocities would present flushing problems leading to incorrect fluid analysis. Some measurements have been attempted previously using non-intrusive techniques such as nuclear magnetic resonance (NMR) and microwaves. NMR has been used successfully for downhole applications by Brown and Gamson(1) and Nikias and Eyraud(2) who were able to distinguish between brine and high viscosity oils. NMR does, however, r'equire a totally non-magnetic containment if the high frequency alternating magnetic fields are to penetrate the core and this is not readily achieved in high pressure laboratory floods. Microwave techniques have been very successfully used by Parsons(3) to determine brine saturations but once again a nonmetallic containmect is required to avoid reflection of the microwave radiation and this reduces its applicability to high pressure experiments. Preference is being given, therefore, to nuclear techniques as they are non-intrusive and are far less sensitive to the effects of pressure containment around the core. Nuclear Techniques

A number of nuclear techniques are potentially of use in the measurement of fluid saturnations within cores. The first technique considered is labelling particular fluids with y-emitting tracers. The concentration of a particular fluid can then be inferred from measurements of radiation as shown in Figure I. The water phase can be labelled by using radioactive forms of its dissolved salts, but the oil phase needs to have a material added to it which is of a hydrocarbon type containing a radioactive element. The main problem with such

485

a technique is that of handling significant volumes of continuously radiating fluids. The method is, however, viable for fluid saturation measurement and is simple, direct and well understood.

W L T l CHANNIL ANALYSIR

F G I GAMMA TRACER METHOD The alternative techniques rely on the response of fluids within the core to bombardment of y-rays or neutrons from an external source which can be turned off when not required. This avoids the problem of handling radioactive fluids. One method of this type which is being investigated is neutron activation. The core is bombarded with neutrons and the resultant y-radiation is detected and analysed using gamma spectroscopy to give a measurement of the relative abundance of the elements within the core. A further alternative centres around the use of deuterium which emits a neutron when bombarded with high energy y-rays. The energy threshold for the emission of a neutron from deuterium in such a reaction is 2.23MeV. Deuterium concentration could then be determined from neutron flux. Many fluid components could be labelled by substituting hydrogen atoms by deuterium. Supplies of heavy water, for example, are readily available at Winfrith and this can be added to B20 for marking the brine phase. A range of deutero-carbons can also be synthesised from D20. The simplest substitute hydrocarbon to produce would be deutero-methane from the reaction of heavy water with aluminium carbide. Preliminary Screening Preliminary tests with the radioactive tracer and y-neutron techniques showed both of these methods to be fundamentally feasible, although each has its own difficulties.. Acceptable count rates, proportional to concentration, could be obtained from reasonable activity levels for each method suggesting thaL further development of these techniques was worthwhile. The absorption of neutrons was examined at an early stage as this was equivalent to the neutron decay logging techniques which have been used for a number of years with pulsed neutron sources downhole to measure local brine saturation ( 4 - 6 ) , or variations of salinity during waterf looding(7). Neutron absorption in a laboratory arrangement was investigated using a 1.5pg.californium source placed close to a sandpack with a porosity of 40% within a 5Omn bore glass cylinder. The source was surrounded by polythene to ensure that the neutron flux entering the sandpack was predominantly thermal and cadmium foil was used around the polythene to provide collimation. The sandpack was saturated with brine over the lower half and oil in the upper half. The sections were separated by a thin polythene interface to maintain a sharp front in saturation and the transmitted neutrons were detected on a glass scintillator. The measurement is based on the neutron absorption cross section in chlorine as a measure of brine saturation as this is the dominant cross section as shown in

486 Table 1 . On t r a v e r s i n g p a s t t h e i n t e r f a c e , however, t h e measured count r a t e f e l l by o n l y 7% which was inadequate f o r d e t a i l e d s a t u r a t i o n measurements. It was concluded t h e r e f o r e t h a t t h i s technique was n o t v i a b l e u n l e s s f l u i d s have t h e i r c r o s s s e c t i o n s i n c r e a s e d by t h e a d d i t i o n of a neutron a b s o r b e r . The d i f f i c u l t y i n t h i s c a s e could then be t h e s e p a r a t i o n of t h e a d d i t i v e from t h e phase it was marking and t h i s method h a s n o t been explored f u r t h e r .

Tests were then c a r r i e d o u t i n v e s t i g a t i n g whether t h e d i f f e r i n g a b s o r p t i o n c r o s s s e c t i o n t o thermal energy n e u t r o n s of hydrogen and deuterium l i s t e d i n Table 1 could be employed, as t h e o r e t i c a l c a l c u l a t i o n s suggested a modest d i f f e r e n c e i n a b s o r p t i o n behaviour could be obtained. P r e l i m i n a r y measurements showed t h a t such d i f f e r e n c e s could be d e t e c t e d b u t n o t on t h a t i m e s c a l e o r r e s o l u t i o n r e q u i r e d t o o b t a i n a s h a r p p i c t u r e of t h e movement of a f r o n t .

Table I Absorption Cross S e c t i o n s (barns) t o 0.09eV Neutrons

Element

H

D

Cross S e c t i o n 0.173 2.6~10'4

0

C

Na

Si

Fe

C1

1 . 8 ~ 1 0 - 3 10-4 0.289 0.083 1.32 16.69

I

10'1

10-1

.

I

loo0

I

CHANNEL N

FIG. 2

x)

m

TYPICAL NEUTRON CAPTURE GAMMA SPECTRUM WITHOUT PRESSURE VESSEL

481

A further technique which was investigated was the spectral analysis of gamma rays following activation by neutron irradiation. Such a method, covering both inelastic scattering and capture of neutrons, has been used by Hertzog(8) for downhole applications to determine the relative quantities of carbon, oxygen, silicon, calcium, iron, chlorine and hydrogen. Our experiments ccncentrated on the neutron capture process as the high energy neutrons needed for inelastic scattering led to shielding problems. The laboratory studies were carried out on a sandpack cofitained within a 50nm bore aluminium tube with a 1 pg californium source as a neutron generator. The initial test results (Figure 2) produced a spectrum showing quite clearly the peaks associated with chlorine. Chlorine concentrations could not, however be obtained to the required accuracy within an acceptable timescale. When the sandpack was placed inside an 18nm thick steel tube to simulate the high pressure rig situation, the spectrum was dominated by iron peaks, with hydrogen and chlorine peaks being reduced to an unacceptably low level compared withthe background level produced by Compton scattering. Because of these major difficulties encountered with neutron absorption and activation techniques it was decidad that reliance should be placed on y-tracer and y-neutron techniques which were then subjected to further development. GAMMA TRACER TECHNIQUES

Radio tracer techniques have to be restricted to y-emitting isotopes as Band y emissions will not penetrate the pressure vessel. As a gamna tracer technique depends on adding a radioactive material to a fluid, it is best achieved when the fluid normally contains materials which can be made radioactive. The possible choice of radioactive material is further restricted by the need for a sufficiently long half life (preferably greater than 1 month) and sufficiently high energy gamna rays (greater than 0.5MeV) to avoid excessive absorption in the pressure vessel around the core. Labelling the brine phase is relatively straightforward, as the naturally occurring chlorides of sodium and caesium are both readily available in radioactive form and their characteristics are sumnarised in Table 2. The oil phase is more difficult as hydrogen and carbon do not have gamma emitting isotopes. A suitable isotope must therefore be wrapped in a hydrocarbon type molecule which will behave as an oil component. It should also have tightly bound electron orbitals and not be strongly electro-positive. This reduced the list of candidate isotopes toSc-46, V-48,Fe-59 and Co-60. This list was further reduced to Fe-59 and Co-60 due to the vast range of organo-metallic chemistry associated with these elements, with a preference for Fe-59 as the very long half life of Co-60 (5.26 years) leads to decontaminatidn and disposal problems. Ferrocene (Figure 3) was therefore selected as the most suitable material, as it contains iron which can be made radioactive, and is one of the simplest organo-metallic molecules, containing only carbon and hydrogen in addition to the iron. Its molecular StruChure suggksts.that it should behave as a heavy liquid oil fraction. The characteristics of Fe-59 are also included in Table 2. Table 2

- Candidate Isotopes for Labelling Fluids

ISOTOPE HALF LIFE

Na-22

cs-I37

Fe-59

2.6 years

30 years

45 days

0.51, 1.28

0.66

1.10,

1.29

488

nc-& , ~cn

wcFIG. 3

CH

FERROCENE MOLECULE.

Preliminary Tests The f i r s t s e r i e s of t e s t s were c a r r i e d o u t on a I c m diameter pure s i l i c a sandpack, set up i n s p e c i a l g l a s s a p p a r a t u s a s shown i n F i g u r e 4 which allowed v i s u a l examination of t h e displacements a t t h e same t i m e a s o p e r a t i n g a t temperatures of around 90°C. The sandpack was 25cm long and t h e displacement tests were c a r r i e d o u t w i t h 3% b r i n e , l a b e l l e d w i t h Cs-137 a t an a c t i v i t y l e v e l of ZOpCi/ml, and medicinal p a r a f f i n . For v i s u a l purposes t h e a c t i v e b r i n e could be marked w i t h sodium f l o u r o s c e i n r and t h e o i l phase by Sudan Red dye. A c o l l i m a t e d sodium i o d i d e d e t e c t o r was used t o measure t h e r a d i a t i o n u s i n g lOcm t h i c k n e s s of lead and a s l i t width of 3 m . C a l i b r a t i o n was c a r r i e d o u t i n s i t u both i n t h e empty tube and i n t h e sandpack a t 100%b r i n e satuEationo. The l a t t e r gave count r a t e s of 3000 per minute. Using a count p e r i o d of I minute t h i s g i v e s a s t a n d a r d e r r o r l e v e l of ?1.8%.

FIG4 APPARATUS FOR GAMMA TRACER DEVELOPMENT TESTS.

489

The experimental prograrrme on this apparatus included:i

downward displacement of inactive brine with active brine (miscible)

ii

downward imniscible displacement of active brine by oil (paraffin)

During the first test a record was kept of the brine level above the sandpack so that the sandpack porosity could be determined both from the velocities of the front, determined by radiation measurement and visual observation of the measured brine level as well as the activity levels in and above the sandpack.

A typical scan of the sandpack for the first experiment is shown in Figure 5 where the characteristic dispersion of the front in miscible displacement can be seen. The porosities calculated (38%) agreed closely, the agreement lying within the experimental uncertainty (22%). When the active brine was displaced with oil (Figure 6) similar measurementsweremade and these indicated a frontal oil saturation of 85%. This was confirmed by direct measurement of the paraffin injected into the core. The results were considered promising as it was clear that accurate measurements were being obtained and development of the technique was transferred t o sandstone cores. At this point the first difficulty with this technique appeared which was adsorption of the tracer within the sandstone.

0

5000

FIG5 DOWNWARO DISPLACEMENT OF UNLABELLEO BRINE BY LABELLED BRINE

0

COUNT )LII MlNUtK 5000

HG.6 DOWNWARD DISPLACEMENT OF LAMLLED BPlM BY OIL.

490 Adsorption When radioactive salt tracers are dissolved in brine they form ions and the metallic components adsorb onto the surface of the rock and particularly onto clay structures within sandstones. This is very noticeable when a low concentration radioactive brine is added to dry sandstone with a substautial fraction of the measured activity eventually coming from the surface of the rock. A series of adsorption tests was, therefore, set up to investigate this behaviour using the sandstones to be used in the high pressure flood experiments. These sandstones, Clashach (20Omd permeability, 13% porosity)and Rosebrae (125Omd permeability, 24% porosity), are Triassic quarry material and have only modest clay contents. In these experiments a rock sample was mounted in a Table Tube (Figure 7) where knowing how much solution should exist within the porous material, the amount of adsorbed isotope could be determined. The salt concentrations were systematically varied and the results for the Clashach and Rosebrae are shown in Table 3. Table 3

- Adsorption

of Tracer on Sandstone

Condition

Adsorbed Activity DissQlved Activit! in Pores

C lashac h a Solution of 6% NaCl + 1 % CsCl + Cs-I37 tracer b Solution of 6% NaCl + 6% CsCl + Cs-137 tracer. c NaOH added to (b) to pH 11 d Solution of 6% NaCl + Na-22 tracer e Sollition of 6% NaCl + 5% MgC12 + 5% CaC12 + Na-22 trace1

I .3 0.53 0.47 0.20 0.12

Rosebrae f Solution of 10% NaCl + 10% CsCl + Cs-137 tracer g Solution of 10% NaCl + 10% CsCl + Na-22 tracer

0.10 0.05

-

-t

FIG. 7

APPARATUS FOP ADSORPTION MEASUREMENT AND TYPICAL GAMMA SCAN

491 In all cases a return to inactive k i n e resulted in the activity in the sample falling to zero. It can be concluded, therefore, that the adsorbed fraction decreased with increasing tracer salt concentrations, that adsorption was reversible, that the addition of divalent salts or increased pH had little effect on adsorption, and that caesium was adsorbed in preference to sodium. The tests were carried out with radiotracer concentrations of IOuCi/ml. The most representative conditions were with brine made of 6% NaCl using a sodium-22 tracer. Under these conditions the radiation from adsorbed isotope was only 20% of that from the isotope dissoloved in the brine. It might be possible to overcome the adsorption problem by pre-saturating the core with active brine before saturating it with oil. If this quantity of tracer then remained adsorbed in the core during a flood experiment, it could be treated as an additional radiation background and measurements could still be made of water saturation albeit at a reduced accuracy. This would require that the rock remained totally water wet throughout and it is more likely that some of the adsorbed material will be displaced during a flood experiment making the interpretation of radiation measurements extremely difficult. Some tests were made in which the sandstone was preflushed with inactive brine in an attempt to saturate adsorption sites. Some improvement resulted from this but the inactive and active ions exchange during the subsequent active displacement. Adsorption of water-borne tracers does, therefore, severcl; limit the power of this technique to measure water saturations, so consideration was switched to the labelling of the oil phase wirh a non-polar, non-ionising material, which should not adsorb and which would allow measurement of the oil phase saturation. Labelling the Oil Phase Ferrocene has been selected as a suitable organo-metallic material for use as an oil tracer as it satisfies the various criteria discussed above and it is readily available in inactive form. To convert it to its radioactive form requires either irradiation in a reactom or synthesis of ferrocene from radioactive iron via the reaction of ferrous chloride with cyclopentadiene using potassium hydroxide as a condensing agent. Investigations of the latter have shown that synthesis is possible, but the main emphasis in the development has been associated with irradiation which is expected to be more econamic. Trial irradiations have been carried out on the PLUTO and DIDO reactors at Harwell for periods of up to 23 days to give a specific activity of about 0.4 mCi/pm. At the end of such an irradiation about 30% of the activity is in ferrocene with the remainder in a material which is insoluble in hydrocarbons. It is believed that this breakdown is induced by the SzilardChalmers reaction(9) which results in the iron being ejected from the molecule under irradiation, allowing the iron to oxidise in the surrounding atmosphere. The two radioactive components can readily be separated by dissolution, filtration and recrystalisation. A typical yield from a standard irradiation would be about 3gm of radioactive ferrocene containing about 1.25mCi of activity. When dissolved in 5 litres of oil to give a specific activity of 25OuCi/litre, the statistical uncertainty in the saturation measurement on a representative core geometry will be less than +3% on a 100% saturation. This accuracy is based on a 9mm slit width, a J O minute counting time, and is derived from preliminary measurements in a representative geometry. Such a concentration is far below the solubility limit of ferrocene in oil, which was found to be about 2.5% at 2OoC and appreciably higher at higher temperature. Several tests have been carried out to examine the partition behaviour of ferrocene between oil and brine by dissolving it at a concentration of about 0.1% in oil and then contacting the mixture with brine at 100°C for several days. The amount of ferrocene transferred to the water phase was then determined colorimetrically or by radiation measurement. Both methods,gave

492

similar results with a partition coefficient less than 10-5 for neutral or alkaline brine but with an increased value of 10-3 for a strongly acid brine (pH-2). As the solubility of ferrocene in brine is so low, this compound will travel with and mark the oil. As quite modest quantities are required to mark the oil, it appears to provide a very suitable method for saturation measurements.

GAMMA-NEUTRON INTERACTION If ferrocene is to be used for labelling the oil phase, and y-emitters are of limited use for labelling the water phase, then an alternative method is required for the measurement of water phase saturations. The gamna-neutron reaction with heavy water has been selected to provide such a method. Such a reaction can occur in any element if it is bombarded by gamnqs with energies exceeding the binding energy, but the second lowest binding energy occurs in deuterium (2.23 MeV). Thus measurement of water saturations can be achieved by using heavy water and bombarding the core with gamna rays with an energy in excess of 2.23MeV. The neutron flux produced is proportional to water saturation. The only element with a lower binding energy is Beryllium-9, which will not be present in the flood experiments. The only convenient g a m a source with a suitable energy level is sodium-24, but this unfortunately has a short half life (15 hrs) which means that special arrangements have to be made for the delivery of sources. An alternative would be to use a y-beam generator but existing collrmercial devices would be too powerful for this application. This technique has been considered here as a means of marking the water phase, as D20 will also have a negligible effect on the physical and chemical characteristics of the water phase. Deuterium could also be used to determine the local saturation of a particular hydrocarbon as deutero-carbons can be synthesised. The simplest would be the production of deutero-methane from the reaction between D20 and aluminium carbide, but other methods such as the Fischer Tropsch synthesis are available to synthesise higher deuterocarbons. Development Te 8 ts Development tests on the gamma-neutron method have been carried out on the apparatus shown in Figure 8. This apparatus consisted of a 2" diameter sandpack contained inside an aluminium tube with a heavy water saturation at one end separated from a light water saturation by a thin polythene film to maintain a sharp saturation front. The sandpack was set up on its own or within a 181m thick steel vessel representing the pressure vessel surrounding the core in a High Pressure Flood experiment. Most of the circumference of the sandpack was surrounded by a polythene block containing BF3 or He3 neutron detectors. The polythene is required to thermalise and reflect neutrons before entering the neutron detectors. Optimisation studies showed that 1 6 of~ polythene was required between core and counters to achieve optimum thermalisation and 50mn beyond the counters for reflection. The remainder of the circumference is taken The sealed source utilised had an up by the source and its collimator. activity of about 100 mCi and was mounted inside a lead collimator system with an adjustable slit allowing a gamma ray beam the full width of the sandpack. The slit design limited the beam to a few millimetres along the length of the sandpack, so that axial variations in saturations can be adequately resolved. In the y-tracer techniques described earlier the detector was collimated, as it is not possible to collimate a source in the fluid. '

The neutrons detectors were connected to a multi channel analyser initially which allowed the spectra to be investigated in detail and compared with those from pure neutron sources, but later tests have used more traditional Harwell 6000 apparatus counting all pulses above a particular threshold level which was set to reject noise.

493

‘OLWHENE BLOCK

FIG. 8

APPARATUS FOR GAMMA -NEUTRON INTERACTION DEVELOPMENT TESTS.

The development experiments were concentrated on saturation measurements through a saturation discontinuity and have allowed the systematic investigation of shielding thickness in the collimator and slit width. Initial tests were carried out using 5Omm thick lead for the collimator, but it became clear that this was insufficient as a significant flux was occurring away f r w the slit position. It was found necessary to increase the lead thickness to 1 2 h to reduce this background gamma flux to an acceptable level. The weight of the collimator system at about 500kg is one of the factors to be taken into account in the design of traversing equipment. The results of scanning through an interface with a thick walled collimator are shown in Figure 9-11. These figures show quite clearly that the step front in saturation has been smeared into a measured S-shape curve where saturations in the range 10%-90% appear over a length of about I a n . Theoretical calculations have been carried out to determine the uncollided gamma flux distribution along the centre line of the sandpack using the relationship

where (ih is the uncollided flux,dOthe source flux, and Mi the total linear attentuation coefficient for the different materials each of thickness ti in the path of the flux, which is a function of X . From such calculations it is possihle to predict the measured piofile with,e.n equation of the form P,(x)

=

I-

la

f(xrl)Pt(xl)dxl

(2)

where Pi,,and Pt are the measured and true profiles respectively and f is a function of the collimator and test section geometry which can be derived analytically or from calibration experiments. Any measured profile can, therefore be deconvoluted to give the true profile by means of the relationship

where the Fourier transform of g is thereciprocal of the Fourier transform of f.

494

1.c ACTUAL DISlRIBUtlO COUNTCUTE

0 1 1 H t O l t t l C ~DISIRIOUIION ~ WllHoUI PNSSURE VESSEL

VESSil

0.6

MEASWD MSV WRH aESSURE

0.4

0.1

C

+I

0

FIG. 9

+2

+4

-

MEASURED PROFILES FOP 0 -100 O/o D 2 0 STEP IN SATURATION. COLLIMATOR SLIT WIDTH 4 mm

1.0 INTERFACE

0 8

COUNT U T E NOIIWALISED 10 1 0 0 Ye 020

Ob

-

04. PROFILES

0.2

-

-

WIYSICAL

I

-40

-30

-lo

-10

1

0

+ 10

1

1

tm

+30

FIC.10 MEASURED SATURATION PPOFILES FOR VARIOUS D20 SATURATIONS KIT WIDTH = 4 mm

4 0

495

A profile derived from equation (21 for a sandpack without a pressure vessel has been included in Figure 9. Close agreement can be observed for most of the profile. The discrepancies at the left hand side of the profile are probably induced by uncertainties in background level and the fact that some collided gamma rays are scattered with energy levels in excess of 2.23MeV and can produce neutrons from deuterium. The predicted width of the front between 10% and 90% saturation levels is 0.8cm which compares satisfactorily with the measured values of about lcm. The signal is also shown in these results to be directly proportional to deuterium concentration. Increasing the slit width in the collimator increases the count rate and, hence, improves the counting statistics, but at the cost of increasing the smearing of the saturation profile.

cnmns WED

ON IS MINUTE COUNT

0

FIC.11

2

4

6

EFFECT OF SLIT WIDTH ON COUNT RATE I00 OIC, D2 0 WITH PRESSURE VESSEL.

Tests have also been carried out on a sandpack with only a short length of light water saturation preceded and followed by heavy water. The results shown in Figure 12 confirm the ability of this technique to determine the length of such a short slug of fluid. In Figures 9 to 12 data are included both with and without a pressure vessel simulation. It is observed that the pressure vessel leads to some attenuation of the neutron flux and further smearing of the saturation profile. These results confirm that the y-n interrogation of deuterium provides a method which gives a good quantitative measurement of the saturation level of deuterium bearing species as a function of axial position and time. It is proposed to use this method for such measurements on high pressure flood experiments.

A further merit of this measurement technique is that it can be used to determine the dispersion coefficient for the core. At the start of an experiment the core is flooded with normal brine prior to oil flooding to set up the starting conditions for a displacement experiment. The brine is then displaced by heavy water brine. This idealised first contact miscible displacement with negligible density or viscosity differences, results in the development of a classical dispersion front and by measuring this profile using the gamma-neutron technique the dispersion coefficient for the core can be derived.

496

f MEASURED PROFILE

I: 1

0 4

-

0.1

-

\f-\ 1

l-f

ACTUAL MOFILL

I

CMS

,

FIG.12 PROFILE ALONG D 2 0 SATURATED SANDPACK WITH 4 C M LENGTH SATURATED WITH H 2 0 . WITH PRESSURE VESSEL. SLIT WIDTH 8 m m

APPLICATION TO HIGH PRESSURE FLOOD TESTS

As a result of the development tests described above it has been decided to use radioactive ferrocene to label the oil phase in the High Pressure Flood Tests and heavy water to label the brine phase using a y-n reaction interrogation method. It is intended that the measurement system should be capable of measuring saturations over the complete length of cores up to 5 metres long, traversing along cores to obtain the axial saturation distribution at intervals which can be as small as Icm. At each position where measurements are required, counting will be carried out for approximately 10 minutes to give sufficiently large counts to ensure reasonable accuracy. Such a period is generally satisfactory for most conditions including a shock front travelling at 0.3mlday which might be typical of North Sea conditions. In the measurement period such a front will have moved only 2mn, which is small in relation to the slit width Although higher rates may have some experimental interest, the errors involved would be mitigated by front smearing induced by capillary forces in inmiscible processes or dispersion in miscible processes. If necessary the counting time could be reduced by increasing the ferrocene concentration and using a higher activity sodium 24 source. It should be noted that these two methods cannot be used simultaneously as the high level of gamma radiation occurring when the sodium 24 source is in use would swamp the radiation coming from the ferrocene. This restriction to one measurement at a time leads, however, to simplification of the apparatus to be used on the flood rigs as only one collimator is required. The apparatus will be similar to that used for development tests (Figure 8) with He3 neutron detectors mounted in the polythene blocks for the y-n method.

497

Detectors are not placed directly helow the core so that the measuring apparatus can be removed readily from the core. When measurement is required of yradiation from the ferrocene, the sodium source will be removed and replaced, within the same collimator, by a sodium iodide crystal detector. Sodium iodide was selected in preference to a Ge(Li) detector to eliminate the need for cooling the crystal to cryogenic temperatures. and becuase of its higher sensitivity. The detectors, fed from separate Em supplies for neutron and sodium iodide detectors, will have their outputs taken to a colllllon multi channel analyser together with the outputs from separate detectors which will be used to measure background radiation levels dimultaneously. h this way the background level can be automatically removed from the measured signal. The multichannel analyser will be integrated into a minicomputer system which will control the flood rigs and carry out data processing. The detector and analyser system has to be calibrated on a representative geometry at 100% saturations of brine and oil. The first high pressure flood rig is currently being constructed but these measurement techniques are now in use in low pressure studies of oil displacement by waterflooding. These experiments are being carried out using brine and tetradecane in the same sandstone materials which are to be used for the high pressure experiments, and encompass both displacement tests and steady state relative permeability measurements.

Conclusions It can be concluded that two viable measurement techniques have been established for the measurement of fluid saturations within the cores of high pressure flood experiments. Labelling the oil 'phase with radioactive ferrocene, which can be prcduced synthetically from active iron or from reactor irradiation. allows the oil phase saturation to be measured. A convenient method for marking the water phase with heavy water and interrogating it via a gamna-neutron interaction to measure the water phase saturation has been evaluated. This method also has p r m i s e for measuring the concentration of a particular component in a hydrpcarbon gas or liquid system by synthesising deutero-carbon additives. Reasonable levels of source activity and conventional counting techniques allow these saturations to be measured within about 10 minutes with a statistical uncertainty of less than k3.Z at the 100% saturation level and at the 25% saturation level the result would typically be 0.25 k0.02. These techniques allow axial and temporal variationc in fluid saturations to be determined as only about Icm of the core length is viewed at any one time snd the detectors aan be traversed along the core. The location of any sharp front in saturation can be accurately determined and although the measurement introduces some smoothing of sharp fronts, it is possible to convert the measured profile back into a more acclirate saturation profile by a deconvolution process. The new tachniques are to be used on the high pressure flood experiments to be carried out at Uinfrith and thcy are already in use there on low pressure experiments.

Acknowledgement This work has been supported by a contract from the UK Department of Energy.

498 REFERENCES 1

-

BROWN, (1960)

I(

J S and W O N , B W: "Nuclear Magnetism Logging", Petroleum Trans. 199-207.

219,

3

NIKIAS, P A and EYRAUD, L E: "Some Examples of Nuclear Magnetism Logging in Three San Joaquin Valley Oil Fields" JPT (Jan 1963) 23-27.

3

PARSONS, R W: Microwave Attenuation A Neu Tool for Monitoring Saturation in Laboratory Flooding Experiments. SPEJ (Aug 1975) 302-309

4

CLAVIER, C. HOYLE W. and MEUNIER, D: "Quantitative Interpretation of Thermal NeiitronDecay Time Logs: Part 1 . Fundamentals and Techniques". JPT (June 1971) 3 743-755.

5

WAHL, J S et al: "The Thermal Neutron Decay Time Log". SPEJ (Dec 1970) 365-,375.

6

RICHARDSON. J E et al: "Methods for Determining Residual Oil with Pulsed Neutron Capture Logs". JPT (May 1973) 593-603.

7

YOUNGBLGOD W E: "The Application of Pulsed Neutron Decay Time Logs to Monitor Waterfloods with Changing Salinity". JPT (June 1980) 987-963.

8

HERTZOG, R C: "Laboratory and Field Evaluation of an Inelastic Neutron Scattering and Capture Gamma Ray Spectrometry Tool". SPEJ (October 1980). 327-340 OVERMAN, T and CLARK, H M: "Radioisotope Techniques". McGraw-Hi11 New York (1960) 378.

9

-

EXPERIMENTAL TECHNIQUES

499

CHARACTERIZATIONOF EOR POLYMERS AS TO SIZE IN SOLUTION ROY DIETZ Division of Materials Applications, National Physical Laboratory, Teddington,Middlesex, TW1I OL W UK

A~STRACT The potential is explored of extending to the characterization of EOR polymers the conventional electrical Sensing zone (ESZ) technique.

Theoretical expectations and experimental factors are discussed. The method is tested with well-characterized fractions of polyacrylamide and some biopolymer Only the samples for which characteristics relevant to EOR use are known. largest solution species can be detected, but those species are significant in detedning technological properties. For polyacrylamides the ESZ response correlated with hydrodynamic volume. For biopolymers there were correlations with screen factor and with viscosity at concentrations of relevance in EOR. The method offers promise for monitoring solutions rapidly for microgel.

INTRODUCTION

The size of solution species is relevant to the possible use of polymers in Solution species must be large enough to give a high viscosity at low concentrations for mobility control, but not so large that they block pores in the substrate and give rise to poor injectivity. A simple means of characterizing polymers as to size in solution would aid the production of improved polymers for mobility control, and could also serve as a means of monitoring solutions for adequate injectivity. The number and size of the largest solution species present control injectivity; estimation of that part of the size distribution gives rise to great difficulties for such conventional techniques as gel permeation chromatography, ultracentrifugation and fractionation followed by independent characterization by light-scattering photometry or viscometry. EOR in two main respects.

It is clear from experiments with filters of controlled pore size (1) (2), from determinations of radii of gyration by light-scattering photometry (3) and from estimates of hydrodynamic volume from viecometry (4) that the size range of In conventional particulate metrology suspensions relevance is some 0.5-1.0 pm. of particles of that size can be characterized by the electrical sensing zone (ESZ) technique. This paper describes an exploratory investigation into the Well-characterized applicability of that technique to dissolved polymer. samples are used to relate the ESZ response to molecular characteristics for polyacrylamide fractions and to rheological characteristics for biopolymers

500 DISSOLVED POLYMER IN AN ELECTRICAL SENSING ZONE Principle and range of the ESZ method

-

In the electrical sensing zone method (Figure 1) a dilute suspension in a salt solution is made to flow through a small orifice (diameter 100 um). Coulostatic circuitry is used to maintain a constant current between electrodes placed on opposite sides of the aperture. When a suspended particle passes through the aperture, the electrolytic resistance is increased by the equivalent of the volume of electrolyte displaced.

T

TO VACWM

AMPLIFER

CIRCUIT

9 CW N T E R

U

M&MOMEl

OSClLLOSCOPE

CONTACT

COUNTER START I STOP

Figure 1.

Schematic of the ESZ method

The constant current is maintained by a voltage pulse of magnitude proportional, to a good approximation, to the size of the suspended particle. Comnercial instruments have discriminator circuits capable of counting and sizing the voltage pulses. The voltage scale can be calibrated in experiments with suspensions of particles of known size. Routine operation is possible with particles greater than some 1 urn in diameter; with precautions to reduce noise, operation with insulating particles of diameter 0.4 um is feasible. Polymer structure in solution Application of the ESZ method to the sizing of dissolved polymer molecules introduces some special features connected with the nature of the solution species. Candidate polymers for EOR use fall into two classes of molecular

501 structure (Figure 2). The synthetic polymers (polyacrylamide, poly(viny1Most biopolymers have pyrrolidone)) can be modelled as flexible chains. structures approximating more closely to rigid rods, at least near ambient temperature; for xanthan there is evidence (5) of a structural transition at temperatures above 60 O C .

>-<

Polymer -polymer interaction

Polymer -solvent interaction

Helical rod

1 Figure 2.

Polymer structure in solution.

Flexible chain polymer molecules pervade m c h larger volumes in solution than the volume of the polymer molecule itself. Within that pervaded volume, It most of the solvent molecules are close to several polymer chain se@ments. turns out that most of the solvent within that pervaded volume is incapable of The hydrodynamic properties of dilute solutions independent hydrodynamic flow. of flexible chain molecules can be treated (6) as those of suspensions of The effective volume of those spheres, consisting largely of bound solvent. spheres, for a monodisperse polymer of molar mass M in solution of concentration c and with an effective volume fraction 4 is Vh =

W N c

For a suspension of spheres, the volume where No is Avogadro's constant. fraction is related to viscosity by

n

= no(l + 2.5++ higher terms)

where n is the solvent viscosity. [n] can%e related to Vh

The measurable limiting viscosity number

502 so that for the low concentrations used in ESZ determinations, the volume of the equivalent sphere can be taken as

1 Real polymer samples are heterogeneous in molar mass and therefore in hydrodynamic volume. For a typical anionic polyacrylamide (molar mass 4000 kg/mol; 20% hydrolysed) the average hydrodynamic radius calculated from Vh is some 80 nm in 0 . 5 M NaC1. There is evidence (7) that much larger molecular aggregates may be present. For a xanthan sample purified by centrifugation, the hydrodynamic properties are consistent (8) with rigid rod molecules, of length some 0.6 pm and diameter some 2 nm. Again there is evidence of much larger solution species (9), particularly in unpurified comnercial material (10). Polymer 'particles' in the ESZ Passage of a solution of a flexible chain polymer through the ESZ aperture corresponds to the passage of spheres of solvent of much reduced mobility. Such a 'particle' will be electrolytically conducting, but the resistance should be higher than that of the same volume of solvent. The salt-containing polymer gels used in electrochemistry to provide electrolytic conduction with minimal It follows that the ESZ signal of a ion transport are a relevant analogy. dissolved flexible chain polymer molecule will be smaller than that of an insulating particle, such as a polymer in latex suspension, of the same size. Biopolymer molecules in rigid rod conformation include smaller quantities of solvent, so that the discrepancy may be smallegbut in general dissolved polymer is to some extent 'transparent' in an ESZ. There is also the question of molecular dynamics. Brownian motion causes the segment density, molecular shape and effective size of a flexible chain molecule to change continuously. Polymer properties are described in terms of average molecular dimensions, where the averaging is both over time for a given molecule and over the population of molecules of given chain length. Those fluctuations will be reflected in dispersion of the ESZ signals; an ideal polymer sample containing only onemolecular species should give signals over a discrete range of apparent size, with a peak at the pulse height corresponding to the most probable size.

EXPERIMENTAL Materials Polyacrylamide fractions were produced by the controlled addition of ethanol to dilute (0.007 g ~ m - ~solutions ) of comaercial polymers, non-ionic and anionic, in water. Fractions were characterized by capillary viscometry (FICA Autoviscometer) and by light-scattering photometry (chrometix larangle Biophotometer) in the solvent (0.01g/cm3 NaCl) used for the ESZ experiments. polymers were gifts from Dr I G Meldrum (BP Research, Sunbury) and Dr I W Sutherland (University of Edinburgh). Polymer solutions were prepared in 'Isoton' a proprietary (Coulter Electronics) saline solution, (ca 0.01g/cm3) supplied for haemacytometry. The effect of electrolyte concentration was studied by using more concentrated saline solution (0.04 g/cm3) filtered through Millipore membranes of pore size 0.1 pm.

503 ESZ measurement requires that only single particles traverse the aperture. The maximum counting rate of the instrument used limits the suspension concentration to 107-108 particles/cm3. For a molar mass of lo4 kglmol, that number concentration corresponds to a mass concentration of 10-10-10’9g/cm3. Solutions within that concentration range were prepared by successive volumetric dilution of parent solutions of polymers of concentration ca 10-3g/cm3; those parent solutions were prepared gravimetrically and with gentle magnetic stirring overnight. ESZ technique The size range of insulating particles to which the ESZ method is conventionally applied extends down to only 1 Um; smaller signals become obscured by background noise. In order to extend the useful range, detailed attention was given to earthing and shielding. The instrument [Coulter ZB] was housed in a Faraday cage, and the mains supply was routed through an isolating transformer. With these precautions the background count was acceptably low at a pulse A height corresponding to an insulating particle of diameter ca 0.4 Irm. polymer latex suspension of that diameter was used to calibrate the size scale. The aperture was of nominal diameter 30 pm and the volume of liquid passed through was constant at approximately 0.05 cm3. Polymer solutions were analysed in the manual mode in order to avoid Each analysis possible artifacts of automatic subdivision of the size range. With the polymer solutions counts were was preceded by a background count. made by reducing the size threshold stepwise throughout the range for which the Duplicate polymer count exceeded the background by a factor of ten or more. determinations were made in all cases; counts were reproducible to within a few per cent except at the extremes of the range. RESULTS AND DISCUSSION ESZ analyses of the polymer solutions are presented as integral distributions of the number of particles per gram of polymer of apparent size greater than the abscissa values, which relate to the calibration with insulating particles. Smooth curves were drawn through 20 points representing counts throughout the size range. Since ESZ transparency is presumably a function of polymer-solvent interaction, and therefore of the chemical structure of the polymer, comparisons are made only between results for polymers of similar s tructure. ESZ response versus molecular properties;

polyacrylamide

The conjecture that the ESZ response of polymer samples of similar chemical structure should correlate with hydrodynamic volume as defined by Four equation 1 was tested in experiments with seven polyacrylamide fractions. fractions of nonionic polymer and three of anionic polymer were characterized by viscometry and light-scattering photometry; the mass-average molar masses A monodisperse sample of molar mass ranged from 3400 to 18200 kg/mol. loo00 kg/mol contains 6 x 10l6 particles/gram. In the ESZ experiments [Figures 3 and 41 the number of particles per gram sensed before the signal to background ratio fell below 10 never exceeded It follows that only a few percent of the particles present were sensed, even allowing for the polydispersity of the fractions. In this estimate no account was taken of possible adsorption of polymer on the glass surfaces. The shape of the measured distributions gave further evidence that only a fraction of the solution species present were detectable; thus most of the curves were rising steeply at the lowest accessible size.

504

The hydrodynamic volumes of the fractions calculated from viscometry and light-scattering photometry are average values and refer approximately to the most abundant species present, which are clearly not detected by the ESZ method, even for the fraction of largest molecular size. The experimental results do not provide, therefore, a critical test of the supposed correlation with hydrodynamic volume. There would be a correlation with the small part of the distribution measurable only if the complete size distributions of the fractions chanced to be of similar shape. Figure 3 shows that larger particles were detectable for the nonionic fraction of largest average hydrodynamic volume throughout the ESZ size range.

.

Non- ionic polyocrylomides

Mm

___---_

----.-

-

I

0.4

Figure 3.

1 0.6

kglmol

pm3

18200

0.031

16700

0.027

17200

0.028

8380

0.0081

1 1 I 1.0 1.2 1.4 Apparent diometer I pm I

0.8

"h

1 1.6

I

1.8

ESZ response of nonionic polyacrylamide fractions

For the anionic fractions (Figure 4) the relation is less clear, but in the ESZ size range below 0.6 pm the recorded distributions follow the order of average hydrodynamic volume. The effect of added electrolyte is also consistent with a relation between the ESZ response and hydrodynamic volume. In more concentrated electrolyte (0.04 g/cm3) results for non-ionic polyacrylamides were little changed, but the number of particles sensed for an anionic polymer fell sharply. It is well known (11) that the radius of gyration and hydrodynamic radius of anionic polyacrylamides fall with increasing electrolyte concentration because the effect of repulsion between carboxyl groups along the chain is reduced.

--

-,---

505 -.I

-

T.

- 1-

-.-r

--

7'

Anionic polyacrylomides

-

!

Mm "h -

\,

kglmol

- 3400 ---- 17700 -.- -..-

11600

pm3

0.0011

0.0072 O.OOL2

\..

Apparent diameter1pm

Figure 4.

ESZ response of anionic polyacrylamide fractions

In summary, the results for well-characterized polyacrylamides are not inconsistent with hydrodynamic volume as the molecular characteristic determining the ESZ response. Only qualitative evidence can be offered since the fraction of particles sensed is small, even for fractions of large molar mass. The ESZ technique in the conventional form employed here is sensitive only to the largest particles present, which may well be molecular aggregates. It is worth noting that such aggregates are thought (12) (13) to be important in determining properties of water-soluble polymers. ESZ response versus rheological properties; biopolymers

The relation between ESZ response and molecular size is more difficult to investigate with biopolymers since fractions of different molecular size but similar chemical structure are not readily accessible, at least at high molar mass. Attempts were made to fractionate xanthan by controlled orecipitation above bi) "C aud by prcparnt ivt. I Iwrilwnticrn c:lii-(iiii.itc,gr;ilIhy h u t without success. Inscead the ESZ response of whole biopolymers was related to rheological properties relevant to use in EOR. Such information was available for a series of experimental biopolymers prepared under contract (OT/F/443) to the Department of Energy at the University of Edinburgh; a commercial xanthan (Keltrol) was included for comparison. Since their thermal stability (14) makes scleroglucans possible candidates for use under North Sea reservoir conditions, a separate comparison was made between three samples. c i a

506 Table 1.

Rheological properties of biopolymers at 3 Screen factor 1 volume 10 volumes

sample

at IS-'

Keltrol

2630

7824

2290

9.64

1.15

<790

9.4

1096

26.5

g/cm3 in salt water

x

Size of filter/vm that retains

20

3

11.28

0.3

1.5

1.8

0.22

7.38

9.36

0.45-0.3

I

ESZ results for biopolymers (Figure 5) were consistent with those of polyacrylamides in that only a small fraction of the particles present were sensed, assuming a plausible molar mass (5000 kg/mol). Similarly the integral distribution of apparent size did not reach a limiting lower plateau. Within those limitations, however, there were clear correlations with properties of significance for EOR use; those pro erties were measured at the University of Edinburgh at a concentration (0.003g/cm ) much higher than that used in ESZ analysis.

!

More large particles were detected (Figure 5) in solutions of the commercial xanthan, Keltrol, than for the remaining polymers; of the samples tested only The viscosity of Keltrol fails to pass in solution through a 1 vm filter.

r

t:.

Biopolymerr

-neltrol

...._. Research

\a*,

' *

\

wrmplc 7824. uncentriluged (upprr) and c.ntri1ug.d (lower) Research rompl. 1.15

.*a,

bscarch romplc 9.4

--. -. I

Figure 5 .

I

I

I

1

ESZ response of biopolymers

5 07

solutions at a shear rate of Is-' follaws the order of the number of particles of apparent size L 1 um, but does not follow that of the number of apparent size 2 0.4 um. The screen factor, after 1 and 10 volumes, follows the former order. Figure 5 also includes the effect of centrifugation (40 krpm) upon the ESZ response of one sample (7824); there was no significant change at apparent sizes below 0.7 pm, but a clear decrease in count above that size. Since centrifugation selectively removes larger particles, the result links directly the ESZ signal to size in solution. Three scleroglucans were available for test (Figure 6); Actigum CSll and L21 were comnercial materials and research sample E was from the University of We have no rheological data for the set, but on the basis of the Edinburgh. correlations established above (Figure 5) one might predict that the screen factor and viscosity at 1s-l would be higher for L21 than both CSll and scleroglucan E, and that the last two would have similar properties.

As with the synthetic polymers studied, the ESZ response of biopolymers In many biopolymer solureflects the few largest solution species present. The tions those species are deformable molecular aggregates termed microgel. correlation between the ESZ response at a concentration such that interparticle interactions can be neglected and rheological properties of the semi-dilute regime in which interparticle interaction is strong suggests that molecular aggregates can affect significantly rheological properties under EOR conditions.

\

Scleroglucanr

-L21

-.- CSll .----Rmearch

sample

0 ApporerM dmrn.1ulpm

Figure 6.

ESZ response of scleroglucans

508 Microgel is also significant (10) (11) in determining injectivity of polymer solutions in porous media. Microgel is sufficiently deformable to pass through small pores at the high shear rate near the injection point, but can block pores A recently suggested (15) at lower shear rates further into the substrate. method for estimating microgel is based upon filtration at a very low shear rate. The ESZ approach has promise as a more rapid and convenient technique. Future developments With some modifications of the very conventional apparatus used, the ESZ technique could well yield more information of relevance to polymer use in EOR. Controlled variation of flow rate through the orifice is desirable; the shear rate in the conventional apparatus is high (- 103s-') and polymer solution species must be deformed in the orifice. The effect of shear rate upon pulse size would Since most of the help to characterize polymer deformation in a shear field. solution species are below the accessible size range in the present work, it is superficially attractive to reduce the aperture rize in order to enhance the signal. The true sizes are larger than the size scale calibrated with insulating particles, however, and there may be advantage in working at slow flow rates Again the in wide apertures and with different electrolyte concentrations. effect of using 'hydrodynamic focussing' to ensure passage through the centre of the orifice where the electrical field is synrmetrical needs to be investigated. S m Y

When used in the mode conventional for particle sizing, but with improved earthing and shielding, the ESZ technique can sense the largest solution species of water-soluble polymers. The response is related to the hydrodynamic volume of polacrylamides, and to rheological properties of biopolymers. The method has promise in monitoring solutions of candidate EOR polymers for microgel and, with some instrumental modification, in more fundamental studies of polymer solutions.

NOMENCLATURE C

M

"lm NO

Vh I) 10

concentration (mass/volume) of polymer molar mass mass-average molar mass Avogadro's constant equivalent hydrodynamic volume of a polymer molecule viscosity of solution viscosity of solvent

[I)] limiting viscosity number 4

volume fraction of polymer in solution ACKNOWLEDGEMENTS

Dr I.W. Sutherland (University of Edinburgh) kindly provided research samples Dr 1.GMeldrum (BP Research) presented some coamercial and rheological data. samples. Molar mass characterization and fractionation was the work of M.A.Francis, and Mrs C.M.LAtkinson carried out the ESZ determinations. The work was carried out under contract (OT/F/524) to the Department of Energy.

509

REFERENCES 1.

SMITH, F.W.; "The Behaviour of Partially Hydrolysed Polyacrylamide Solutions in Porous Media" J. Pet. Tech. (Feb 1970), 148-156

2.

SZABO, M.T.; "Molecular and Microscopic Interpretation of the Flow of Hydrolyzed Polyacrylamide Solution Through Porous Media" SPE 4028, presented at SPE 47th Fall Conference, San Antonio (1972) KLEIN, J and CONRAD, K-D. ; "Characterization of Poly(acry1amide) in Solution". Makromol. Chem. (1980), 181,227-240 UNSAL, E., DUDA, J.L. and KLAUS, E.; "Comparison of Solution Properties of Mobility Control Polymers" in JOHANSEN, R.L. and BERG, R. (Eds) "Chemistry of Oil Recovery" ACS Washington (19781, 141-170

3.

4.

5.

HOLZWARTH, G.; "Conformation of the Extracellular Polysaccharide of Xanthanomae campestrid'. Biochemistry (1976) 4333-4339

6.

TANFORD, C.; "Physical Chemistry of Macromolecules". Wiley (1961) 333-344 'Caracterisation BOYADJIAN, R., SEYTRE, G., BERTICAT, P. and VALLET, G. physico-chimique de Polyacrylamides utilises c m e Agents Floculants'. Euro. Polym. J. (1975) 11 401-407 "Polyelectrolyte Behaviour of a Polysaccharide RINAUW, M. and MILAS, M. from Xanthanomas canpestris" Biopolymers (1978) 17 2663-2678

7.

8.

9.

SOUTHWICK, J.G., LEE, H., JAMIESON, A.M. and BLACKWELL, J. "Self-association of Xanthan in Aqueous Solvent Systems" Carbohydrate Res. (1980) 2 287-295

10.

KOHLER, N. and CHAWETEAU, G.; "Polysaccharide Plugging Behaviour in Porous Media: Preferential Use of Fermentation Broth". SPE 7425. Paper presented at SPE 53rd Fall Conference, Houston (1978) 'Water-soluble Polymers in MACWILLIAMS, D.C., ROGERS,'J.H. and WEST, T.J.; Petroleum Recovery" in BIKALES, N.M. (Ed). "Water-soluble Polymers" Plenum (1973) 106-124 "Influence of Molecular Aggregates on Drag DUNLOP, E.H. and COX, L.R.; Phys. Fluids (1977) 20 S203-S213 Reduction".

11.

12. 13. 14. 15.

"On the Real Molecular Weight of Polyethylene Oxide of High WOLFF, C. Canad. J. Chem. Eng. (1980) 2 634-636 Molecular Weight in Water". DAVISON, P. and MENTZER, E.; "Polymer Flooding in North Sea Oil Reservoirs" Paper presented at SPE 55th Fall Conference Dallas (1980) SPE 9030. CHAWETEAU, G and KOHLER, N.; "Influence of Microgels in Xanthan SPE 9295 Polysaccharide Solutions on their Flow through Porous Media". Paper presented at SPE 55th Fall Conference, Dallas (1980)

This Page Intentionally Left Blank

551

EXPERIMENTAL TECHNIQUES

VISUALISATION OF THE BEHAVIOUR OF EOR REAGENTS IN DISPLACEMENTS IN POROUS MEDIA ERIC G. MAHERS, ROBERT J. WRIGHT, RICHARD A. DAWE Department of Mineral Resources Engineering, Imperial College,London SW7 2BP

ABSTRACT Micromodels have been successfully employed to observe directly displacement processes, and have assisted in understanding the physics of the complex fluid phenomena involved in Enhanced Oil Recovery. Both miscible and surfactant displacement sequences are reported here. The models have been produced by etching the pores into nylon, from which replicas in epoxy resin have been made. Computer graphics and microfilm facilities have been used to produce accurately drafted network photomasks. INTRODUCTION The mathematical description and prediction of fluid flow behaviour has been much assisted by direct observation. Although this is not possible in real porous media, models can be made in transparent materials which permit direct observations within the pores of fluid interactions, displacements and entrapments. These models may be monolayer packs of glass beads, as used by Chatenever (1) and Egbogah ( 2 ) , or two dimensional etched networks. Mattax and Kyte ( 3 ) , Michaels et a1 (4), Davis et a1 (5) and Wardlaw (6) have used etched glass models. Mattax's network comprised of a rectangular array of straight channels of similar width but varying length. He used this model to study the mechanism of water flooding, with regard to relative permeabilities and wettability. He described the distribution of the fluids and the effect of wettability on areal sweep efficiency, but did not extend this work to cover EOR mechanisms. Michaels et a1 used the same micromodel to analyse how changes in surface wetting, by the injection of aqueous hexylamine, might mobilise entrapped oil. They concluded that the observed stimulation of oil production was the result of transient changes in Davis et a1 made use of a commercial overlay shading medium to wettability. produce an irregular, random design. They used this model to qualitatively demonstrate the displacement of oil and water by the microemulsions used in A film is available from Marathon Oil the various Maraflood processes. Company showing the displacements of oil and water by micellar solutions specially formulated for selected U.S. crude?. Wardlaw employed a heterogeneous, rectangular network with varying pore width. He describes the effect of pore throat size ratio on displacement efficiency, and drainage-imbibition cycles. Although he recognised the importance of pore connectivity and throat sizes on displacement mechanisms, he had not fully explored these factors in his networks.

512 The pores produced by etching into glass have been V-shaped in cross section, larger in width than those found in common reservoir rocks, usually very shallow, and with high surface roughness. This type of channel topology does not correctly scale capillary pressure effects. Special network patterns of realistic pore sizes have not, as far as we know, been incorporated into any model designs to study experimentally their effects on displacement phenomena. The objective of this work is to understand the microscopic mechanics of low interfacial tension and miscible enhanced oil recovery processes by using micromodels. In our experiments we are exploring: Pore network geometry and its effect on capillary pressure, displacement and entrapment, by varying pore shapes and throat sizes, and the connectivity of the pores, which, with the size distribution, defines the degree of freedom of route. The scale and type of network heterogeneity, and the mechanisms by which areas of bypassed oil can be contacted and mobilised through diffusion or reduced interfacial tension. Diffusion and mass transfer phenomena and the phase behaviour of ternary systems. Various alcohols can be used to simulate the different types of miscibility; 1.e. preferentially oil or water soluble, and first or multiple contact.

CONCEPT OF THE MICROMODEL The micromodel networks to be described are two-dimensional and it is therefore pertinent to discuss first the validity of results from these experiments. Any two pores within a feal porous medium may be connected through a number of routes in three-dimensional space. If these pathways were rotated about a line between these two pores such that they lay wholly within a plane, a high porosity, two dimensional network would evolve. Although two-dimensional networks cannot allow bicontinua in the manner that three-dimensional models can, where the pathways can intertwine ( e.g. in the manner of a double helix), simultaneous parallel flow is still permitted. This concept of high porosity, high coordination number networks lies at the heart of our micromodel designs.

NETWORK DESIGN

Ae already indicated, most networks previously employed have been of random or simple design. In our early work a photoreduced ‘Letratone’ texture was used to obtain networks which were homogeneous overall, but had variable pore structures on the microscopic scale. The pore ‘necks’ were of 10-30 microns in width with the pore ‘bodies’ being 50 to 100 microns. Figure 1 shows the etched network used. In an attempt to simulate more closely the heterogeneous microstructure of natural media, we have developed models with layered structures, figures 2 through 4, and some with additional serial variations, such as shown in figure 5. The latter type, with their high degrees of freedom, were designed to yield fairly realistic, and approximately predictable, relative permeability and capillary pressure functions.

A doublet network, similar to figure 6, was designed to demonstrate the effects of two pore sizes in parallel. Initially, it was drafted by hand and then photographed to create the photomask for etching.

513 Accurately drafted networks have now been produced using computer graphics and microfilm facilities; this method also enables the pore parameters to be easily varied. A unit cell is composed which is repeated to build up the model. Figures 6 through 9 have been produced in this manner; where the pores are in white. The doublet network of figure 7 has abrupt changes in pore width, which contrast with the 45 degree divergence in the earlier design ( figure 6). Figure 8 illustrates the ability to vary the pore parameters. Although figure 9 is a regular array, an attempt has been made to create a smooth variation in channel width, with the walls comprised of arcs of circles. The pore throat to body ratio is 1:5. Development of this type of network is under way to investigate the effects of channel angularity.

Figure 1

Letratone etched network

Figure 2 Parallel channel design

514

Figure 3 Parallel channel model with obstructions

Figure 4 Network with high permeability central streak

Figure 5a Parallel design with additional serial variations

515

Figure 5b

6a

Serial model showing inlet ports

6b

Figure 6 Pore doublet networks (computer drawn)

Figure 7

Doublet network with abrupt pore necks (computer d r a m )

516

Figure 8 Variation of pore parameters

Figure 9 Regular network of curved channels (computer drawn)

CONSTRUCTION OF THE MICROMODEL The micromodels are produced by etching the pores into nylon film. This is a process commonly used for making printing plates, e.g. using BASF Nyloprint, and has also been used by Bonnet and Lenormand (7). Such photoetching methods enable greater control over pore geometry than chemical etching, and can hazards of easily be done in the laboratory, without involving the hydrofluoric acid.

517 Detailed procedure The procedure is illustrated in figure 10. The photographic negative of the network is placed over the nylon and placed under an ultra violet light source. An exposure time of about one hour was found to be adequate when the source (Philips HPW 125W F/70/2) was 200 mm from the negative, with a 10 mm diameter aperture placed midway in between. For deep pores it appears to be necessary to have a small air gap between the negative and the nylon, but the reason for this is not yet fully understood. The unexposed regions are then etched away by washing in a mixture of 90% (by volume) methylated spirits and 10% water at 35OC, for about 30 minutes. A turbulent stream of liquid 1s maintained across the surface of the nylon by circulation through a centrifugal pump. When etching is complete, the model is dried with warm air and exposed to ultra violet radiation for a further five to ten minutes to set the pore surfaces.

Ultra Violet Light

, q '

Negative

(a)

R

Air Gap Photosensitive Nylon Rigid Backing Plate

(b)

1-1

((1

1-1

Unexposcd regions etched away. and then re-exposed to ultra violet.

-Perspex

.-.

Plate

Resin I

Figure 10 Etching procedure

In our early work we performed flow experiments directly with the nylon etchings, however these were found to suffer from significant sorption of dyes and solvents. Consequently we used the etchings as bases for preparing silicone'rubber moulds (Hopkin and William Sllastic 3110 RTV and Dow Corning Catalyst l), from which rigid, non-absorbent epoxy resin replicas are cast, which accurately reproduce the microstructure of'the nylon model. Araldite MY753, MY951 hardener, is a suitable resin for this purpose. We now have a relief structure on which a top needs to be secured, to form a two-dimensional pore network. To preserve uniform wettability, epoxy resin film has been produced in the laboratory, which can be sealed onto the epoxy cast by one of several methods:

518 1.

The pores are filled with wax and then resin poured on top. The wax was removed by heating the model and injecting hot fluid, e.g. kerosene. This is a delicate operation with which we have had only limited success, however a similar method was reported by Bonnet and Lenormand (7).

2.

The resin film is sealed on by external pressure, using screw clamps as shown in figure 11. This allows the model to be dismantled and cleaned easily. However, the seal is not always perfect and the film tends to depress into the pores, resulting in an unknown, and variable pore depth. The seal can be improved by placing the assembled model in an oven at 65OC for one or two hours. This creates a weak adhesive seal at resin-resin contacts through increased surface interaction and plastic deformation.

/

6 mm Perspex Plates \

Resin Costing Resin Film Cushion

Figure 11

3.

Micromodel seal by external pressure

The best method discovered to date is to coat the perimeter of the model with epoxy, and gently press the resin film on top. This is to prevent leakage while a solution of resin in methylated spirits is injected into the pores. After two to three hours a thin, wetting resin film will have been deposited. Injection of pure methylated spirits removes any excess resin leaving a bonding film in the tiny crevices; especially between the top of the pore walls and the sealing film. This method maintains constant pore geometry over a series of experiments, and allows short working distance microscope objectives to be used. Surface flatness is improved by using a thick resin film or block.

TOPOLOGY OF THE MICROMODEL PORES Interfacial curvature, and therefore capillary pressure, is governed by the In pore shape (the angle of divergence), contact angle and pore dimensions. order to ensure that the capillary pressure and viscous resistance are controlled by the dimensions within the plane of the network, it is necessary for the depth of the pores to be constant and of the same order as the width. For widths greater than 50 microns, the depth tends to be constant at about 50 microns. Controlled pore widths at least as small as 20 microns are possible. Figure 12 shows the square shape of the pores in contrast to the V-shape of glass etchings.

5 19

Figure 12

Shape of the pores of a resin cast of the early doublet model

DISPLACEMENT STUDIES Displacements within the micromodels were observed through a microscope and recorded in colour on videotape or still photographs. The floods were carried out at low flow rates of less than 50 mm/hr (four ft/day) by means of a variable rate syringe pump. The fluids were introduced into the models through the valve arrangement shown in figure 13. This eliminated dispersion in the entry tube, thereby ensuring injection of uncontaminated fluid.

Inlet 1

Inlet 2

Bypass

I Figure 13

Valve arrangement for the injection of fluids into the micromodels

5 20 Use of dyes Dyes were used to aid the visualisation of the fluids. Alternate injection of dyed and undyed, but otherwise identical, fluids highlighted the flow pathways, clearly showing the stagnant regions (figure 18). The distribution of this stagnant fluid is an important factor influencing the efficiency of an EOR flood. The water-soluble dyes used in these experiments were Methylene Blue, Nigrosine Black and ICI Lissamines. The oils were dyed with ICI Waxolines. These dyes are, however, surface-active and their effect on wettability and interfacial phenomena should be taken into account when analysing results. Mobilisation of oil The mechanics of oil ganglia mobilisation in straight capillaries of varying Under these cross sectional area have been described by Arriola et a1 (8.9). conditions an EOR chemical can contact the downstream interface only through a wetting film surrounding the ganglion, 1.e. a contact angle of 180 degrees measured through the globule. In a two-dimensional network this contact can be achieved through neighbouring pores. These parallel routes also affect the viscous pressure drop across the ganglion, thereby determining the reduction in interfacial tension required to mobilise the drop immiscibly. This discrepancy between single pore and network studies has been discussed by Stegemeier ( l o ) , and is effectively demonstrated by the pore doublet models. Simulation of miscible processes Alcohols were employed to simulate miscible displacements. The wide variety of alcohols available permits a spectrum of single and multiple contact miscible systems to be studied. For instance, low molecular weight alcohols can be used to model carbon dioxide injection. The partitioning of carbon dioxide between the aqueous and oleic phases is a function of pressure, and is reflected in the choice of ternary systems. This has been discussed by Stegemeier (lo), Totonji and Farouq All (111, and Orr and Taber (12). Examples of displacement processes Figures 14 through 18 illustrate fluid displacement and distribution in the Letratone and doublet (hand drafted) models. Red and blue dyes were used in these experiments which, although clearly distinguishable in the original colour slides, appear as only slightly differing tones in these photographs. The interfaces are, however, well defined through light scattering at refractive index discontinuities. We are also investigating techniques to quantitatively study fluid concentrations as functions of both position and time. Absorption of light by the dyes can be exploited to show dispersion and diffusion. It shocld be noted that because the diffusion and mass transfer of the dyes may be different to those of the fluids, and that the dyes may suffer dispersion through adsorption within the system, corrections need to be made to any measurements. It is therefore more desirable to utilise methods which exploit the refractive index properties of the liquids, e.g. interferometry. Dynamic recordings of displacement sequences have been made on Sony U-matic videotape, and are held by the Professor of Petroleum Engineering, Imperial College. In the following photographs flow is from left to right.

521

Figure 14 High tension, immiscible displacement of non-wetting fluid (dark tone) by a wetting phase of equal vicosity, in the Letratone model.

100 pm

Figure 15

Residual non-wetting phase (dark areas) behind the flood figure 14.

front

of

522

Figure 16

Displacement of water by Carnation oil, of viscosity 0.019 Pa.8, in the doublet network. The oil clearly preferred the large pores and entrapped the water within the smaller channels.

Figure 17

Illustration of a Haine's jump as the oil entered a large pore. The fluid interface moved during the exposure time.

523 1mm

i -1

/ Water

\

011

\I

Figure 18a

Water

Oil

- I

I\

1 mm

Water

Oil

Figure 18b

Figure 18 Doublet model, initially fully saturated with Carnation o i l , which was partially displaced by water, followed by a dyed oil flood. Subsequent injection of undyed oil highlighted the stagnant regions.

524

Quantitative results The Letratone micromodels were used to study low tension displacements. As well as purely visual results, quantitative measurements were obtained from photographs in conjunction with flow rate data; viscosity and interfacial tension parameters were determined separately. Figure 19 shows the observed residual oil (as a percentage of the total pore volume) as a function of Capillary Number, for both high and low tension (petroleum sulphonate / kerosene) displacements. The Capillary Number was increased in steps by adjustment of the flow rate, and the remaining volume of oil measured. Some lower residuals were produced by Capillary Number 'shock' (sudden reduction in interfacial tension) at a surfactant displacement front, where microemulsions were often formed.

High tenvm Low tension

0 0

40

%

30

I-

0

O

0

0

0

0

0

0

20

O

D

0

10

0

-5

-6

-3

-2

Figure 19 Residual oil saturation as a function of Capillary Number, Letratone model

in

the

Figure 20 illustrates the measured residual ganglion length distributions (taken in the mean flow direction). Clearly, blobs of oil longer than 500 microns are mobilised by increasing the Capillary Number within this range, while the atable globules at high Capillary Number are of the same order of size as the individual pores.

525 Fraction o f

Total NO

(9

0.6

0 5

........

1 x10

-5

----- I x10-L - 6 1 1 0- 3

0.-

..... . . . . . . .

0.3

1

0.2

J

............

0.1

....................... 0

530

1933

1500

2330

Ganglion Length ipml

Figure 20

Size distributions of residual values of Capillary Number.

oil

ganglia for three different

CONCLUSIONS Micromodelling techniques have been developed to gain insight into the physics of reservoir miscible and surfactant displacement processes by observations of alcohol and low interfacial tension systems at ambient temperature and pressure. FUTURE WORK We intend to develop the design of networks to relate micromodel displacement results to real reservoir rocks through pore size distribution and connectivity

.

Holographic interferometry is currently being employed to investigate the role that diffusion can play in the recovery of oil entrapped by small scale heterogeneities. Techniques for producing castings in glass of the nylon examined to create more strongly water-wet models.

etchings

are

being

ACKNOWLEDGEMENT The authors would like to thank the Department of Energy and the Science and Engineering Research Council for their support of this research, Professor Colin Wall for his encouragement, and Mr Martin Hughes for technical advice. NOMENCLATURE

v

= superficial (average interstitial) velocity, mls

y

= interfacial tension, N/m

-

= viscosity, Pa.s ,S residual oil saturation The Capillary Number is defined by: Nc= p V 1 y

526

REFERENCES 1.

CHATENEVER, A., and CALHOUN, J.C.; "Visual Examinations of Fluid Behaviour in Porous Media Part 1". Trans., AIME (1952) 195, 149-156

2.

EGBOGAH, E.O., and DAWE, R.A.; "Microvisual Studies of Size Distribution of Oil Droplets in Porous Media", Bull. Can. Pet. Geol. (June 1980) 2. 200-210

3.

MATTAX, C.C., and KYTE, J.R.; "Ever See a Water Flood?", Oil and Gas Journal (Oct 1961) 2, 115-128

4.

MICHAELS, A.S., STANCELL, A., and PORTER, M.C.; "Effect of Chromatographic Transpart in Hexylamine on Displacement of Oil by Water in Porous Media", SOC. Pet. Eng. J. (Sept 1964) 4, 231-239; Trans., AIME, 231

-

-

5.

DAVIS, J.A., and JONES, S.C.; "Displacement Mechanisms of Micellar Solutions", J. Pet. Tech. (Dec 1968) 3, 1415-1428; Trans., AIME, 243

6.

WARDLAW, N.C.; "The Effects of Pore Stucture on Displacement Efficiency in Reservoir Rocks and in Glass Micromodels", SPE/DOE 1 s t Joint Symp. on EOR, Tulsa, Olklahoma (April 1980) 346-352; SPE paper 8843

7.

BONNET, J., and LENORMAND, R.; "Constructing Micromodels for the Study of Multiphase Flow in Porous Media", Revue de L'Inst. Franc. du Pet. (1977) 42, 477-480

8.

ARRIOLA, A., WILLHITE, G.P., and GREEN, D.W.; "Trapping of Oil Drops in a Noncircular Pore Throat", SPE paper 9404, SPE Annual Fall Meeting, Dallas (Sept 1980)

9.

ARRIOLA, A., WILLHITE, G.P.. and GREEN, D.W.; "Mobilization of an Oil Drop Trapped in a Noncircular Pore Throat upon Contact with Surfactants", SPE paper 9405, SPE Annual Fall Meeting, Dallas (Sept 1980) #

10.

STEGEMEIER, G.L.; "Mechanisms of Entrapment and Mobilization of Oil in Porous media", Improved Oil Recovery by Surfactant and Polymer Flooding, ed. Shah, D.O., and Schechter, R.S., Academic Press, Inc., New York (1977) 55-91; 81st Nat. Meeting AICHE, Kansas City (April 1976)

11.

TOTONJI, A.H.M., and PAROUQ ALI, S.M.; "Solvent Flooding Displacement Efficiency in Relation to Ternary Phase Behaviour", SOC. Pet. Eng.J. (April 1972) 12, 89-95

12.

ORR, F.M., and TABER, J.J.; "Displacements of Oil by Carbon Dioxide", Annual Report, U.S. DOE/MC/03260-4 (1980)

527

THERMAL RECOVERY METHODS

THE INTERPLAY BETWEEN RESEARCH AND FIELD OPERATIONS IN THE DEVELOPMENT OF THERMAL RECOVERY METHODS J. OFFERINCA, R. BARTHEL and J. WEIJDEMA

KoninWijke Shell Explomtive en Produktie Labomtorium, Rijswijk, The Netherlands (Shell Research B. V.)

ABSTRACT The role of research in the development of thermal recovery processes is discussed, viz: steam drive, steam soak, hot-water drive and in-situ combustion. The importance of feedback from field experience to research is pointed out. Five periods are distinguished: 1. Early and mid-fifties when mainly laboratory work was carried out. 2. Late fifties and early sixties when the processes were tested in field pilot projects. 3. Mid-sixties to early seventies when large steam-soak projects were started and research experiments were carried out in large physical models. 4. Mid-seventies to early eighties when the number of steam projects has been increasing fast. The design of these projects is being carried out with the aid of nmerical simulators. 5. The present, when new techniques and applications for thermal methods are under investigation. It appears from this historical survey that in particular the interplay between research and the field is stimulating for new developments.

INTRODUCTION Present worldwide recovery of oil by EOR methods is estimated to amount to some 600 000 bbl/d. Nore than 80 per cent of this production is by thermal methods of which steam drive and steam soak take the major part. Usually thermal methods have been applied so far in reservoirs containing medium to heavy oil or tar. Thermal methods are the oldest EOR methods. They have been developed during the past thirty years, partly in the laboratory and partly in the field. The object of this paper is to show where research and field operations have stimulated each other in developing these processes or where, occasionally, one or the other came to a dead end. The paper is therefore presented in the form of a historical review. It is unavoidable that some of the material of older reviews such as, for instance, by RAMEY(1) (1967) and RARMSEN(2) (1971) on steam and hot-water injection and by DIETZ(3) (1970) on in-situ combustion will be repeated. However, we believe it fulfils a useful purpose. Firstly, because these reviews are now 10-14 years old and thus only cover half of the period of interest and, secondly, because we tend much more to discuss in retrospect the role of research.

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If we sometimes seem to overemphasise Shell's role in the history of thermal recovery, this is not done intentionally but is mainly due to easier accessibility to reports and to the people who made part of this history. We are aware of the fact that similar developments to those within Shell research have also taken place in other companies. If this explanation is not fully satisfactory, it may even stimulate some petroleum engineer with a vocation for historian to write an "objective" history on the development of thermal processes. In the following we do not present descriptions of the basic thermal processes. For those who are not familiar with these ample literature references are given in this paper.

EARLY AND MID-FIFTIES

In an internal Shell Report of 1951 entitled "Higher ultimate recovery by heating the reservoir", it is stated that: "The idea of heating an oil reservoir in order to decrease viscosity and consequently increase recovery is not new. Already in 1917 .I1 Then follows a long list of papers and patents containing suggestions for heating methods. A considerable number of these ideas date from before the second world war(1). Even some early field applications are mentioned. 'In retrospect, however, these tests should be considered to be isolated events having no followup. The actual rise of the thermal recovery methods did not occur before the early fifties. Prom then on, a continuous flow of papers on research investigations and field experiences has been maintained, which has not yet stopped. It is interesting to note that in the internal Shell report mentioned above (part of which was later published (4)) some exotic heating methods were suggested which also nowadays regularly appear in the literature, such as application of sonic waves, electromagnetic radiation, electric conduction between electrodes in wells, injection of oxygen (instead of air) and even letting down an atomic bomb into a well. Although these methods were rejected (mainly on economic grounds) it still seems recommendable to re-evaluate these techniques regularly vith changing economic conditions, new technical developments or even for deviant oil formations. It is, furthermore, surprising to realise that in this early period attention was mainly directed to in-situ combustion. The reasons for this are that air injection was considered to be easier than, for instance, steam injection and that it requires less fuel at the surface.

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-In,s;tz

cebysii_onThe first field trials on in-situ combustion were carried out by Sfnclair Research and by Magnolia Petroleum Corporation in the U.S. Sinclair (5) experimented with injection of air/fuel gas mixtures in a shallow oil sand. Ignition was achieved by means of a gas burner. They demonstrated the propagation of a combustion wave which left a clear burnt sand. Supporting laboratory experiments demonstrated that the oil in the formation could be moved by the front edge of the heat wave. Magnolia first tried out ignition of underground combustion in a three-well test using an electric heater (6) and then carried out a successful in-situ combustion drive in a 30 acre inverted five spot (7). These early field trials stimulated research in various companies. In laboratory tube experimentation process variables were determined, such as minimum air flux for self-sustained combustion, fuel availability dependent on oil type, and frontal advance rate in relation to air rate (8).

529 An extensive study of combustion processes in oil sands led to a description of the drive mechanism of the process (9). In experiments in glass tubes oil-bank formation was made visible. Thermal analysis, using a pack of oil sand fluxed with air, showed that the reaction between oxygen and oil proceeds in two major steps; in a lower temperature regime (below 3000C) the oil molecules lose comparatively more hydrogen than carbon in reaction with the oxygen, leaving a carbon-rich coke-like residue which is subsequently burnt off in a temperature range of 300 to SOOOC.

Rot-yatez inlectzoz The method that was, at least at Shell in that period, considered as second best is hot-water injection. Therefore a feasibility study was carried out on the applicability of this process in the Schoonebeek field in the' Netherlands. This field, which had once been called a play-ground for petroleum engineers specialised in thermal recovery, contains oil of 25OAPI with an initial viscosity of 180 cP. It consists of two parts: the highpressure (70 bar) waterdrive area and the low-pressure (10 bar) solution gas drive area. The total SMIIP is l.Zx109 bbl. Hot water was intended to be injected into the waterdrive area. As it was realised that the temperature distributions in the water and the oil zone are the determining parameters of the process, an analytical model was developed to determine these temperature distributions. This model, still known as the lauwerier model (lo), mainly consists of a procedure for calculating heat losses in the formations over- and underlying the hot-water zone. It enables the average water and the average oil temperature to be calculated at a certain time and thus the average viscosities and the mobility ratio. The recovery as a function of time can then be approximated from this varying mobility ratio. Furthermore, scaled laboratory experiments were carried out to confirm the model for an actual situation with a hot-water tongue underrunning the oil. From economical calculations it appeared that the process could be profitable provided cheap fuel is available (4).

-Steam injectlo! In the meantime also, a start had been made with tube experiments on the steam-drive process (11). It appeared in these one-dimensional experiments that a steam zone with a stable front develops, in front of which the temperature decreases gradually to the initial temperature. Further important observations were the low residual oil saturation in the steam zone, the relative independence of the process to oil viscosity and sand permeability and again the dominating effect of heat losses to over- and underlying formatione.

LATE FIFTIES AND EARLY SIXTIES After the preceding period of (mainly) laboratory investigations, a period had now come of active field testing of the studied processes. All three processes were tested by Shell in the Schoonebeek field: Rot-water drive in the high-pressure water-drive area and in-situ combustion and steam drive in the low pressure solution gas-drive area. In the heavy-oil fields of the Bolivar Coast in Venezuela ( 10-1SoAPI), steam drive and in-situ combustion were tested in the PIene Grande field and the Tia Juana field.

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-1nZsit-U combysJionIn designing an in-situ combustion test at that time, ignition was considered a matter of particular concern. Ignition procedures using powerful well heaters to heat the formation round the injector to combustion wave temperatures (some 300°C or more) (5,6), or by use of reactive chemicals (12.13) all had their specific drawbacks, often necessitating well repairs and repeated trials (3). At Schoonebeek, for instance, ignition was achieved in the three injectors of the triple seven-spot by squeezing-in concentrated nitric acid as a strong oxidiser. In one of the injectors, however, an explosion occurred, tearing up a tubular section. Aa in the South Belridge field test spontaneous ignition had quite unexpectedly occurred after prolonged air injection (4), interest in this manner of starting in-situ combustion led to the development of a predictive method for spontaneous ignition, based on low-temperature oxidation rates of oil sands (15). Predictions for the Tia Juana test site in Venezuela led to the decision to rely on spontaneous ignition, which actually occurred some five weeks after air injection. Later, on basis of the predictive model, it was formulated that by heating the formation round the well bore gently and gradually to only some 100% with a low-powered well heater or by steaming the injector, a smooth well-controlled ignition could be achieved after one or two days' air injection (16.17). By steaming the injector a smooth ignition was obtained in the Tia Juana wet in-situ combustion test in 1965, discussed below. Although much experience had been gained with both in-situ combustion pilots at Schoonebeek and Tia Juana, they were considered economically unsuccessful. Oil returns were low, mainly due to rapid up-dip channelling of the air. In the meantime a theoretical one-dimensional model study had been made on the tolerance of a dry combustion wave to w e e r injected simultaneously with the air (18). The water evaporates to steam in the hot burnt-out zone and the steam carries the heat downstream through the combustion zone. The effect of such heat recuperation is two-fold: the steam stabilises the propagation of combustion by preheating the oil and, most important, the growing steam zone effectively sweeps the mobile oil far ahead of the combustion wave. As a result, less air is needed for the combustion-drive process, so that compressor capacity can be reduced, thus economising on investment and running costs. The optimum tolerable water-injection rate relative to the airinjection rate was found to be the one at which the evaporation front moves steadily and closely behind the combustion wave. Baaed on the relatively high oxidation rates of oil in the lowtemperature range found in combustion kinetic studies (19,20,21) a series of laboratory tube experiments was carried out at 40 bar, in which the waterinjection rate was deliberately increased to far above the quoted tolerance limit (22). It appeared that as the water under these conditions enters the combustion zone and evaporates, it suppresses the combustion temperature to near-saturated steam temperatures, with the result that the less reactive coke (final oxidation step) remains unburnt. It was shown that, in spite of partial quenching of the combustion, a steady progress of the heat wave is ensured, while achieving a further important economisation on the air requirements. The experimental results fitted a simple theory which showed that in partially quenched combustion the speed of the combustion wave is no longer governed by the air-injection rate (as in dry and "normal" wet combustion) but by the water-injection rate and that the air requirement per unit formation volume decreases with increasing water-injection rate. Later, more refined theories on "superwet" combustion were developed (23,24) which were reviewed in Ref. (3). Seemingly different experimental observations by others (25) appeared to fit in with these theories (26).

531 On the basis of their experience with wet and superwet combustion in onedimensional models, Shell decided at an early stage to try out wet combustion in the field. In 1962, the triple seven-spot dry combustion test at Schoonebeek was converted into a wet combustion project (3). The test was terminated in 1965 after a severe production decline had set in, presumably caused by an overall formation plugging, while in addition several injectors and producers suffered from corrosion. Although the test was not considered an economic succese, it had shown that while injecting water simultaneously with the air, more than three times as much tertiary oil could be produced per unit volume of air than during the dry combustion phase. In Venezuela, a wet combustion drive test was carried out in a seven-spot in the Tia Juana field, in the period 1965 to 1968 (3). Compared to Schoonebeek, where conditions were rather in the range of 'normal' wet combustion, water/air injection ratios were chosen to be twice as large, to reach the range of partially quenched combustion of the laboratory experiments. Temperature profiles determined in observation wells and in producers remained below 20OoC. Though speculative, this might be taken as an indication that the combustion has'perhaps indeed proceeded in the partially quenched mode. The test made a m a l l net profit. Although much uncertainty arose concerning how much oil should be attributed to the effect of the wet combustion drive ( 3 , probably at least twice as much tertiary oil had been produced per unit volume of air as compared with the Schoonebeek test.

-Steam

@JectAoz The most important event of this period is probably the discovery of the steam-soak process in 1959 in the Mene Grande field (27). The process was discovered rather accidentally when, during the planned,steam drive, steam eruptions around an injector made it necessary to relieve the reservoir pressure by backflowing the injector. It appeared then that the well continued to flow at a rate of more than 100 bbl/d oil at a relatively low watercut, whereas surrounding producers had been pumped before steam injection at oil rates varying from 3 to 10 bbl/d. Further testing was carried out in the Tia Juana field, the favourable r.esults of which prompted a large scale project. In the meantime also, Shell Oil tested the process successfully in its Yorba Linda field in California (28) which was the start of the large-scale applications of the process in the Californian heavy oil fields. In retrospect, this accidental discovery has been mentioned as being more or less inevitable (29). Others consider "the observation of a phenomenon, the reallsation of its value and the initiative to apply it" to be less obvious (30). An interesting question in this respect is: Why has this process been discovered in the field and not been proposed by research? Afterwards, the idea to reduce the pressure drop around a production well by heating seems rather obvious. Same simple calculations could have demonstrated that this effect would last a reasonable time. A possible answer to the question why this idea has never been proposed is that, even if anybody had the idea, he probably would have rejected it himself because he would expect to produce mainly water. Even in recent literature different explanations (31,321 are given for the low water cut during the production phase. The steam-drive projects in Schoonebeek (33) (4 injectors and 8 producers) and in Tia Juana ( 3 4 ) (7 injectors and 24 producers) both proved to be a technical success. Additional oil recoveries from the test areas were estimated to be 38% and 21% STOIIP for Schoonebeek and Tia Juana respectively. In both projects it appeared that owing to gravity the steam flows only

532 through the upper part of the formation. The lateral flow patterns in both projects were far from symmetric. This phenomenon can partly be accredited to the dips of the reservoirs ( 6 . 5 O in Schoonebeek and 3O in Tia Juana) but is also due to heterogeneous sand developments. For correct interpretation of such projects it is important to know the volumetric development of the steam zone. At that time only theories describing the developnent of a one-dimensional steam zone were available. The thickness of the steam zone which determines the vertical sweep efficiency, had to be derived from field observations. These thicknesses were estimated to be between 7 and 1 1 m. It followed from the analyses that oil was not only displaced by free steam but also by condensation water, in Tia Juana even in equal amounts. The Schoonebeek project was extended to adjacent areas. In the meantime it had become apparent from the steam-soak tests in the Tia Juana field that a combination of reservoir compaction and steam soak could maintain primary recovery for a considerable period. It was therefore decided for the near future to discontinue steam-drive activities in the Bolivar Coast fields. HoL-Earei &nJeEt&oz Although the hot water injection test in the Schoonebeek field (2 injectors and 7 producers) proved to be reasonably successful, it appeared that the process is much more complicated than was initially envisaged (35). Water breakthrough occurred much earlier than expected. Later studies based on model experiments showed that the process is intrinsically subject to lateral instability and that the hot water tends to concentrate in a few tongues. Nevertheless, the performance in the Schoonebeek field was attractive enough to extend the project over a considerable part of the high pressure waterdrive area. In some parts of the reservoir hot-water injection is still being carried out. This is a quite exceptional situation since most early pilot projects were discontinued because of poor areal sweep efficiency. An explanation for the acceptable performance of Schoonebeek could be its relatively low initial oil viscosity of 180 CP (180 mPa.6).

MID-SIXTIES TO EARLY SEVENTIES This period shows a spectacular increase in the number of steam-soak projects at the cost of the other thermal processes. Within a period of ten years the production of heavy oil due to this process increased in California to about 130 000 b/d and in Venezuela to an even higher level. Although by its nature only a stimulation procese, it enables at relatively low costs production from undepleted reservoirs which would otherwise only produce at very low rates. Theoretical (36,37) and experimental (38) studies were carried out to investigate the performance of the process and to define optimal injection and production schemes. The effect of a number of parametere had to be investigated, among which slug size, cycle length, number of cycles, soaking time, etc. Although at that time the complete set of flow- and heat transport equatione could not yet be solved, the simplified equations were already being solved numerically with the aid of the computer. The most advanced models did not predict the performance purely based on physical input parameters but had to be matched to actual well performance. Answers to important questions concerning whether a particular reservoir at its particular stage of depletion was suitable for steam soaking still very often had to be found by field trials. So far we have only mentioned the Californian and Venezuelan Bolivar Coast heavy oil fields as targets for thermal recovery but not the even more important heavy oil sands of Canada and the Orinoco belt in Venezuela.

533 In this period attention in Venezuela was mainly directed to the Bolivar Coast rather than to the Orinoco belt. In Canada, however, the first pilots were started as early as 1957 (39). Amoco started a field programme in which dry and wet combustion were tested. Also, reversed combustion was tried out. To obtain injectivity, fracturing of the formation appeared to be necessary. As a follow-up to many years of testing, a relatively large in-situ combustion test is currently being carried out in co-operation with the AOSTRA. A special condition exists in the site of AOSTRA and Shell Canada where the oil zone is underlain by a zone with a high water saturation which is more permeable than the oil sand. No fracturing is required to inject steam in this zone. From the field-testing programme which started in 1963, a cyclic steaminjection recovery scheme has been developed which is at present being tested in a seven-7-spot pattern. Physical model experiments with vacum models were carried out to investigate the performance of this project ( 4 0 ) . In all field trials on the various thermal processes it had appeared that, however well the process might be understood in a onedimensional tube experiment, this understanding did not guarantee reliable predictions for an actual field performance. Areal distribution of the injected fluid and fluid segregation due to density difference play a major role. To study these phenomena, three-dimensional model experiments were carried out which were scaled to actual reservoir conditions. Two different types of models were applied: high-pressure models and vacuum models. Not only was it necessary to develop all kinds of new laboratory techniques but also to derive scaling rules. In the tests usually field symmetry elements were simulated consisting of a few injection and production wells. In the earlier high-pressure models, temperatures and pressures were equal to (which is essential for ISC experiments) or approaching those in the field. Typical dimensions for these sand-filled models were 3 m x 1.5 m x 0.15 m. To enable maintenance of the high pressures, the models were contained in bulky pressure vessels. To simulate dip effects, the vessels could be placed in a tilted position.

In hfgh-pressure model experiments on wet in-situ combustion, using a medium viscosity (Schoonebeek type) oil, surprising observations were made (3). As expected, the injected air rapidly moved to the top of the formation, driving a combustion spearhead to the production wells, finally resulting in a tilted coke deposit (41). Temperature observations showed, however, that at several spots and at several moments combustion in the burnt-out zone revived. This was an indication that oil was being driven upwards by the growing underlying water tongue. Also, it was observed that the combustion heat made itself felt to near the bottom of the sand pack. Thus, an effective recovery mechanimn was recognised by which a considerable amount of the oil is driven upwards by the invading water tongue into the hot regime near the top of the formation where the oil becomes much more mobile and is easily driven toward the producers. A similar effective flow regime has been discovered earlier (42) for a water drive in a reservoir having a high mobility streak along the top. Occurrence of this specific flow regime would explain why model experiments, run at a given water-injection rate but with air-injection rates differing by a factor of 4, showed practically identical recovery curves ending at an ultimate recovery of more than 1.5 higher than that obtained in a comparable plain water drive. It would be interesting to experiment with m o d e m computer simulators and assess how far the air injection rate can be reduced without affecting these favourable recovery results. Furthermore, it might be investigated to what

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extent the sketched recovery mechanism would remain operative in reservoirs containing heavier oil, e.g. as in Tia Juana, with greater mobility contrasts to water and air. In retrospect, it is noted that the concept of partially quenched combustion, being a marked step forward in combustion control, has been developed on basis of the frontal drive laboratory experiments and corresponding theories. These research activities have led, however, to an effective recovery process in which a mechanism other than partially quenched combustion also plays a role.

In steam-drive model experiments particular attention was paid to the development of the steam zone. Also, the utilisation of the heat injected was studied. From these experiments an analytical theory ( 4 3 ) could be derived which predicts the shape and the growth of the steam zone by making use of the concept of a pseudo-mobility ratio between oil and steam. In experiments directed to the Schoonebeek field trials ( 3 3 ) it was observed that steam followed the downdip draining hot condensate and thus broke through in a downdip well. This phenomenon had also been observed in the field. Agreement between field- and model observations was satisfactory. Vacuum models to predict reservoir performance under steam drive were in particular applied by Shell Dev. Co. ( 4 4 ) . In vacuum models a rigid structure is obtained by imposing a vacuum on a packed bed of glass beads confined between two plastic sheats. Although these models were initially developed for low temperatures, they could also be applied for low temperature steam at the sacrifice of correct matching of the ratio between latent and sensible heat. The advantages are that they are much simpler to use and safer. Information from model experiments was thus obtained for complicated field projects such as for example Mt. Poso ( 4 4 ) , Midway Sunset, Yorba Linda and Peace River (40).

MID-SEVENTIES TO EARLY EIGHTIES In the last ten years it has become more and more clear that the competition between the three thermal processes has been won by steam. After the oil crisis of 1973, the demand for heavy oil has increased and in particular in the U.S. many existing steam projects have been extended and new projects started. Many reservoire which have already been producing for 10 to 15 years under steam soak are now being converted to steam drive combined with steam soak. To give an order of magnitude of these projects ( 4 5 ) : Many of them are producing in the range of 1000 to 5000 b/d. Large projects are Getty's Kern River Project with a production due to steam injection of 52,000 b/d, Shell's Hount POSO project with 20,000 b/d and Texaco's San Ardo project with 22,000 b/d. Another important large steam drive project is being carried out by Maraven in Venezuela in a nearly depleted part of the Tia Juana field ( 4 6 ) . Although a large project on a commercial scale with a production rate of about 20,000 b/d, It is still considered to be of an exploratory nature for the wider application of steam drive in the Bolivar Coast heavy-oil fields. For comparison, we mention some of the largest ongoing in-situ combustion projects: The Rumanian project I n the Suplacu de Barcau field ( 4 7 ) with an oil production of about 6500 b/d, Getty's project in the Bellevue field in Louisiana with about 2800 b/d and Mobll's project in the South Belridge field with 1900 b/d. Most of these projects are technically considered to be successful and profitable. This means that although steam is by far the most successful thermal method, in-situ combustion should certainly not be considered obsolete.

535 The main reservoir-engineering problem in designing new projects is the lack of simple and reliable performance prediction methods. Until the early seventies, a selection had to be made from extrapolation of pilot projects or more or less similar other projects, time-consuming scaled model experiments in the laboratory and a few simplified analytical models. In the field of steam drive, a number of analytical methods for computing the volume and the shape of the steam zone have been derived over the years. The common basis of these various models is a procedure to account for the heat losses from the steam zone to over- and underlying formations. Furthermore, an attempt is made to disconnect the coupled heat transport equations (conduction and convection) and those for fluid flow (water, oil and steam). In one case this is done by neglecting fluid flow completely (Marx and Langenheim ( 4 8 ) ) , in another case by taking fluid flow partially into account to arrive at a better analysis of the heat distribution in front of the steam zone (Mandl and Volek ( 4 9 ) ) . A severe limitation of both approaches is that they describe only the development of a one-dimensional steam zone and do not predict its thickness. The method of Neuman (50) predicts areal and vertical development, assuming this is only determined by heat conduction and convection. Van Lookeren (43) assumes that the shape of the steam zone is determined by gravity and viscous forces but has to simplify the heat distribution. Nevertheless, some of his predictions check quite well within a defined range of applicability with observations from laboratory experiments. With the aid of these analytical models it is possible to approximate the volune of oil displaced by steam. No straightforward methods existed to predict the volume of oil displaced by the hot condensate; neither did methods to take areal effects into account. This could only be done with the scaled model experiments and since the mid-seventies with a numerical simulator. A lot has already been said in literature on the advantages and disadvantages of physical and numerical models (51). The consensus nowadays is, more or less, that physical experiments should provide the physical insight, and that the quantitative effect of any physical parameter could be investigated with the aid of the numerical simulator. This means that geometrically scaled model experiments as carried out in the late sixties and early seventies, will no longer be carried out in the future, since geometrical effects can much more easily be studied with a numerical simulator than with a physical model. The main development in thermal simulators, or in particular those Simulators that can handle hot water and steam is connected with the increasing capacity of the computers: increasing speed and memory space. These factors enable the study of more details by means of the application of more grid blocks and acceptable runtimes made possible by replacing the older explicit methods by implicit methods. Numerical simulators for the in-situ combustion process are not new either: One of the first mentioned in the literature dates from ae early as 1965 (52). However, owing to the complexity of the process, their development is far less advanced than in the case of steam models. One of the major problems in simulating field performance is the fact that the essential phenomena occurring in the combustion zone of a few metres thick have to be represented for practical reasons in grid blocks with sizes in the range of 10 m and more. PRESENT DEVELOPMENTS The developments which are at present taking place in the field of thermal recovery can be grouped in the following way: a. follow-up methods for ongoing steam projects. b. new thermal methods for the recovery of heavy oil. C. search for new targets for thermal methods. d. improvement of existing and development of new equipment.

536 Each of these groups is discussed briefly: a. The need for follow-up processes is felt in particular in steam-drive projects which have been in progress for a couple of years, in which steam breakthrough has already taken place and where the oil-steam ratio is declining. In reservoirs with medium viscosity oil (e.g. Schoonebeek) water injection or (if present) a strong aquifer may cause collapsing of the steam zone when steam injection is discontinued. In this way, relatively cold oil may be pushed into the hot formation. As the heat stored in the reservoir is utilised very efficiently, in this way, high oil/steam ratios may be obtained. It is clear that this process is not suitable for heavyoil reservoirs. Nevertheless, water injection, with or without caustics, needs further consideration. A promising method to improve the sweep efficiency of steam drive seems to be the application of blocking agents ( 5 3 , 5 4 ) , such as foams to divert steam into unswept areas. This method is under active study at various companies and institutes, both in the field and in the laboratory. b. As already mentioned above, re-evaluation of heating heavy oil reservoirs by electromagnetic radiation or electric conduction regularly occurs. The major economic drawback of these methods is the low thermal efficiency inherent in the generation of electricity. Also, the interest in the injection of oxygen (instead of air) for insitu combustion has been revived ( 5 5 , 5 6 ) . The potential advantage of oxygen would lie in suppression of early breakthrough of large quantities of hot combustion gases in the production wells. Methods which may become of interest with increasing oil prices are combinations of mining techniques and thermal methods (57) to increase recovery and reduce heat losses. C.

With a very few exceptions, all thermal projects have been carried out in reservoirs containing heavy oil. Light-oil reservoirs were not considered because water is generally considered to be a cheaper driving fluid. If the residual oil remaining after water drive is considered to be a target, thermal methods should also be taken into account. Although not all proven to the same degree, injection of steam and hot water as well as in-situ combustion may be considered. Steam distillation,(or strip) drive in lightoil reservoirs is a process which has been technically proven both in the field (58) and in the laboratory (59). Residual oil saturations in the steamed-out zone are in the range of 3 to 8%. The economic weak points of the process are its high initial investment and high operation costs (fuel). Further study on the economic viability of the process seems necessary. The technical feasibility of in-situ combustion in a watered-out light oil reservoir has already been demonstrated in the mid-sixties by Amoco in the Sloss field in Nebraska (60). A potential process for high-pressure reservoirs might be derived from the property of hydrocarbons to dissolve in water at near-critical conditions. In practice, this means that the pressure should be above 200 bar and the temperature above 300°C. This means that this process is, anyhow, limited to deep reservoirs. Russian investigators (61) claim to have obtained high recoveries in tube experiments. Which crudes are suitable candidates for this process needs further investigation, as well as the economic viability of the process. Technical limitations can also be caused by the design of the deep injection wells. A completely different type of target where thermal methods seem promising are fissured limestone reservoirs. These reservoirs often consist

537 of very low permeable matrix blocks containing nearly all the oil and a highly permeable fissure (or fracture) system (62). Drive processes have a very low recovery because the oil in the matrix blocks is bypassed by the drive fluid (either water or gas). Water imbibition does not occur or is very weak because the rock is oil-wet or neutral-wet. Gravity drainage is often hampered by capillary forces, the low permeability of the matrix rock and sometimes by the high viscosity of the oil. The effect of heat can be manifold (63,64): expulsion of oil from the matrix blocks due to swelling and gas development within the matrix blocks (oil vapours and steam), improvement of gravity drainage and countercurrent imbibition due to viscosity reduction and reduction of the capillary retention. Both heavy and light oils come into consideration. Heat can be supplied by either injection of steam or hot water or by insitu combustion. An important requirement for these processes to be effective is that the average fissure spacing should not be too wide to enable sufficient heat penetration into the matrix blocks. d. Although in the field it is very often an area of serious problems, engineering of thermal projects has not been discussed so far in this paper. We will briefly touch on some of the major problem areas encountered with steam injection and some of the developments taking place in this field. These major problem areas are: water treatment, boiler design (efficiency, H2S emission, resistivity to feedwater and fuel), thermal well completions, production of sour gas due to thermal cracking and production of oil-water emulsions. These problems cannot be considered separately: water treatment and boiler design are fully interwoven and are furthermore determined by the properties of the available water. With the generation of steam downhole which is, at present, being actively investigated (65,66), a number of these problems is circumvented, such as boiler efficiency, H S emission and well completion. Mechanical problems in hoz wells which increase with the depth of the wells are tackled by testing various insulations and high-temperature packers (67). The problems do not seem to be solved easily.

CONCLUDING REMARKS

In the early period much was expected of the in-situ combustion process with hot-water drive in second and steam drive in third place. At present, much more oil is produced by steam than by the two other processes. Steam soak, although not a drive process, has produced most of the "thermal" oil in the world. This process was discovered in the field and not proposed by research. Looking at the way the three processes were developed, it appears that hot-water drive fallowed the sequence: desk study laboratory experiments pilot test. In the case of steam drive, laboratory experiments preceded the detailed desk study. In-situ combustion research was prompted by very early pilot tests.

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From the above observations, one tends to conclude that all three phases (desk study, laboratory experiments and pilot test) are essential in the development of the process, while the sequence seems to be of less importance. On the other hand, it is very important really that all phases have been passed through. Research without field testing may lead to sterile hobbyiem and field testing without detailed preceding and following interpretation studies does not produce more than an abundance of poorly understood data.

538 REFERENCES 1.

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15. 16.

17.

RAMEY, H.J.; "A current review of oil recovery by steam injection", Proc. 7th World Petrol. Congr. Vol. 3, pp. 471-476. RARMSEN, G.J.; "Oil recovery by hot-water and steam injection", Proc. 8th World Petrol. Congr. Vol. 3, pp. 243-251. DIETZ, D.N.; "Wet Underground combustion. State of the art", J. Pet. Tech. (May 1970) 605. VAN HEININGEN, J. and SCHWARZ, N.; "Recovery increase by thermal drive", Proc. 4th World Petrol. Congr. Section 11, pp. 299-311. GRANT, B.F. and SZASZ, S.E.; "Development of an underground heat wave for oil recovery", Trans. AIME ( 1 9 5 4 ) z 108. KUNH, C.S. and KOCH, R.L.; "In-situ combustion newest method of increasing oil recovery", Oil and Gas J. (Aug. 10, 1953) 52, No. 14, p. 92. MOSS, J.T., WHITE, P.D. and McNIEL, J.S.; "In-eitu combustion process results of a five-well field experiment in Southern Oklahoma", Trans. AIME (1959)=, 55. WEINAUG, C.F. et al., editors; "Thermal recovery processes", Petrol. Trans. Reprint Series No. 7, SOC. of Petrol. Engineers AIME 1964. TADEMA, H.J.; "Mechanism of oil production by underground combustion", Proc. 5th World Petrol. Congr. (1959) Sec. 11, paper 22,279. LAUWERIER, H.A.; "The transport of heat in an oil layer caused by the injection of hot fluid" , Appl. Sci. Res., Section A, Vol. 5, pp. 145-150. SCHENK, L.; "Steam drive Results of laboratory experiments and first field testa in Mene Grande, Venezuela", Symposium on Thermal Recovery Methods, Caracas 1965. TADEMA, H.J. and QUANT, J.Th.; "Process for igniting hydrocarbon materials present within oil bearing formations" , U.S. Patent 2,863,510 (Dec. 9, 1958). TADEMA, H.J. and QUANT, J.Th.; "Recovery of oil by combustion in-situ", Dutch Patent 87145 (Jan. 15, 1958). GATES, C.F. and M Y , H.J.,Jr.; "Field results of South Belridge thermal recovery experiments", Trans. AIME (1958) 213 236. TADEMA, H.J. and WEIJDEMA, J.; "Spontaneous ignition of oil sands", Oil & Gas J. (Dec. 14, 1970). 70-80. WEIJDEMA, J. and ZELDENRUST, H.; "Formation ignition with moderate preheating", Dutch Patent Applic. 297100 (Oct. 1963); Venezuelan patent specific. 14629. STRANGE, L.K.; "Ignition: key phase in combustion recovery", Petrol. Engin., November 1964, p. 105, and December 1964, p. 97.

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539 18. DE HAAN, H.J.; "In-situ steam generation. The case of frontal displacement", (November 1961, unpublished). 19. WEIJDEMA, J.,; loZurOxydationskinetik Kohlenwasserstoffe in poroesen Media in Bezug aug underirdische Verbrennung", Erdol und Kohle, Erdgas, Petrochemie (Sept. 1968) 21 520. (Determination of the oxidation kinetics of the in-situ combustion process). 20. BURGER, J.G. and SAHUQUET, B.C.; "Chemical aspects of in-situ combustion. Heat of combustion and kinetics", SOC. Petr. Eng. J., (October 1972), 410-422. 21. FASSIHI, M.R., BRIGHAM, W.E. and RAMEY, H.J.,Jr.; "The reaction kinetics of in-situ combustion", Paper SPE 9454, presented at Dallas (Tex.), September 21-24, 1980. 22. DIETZ, D.N. and WEIJDEEU, J.; "Wet and partially quenched combustion", J. Pet. Tech. (April 1 9 6 8 ) E 411. 23. BECKERS, H.L. and HARMSEN, G.J.; "The effect of water injection on sustained combustion in a porous medim", Soc. Pet. Eng. J. (June 1970) 145-163. 24. BASKIR, E., BECKERS, H.L., DIETZ, D.N., TER HAAR, L.G.J. and KRUIZINGA, J.H.; Shell Research (unpublished). 25. PARRISH, D.R. and CRAIG, F.F.,Jr.; "Laboratory study of a combination of forward combustion and waterflooding the COFCAW process", J. Pet. Tech. (June 1969) 753-761. 26. HARMSEN, G.J.; "A note on COFCAW', J.Pet. Tech. (July 1969) 801. 27. DE H M N , H.J. and VAN LOOKEREN. J.; "Early results of the first large-scale steam soak project in the Tia Juana field, Western Venezuela", J. Pet. Tech. (Jan. 1969), pp. 101-110. 28. STOKES, D.D. and DOSCHER, T.H.; "Shell makes a success of steam flood at Yorba Linda", Oil and Gas J. (Sept. 2, 1974). pp. 71-78. 29. RAMEY, H.J.; "Thermal recovery - A troublesome neophyte", Interview in J. Pet. Tech. (Jan. 1969). pp. 7-8. 30. DIETZ, D.N.; "Letter to the Editor", J. Pet. Tech., July 1969, p. 862. 31. PRATS, H.; "A current appraisal of thermal recovery", SPE 7044. 32. COATS, K.H., RAMESH, A.B. and WINESTOCK, A.G.; "Numerical modelling of thermal reservoir behavior", Proc. of the Canada-Venezuela Oil Sands Symposium 1977, pp. 399-410. 33. VAN DIJK, C.; "Steam drive project in the Schoonebeek field, the Netherlands", J. Pet. Tech. (March 1968), pp. 295-302. 34. DE HAAN, H.J. and SCHENK, L.; "Performance analysis of a major steam drive project in the Tia Juana field, Western Venezuela", J. Pet. Tech. (Jan. 1969), pp. 111-119.

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540 35. DIETZ, D.N.; 36. 37. 38.

39. 40. 41. 42. 43. 44. 45. 46.

47. 40. 49. 50.

51. 52. 53.

"Hot-water drive", Proc. seventh World Petrol. Congr. Vol. 3 , p 451. BOBERG, T.C. and LANTZ, R.B.; "Calculation of the production rate of a thermally stimulated well", J. Pet. Tech. (Dec. 1 9 6 6 ) , pp. 1613-1623. OFFERINGA, J.; "A mathematical model of cyclic steam injection", Proc. 8th World Petrol. Congr., Vol. 3 , pp. 227-234. NIKO, 8. and TROOST, P.J.P.M.; "Experimental investigations of the steam-soak process in a depletion-type reservoir", SPE 2978. NICHOLLS, J.H. and LIJHNING, R.W.; "Heavy oil sand in-situ pilot plants in Alberta (Past and Present)", Proc. of the Canada-Venezuela Oil Sands Symposium 1977, pp. 527-538. PRATS, M,; "Peace River steam drive scaled model experiments". Proc. of the Canada-Venezuela Oil Sands Symposium 1977, pp. 346-363. PRATS, M., JONES, R.F. and TRUIT, N.E.; "In-situ combustion away from thin horizontal gas channels", Soc. Pet. Eng. J. (March 1 9 6 8 ) . 1 8 . VAN DAALEN, F., VAN DOMSELAAR, H.R. and HOOYRAAS, H.; "Method of producing liquid hydrocarbons from a subsurface formation", U.K. Patent specification 1,112,956 (April 7, 1 9 6 6 ) . VAN LOOKEREN, J.; "Calculation methods for linear and radial steam flow in oil reservoirs", SPE 6788. STEGEMEIER, G.L., LAUMBACH, D.D. and VOLEK, C.L.; "Representing steam processes with vacuum models. SPE 6787. MATHENY, S.L.; %OR methods help ultimate recovery", Oil and Gas Journ. (March 3 1 , 1 9 8 0 ) , pp. 79-124. VAN DER KNAAP, W.; "M-6 steam drive process. Preliminary results of a large scale field test", SPE 9452. PETCOVICI, V.; The experience of the Rumanian petrolem engineers with thermal recovery", Congreso Panamericano de Ingenieria del Petroleo, Mexico 1979. MARX, J.W. and LANGENHEIM, R.N.; "Reservoir heating by hot fluid injection", Trans. AIME ( 1 9 5 9 ) pp. 312-315. MANDL, G. and VOLEK, C.W.; "Heat and mass transport in steam drive processes", SOC. Pet. Eng. J. (March 1 9 6 9 ) , pp. 59-79. N",C.H.; "A mathematical model of the steam drive process Applications", SPE 4757. PAROUQ, AL1,S.M. and REDFORD, D.A.; "Physical modelling of in-situ recovery methods for oil sands", Proc. of the Canada-Venezuela Oil Sands Symposium 1977, pp. 319-326. GOTTPRIED, B.S.; "A mathematical model of thermal oil recovery in linear systems", J. Pet. Tech. (Sept. 1 9 6 5 ) , 196-210. DOSCHER, T.M. and IIAMMERSHAIMB, E .C.; "Field demonstration of steam drive with ancillary materials", SPE/DOE 9777.

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541 54. ESON, R.L.

55. 56.

57.

58.

59. 60. 61. 62. 63.

64.

. 65. 66. 67.

and FITCH, J.P.; "North Kern front field steam drive with ancillary materials", SPEfDOE 9778. ANON.; "ARC0 wants to test oxygen for in-situ", Enhanc. Recov. Week, November 10, 1980. PUSCH,.. !:; "Tertiarolgewinnungsverfahren Die Untertageverbrennung mit Sauerstoff kombiniert mit Wasserinjektion (ISCOWI)", Erdbl und Kohle-Erdgas-Petrochemie (Jan. 1977) 2, 13-25. BETC-STAFF; "Technical constraints limiting application of enhanced oil recovery techniques to petroleum production in the United States", DOE/ BETCf RI-80f 4, May 1900. KONOPNICKI, E.F., TRAVERSE, E.F., BROWN, A. and DEIBERT, A.D.; "Design and evaluation of the Shiells Canyon field steam distillation drive project", SPE 7086. HAGOORT, J., LEIJNSE, A. and VAN POELGEEST, F . ; "Steam-strip drive: A potential tertiary recovery process", SPE 5570. PARRISH, D.R., POLLOCK, C.B., NESS, N.L. and CRAIG, F.F.; "A tertiary COFCAW pilot test in the Sloes Field, Nebraska", J. Pet. Tech. (June 1974), pp. 667-675. CHEKALJUR, E.B. et al.; "Method of recovering oil from an oil bearing bed", British Patent Appl. No. 15256/71. REISS, L.H.; "The reservoir engineering aspecte of fractured formations", IFP, Editions TECHNIP, Paris 1980. SAHUQUET, B.C. and FERRIER, J.J.; "Steam drive pilot in a fractured carbonated reservoir Lacq Superieur field" , SPE 9453. DE VRIES, A.S.; "Aspects of enhanced recovery in densely fissured carbonate reservoirs containing heavy oil", Congreso Panamericano de Ingenieria del Petroleo, Mexico 1977. WRIGHT, D.D. and BINSLEY, R.L.; "Feasibility evaluation of a downhole steam generator", SPEfWE 9775. FOX, R.L., DONALDSON, A.B. and MULAC, A.J.; "Development of technology for downhole steam production", SPEfDOE 9776. JOHNSON, D.R. and FOX, R.L.; "Examination of techniques for thermally efficient delivery of ateam to deep reservoirs", SPE 8820.

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543

THERMAL RECOVERY METHODS

US. DEPARTMENT OF ENERGY R&D ON DOWNHOLE STEAM GENERATOR FOR THE RECOVERY OF HEAVY OIL RONALD L. FOX Sandia National Laboratories

J. J. STOSUR

US.Department of Energy ABSTRACT The energy loss associated with delivering steam from surface generators to the reservoir is one of the factors that has limited most commercial steaming operations to relatively shallow oil bearing formations (about 1000 feet). The Sandia National Laboratories under contract to the U. S. Department of Energy has initiated an ambitious program for the developnent and field testing of a downhole steam generator. The advantages are impressive: exceptionally high overall thermal efficiency; good potential for alleviating air pollution from generating steam at the surface, andj significant economic benefits from accelerated oil recovery due to the introduction of combustion products along with steam. W o designs are being developed: a low pressure and a high pressure steam generator. The low pressure combustion design transfers energy to water through a heat exchanger, thus enabling the combustion process to be conducted at a pressure less than the injection pressure; a high pressure combustion design mixes the combustion gases directly with water, resulting in the injection of steam and combustion gases into the reservoir.

Field testing of a high pressure combustion generator was carried out in a shallow reservoir (275 meters) to determine if the system was conpatable with field conditions, if recovery with this device resulted in modifications to the reservoir or produced crude, and to assess the injection of combustion gases into the formation as a method of reducing air pollution associated with steam injection. Follow on field tests have examined the performance of the device for downhole operations in reservoirs below 700 meters. INTRODWTION THE U. S. Department of Energy initiated developnent of tools for production of steam at the oil producing formation in 1978. The technical implementation of the developnent and testing program is being carried out by the Sandia National Laboratories as part of the Department of Energy's Project DEEP STEAM. The DEEP STEAM project incompasses development of methods for application of conventional steam drive to deep reservoirs as well as the downhole steam generator program. The project provides for the conception, feasibility analysis, laboratory testing, and field testing of methods for downhole production of steam. W o concepts for downhole production of steam for drive operations have been

selected for comparative development.

The two designs differ in method of

544 t r a n s f e r r i n g h e a t from h o t combustion g a s e s t o produce steam. A low p r e s s u r e combustion design t r a n s f e r s energy t o water through a h e a t exchanger t h u s e n a b l i n g t h e combustion process t o be conducted a t a p r e s s u r e less than t h e i n j e c t i o n p r e s s u r e t a high p r e s s u r e cornhuetion design mixes t h e combtistion gases d i r e c t l y with w a t e r , r e s u l t i n g i n t h e i n j e c t i o n o f steam and combustion gases i n t o t h e reservoir. The high p r e s s u r e c o m h s t i o n design has been u t i l i z e d i n a series of f i e l d experiments, and t h i s paper p r e s e n t s t h e s t a t u s of downhole steam generator technology a s revealed i n t h e s e experiments.

DOWNHOLE STEAM GENERATOR PROGRAM The developaent of technology f o r downhole steam production h a s been c a r r i e d o u t a t t h e Sandia N a t i o n a l Laboratories and under c o n t r a c t 'with Rockwell I n t e r n a t i o n a l , Rocket%ne Division, and with Foster-Miller Associates. The design and t e s t i n g of a l o w p r e s s u r e combustion generator h a s been pursued a t Rocketdyne. A high p r e s s u r e combustion downhole steam g e n e r a t o r is under development a t Poster-Miller. The Sandia National Laboratory is i n v e s t i g a t i n g a high p r e s s u r e g e n e r a t o r which d i f f e r s from t h e Foster-Miller design i n t h e method f o r o b t a i n i n g c l e a n combustion a t p r e s s u r e s r e q u i r e d f o r steam i n j e c t i o n operations. The f i e l d tests which have occurred t o d a t e have u t i l i z e d t h e Sandia Systems. The f i e l d t e s t i n g h a s included t h e s e experiments: T e s t A:

Test 8:

Test C:

Intermediate term test of e q u i p e n t on s u r f a c e with i n j e c t i o n i n t o shallow reservoir. I n s t a l l a t i o n and recovery of t h e g e n e r a t o r from a deep w e l l . Intermediate term t e s t of equipment i n downhole o p e r a t i o n s i n a deep r e s e r v o i r .

The c o n d i t i o n s f o r T e s t A were f o r 3 t o 4 months o f continuous o p e r a t i o n u t i l i z i n g o i l f i e l d water and u t i l i t i e s with i n j e c t i o n of t h e g e n e r a t o r T e s t A w a s performed i n t h e Kern River e f f l u e n t i n t o a 270 m deep reservoir. F i e l d of C a l i f o r n i a i n cooperation with Chevron, USA d u r i n g January-May, 1980. The c o n d i t i o n s f o r T e s t B were t o i n s t a l l and r e t r i e v e a downhole g e n e r a t b r below 7 0 0 m i n a s t a n d a r d o i l f i e l d c a s i n g with a mechanically set packer b e l o w t h e device. T e s t R w a s performed near Lovington, New MBxico, i n cooperation with ARC0 O i l and Gas d u r i n g September 1980. The c o n d i t i o n s f o r T e s t C were f o r 3 t o 4 months o f continuous downhole o p e r a t i o n i n a r e s e r v o i r a t a depth greater t h a n 7 0 0 m. The r e s u l t s of t h e s e tests a r e given i n t h e r e m i n d e r of t h i s paper.

SHALulw WELL OPERATIONS Steam Generator. The d i r e c t c o n t a c t steam/generation concept was chosen f o r t h e preliminary f i e l d test. A c o m w r c i a l l y a v a i l a b l e steam g e n e r a t o r u n i t w a s sought t o minimize t h e d e v e l o p e n t time r e q u i r e d t o perform a test. V a p o r Energy Co. of Grand P r a i r i e , Texas, produced a d i r e c t contact g e n e r a t o r of s l e n d e r c y l i n d r i c a l geometry. These u n i t s had been p r e v i o u s l y o p e r a t e d a t pressures up t o 100 p s i g . A s p e c i a l l y designed u n i t whic could approxfmate dimensions f o r d a m h o l e operation w a s procured f o r 5 x 10' b t u / h r a t 3000 p s i with a n o u t s i d e dicrmeter of 6.5 inches. The design is i l l u s t r a t e d i n Figure 1 and is designated "before." I n t h i s design propane vapor is brought i n t o t h e a i r stream i n e i t h e r one or both i n l e t s i n d i c a t e d i n t h e f i g u r e . The propane and a i r are mixed as t h e y t r a v e l d a m t h e channel. I g n i t i o n is by spark p l u g and occurs a t t h e area expansion. Water is passed up an annulus o u t s i d e t h e combustion r e g i o n and is e n t r a i n e d i n t o t h e combustion gases. As t h i s mixture passes d w t h e i n a i d e o f t h e steam generator, v a p o r i z a t i o n o f t h e water occurs r e s u l t i n g i n a mixture of Steam and cornbustion products (mainly COz and Nz). A.

545 AIR

I

PROPANE

AIR

IK)DIFICATIONS

Propane Delivery/Mi.Xing nixture velocity Wall Propagation Water Paaaages Water Entrainment Ignition

3 WATER

WATER

BEFORE

Figure 1.

ARER -

Direct contact Stoam Generator eefore an3 After Modification

T h i s design was tested a t Sandia a t p r e s s u r e s o f 100 p s i g or lower. The pressure l e v e l w a s l i m i t e d by t h e vapor p r e s s u r e of propane a t t h e e x i s t i n g ambient temperature. S e v e r a l s h o r t c d n g e of t h i s system f o r t h e f i e l d test applicat i o n w e r e noted. These problems w e r e resolved by t h e following modifications: 1. I n o r d e r t o provide propane v a k r a t pressures above 400 peia, l i q u i d propane is f i r s t pumped t o pressure. Then t h e propane l i q u i d is p a r t i a l l y vaporized by h e a t t r a n s f e r from two sources: 1) propane is c i r c u l a t e d through t h e f l a n g e which a t t a c h e s t h e mixer s e c t i o n t o t h e combustor s e c t i o n ( t h e f l a n g e is heated by conduction from t h e flame zone)# and 2 ) propane i a then c i r c u l a t e d through a j a c k e t around t h e a i r l i n e ( t h e a i r is warm because of compression h e a t ) . These t w o zones are s u f f i c i e n t t o cause p a r t i a l vaporiz a t i o n of t h e propane. The r e s u l t i n g flaw t h e n passes down a tube and i s i n j e c t e d i n t o t h e a ir stream through f o u r h o l e s which are 0.030" dia. The h o l e s are normal t o t h e air flaw t o achieve p e n e t r a t i o n and improved mixing o f t h e t w o streamer. A l l s u r f a c e s i n t h e mixing s e c t i o n are m t h t o e l i m i n a t e s t a g n a t i o n regime ( f l a w , holdern). The w a l l c o o l i n g has t h e e f f e c t of r e d u c i n g temperatures i n t h e boundary l a y e r which eliminate. flame propagation up the walls.

The diameter of t h e mixing s e c t i o n was decreased from 1.5 i n c h e s t o 1.27 2. inches. This h a s t h e e f f e c t of i n c r e a s i n g t h e flow v e l o c i t y by 40% which decreased t h e p o s s i b i l i t y of burn-back. 3. The water paenage w a s modified to i n c l u d e a s l e e v e which separates t h e water and c o m h s t i o n zone t o a p o i n t a t which combustion i s e s s e n t i a l l y cow p l a t e . Two b e n e f i c i a l e f f e c t s arise from t h i s modiCication: 1) greater ease of i g n i t i o n , and 2 ) better combustion e f f i c i e n c y . A n i n t e r m e d i a t e step i n t h i s modification w a s f o r t h e o r i g i n a l f a b r i c a t o r ( V a p o r Energy) t o i n s t a l l a s l e e v e f o r t h i s purpose, with Sandia's concurrance. However, a f t e r approximately 20 h r s o p e r a t i o n with t h i s modification, t h e s l e e v e was aeverely damaged. This w a s apparently due t o t h e s l e e v e n o t being f u l l y wetted by water. Hence, t h e f i n a l modification included a l i p on t h e end of t h e deem t o restrict water flaw and i n s u r e t h a t t h e annulua remained f u l l y wetted.

546 Approximately 30 s l o t s w e r e machined through t h i s l i p t o allow water passage, even a f t e r thermal expansion d u r i n g operation. Additionally, t h e water passage gap a t t h e t o p o f t h e combustor was increased from 0.040" t o 0.100" so t h a t it would n o t close upon thermal expansion. Further, t h e area of c o n t a c t between water and t h e top cap w a s i n c r e a s e d by extending t h e a r e a expansion f u r t h e r i n t o t h e combustor. 4.

I n s t e a d of spark i g n i t i o n , t h e f i n a l design u t i l i z e d a flow plug f o r ignit i o n . This modification f a c i l i t a t e d ease of s t a r t i n g a t high p r e s s u r e l e v e l s without use o f an e x o t i c pover source. The above modifications a r e t h e hasis of a p a t e n t a p p l i c a t i o n f i l e d by DOE. B. Kern River F i e l d T e s t Results. The DEEP STEAM test s t a r t e d with t h e i n j e c t i o n of steam and combustion products i n t o t h e reservoir on February 6 , 1980, a f t e r one week of o p e r a t i o n s t o c a l i b r a t e equipnent and t o i n s t r u c t personnel i n t h e o p e r a t i o n o f t h e system. The test w a s scheduled f o r and w a s conducted on a 24-hour, 7-days a week basis.' A f t e r t h e s t a r t up on February 6 t h e t e s t w a s run f o r 109 days t o May 15. During t h a t p e r i o d t h e test was i n t e r r u p t e d 51 times: 8 f o t power and water

f a i l u r e s which were s u p p l i e d by o t h e r s , 12 w e r e d e l i v e r a t e shutdowns, and t h e remaining 31 were represented by problems with t h e f u e l supply, computer, instruments and people. The only major down p e r i o d was from March 7 through March 20 and was caused a d e t o n a t i o n being propaqated upstream through t h e a i r l i n e due t o o i l i n t h e l i n e . The run t i m e excluding t h i s p a r t i c u l a r problem w a s 80% o f t h e t o t a l t e s t time. The shallow r e s e r v o i r f i e l d test a t Kern River demonstrated t h e f i e l d performance of t h e generator system and t h a t n e g l e c t a b l e material c o r r o s i o n w a s encountered with t h e low s u l f u r LPG f u e l . The combustion g a s e s moved r a p i d l y through t h e r e s e r v o i r , reaching production wells i n t h e 2 ~ acre 5 5-spot p a t t e r n w i t h i n 18 h r s . The o i l produced d i d n o t e x h i b i t any special emulsions due t o presence of t h e combustion gases. The e f f e c t of i n j e c t i n g t h e combustion gases i n t o t h e r e s e r v o i r reduced t h e environmental inpact due t o atmospheric exhaust o f NOx and SOx. TEST OF GENERATOR INSTALLATION AND RETRIEVAL The downhole g e n e r a t o r r e q u i r e s s u p p l i e s of f u e l , water, and o x i d i z e r t o produce steam a t t h e sand face. Multiple s t r i n g s must be run t o supply t h e g e n e r a t o r A t e s t t o determine proceedure f o r i n s t a l l a t i o n o f t h e with t h e s e f l u i d s . device below 700 meters w a s performed i n l a t e September 1980.2 The g e n e r a t o r u t i l i z e d i n t h i s test w a s 15 meters long and designed f o r i n s e r t i o n with a 18 cm diameter casing. The m u l t i - s t r i n g supply c o n s i s t e d of t w o j o i n t e d t u b u l a r s , t w o small diameter continuous t u b u l a r s , and an electrical c o n t r o l cable.

set Baker AB-1 packer w a s l o c a t e d below t h e generator. The packer w a s set a f t e r t h e generator w a s i n place. The m u l t i s t r i n g d e l i v e r y system w a s p r e s s u r e t e s t e d before s e t t i n g of t h e packer, a f t e r s e t t i n g , and a f t e r release of t h e packer. The t e s t demonstrated t h a t t h e i n t e g r i t y o f t h e system w a s maintained a t a l l s t a g e s of i n s e r t i o n and r e t r i e v a l . A mechanically

DEEP DOWNHOLE OPERATION The g e n e r a t o r design which w a s t e s t e d i n t h e shallow t e s t i n t h e Kern River F i e l d h a s been r e p l a c e d by a design which o p e r a t e d on l i q u i d f u e l s ( d i e s e l No. 21. The l i q u i d f u e l design w a s developed i n o r d e r t o have wider applicat i o n by u s i n g more abundant f u e l s .

541 A site for testing of the generator in a reservoir below 700 m was selected in the Wilmington Field in California. The test was carried out in cooperation with the City of Long Beach, California, and the Long Beach Oil Developnent Co. A new injection well was drilled for the test while existing production wells were utilized to form a five-spot 5-acre pattern. The injection well was directionally drilled at a 36 degree angle, the total length of the well is 830 meters. The generator was inserted on June 19, 1981. The continuity of supply lines was tested and the responces of the reservoir to gas injection were studied after insertion of the device. The generator was ignited on June 22, 1981. The computerized ignition was achieved without incident, and continuous operation of the generator has proceeded ignition. The arrival of combustion gases at production wells was observed on June 26. The intermediate term test is scheduled for completion during September 1981. A longer term follow on test may be performed in the same location for a total operation time of one year. CONCLUSIONS The DOE program for development of a downhole steam generator for recovery of heavy oil from deep reservoirs has proceeded through a series of successful field tests. The ability of the device to eliminate heat losses and reduce environmental impact of steam drive has been demonstrated. The operational characteristics of the device in deep downhole operations are being evaluated in current field testing.

REFERENCES 1.

Mulac, A. J., et al, Project DEEP STEAM PrelMnary'Field Test, Sandia National Laboratories Report SANDBO-2843, April 1981

2.

Hulac, A. J., et al, Multiple String Demonstration Test for Project DEEP STEAM, Sandia National Laboratories Report SANDBO-2872, April 1981

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THERMAL RECOVERY METHODS

549

STEAM DRIVE - THE SUCCESSFUL ENHANCED OIL RECOVERYTECHNOLOGY TODD M.DOSCHER and FARHAD CHASSEMI Department of Petroleum Engineering, Universiw of Southern calfomirr, Los Angeles, Gzlvornia 90007 I . ABSTRACT

Continued work w i t h p h y s i c a l l y s c a l e d models of t h e steam d r i v e process has confirmed earlier conclusions t h a t t h e process should be viewed as being c o m p r i s e d of t w o d i s t i n c t componenta: t h e h e a t i n g of t h e o i l a t t h e i n t e r f a c e b e t v e e n t h e o i l column and t h e o v e r r i d i n g s t e a m , and t h e n t h e displacement of t h e heated oil by an e x c e p t i o n a l l y high v e l o c i t y gas (steam vapor) drive. The s t u d i e s d e s c r i b e d h e r e i n were c o n d u c t e d t o v a l i d a t e c e r t a i n hypotheses t h a t r e s u l t from t h e a p p r e c i a t i o n of t h e foregoing mechanism by which t h e eteam d r i v e operatea. In general, a l l t h e s e hypotheses have been proven

.

The o i l steam r a t i o , when communication between i n j e c t i o n and producing w e l l s is e s t a b l i s h e d e a r l y , is not dependent upon r e s e r v o i r thickness when r e c o v e r i n g m o d e r a t e l y v i s c o u s c r u d e o i l s . The o i l steam r a t i o s i n a wide r a n g e of f i e l d o p e r a t i o n s , i n k e e p i n g w i t h t h i s c o n c l u s i o n , are shown t o f a l l w i t h i n a very MKKOW band of values. Perhaps t h e most novel conclusion a r i s i n g from t h i s study, i n t i m a t e d by t h e work of o t h e r s i n t h e p a s t , is t h a t t h e steam d r i v e is a p o w e r f u l p r o c e s s f o r r e c o v e r i n g h i g h g r a v i t y crudes, even w a t e r f l o o d r e s i d u a l s i f high i n j e c t i o n r a t e s of high q u a l i t y steam can be achieved. The s u b s t i t u t i o n of i n e r t gas f o r some of t h e steam i n a mature steam d r i v e can s i g n f i c a n t l y i n c r e a s e t h e t h e r m a l e f f i c i e n c y b u t i t is n o t c e r t a i n , a t t h i s t i m e , t h a t t h e economic ef f l c i e n c y would thereby be increased. F i n a l l y , t h e observed e f f e c t of t h e v i s c o s i t y of t h e crude a t steam temperature on t h e e f f i c i e n c y of t h e p r o c e s s . t h r e a t e n s t h e p o s s i b i l i t y of u s i n g t h e steam d r i v e f o r u n a s s i s t e d recovery of t r u l y viscous crudes and bitumens. 11. INTRODUCTION

The s t e a m d r i v e was f i r s t a t t e m p t e d i n t h e Hene Grande f i e l d I n Venezuela i n t h e l a t e W e where its f a i l u r e gave rise t o t h e use of c y c l i c ateam s t i m u l a t i o n f o r a c c e l e r a t i n g t h e recovery of crude o i l from r e s e r v o i r s c o n t a i n i g viscous Crude.. Eowever, during t h e subsequent decade experiments w i t h t h e steam d r i v e i n t h e San J o a q u i n V a l l e y of C a l i f o r n i a and i n t h e Athabasca bitumfoou8 8ands of Canada proved t h a t i t w a s a v i a b l e scheme f o r recovering viscous crud- and c e r t a i n bitumens. Today, p r o d u c t i o n i n C a l i f o r n i a as a r e s u l t of b o t h c y c l i c s t e a m i n j e c t i o n and steam d r i v e OperatiOM is approximately 400,000 b a r r e l s of o i l a day, or 40% o f t h e 8tate.8 t o t a l . Recovery e f f i c i e n c y in aome m a t u r e o p e r a t i o n e is d r e 8 d y well over 50% of t h e o r i g i n a l oil i n p l a c e and is

550 projected t o approach 70%. a v a l u e t h a t is achieved i n only a few r e s e r v o i r s t h a t a r e e x p l o i t e d by c o n v e n t i o n a l technology. C u m u l a t i v e r e c o v e r y f r o m r e s e r v o i r s subjected t o steam i n j e c t i o n i n C a l i f o r n i a is now approaching 1.5 b i l l i o n b a r r e l s of o i l . The s t e a m d r i v e h a s been i n t e n s i v e l y s t u d i e d i n t h e Department of P e t r o l e u m E n g i n e e r i n g of t h e U n i v e r s i t y of S o u t h e r n C a l i f o r n i a u s i n g p h y s i c a l l y s c a l e d models. The r e s u l t s of t h e s t u d i e s have c o r r o b o r a t e d a number of conclusions t h a t had been e m p i r i c a l l y reached by s t u d i e s of f i e l d operations and i n a d d i t i o n have provided f u r t h e r i n s i g h t i n t o t h e mechanism by which t h e a t e a m d r i v e f u n ~ t i o n s ~ , ~ , 3One , ~ . of t h e most i m p o r t a n t conclusions from t h e s e s t u d i e s is t h a t t h e e f f i c i e n c y of t h e steam d r i v e i s a function of t h e v i s c o s i t y of t h e crude o i l a t steam temperature. This i n t u r n l e a d s t o t h e f u r t h e r c o n c l u s i o n s t h a t t h e s t e a m d r i v e may n o t be a s e f f i c i e n t as may have been surmised f o r t h e recovery of extremely viscous bitumens and may be t h e u l t i m a t e recovery scheme f o r t h e recovery of high g r a v i t y crude o i l s . I n t h e c l a s s i c a n a l y t i c a l d e r i v a t i o n of t h e way i n which a steam d r i v e functions, a t t e n t i o n is focussed on t h e development of a steam zone, which o c c u p i e s t h e e n t i r e c r o s s s e c t i o n of t h e r e s e r v o i r , and f r o m which o i l i s assumed t o be depleted t o some n a t u r a l l y determined r e s i d u a l o i l s a t u r a t i o n . The f a c t i s , however, t h a t t h e p r e s s u r e r e q u i r e d t o f r o n t a l l y d i s p l a c e a Viscous o i l bank a t an appreciable (economic) r a t e can r a r e l y be applied i n a r e a l reservoir. Reported f i e l d r e s u l t s have demonstrated t h a t steam does not f r o n t a l l y d i s p l a c e heavy o i l i n a s t e a m d r i v e o p e r a t i o n . I n j e c t e d s t e a m i n i t i a l l y e n t e r s t h e formation through a depleted o r w e t i n t e r v a l , a f r a c t u r e , or, i n unconsolidated formations, a f l u i d i z e d i n t e r v a l . I n a s u c c e s s f u l steam d r i v e i n r e s e r v o i r s c o n t a i n i n g v i s c o u s crude, t h e steam p e n e t r a t e s t o t h e producing w e l l q u i t e e a r l y i n t h e l i f e of t h e operation. Without t h i s , t h e i n f l u x of o i l i n t o t h e p r o d u c i n g w e l l would s t i l l b e l i m i t e d by t h e h i g h v i s c o s i t y of t h e r e s e r v o i r crude. Even i f t h e i n i t i a l s t e a m e n t r y i s n o t t h r o u g h a d e p l e t e d zone a t t h e t o p of t h e o i l s e c t i o n , t h e n t h e s t e a m soon m i g r a t e s t o t h e t o p i f t h e r e l a any s i g n i f i c a n t v e r t i c a l p e r m e a b i l i t y a t a l l . D e p l e t i o n of t h e o i l t o a v e r y low s a t u r a t i o n o c c u r s i n t h e i n t e r v a l t h r o u g h which t h e steam f l o w s , and w i t h t i m e t h e d e p l e t i o n e x t e n d s d ~ w n w a r d s ~ ,I~n. t h e s c a l e d p h y s i c a l model s t u d i e s , t h i s v e r t i c a l extension of t h e s t e a m zone can b e f o l l o w e d i n some d e t a i l . The h e a t e d c r u d e a t t h e i n t e r f a c e b e t w e e n t h e steam and t h e o i l column i s s t r i p p e d o f f o r d r a g g e d along by t h e flowing steam. This s t r a t i f i e d flow of steam i s of course not unexpected i n v i e w of its very low d e n s i t y i n comparison t o t h e d e n s i t y of t h e r e s e r v o i r f l u i d s . However, t h e u n e x p e c t e d r e s u l t i s t h a t t h e f l o w i n g steam i s capable of d r i v i n g t h e o i l s a t u r a t i o n down t o such low levels. The i n t e r f a c i a l t e n s i o n of o i l a g a i n s t s a t u r a t e d s t e a m h a s been v e r i f i e d i n our l a b o r a t o r i e s t o b e l i t t l e d i f f e r e n t from t h a t o i l a g a i n s t vater, and t h e r e f o r e i t a p p e a r s t h a t t h e o n l y p a r a m e t e r t o which t h e low r e s i d u a l can be a t t r i b u t e d is t h e high v e l o c i t y of t h e gas (steam vapor). I t m i g h t b e n o t e d t h a t t h e i n j e c t i o n of 500 b a r r e l s of s t e a m p e r day i n t o a r e s e r v o i r a t a n a v e r g e p r e s s u r e of 200 p s i . i s e q u i v a l e n t ( n e g l e c t i n g condensation) t o t h e i n j e c t i o n of 6 M M SCFD of an i d e a l gas. The r e s u l t i n g v e l o c i t i e s on 2.5 t o 6 a c r e spacing ( t h e u s u a l spacings f o r steam d r i v e w i t h I n j e c t i o n rates of 500 b a r r e l s p e r d a y ) when c o u r s i n g t h r o u g h a 2 5 f o o t depleted zone are very high; of t h e o r d e r of 100 f e e t p e r day. Of course, a s i g n i f i c a n t f r a c t i o n of t h e i n j e c t e d steam condensea, but o f f s e t t i n g t h i s somewhat is t h e f a c t t h a t t h e production p r e s s u r e is less than t h e i n j e c t i o n p r e s s u r e and t h e r e f o r e t h e uncondensed steam w i l l expand and f u r t h e r i n c r e a s e i t s v e l o c i t y through t h e reservoir.

551 111. THE OIL STEAM RATIO

- THE MEASURE OF SUCCESS

The amount of o i l produced p e r u n i t q u a n t i t y of steam i n j e c t e d is t h e most i m p o r t a n t c r i t e r i a f o r j u d g i n g t h e s u c c e s s of a s t e a m i n j e c t i o n project. This is so because t h e amount of energy used t o generate the steam i n even t h e most s u c c e s s f u l p r o j e c t s i s a s u b s t a n t i a l f r a c t i o n of t h e p r o d u c e d o i l . The v a l u e of t h e f u e l i s o v e r w h e l m i n g l y t h e l a r g e s t s i n g l e component of t h e c o s t of producing o i l by steam i n j e c t i o n . D u r i n g t h e 60's Marx and Langenheim7 p u b l i s h e d a p r o c e d u r e f o r c a l c u l a t i n g t h e g r o w t h of a s t e a m zone a s a f u n c t i o n of steam i n j e c t i o n r a t e , t i m e of I n j e c t i o n , r e s e r v o i r dimensions, and t h e thermal p r o p e r t i e s of t h e r e s e r v o i r and t h e cap and base rocks. Mandl and Volek8 l a t e r undertook a somewhat more d e t a i l e d a n a l y s i s of t h e mass and t h e r m a l b a l a n c e s a t t h e condensation f r o n t and developed a somewhat improved a n a l y t i c a l technique f o r e s t i m a t i n g t h e g r o w t h of t h e s t e a m zone. S u b s e q u e n t l y M y h i l l and Stegemeier9 c o d i f i e d Mandl and Volek's a n a l y s i s t o permit ready c a l c u l a t i o n of t h e o i l s t e a m r a t i o a s a f u n c t i o n of a v a r i e t y of o p e r a t i n g c o n d i t i o n s and w e l l spacings. I t 1s important t o n o t e t h a t t h e o i l steam r a t i o s c a l c u l a t e d by these methods a r e f o r u n i f o r m s a n d s ( a l t h o u g h a l l o w a n c e can be made f o r unproductive but permeable l a y e r s disseminated through t h e r e s e r v o i r sand). Also, i t is assumed a t t h e o u t s e t of t h e s e c a l c u l a t i o n s t h a t t h e i n j e c t i o n r a t e of steam i s e s t a b l i s h e d o r assumed s i n c e t h e a n a l y s i s i s s t r i c t l y a t h e r m a l one and d o e s n o t t r e a t t h e q u e s t i o n s r e l a t e d t o f l u i d flow. Eventually, numerical methodslO were developed f o r p r e d i c t i n g t h e performance of a s t e a m d r i v e . I t soon became o b v i o u s t h a t f o r t h e presumed r e s e r v o i r c o n d i t i o n s i n most heavy o i l r e s e r v o i r s d i d n o t p e r m i t t h e i n j e c t i o n of steam a t t h e r a t e s observed i n f i e l d operationa. I n o r d e r t o overcome t h i s d e f i c i e n c y , a n e x t r a o r d i n a r y h i g b c o m p r e e s i b i l i t y was a s s i g n e d t o t h e r e s e r v o i r . The i m p o r t a n t a d v a n t a g e of t h e n u m e r i c a l a n a l y s i s o v e r t h e a n a l y t i c a l one is t h e a b i l i t y of t h e former t o include more than one l a y e r and t h u s p e r m i t t h e d e v e l o p m e n t of t h e o b v i o u s g r a v i t y o v e r r i d e of t h e steam. By making s u i t a b l e adjustments i n t h e i n p u t parameters t o g e t a match of t h e p e r f o r m a n c e of p a r t i c u l a r o p e r a t i o n s , t h e r e s u l t i n g n u m e r i c a l a n a l y s i s can be presumed t o be a generalized s i m u l a t i o n of t h e steam drive process.

Both t h e a n a l y t i c a l and n u m e r i c a l models of t h e steam d r i v e p r o c e s s p r e d i c t a s i g n i f i c a n t e f f e c t of r e s e r v o i r t h i c k n e s s on t h e o i l steam r a t i o , a c e F i g u r e s 1 and 2. T h i s comes a b o u t f r o m t h e f a c t t h a t when f r o n t a l displacement occurs, t h e h e a t l o s s a t t h e cap and base rock ie independent of t h e r e s e r v o i r t h i c k n e s s . Hence, t h e t h i c k e r t h e r e s e r v o i r , t h e g r e a t e r t h e f r a c t i o n of t h e i n j e c t e d h e a t t h a t is captured w i t h i n t h e reservoir. Recent reviews of t h e performance of steam d r i v e operations i n d i c a t e t h a t a much lower range of o i l steam r a t i o s occur i n f i e l d operations than would be expected from t h e r e s u l t s of t h e s e c a l c u l a t i o n s . The average of 7 c u r r e n t and completed steam d r i v e o p e r a t i o n s i n t h i c k sands, I n excess of 70 f e e t and a p p r o a c h i n g 200 f e e t , r e p o r t e d i n a r e c e n t s t u d y l l is o n l y 0.22 w i t h a standard d e v i a t i o n of only 0.06. On t h e o t h e r hand, t h e a v e r e fe;rlqfeam d r i v e s i n t h i n n e r s a n d s , r a n g i n g f r o m 18 f e e t t o 50 f e e ttt4, €9; i s s t i l l 0.20, r a n g i n g from 0.15 t o 0.25. F u r t h e r , t h e r e c o v e r y e f f i c i e n c y f r o m two of t h e s e r e l a t i v e l y t h i n r e s e r v o i r s , viz., Slocum and San Joaquin have been reported t o have approached 80%. This anomalous behavlor of t h e o i l steam r a t i o combined with t h e observed o v e r r i d e of s t e a m s u g g e s t e d t h a t t h e p e r f o r m a n c e of steam d r i v e s , a t

552

Fig.2. Fig.1.

E f f e c t of O i l Sat.,Reservoir Thickness and NetIGross R a t i o on O/S R a t i o

E f f e c t of Res. Thickness on O i l / Steam R a t i o

l e a s t when d e a l i n g w i t h v i s c o u s c r u d e s , is n o t c o r r e c t l y e s t i m a t e d by a n a n a l y s i s t h a t assumes f r o n t a l displacement. The e a r l y work on t h e p h y s i c a l model e x p e r i m e n t s 1 * 1 6 i n d i c a t e d t h a t t h e p r o d u c t i o n of o i l o c c u r s a t a ( v e r t i c a l l y ) moving boundary between t h e o v e r r i d i n g steam zone and t h e o i l column. C o r r e l a t i v e with t h i s performance is t h e e x i s t e n c e of t h e f o l l o w i n g occurrences : 1. There is an optimum ateam i n j e c t i o n rate f o r a given spacing between i n j e c t i o n and production wells. Thin phenomenon had been observed i n Kern River o p e r a t i o n s sometime earlied’.

2- The o i l s t e a m r a t i o i n v i r t u a l l y l i n e a r l y r e l a t e d t o t h e q u a l i t y of t h e I n j e c t e d steam. This r e s u l t i s i m p l i c i t i n t h e Mandl Volek analysis. Rot v a t e r i s v i r t u a l l y i n e f f e c t i v e i n r e c o v e r i n g any s i g n f i c a n t q u a n t i t y of viscoua crudes.

3. The o i l steam r a t i o i n a f u n c t i o n of t h e v i s c o s i t y of t h e v i s c o u s c r u d u at ( t h e average) steam t e m p e r a t u r e . F o r l o d e r a t e l y v i s c o u s c r u d e s t h e r a t i o a p p e a r s t o b e a f u n c t i o n of t h e h a l f power of t h e i n v e r s e of t h e s t e a m temperature v i 8 c o s i t y . Figure 3. This observation has s e r i o u s i m p l i c a t i o n s f o r t h e a p p l i c a b i l i t y of t h e steam d r i v e proceas t o highly viscous bitumens f o r which a very high steam temperature vould be required. It vould appear t h a t t h e r e s u l t i n g o i l steam r a t i o vould f a l l t o uneconomic valuea (below 0.12’1) when t h e produced crude is used as f u e l f o r g e n e r a t i n g steam. The f a l l i n t h e o i l steam r a t i o would b e f u r t h e r e x a c e r b a t e d by t h e l o w e r f r a c t i o n of t h e l a t e n t h e a t and t h e lower s p e c i f i c volume of t h e steam a t high temperatures (pressures).

4. The p e r m e a b i l i t y of t h e f o r m a t i o n , above a d a r c y , h a s v i r t u a l l y no e f f e c t on t h e o i l steam r a t i o . D e t a i l e d i n v e s t i g a t i o n s have n o t been conducted a t lower p e r m e a b i l i t i e s , but t h e r e i s a suggestion t h a t very low p e r m e a b i l i t i e s have a depressing e f f e c t on t h e o i l ateam r a t i o .

553

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VISCOSITY OF OK AT STEAM TEMPERATURE (CD)

Fig. 3. OilfSteam R a t i o as a Function of Reservoir F l u i d Viscosity

5. Diurnal i n j e c t i o n of steam, as would occur i f steam was generated by 80kr devices, does not s e r i o u s l y a f f e c t t h e o i l steam r a t i o as long as t h e t o t a l d a i l y rate is t h e same as in continuous i n j e c t i o n 3 -

The c u r r e n t study was t h e r e f o r e designed t o i n v e s t i g a t e j u s t why t h e 80 less in a c t u s l o p e r a t i o n s t h a n would b e p r e d i c t e d by a n a l y t i c a l and numerical models, and in a d d i t i o n , vhy t h e o i l rteam r a t i o 8 a p p e a r t o f a l l w i t h i n a n a r r o w band of v a l u e s f o r r e s e r v o i r s h a v i n g a w i d e r a n g e of t h i c k n e s r e s . F u r t h e r , b e c a u s e of t h e i n c r e a s i n g v a l u e of t h e o i l #team r a t i o w i t h a d e c r e a 8 e in o i l v i s c o r i t y , i t W a s decided t o i w e 8 t i g a t e j u a t how high a n o i l ateam r a t i o could be achieved in t h e d i r p l a c e m e n t of h i g h g r a v i t y c r u d e s , p a r t i c u l a r l y a t r e r i d u a l O i l ( t o water flood) maturations.

a i l rteam r a t i o a p p e a r s t o be

F i n a l l y , becaume t h e steam d r i v e p r o c e r s appearr t o be comprised of two rcchanism8: f i r s t l y , t h e h e a t i n g of t h e o i l a t t h e steam o i l i n t e r f a c e , and 8econdly t h e displacement of t h e o i l from t h a t i n t e r f a c e by t h e f l w of t h e at-m vapor; t h e s u b s t i t u t i o n of n i t r o g e n f o r some of t h e ateam that part was invertigated. used f o r displacement alone and not f o r h e a t i n g

-

-

I V . THE EFFECT OF RESERVOIR TH1CB;NESS

The e x p e r i m e n t a l p r o c e d u r e s and t e c h n i q u e s u8ed in c a r r y i n g o u t t h e p h y s i c a l y s c a l e d model experimenta have been thoroughly d e t a i l e d in earlier 8 t u d I e ~ ~ ' * Tables ~~~~1 . rummrires t h e prototype and model parameters f o r t h e experiment8 conducted w i t h viscous o i l 8 in t h i s study.

554

TABLE

1

PROTOIYPE AND CORRESPONDING MODEL PAWTERS

Parameter

I n i t i a l Res. Temp., "F Pressure, psi.

Prototype Lloydainster Reservoir

Mdel

75

3s

In j eet ion

500

8.S

Production

50

5.0

2;

0.354

Sand T h i c h e s s . f t Permeability. Darcy Porosity, I

1

550

53

55

Steam I n j e c t i o n Temp., "F

186

z

2

I n i t i a l Gas S a t u r a t i o n , O i l Gravity, "API

14

11.8

Steam Quality, I

7s

27 .l

1

76.9

Scaling Factor

Flow Rate, (P-B/D, ?(-cc/min)

1000

186

Time (P-year, M-minute)

1

85.7

P a t t e r n Area (P-acre. M-ft')

5

4.6

Distance of I n j e c t o r t o R o d u c n . f t

so

4.29

TheriPrl conductivity, B N / h r . f t .*F a)

overburdon

1.09

1.15

b)

uaderhrrdm

1.1

1.o

O i l Viscosity. cp a) r e s e r v o i r tamp.

b)

stem temp.

100,000 28

'

1000

5.8

Figure 4 shows t h e r e s u l t s obtained f o r a 26 f o o t t h i c k prototype on 5 a c r e r p a c i n g ( o r f o r a 1 3 f o o t t h i c k r e s e r o i r o n 2.5 a c r e a p a c i n g a t h a l f t h e i n d i c a t e d I n j e c t i o n rate. o r f o r a 52 f o o t r e s e r v o i r on 10 acre spacing a t double t h e i n d i c a t e d i n j e c t i o n rate). A conpariron of t h i s d a t a w i t h t h e

555 r e s u l t s obtained earlier f o r t h e 70 f o o t prototype, Figure 5, i n d i c a t e s t h a t t h e optimum stem i n j e c t i o n rate is i n t h e same range f o r both models; i t is n o t d e p e n d e n t on t h e t h i c k n e s s of t h e f o r m a t i o n . F i g u r e 6 compare8 t h e p e r f o r m a n c e o f t h e optimum steam i n j e c t i o n r a t e i n t h e two models. (The I n i t i a l , q u i t e pronounced d i f f e r e n c e i n t h e two runs is due t o t h e f a c t t h a t i n t h e later work w i t h t h e t h i n n e r r e s e r v o i r t h e i n i t i a l few hundreths of a pore volume of o i l t h a t was produced was not a t t r i b u t e d t o t h e steam drive.) Earlier c o n c l u s i o n s b a s e d on f i e l d o b s e r v a t i o n t o t h e e f f e c t t h a t t h e optimum rate is a f u n c t i o n of t h e a c r e f e e t i n t h e p a t t e r n area was probably due to t h e f a c t t h a t a l l t h e p a t t e r n s had t h e same thicknes.

" J

0.15

6 W

F 0.H)

2 0.05 0

L 1.0

0.5

,

1.5

2.0

Prololype Permeobilily. dorcy 1.0 Oil roturolion. Y. 90 Sand Ihichner;. I 1 26 irao. ocre . Oil vixosily 01 s l a m lemo Averow rleom awlily. Y. 65 Stcorn- pressure, Psib 190-270 Po$osity. ,% , 33 2.5 3.0 3.5 40 4.5

STEAM INJECTED. EQUIVALENT WATER. P.V.'r

Pig. 4. E f f e c t of I n j e c t i o n Rate on Oil/Steam R a t i o

a

L I-

0.25-

(196.4

B/o

0.90-

2393 V

I

0

l

t

1.0

l

a

r

2.0

l

l

r

3.0

l

r

L

4x

STEAM INJECTED, EOUIVALENT WATER, P.V.' r

Pig. 5. E f f e c t of I n j e c t i o n Rate on Oil/Steam R a t i o

I I

556

n f

Thiarludy Eorlicr studies'

0.30

744 B/a

657.5

B/O

1.0 2.0 3.0 4.c STEAM INJECTED, EOUIVALENT WATER, P.V.'s

Fig. 6. Comparison of OilfSteam Ratio f o r Thick and Thin Sand

The s t e a m q u a l i t y uaed i n t h e 70 f o o t p r o t o t y p e r u n s a v e r a g e d 4 5 % whereas t h e steam q u a l i t y f o r t h e 26 f o o t NN)averaged 65%. C a l c u l a t i o n s based on f r o n t a l d r i v e theory i n d i c a t e t h e o i l steam r a t i o i n t h e f i r s t f i v e years should be somewhat h i g h e r f o r t h e t h i c k r e s e r v o i r than t h a t observed i n t h i s work. and j u s t s l i g h t l y h i g h e r f o r t h e t h i n reservoir. Discounting t h e e f f e c t of s t e a m q u a l i t y , t h e r e s u l t s f o r t h e two r e s e r v o i r s would b e v i r t u a1l y i d e n t i c a l . Given t h a t t h e d e s c r i p t i o n of t h e steam d r i v e presented e a r l i e r , viz., t h a t t h e s t e a m o v e r r i d e s t h e o i l column and g r a d u a l l y s t r i p s t h e h o t o i l f r o m t h e i n t e r f a c e b e t w e e n t h e l a t t e r and I t s e l f , t h e r e i s no r e a s o n t o a n t i c i p a t e a s i g n i f i c a n t e f f e c t of r e s e r v o i r t h i c k n e s s on t h e p r o c e s s . I n d e e d , t h i s i s what t h e f i e l d r e s u l t s i n d i c a t e . T h e a l m o s t c o n s t a n t o i l steam r a t i o observed i n t h e wide range of steam d r i v e n r e s e r v o i r s r e p o r t e d above i s i n a g r e e m e n t w i t h t h e r a n g e of o i l steam r a t i o , 0.15 t o 0.20 observed i n t h e p h y s i c a l l y s c a l e d model runs w i t h viscous crudes. A s i m p l e mathematical f o r m u l a t i o n of t h e displacement of o i l a t t h e moving boundary h a s been d e v e l o p e d which l e a d s t o t h e p r e d i c t i o n of j u s t s u c h a r a n g e of values f o r t h e o i l steam ratio16.

V. EFPECT OF FLUID VISCOSITY Figure 7 shows t h e r e s u l t s f o r t h e 26 f o o t prototype r e s e r v o i r when t h e prototype r e s e r v o i r f l u i d has a v i s c o s i t y a t steam temperature of only 0.4 c e n t i p o i s c , s l i g h t l y g r e a t e r than water would have a t t h e same temperatureA c o m p a r i s o n of t h i s p r o d u c t i o n h i s t o r y w i t h t h a t of t h e more v i s c o u s r e s e r v o i r f l u i d s quickly shows t h a t displacement of t h e l o w v i s c o s i t y f l u i d by 8te.m r e s u l t s i n a u c h higher o i l steam r a t i o . F i g u r e 3 shows t h e o i l a t e a m r a t i o a s a f u n c t i o n of v i s c o s i t y of t h e o i l a t steam t e m p e r a t u r e . The d a t a p o i n t f o r t h e t h r e e h i g h e s t v i S c o s i t Y f l u i d s were obtained i n t h e earlier s t u d i e s i n a 70 f o o t prototype, and t h e d a t a p o i n t f o r t h e l o w e s t v i s c o s i t y f l u i d i s t h e one d e s c r i b e d i n t h i s study adjuated downwards because of t h e h i g h e r q u a l i t y of t h e steam t h a t was used. It i 8 apparent t h a t f o r t h e same o i l s a t u r a t i o n , t h e o i l steam r a t i o COOtiruw t o I n c r e a s e as t h e v i s c o s i t y of t h e r e s e r v o i r f l u i d decreases.

557

0

t.

I

'

9

'

a5

fi

1 ' 1

a

'

' ' ' '

I

a

' '

1.0 1.5 STEAM INJECTED, EOUIVALENT W A E R . P.V.'s

I

;

0

Fig. 7. Oil/Steam Ratio History for Low Viscosity Fluid

A comparison of the steam (and therefore temperature) distribution i n the reservoir for the displacement of a viscous fluid and one with a low viscosity Is quite informative. Figures 8 .and 9 show the temperature distribution for the displacement of the heavy oll'and the mobile oil, respectively, after the Injection of an amount of steam generated from 0.5 pore volume of liquid water. Figures 10 and 1 1 portray the temperature distribution after the injection of 1.5 pore volumes.

c- FLOW DIRECIIOI

Fig. 8 . Temperature Dirtribution for the Heavy Oil of Steam Injected After 0.51 P.V.'r

558 FLOW DIRECTION

Fig. 9 . Temperature D i s t r i b u t i o n f o r t h e L i g h t O i l A f t e r 0.5 P.V.'s of Steam I n j e c t e d

c-FLOW

DIRECTION

Fig. 10. Temperature D i s t r i b u t i o n f o r t h e Heavy O i l A f t e r 1.5 P.V.'s of Steam I n j e c t e d

I t should be noted t h a t w i t h a d e c r e a s e i n v i s c o s i t y of t h e r e s e r v o i r f l u i d t h e t e m p e r a t u r e d i s t r i b u t i o n i n d i c a t e a t h e mechanism is g r a d u a l l y t a k i n g o n t h e a s p e c t s of a f r o n t a l d i s p l a c e m e n t . T h i s a g a i n s h o u l d b e a n t i c i p a t e d s i n c e w i t h d e c r e a s i n g v e l o c i t y t h e a v a i l a b l e p r e s s u r e can indeed d i s p l a c e t h e bank of r e s e r v o i r f l u i d . The o i l s t e a m r a t i o s h o u l d now b e e x p e c t e d t o a p p r o a c h t h e v a l u e s p r e d i c t e d by t h e f r o n t a l d i s p l a c e m e n t analyses, and indeed i t does. An e a r l i e r numerical s t u d y a l s o i n d i c a t e d t h a t into a t h e o v e r r i d e of steam decreased s i g n i f i c a n t l y when i n j e c t i n g a t e r e s e r v o i r t h a t had been water flooded t o a r e s d i u a l o i l s a t u r a t i o n f f .

559 C-

FLOW DIRECTION

Fig. 11. Temperature D i s t r i b u t i o n f o r t h e Light 011 A f t e r 1.5 P.V.'s of Steam I n j e c t e d

V I . STEAM DRIVE OF A RESIDUAL. O I L SATURATION

The r e l a t i o n s h i p of t h e o i l s t e a m r a t i o t o oil v i s c o s i t y , F i g u r e 3, i n d i c a t e s t h a t a steam d r i v e i n a r e s e r v o i r having a 33 percent porosity and s a t u r a t e d w i t h water w i l l p r o d u c e t h e l a t t e r a t a r e s e r v o i r w a t e r l s t e a m i n j e c t e d r a t i o of 0.7 a f t e r t h e i n j e c t i o n of 1.0 pore volume of steam. Even h i g h e r . i f t h e q u a l i t y of t h e i n j e c t e d steam a t t h e s a n d f a c e Is above 65% and t h e p r e s s u r e is less than the prototype value of approximately 250 p s i used i n our s t u d i e s . I f t h e r e s e r v o i r is n o t 100% s a t u r a t e d w i t h water, b u t c o n t a i n s a r e s i d u a l s a t u r a t i o n of a low v i s c o s i t y crude o i l which i r displaced more or less I n p r o p o r t i o n t o i t s s a t u r a t i o n i n t h e r e s e r v o i r ; t h e n t h e r e s u l t i n g o i l steam ratio would be a n t i c i p a t e d to be ( 0 . 7 ~ ~ ~ ) .

For a r e s i d u a l s a t u r a t i o n of 0.25, or g r e a t e r , t h e r e s u l t i n g o i l steam r a t i o would be 0.18, or g r e a t e r ; as high or h i g h e r than t h e o i l rteam r a t i o s e x p e r i e n c e d I n t h e steam d r i v e of heavy o i l s . The r e s u l t s of a model experiment With a r e s i d u a l s a t u r a t i o n of 22% of a prototype crude o i l having a v i s c o s i t y of 0.15 c e n t i p o i s e at a steam temperature of 401% are shown I n F i g u r e 12. The o i l a t c a m r a t i o is 0.21 a f t e r t h e r e c o v e r y of 32% of t h e r e s i d u a l o i l , and t h e o i l steam r a t i o i n m t i l l 0.14 a f t e r t h e r e c o v e r y of 50% o f t h e oil i n p l a c e . I t is I m p o r t a n t t o n o t e t h a t r e a c h i n g s u c h h i g h o i l steam r a t i o s is d e p e n d e n t b o t h on a s u i t a b l y h i g h steam i n j e c t i o n r a t e and a s u f f i c i e n t l y h i g h p o r o s i t y . However, t h e r e s u l t s do n o t a p p e a r t o b e dependent on d i s t i l l a t i o n e f f e c t s , as had been Suggest by previous workers studying t h e recovery of r e s i d u a l o i l by a steam driveTib. Further, t h e mere f a c t t h a t a h i g h oil s t e a m r a t i o is r e a l i z e d is n o t a u f f i c i e n t t o i n d i c a t e t h a t a n economic steam d r i v e o p e r a t i o n is f e a s i b l e . C e r t a i n l y , an economic operation would be a t hand i f n o a d d i t i o n a l w e l l d r i l l i n g c o s t a are e n c o u n t e r e d i n i m p l e m e n t i n g t h e d r i v e ; however, If many new w e l l s had t o b e d r i l l e d i n r e l a t i v e l y t h i n sands ( r e s u l t i n g i n a high c a p i t a l investment p e r recovered b a r r e l ) , t h e advantages of high o i l steam r a t i o s might be overcome-

5 60

0.b

1

I

I

I

1

I

I

I

FROTCkYPE mldIhal a1 22%

pc-d .cP

401

0.15

R O S W P W -

26

-.

M

Y

x

.

33

LzQsfm-0,

Rk

P I

a0

I

I

I

I

I

X

B I

P I

7o

m774 1

40 60 80 100 OIL REcwup(, x O.O.I.P. Fig. 12. Cum. Oil/Steam R a t i o h i a t o r y f o r Waterflood Residal O i l 0

20

VII. EFFECT OF CO-INJECTION OF NITROGEN AND STEAM

Figure 13 compares t h e performance of t h e steam d r i v e of a viscous 011 w i t h w i t h t h a t i n v i r t u a l l y t v o i d e n t i c a l r e s e r v o i r s i t u a t i o m i n which t h e i n j e c t i o n of steam and n i t r o g e n was s u b s t i t u t e d f o r t h e I n j e c t i o n of steam alone af t e r one p o r e volume o f s t e a m had a l r e d y b e e n i n j e c t e d . I n Run 36 s t e a m and n i t r o g e n were ~ i m u l t a n e o u a l yi n j e c t e d , and in Run 37 s l u g s O f n i t r o g e n vere a l t e r n a t e d w i t h t h e steam.

0

*

rb

ab

io

Fig. 13. Nitrogen as a Steam Additive Compring t h e r e a u l t a of Run 36 and 37 w i t h t h e c o n t r o l . Run 38. i t is a p p a r e n t t h a t oil p r o d u c t i o n l a b e i n g m a i n t a i n e d e v e n though a t e a m i n j e c t i o n is c u r t a i l e d a a a r e a u l t of t h e a n c i l l i a r y e f f e c t of t h e i n j e c t e d i n e r t gas. T h e r e r e a u l t a c l e a r l y show t h a t i n a a t e a m d r i v e o p e r a t i o n t h e a t e m l a playing t h e u l t i p l e role a l r e a d y described. A t t h i s t i r e , i t is n o t c l e a r t h a t t h e r e would b e a marked economic g a i n i n t h e a u b a t i t u t i o n of an i n e r t g a a f o r mome of t h e a t e a m i n a m t u r e steam d r i v e because of t h e u n i t c o a t of compreaaed, i n e r t gaaaea. Bovever. t h i s l a n o t l i k e l y t o b e t r u e i n l a r g e i n a t l l a t i o n s a t t h i n time. and may

561 n o t b e t r u e a t a l l i n t h e f u t u r e as t h e c o s t of e n e r g y c o n t i n u e s t o e s c a l a t e . T h e r e is a f a r l a r g e r component of e n e r g y c o s t s i n t h e u n i t c o s t of steam than t h e r e i r t h e u n i t c o s t of i n e r t gas. VII. CONCLUSIONS

The continued study of t h e steam d r i v e i n p h y s i c a l l y s c a l e d models, and c o r r e l a t i v e o b s e r v a t i o n s made on r e p o r t e d steam d r i v e o p e r a t i o n s i n t h e f i e l d lead t o t h e f o l l o w i n g conclusions: 1. The o i l steam r a t i o i n r e s e r v o i r s vhich c o n t a i n a moderately viscous crude o i l , and i n which rteam o v e r r i d e s t h e oil column w i l l a u b s t a n t i a l l y be t h e same r e g a r d l e s s of r e s e r v o i r thickness. The most probable range f o r t h e oil steam r a t i o v i l l be 0.15 t o 0.20. This conclusion presumes t h a t adequate i n j e c t i v i t y and c o m m u n i c a t i o n b e t w e e n i n j e c t i o n and production wells has been recured. The recovery e f f i c i e n c y i t r e l f w i l l decrease as t h e r e s e r v o i r t h i c k n e s s i n c r e a s e s much beyond 50 or 60 feet.

2. Because of t h e h i g h e r steam t e m p e r a t u r e s r e q u i r e d t o a c h i e v e r u f f i c i e n t m o b i l i t y of r e s e r v o i r crude, t h e oil steam r a t i o i n r e s e r v o i r s vhich c o n t a i n very viscous crudes are n o t l i k e l y t o p e r m i t economic recovery u n l e s s a f u e l c h e a p e r t h a n t h e c r u d e oil i t s e l f is u s e d f o r g e n e r a t i n g

rteam. 3. The oil steam r a t i o i n c r e a s e s markedly as t h e v i s c o s i t y of t h e r e s e r v o i r crude decreares. Thin is due t o t h e more e f f i c i e n t s t r i p p i n g of t h e h e a t e d f l u i d a t t h e oil steam i n t e r f a c e . An t h e v i s c o s i t y of t h e r e r e r v o i r f l u i d s d e c r e a s e t o t h a t of vater, t h e d i r p l a c e m e n t g r a d u a l l y c o n e r t s t o a f r o n t a l a d v a n c e and t h e e f f i c i e n c y of d i s p l a c e m e n t of t h e r e s e r v o i r f l u i d a i n c r e a s e s s t i l l f u r t h e r . The i n c r e a s e i n t h e oil rteam r a t i o is s u f f i c i e n t t o i n d i c a t e t h a t 10numerous s i t u a t i o n s v a t e r f l o o d r e r i d u a l oil a a t u r a t i o r u can be economically recovered by a rteam drive. (An e x t e n s i o n of t h e rame argument MY i n d i c a t e t h a t UUY resewoirr containing high g r a v i t y c r u d u may be more e f f i c i e n t l y e x p l o i t e d by a steam d r i v e than by a vater flood.

4. An i n e r t g a r s u c h a s n i t r o g e n c a n b e r u b s t i t u t e d f o r a s i g n f i c a n t f r a c t i o n of t h e ateam, t h a t would o t h e r w i r e be i n j e c t e d i n t o a mature steam f l o o d , r t o m a i n t a i n t h e p r o d u c t i o n of oil and a c h i e v e a h i g h e r o i l f s t e a m ratio. The economic a d v a n t a g e of ouch a r u b r t i t u t i o n v i l l become more s i g n f i c a n t M t h e v a l u e of t h e crude oil i t r e l f increases. 5. A n i m p l e c o n c e p t u a l model f o r t h e steam d r i v e v h i c h c o m p r i s e s t h e o v e r l a y of t h e rteam, t h e h e a t i n g of t h e oil a t t h e r e s u l t i n g oil ateam i n t e r f a c e , and t h e displacement of t h e heated o i l by t h e g a s d r i v e accounts f o r v i r t u a l l y a11 of t h e observatione made on rteam d r i v e o p e r a t i o n s i n t h e f i e l d and i n t h e l a b o r a t o r y p h y a i c a l l y s c a l e d models.

9111. REFERENCES 1. D o r c h e r , T. M., at. al.; "Scaled P h y s i c a l Models of t h e Steam D r i v e Process", Annual R e p o r t , C o n t r a c t EP-76-S-03-0113 36 PA, U n i t e d S t a t e s Department of Energy, Oakland, C a l i f o r n i a 2. Doacher, T. M., and Baung, V.; "Steam Drive P e r f o r m a n c e Judged f r o m Use of P h y s i c a l Modelr", O i l and Gas J. ( O c t 1979) 52

562 3. Doscher, T. U., Ghassemi, F., and Omoregie, 0. S.; "The A n t i c i p a t e d Effect of D i u r n a l I n j e c t i o n on S t e a m D r i v e E f f i c i e n c y " , P a p e r SPE 8885 preaeated a t SPE 50th C a l i f o r n i a Regional Meeting, Lo8 AngeleS, A p r i l 9-11, 1980 4 0 Ree, S. W., and Doscher, T. U.; "A Uethod, f o r p r e d i c t i n g O i l Recovery by Steamflooding Including t h e E f f e c t of D i s t i l l a t i o n and G r a v i t y Override", SOC. Pet. Eng. J. (AUg 1980) 249-266

.,

5. B l e v i n s , T. R and B i l l i n g s l e y , R. R.; "The Ten P a t t e r n Steam F l o o d , Kern River Field", J. Pet. Tech. (Dec 1975) 1505-1514

6. Neuman, C. 8.; "A W a t h e m a t i c a l M o d e l o f S t e a m D r i v e P r o c e s s Applications", Paper SPE 4757 Presented a t SPE 45th Annual Ueeting , Held i n Ventura, A p r i l 2-4, 1975 7. Uarx, J. W., and t a n g e n h e i m , K. H.; Injection", Trans., AIIIE, 216, 312-315

" R e s e r v o i r H e a t i n g by Rot F l u i d

8. Uandel, G., and Volek, C. W.; "Reat and Mass T r a n s p o r t i n Steam D r i v e Process", SOC. Pet. Eng. J. (Uar 1969) 59-79

M y h i l l , 1. A*, a n d S t e g e m e i e r , G. L.; "Steam-Drive 9. Prediction", J. Pet. Tech. (Fib 1978) 173-182

C o r r e l a t i o n and

10. Comma, E. a; " C o r r e l a t i o n s f o r P r e d i c t i n g O i l Recovery by Steamflood", J. Pet. Tech. (Feb 1980) 325-332 11. Farouq A l i , S. X., and U e l d a u , R. F.; " C u r r e n t Steamf l o o d Technology", J. Pet. Tech. (Oct 1979) 1332-1342 12. B a l l , A. Lo, and Bowman, R. W.; "(Tperation and P e r f o r m a n c e of t h e Slocum Thermal Recovery Project", J. Pet. Tech. (Apt 1973) 402-408

13. B l e v i n s , T. B., A B e l t i o e , B. J., and K i r k , R. S.; " A n a l y s i s of a Steam Drive P r o j e c t , Inglewood Field, California", J. Pet. Tech. (Sept 1969) 11411150

14. Wooten. R. W.; "Case H i e t o r y of a S u c c e s s f u l 1 Steamf l o o d P r o j e c t - L o c o Field", Paper SPE 7548 Presented a t 53rd SPE Annual Meeting, Houston, O c t 13, 1978 15. Greaser, G. R., and S h o r e , R. A.; " S t e a m f l o o d P e r f o r m a n c e in t h e Kern River Field", Paper SPE 8834 , Presented a t F i r s t J o i n t SPE/DOE Symposium,

Tulsa, A p r i l 20-23, 1980 16. Doscher, T. M., and Ghassemi, F.; "The E f f e c t of R e s e r v o i r T h i c k n e s s and low V i s c o s i t y F l u i d on The S t e a m Drag P r o c e s s " , P a p e r SPE 9897, Pre6ented a t The C a l i f o r n i a Regional Meeting, Bakersfield, March 25-26, 1981 17. B r u s e l l , C. G., and P i t t m a n , G. U.; "Performance of S t e a m D i s p l a c e m e n t in t h e Kern River Field", J. Pet. Tech. (Aug 1975) 997-1004

18. S t e g e m e i r , G. L., Laumbach, D. D., and Volek, C. W.; ' a e p r e s e n t i n g Steam P r o c e s s w i t h Vacuum Uodels", P a p e r SPE 6787, P r e s e n t e d a t 52nd SPE Annual F a l l n e t t i n g , Denver, Oct 9-12, 1977 1% A y d e l o t t e , S. R., and Ramesh, A. B.; "Economic F e a s i b i l i t y of Steam D r i v e i n L i g h t O i l R e s e r v o i r s " , P r e s e n t e d a t 5 t h Annual DOE Symposium, T u h a , Auguat 22-24, 1979 20. Bagoot, J. L e i j n s e , A., and Van P o e l g e e s t , F.; "Steam S t r i p Drive: A P o t e n t i a l T e r t i a r y Recovery", J. Pet. Tech. (Dec 1976) 1409-1419

THERMAL RECOVERY METHODS

563

DOWNHOLE STEAM GENERATION USING A PULSED BURNER D. A. CHESTERS, C. J. CLARK and F. A. RIDDIFORD BP Research Centre, Chertsey Road, Sunbury

ABSTRACT The recovery of viscous crude oils using downhole steam generation provides a significant rnprovement in t h e m 1 efficiency over surface steam generation. It is also 1 kely to be an economically viable solution for oil recovery at depths greater than 30%. In addition, by discharging combustion products into the formation, the technique is virtually pollution free and provides a source of C02 to assist viscosity reduction. The operation of a continuously fired, high intensity burner within the confines of an oil well, hwever, presents a number of technical problems, the most intractable of which relates to the selection of materials to operate at high burner temperatures.

In order to obviate these difficulties BP has been developing a eystem based upon a pulsed burner. The unit operates in a "quasi" detonation m d e and achieves the overall required combustion intensity as a series of high intensity, short duration pulses. Steam is produced by atomi8ing water into the high velocity combustion products, the quantity of steam being governed by ignition frequency and mixture flow rate. The feasibility of this eystem has been demonstrated on a 75 m test wen. A high pressure test rig, designed to simulate oil well conditions at greater

depths, has been built to test pulsed burners operating on both gaseous and liquid fuels. To date, operating experience on this scale has been obtained only on gaseous fuels. Under pulsating conditions, the temperatures on the combustion chamber walls are close to that of saturated eteam at the operating pressure. Current developments are being directed towards liquid f'uel operation, with the ultimate objective of proving a system on residual fuel. INTRODUCTION Dohnhole steam generation for the recovery of viscous crude oils offers a number of potential advantages over conventional surface methods. In particular, it is predicted from numerical simulation of the downhole steam generation process that the combined injection of steam and combustion derived C02, which assists in viscosity reduction, will significantly increase recovery rates compared to conventional steam drive (1). As a result of this interaction, it is also predicted that the operating cost per barrel of recovered crude oil is independent of depth up to-1500 m (1). Since surface and well thermal losses are eliminated, the technique is also more thermally efficient, an advantage that becomes progressively more significant as deeper reservoirs are prcbed and higher pressures encountered. Downhole steam generation therefore appears to be an attractive solution to thermal recovery in deep reservoirs.

564

The advantages of downhole steam generation were recognised a number of years ago when the US Department of Energy set up the research programme "Project Deep Steam". This project has resulted in the development of indirect (low pressure combustion ( 2 ) ) and direct (high pressure combustion (3)). methods of downhole steam generation. In the indirect method, steam is generated within a downhole heat exchanger and the combustion gases are ducted back up the well casing. Pressures are, therefore, only those required to maintain the flow of reactants and products within the system. In the direct method, however, water is flashed directly to steam by the combustion gases and the mixture injected into the formation. Combustion therefore takes place at reservoir pressure. Both systems have reached an advanced state of development and have been tested downwell (4.5). The operation of high output continuous burners within the confines of M A o i l well, however, presents a number of technical problems. In particular, the very high heat fluxes encountered within the canbustion chamber coupled with the degree of mixing required to achieve high combustion intensities necessitate careful attention to cooling and fuel/air mixing. The problems are accentuated in high pressure applications where the technology literally enters the space age; advanced rocket engines using exotic f'uels rarely exceed pressures of 70 bar. The design of a continuous burner and associated downhole hardware is therefore complex and requires the use of highly specialised materials. Field experience gained to date has already highlighted the importance of these pnrticular areas (6).

In order to overcome the potential problems of a continuously fired downhole burner, Bp have developed a downhole steam generator that operates in a pulsed combustion mode. This paper deals with the current state of the development and discusses:( a ) the principles of operation and general construction of a pulsed downhole s t e m generator; operational experience of a methane fired downhole steam generator; (b) current progress in the development of a liquid fuel fired burner. (c)

MIXING MAD

SURFACE ROUGHNESS

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01 INOUCtlOLl

bj IWllDN

d

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d j EIHAVS1

Figure 1. Schematic Diagram of the Individual Phases in the Firing Cycle of a Pulsed Burner.

565

DESCRIPTION OF A PULSED DOWNHOLE STEAM GENERATOR The essential difference between the BP downhole generator and those being developed elsewhere i s that it operates i n a pulsed mode rather than i n a continuous mode. Within t h e pulsed burner, combustion occurs by the r e p e t i t i v e f i r i n g of discrete volumes of f'uel/air mixture. The individual phases i n t h e f i r i n g cycle are sham schematically i n Figure 1. A t the s t a r t of the f i r i n g cycle (Figure l a ) , fuel and a i r a r e introduced from separate supply l i n e s a t one end of a tube roughened over part of i t s length. The tube i s f i l l e d over i t s e n t i r e length with f u e l / a i r mixture. On ignition

(Figure l b ) flames propagate both upstream and downstream. The pressure r i s e within the combustion tube modulates the reactant flow and the upstream propagating flame i s extinguished at t h e mixing head (Figure l c ) . AB a r e s u l t of turbulence induced acceleration, the flame within the roughened tube reaches a velocity that i s about 25% of the detonation velocity of the f u e l / a i r This corresponds t o a pressure r a t i o across the flame mixture (-500 ms-1). front of 2.5. The flame and associated shock structure propagate as a coupled system or "quasi" detonation, the velocity of which i s determined primarily by the roughness of the tube walls. A detailed description of the propagation mechanism i s given i n Ref 7. In the final phase of the cycle (Figure l a ) combustion gases a r e exhausted from the burner a t high velocity. Since t h e i r residence t i m e v i t h i n the burner i s short, l i t t l e heat i s transferred t o the canbustion tube w a l l s ; f o r the greater part of the cycle the tube i s f i l l e d with r e l a t i v e l y low temperature gares. The power output, and hence potential steam output of a pulsed burner, i s determined by the frequency with which each discrete volume of reactants, t h a t is the volume of the combustion tube, i s ignited. Power output is simply adjusted by varying f u e l / a i r f l o w r a t e and ignition frequency. The upper l i m i t t o power output i s theoretically determined by t h e maximum propagation velocity t h a t can be achieved i n a roughened tube. In practice, however, power output i s limited by a r e a l i s t i c frequency aad fuellair f l o w rate. For burners presently being designedran output of 10 Mw ( - 2000 bbl steam/day*) a t a depth of fib m i r believed t o be achievable. An operating pressure of 70 bar has been selected M a t a r g e t f o r t h e i n i t i a l phase of burner development. A specifioation f o r such a burner i s given i n Table 1. Table 1 Typical Specification f o r a 10 MW Pulsed Burner Operating at 70 bar Principal Burner Charact e r i s t i c s I

Diameter of canbustion tube Overall diameter of generator Length of combustion tube Overall length of generator Heat output range Ignition Frequency a

89 nun 127 nun

I

1.3 m

4.0 m

I

I

0-1oMw

0 - 5 HZ

This i s defined as the number of barrels of water converted t o steam.

566 A comparison of the combustion intensities that can be achieved in continuously fired high intensity combustion systems is given in Table 11. Examination of these data shows that the combustion in a pulsed burner is only exceeded by the most exotic systems. Table I1 Comparison of Typical Combustion Intensities Achieved in High Intensity Combustion Systems. Combustion System

Operating Pressure (bar)

Steam boiler

Combustion Intensity m/m3 1 - 3

Gas turbine

4

370

Ram jet

5

750

Rocket engine Pulsed burner

35

70

105 1.3 103

Although high combustion intensities may be achieved using a pulsed burner, the fact that flame stabilisation is not required and that the entire combustion tube is available to mix fuel and air prior to combustion, permits significant simplification in the design of the mixing head and combustion tube. In addition, because of the low wall temperatures that result from a pulsed mode of operation, the burner requires only simple cooling and may be constructed from conventional materials. That low w a l l temperatures are indeed measured during normal operation is demonstrated in Figure 2a. These data were obtained from thermocouples set in the wall of a burner operating at a pressure of 7 bar. It is seen that the wall temperature is highest nearest the mixing head and that it drops to well below the saturation steam temperature some distance downstream. If, however, the burner changes to a continuous mode Of operation, the change in wall temperature is dramatic. The effect is shown in Figure 2b. The short duration plateau, followed by a rapid temperature rise, indicates a change to film boiling within the water jacket. Continuous operation under these conditions would result, after a few minutes operation, in total failure of the unit. In the prototype burner, instrumentation is included to sense such an event and initiate shut down. The overall design of the entire downhole steam generator is shown schematically in Figure 3. Fuel and air are supplied to the burner through a dual string system, with the ignition and instrumentation lines strapped to the air line. The upper part of the assembly comprises instrumentation and ignition packages which provide, respectively, a continuous monitor of combustion performance and ignition control. Fuel and air are injected into the combustion tube and the ignition cycle is initiated, as already discussed. Water is sprayed directly into the combustion chamber via an annular water jacket. The water is flashed directly to steam and the resulting mixture of steam and combustion products is injected into the formation. A high pressure packer prevents the escape of steam up the annulus. Small scale experimental burners of this general design have been successhiLly operated on gaseous fuel (methane and hydrogen) in a high pressure test rig. Limited field work has also demonstrated that the system represents a practical means of downhole steam generation. Burners are currently being developed to use

567

liquid fuels (ranging from middle distillate to residual fuels) to meet a variety of operational requirements. Each of these aspects of the deve1opner.f is now separately discussed. uo-

”’

1E~PERATURERANCERECORDEDON INSIDE AND WTSIOE OF COMEWTION

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100

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8ca

Figure 2a Temperature p r o f i l e along t h e combustion tube of a prototype 0.25 MW pulsed burner during operation a t 7 b a r .

SHUl DOWN OF BURNER

a

5

la

E

20

TIME (SECONOS)

Figure 2b Variation of combustion tube well temperature with time following a change to continuous operation at 2 bar.

a

568

FUEL!

..

.

'

. . NEL AND AIR PASSED DOWN WELL USING INDIVIDUAL SUPPLY PIPES WATER . PASSED DOWN ANNULUS

Figure 3

- Schematic diagram of

PUSED BURNER

WATER INJECTK: . NOZZLES .c\s \

r;..

F9::

CONNECTING

...

WlOP

a prototype Pulsed Downhole Steam Generator

.

y\

569

P

u

0

0

5

k

ti d

a

B

4 General arrangement diagram of the 0 . 5 MW burner used i n f i e l d trials .PI

Figure

570 OPERATIONAL EXPERIENCE OF A DOWNHOLE GAS FIRED GENERATOR A s e r i e s of experiments

w a s carried out i n a water well d r i l l e d i n t o Bunter Sandstone and located i n the Midlan&' gas f i e l d . The aim of t h e work w a s t o prove t h e operation of a pulsed burner i n a downhole environment. The burner was designed t o operate on l o c a l l y available methane a t depths of up t o 75m. The t e s t burner had a maximum diameter of 0.13m, a length of 1.0 m and a combustion tube volume of 0.007 m3. 2 Hz, giving The f i r i n g frequency was 0.5 heat output i n t h e range 0.125 0.5 MU. A general arrangement drawing of the t e s t burner i s given i n Figure 4 . Water, f u e l and a i r were fed i n separate l i n e s through a h i pressure bellows aeal. Ignition was achieved by means of a h1sh energy (10 J aeroengine i g n i t e r situated a short distance downstream of the mixing head; i n t h i s design the mixing head i s located under the packer.

-

-

?

During the early stages of the t r i a l , d i f f i c u l t i e s were experienced with the ignition system; short c i r c u i t s within t h e high tension u n i t s and leads resulted i n the t e s t being discontinued a f t e r a few hours' operation. Tests were resumed w i t h an improved i g n i t i o n system which enabled continuous operation f o r 24 hour periods a t a depth of 75 m. Although the burners operated f o r only a limited period, t h e work did demonstrate t h a t downhole operation of a pulsed burner i s technically possible. I n addition, it highlighted a number of deficiencies i n the system t h a t required further development. In particular, it was c l e a r t h a t the design of a r e l i a b l e ignition system i s of c r i t i c a l importance t o the successful operation of the burner. A closer integration of t h e burner and packer assembly was a l s o recognised as being an important requirement for downhole burners.

CURRENT PROGRESS I N THE DEVELOPMENT OF A LIQUID FUEL BURNER I n i t i a l development work on t h e pulsed downhole burner was carried out using hydrogen or methane as f u e l . Owing t o e c o n d c / p o l i t i c a l constraints, gas supplies may not always be available f o r downhole stem generation. It i s considered e s s e n t i a l , therefore, that a downhole burner should be capable .of operating on a range of fuels. For t h i s reason, the developent has been extended t o l i q u i d fuels with the ultimate aim of operating on residual fuel or produced crude. The operation on a l i q u i d f u e l presents a number of d i f f i c u l t i e s f o r both pulsed and continuous burners. For the pulsed burner, the greatest d i f f i c u l t y i s associated with t h e i n i t i a t i o n of a "quasi" detonation. I t i s generally agreed ( 8 ) t h a t , i n two phase detonations, f u e l droplets are broken up by secondary a t d s a t i o n t o produce a combustible mixture of f u e l micromist (micron s i z e droplets) and hot oxidiser i n the wake of each parent droplet. The l a r g e surface area between micromist and oxidiser enables chemical reaction t o occur a t a r a t e t h a t i s s u f f i c i e n t l y rapid t o support the incident shock front. A similar mechanism generates the "quasi" detnnation. In order tQ i n i t i a t e a d i r e c t detonation i n a fuel/air mixture, a f i g h energy ignition source is required, t h e precise energy requirement being dictated by t h e overall induction period of t h e reaction. In a gaseous system the induction period i s governed s o l e l y by chemical processes, whilst i n a heterogeneous system both physical and chemical processes play a role. A s a r e s u l t , t h e induction period and hence t h e energy requirement f o r d i r e c t i g n i t i e x is greater f o r heterogeneous systems. O f t h e physical parmetkrs, droplet s i z e plays a key r o l e i n the (9). i n i t i a t i o n and propagation of a detonation

The operation of a pulsed burner on liquid fuels has therefore necessitated the development of two key areas of burner operation, namely: (a) Fuel atomisation and mixing. (b) High energy ignition systems.

To date, a burner has been successfully fired at atmospheric pressure on liquid kerosene. Within the burner, atomization is effected by a ring of twin fluid atomising nozzles using combustion air as the atmising medium. Detonation is initiated by a high energy source generating approximately 250 J at each ignition event. This system operates on an energy awentation principle triggered by a plasma plug. The latter has overcome the problem of igniter reliability, discussed previously. The plasma plug is a recent developnent (lo) and operates in a surface discharge fashion, the main discharge taking place within the confines of a small cavity.

In this mode of operation the breakdown voltage is lower than that required for a conventional air gap and, furthermore, exhibits a smaller pressure dependence. Trigger voltages are maintained at an acceptable level even at pressures of 70 bar. The plasma plug has the additional advantages of a variable output, an enclosed electrode assembly and a self-cleaning action. These features have enabled plasma plugs to be operated reliably in laboratory test rigs at high pressure. Future work e l l be directed towards developing burners to operate on fuels of laver volatility.

1. A burner that operates in a pulsed mode, rather than in a continuous mode, offers a number of advantages for downhole steam generation. These include:-

(a) (b) (c) (d)

low burner temperature; relatively simple construction from conventional materials; high combustion intensities; high turndown ratio

2. A s t e q generator incorporating the principle of pulsed combustion has been successfully demonstrated downhole.

3. A reliable ignition system is an essential requirement for a burner operating in a pulsed continuous mode.

4. A n atmospheric pulsed burner has been successflilly operated on liquia kerosine using a high energy ignition source.

ACKNOWLEDGEMENT Permission to publish this paper b s been granted by the British Petroleum Company Limited.

The authors acknowledge the support given by the European Economic Community.

572

1.

BADER, B.E. and FOX, R.L.; "The Potential of Downhole Steam Generation t o t h e Recovery of Heavy O i l s " , UNITAR 1 F i r s t International Conference on the Future of Heavy Crude and Tar Sands, Edmonton, Alberta 4 12 June 1980.

-

2.

WRIGHT, D.E. and BINSLEX, R.L.; "Feasibility Evaluation of a Downhole Steam Generator"; SPE/DOE 9776, Paper presented t o the Second Joint Symposim on Enhanced O i l Recovery of t h e Society of Petroleum Engineers, Tulsa, Oklahoma, 5 8 April 1981.

-

- Pre1hrinax-y

3.

MULAC, A.J., e t a l ; " R o j e c t Deep Steam Bakersfield, California, SAHD 80 2843.

4.

"Downhole u n i t s a i d t o be ready f o r sale"; Enhanced Recovery Week, May 11, 1981.

5.

"Test s l a t e d f o r damhole steam generator"; O i l and Gas Journal, March 30. 1981.

6.

JOHNSON, D.R., e t al; Project Deep Steam Quarterly Report, July 1 September 30, 1980.

7.

LEE, J.H.S. and MOEN, 1.0.; "The Mechanism of Transition fram Deflagration t o Detonation i n Vapour Cloud Explosions", Prog. Energy Combust. Sci., (1980) 6, 359 389.

-

Field Test

-

-

8.

DABORA, E.K. and WEINBE3GER, L.P.; "Present Status of Detonations i n Two-phase Systems"; Acta Astronautica (19741, 1, 361 - 372.

9.

LU, P.L., SLAGG, N. and FISHBURN; B.D.; "Relation of Chemical and Physical Processes i n Tvo-phase Detonations", Acta Astronautica (19791, 6, 815 826.

10.

ASIK, J.R., PIATKOLSKI, P., FOUCHER, M.J. and RADO, W.G.; "Design of a Plasma Jet Ignition System f o r Autanotive Application "(No 7703551, Society

-

of Automotive Engineers, International Automotive Engineering Congress and Exposition Cob0 H a l l , 28th February 1978.

THERMAL RECOVERY METHODS

573

HOT CAUSTIC FLOODING R. JANSSEN-VAN ROSMALEN and F. Th. HESSELINK Koninklijke Shell Explorative en Roduktie Luboratorium, Rijswijk, The Netherlands (Shell Reseurch B. V.)

SUMHARY

A chemical recovery method used as a follow-up to or in combination with thermal methods is restricted to processes that are not too sensitive to elevated temperatures and temperature gradients. Caustic flooding is one of the few processes which can meet these requirements. Three different recovery mechanisms can be created by varying the salt content and/or adding extra chemicals to the caustic slug. The caustic process at high salinities is regarded to offer the best prospects for "hot caustic", since the process does not require extra chemicals (e.g. polymer) for mobility control. In our studies on caustic floods, laboratory experiments have shown that an increase in temperature can be favourable for in-situ emulsification and, once an emulsion is formed, can drastically influence the flow properties of the emulsion. For a caustic flood following a hot water drive, a minimum shear rate was found to be necessary for emulsification. In the caustic flooding experiments where a mobile emulsion was formed, oil recoveries superior to those of a comparable hot-water flood have been obtained. In one-dimensional packs of reservoir sand a hot caustic flood recovered 16-18% PV additional oil after a hot water drive. The sweepimproving effects of a sufficiently mobile caustic emulsion are expected to give a substantially higher additional recovery in a real three-dimensional flood

.

1. INTRODUCTION Caustic flooding is an enhanced oil recovery method which is based on the principle that organic acids, naturally occurring in some crude oils, can react with the alkali of the caustic injected. This chemical reaction leads to the formation of surfactants at the oil-water interface, resulting in a decrease in interfacial tension between the oil and the water phase and in insitu emulsification when a caustic solution of suitable alkalinity is injected into an oil-bearing formation. A basic requirement for the caustic recovery method is that the oil contains a sufficient amount of natural acids. In this connection an acid n m b e r of about 1 mg or higher is desirable (+> (2> but active caustic systems have also been reported at lover acid n m b e r e (2). This activity is, among other things, related to the percentage of natural acids having a sufficiently high molecular weight to be effective in reducing the oil-water interfacial tension.

574

Several mechanisms have been proposed to describe the effect of caustic injection on the recovery of oil. Johnson (2)has given an overview of the different mechanisms involved in caustic flooding, such as emulsification and entrapment (L),wettability reversal (L) (5) (i) and emulsification and entrainment (2). Recently Meyer et a1 have summarised data on field tests, and related the results to caustic concentrations and salt contents of the floods. Their status report shows that different recovery mechanisms are dominating in the various caustic flooding field trials. In the present paper the effect of an increase in temperature on the caustic flooding process will be discussed. A method of this kind is indicated in Ref. 8. The application of "hot caustic" may be considered for the following reasons. In some cases a hot caustic injection may yield increased oil recoveries, while at reservoir temperature the injection would not lead to a better performance in comparison with a plain water drive. It should be noted that injection of hot caustic into an ambient temperature reservoir may require preheating of the reservoir, since the thermal front will move through the reservoir at a much slower rate than the caustic front. In other cases the reservoir may already have been preheated by a steam drive or a hot water drive. A chemical recovery method to follow up these thermal methods is restricted to processes that are not too sensitive to high temperatures and temperature gradients as occur in preheated zones. Such conditions adversely affect a surfactant or polymer flood. The prospects offered by a foam or caustic process are more promising under conditions as described above. The scope of the present study is to provide an indication of: - which caustic recovery mechanism can best be chosen at elevated temperatures. - how the parameters that are important for a caustic process are influenced by an increase in temperature. the oil recovery when applying hot caustic flooding.

(z)

-

The investigation of caustic flooding I n conjunction with a thermal project is especially relevant, since the high-acid-number crudes suitable for caustic flooding are usually low-gravity crudes for which thermal EOR processes are often considered. The preceding steam flood may even have increased the acid number of the crude.

(1>

2. THE CAUSTIC PROCESS 2.1.

Principal recovery mechanisms The interfacial tension between the oil and the water phase as well as the type of emulsion formed during caustic flooding have been found to be dependent on the salinity of the caustic injected (2)(L). This means that the recovery mechanism is likewise affected by salinity. Reisberg and Doscher (2) have reported that caustic solutions used in conjunction with surfactants were effective in increasing oil displacement. The combination of an alkaline solution with a co-surfactant was also mentioned for the formation of a microResearch on the application of emulsion to be injected into a reservoir (10). polymers in caustic flooding to provide mobility control is in progress (2)

(11)(12).

In order to catalogue the variety of alternatives for the caustic process, we would propose to classify the caustic recovery mechanisms (see Fig. 1) in parallel with the various mechanisms identified in surfactant floodinn. -. as follows: The under-optimum system. At low salinity of the caustic injected a non-viscous oil-in-water emulsion is formed. This system is often formed at sodium ion

-

I -

575

I

UNDERQPTIMUM

I

FRESH WATER O/W EMULSION CONTINUOUS PHASE:

I

OIL +CAUSTIC

1

I

OPTIMUM

I

OVER-OPTIMUM

-

SALINE WATER WIO EMULSION CONTINUOUS PHASE! OIL

LOW VlscOSlry

0 7 G= + MOBILITY CONTROL

OILBANK

,-,

FIG.! :CAUSTIC RECOVERY MECHANISMS concentrations lower t an 0.5 mol/l. Oil/water interfacial tensions (IFT) can be very low (< lo-’ mN/m). Oil recovery can be increased either by entrament of emulsified oil drops in the pore throats, reducing water mobility (A), or by very low interfacial tension, leading to reduced residual oil saturation through a favourable capillary number (13). In the first case an improvement in sweep efficiency is achieved. In general, however, the latter mechanism is more common; it may lead to oil bank formation in cases where interfacial tensions are sufficiently low. Mobility control (polymer, foam) is required for stable displacement 0’: such an oilbank. The oEtimum system. i i S ; ~ p t ~ ~ s a ~ i o n ~ r ’ t amount he of salt and/or the addition of surfactants interfacial tensions may become ultra-low, so that capillary-trapped oil is mobilised and an oilbank is formed. This system also requires mobility control.

(z),

2!rover:sptL!E!?-syelem,

At high salinities a viscous water-in-oil emulsion is formed (2). Interfacial tensions are reduced somewhat. Once an emulsion bank has formed, caustic fingers through the emulsion bank are converted into emulsion, sealing off the finger. Extra oil recovery is obtained by improved mobility, leading to a better areal and vertical sweep efficiency in the reservoir. In addition, the increased viscosity of the viscous emulsion drive, combined with the reduced IPT, may (at least in the laboratory) cause such an increase in the capillary number that residual oil becomes mobilised, leading to oilbank formation ahead of the emulsion drive.

576 An application of the over-optimum caustic system, not shown in Fig. 1, is the possible permeability reduction of a water-flooded zone by emulsion formation. This would divert the main flow direction and consequently improve the sweep efficiency.

The over-optimum system seems to be most suitable in the case of a hot caustic process, since this system provides its own mobility control by the formation of a viscous emulsion. The other two systems would generally require the addition of extra chemicals, which would make the process more sensitive to temperature, and also more complicated and costly. 2.2.

Parameters for the over-optimum system The parameters that are of importance for caustic flooding are schematically given in Pig. 2. When a caustic solution is injected into a ACID OIL

-

SALINITY REDUCED INTERFACIAL TENSION

COALESCENCE

FIG. 2 : INTERACTION-DIAGRAM FOR CAUSTIC FLOWING

reservoir, part of the caustic is used to form surfactants, and part of it is depleted by interaction with rock and reservoir water. This interaction is highly dependent on type of rock, pH and composition of the caustic solution, reservoir salinity and temperature (14).If depletion is excessive, it may accordingly retard or even prevent the onset of increased oil production (12). The surfactants formed in situ, will reduce oil-water interfacial tension. Since the water phase is saline, this reduction is not drastic. Divalent ions (Ca*,Mg*) may be detrimental to the process, leading to the formation of less interfacially active soaps (see Fig. 3). Calciun is much more detrimental than magnesium in this respect. The calcium concentration in the water should therefore be controlled by the addition of chemicals to the flood water. For instance, addition of soda ash (Na Cog) to the allcaline water causes most of the calcim ions originally present $0 precipitate as calcim carbonate. As a result of reduced interfacial tensions, emulsification is promoted under the action of interfacial tension gradients (Marangoni effects which may result in turbulence at the oil/water interface) and/or by an extra mixing effect (see Fig. 2) generated by external shear forces. In general, no extra mixing energy is required to form an oil-in-water emulsion, since in that case interfacial tensions are much lower. Wettability reversal of the rock to oilmay play a role in the formation of a stable water-in-oil emulsion. wet (2) Flow behaviour of the emulsion, in relation to droplet size is an important aspect for the overall flooding behaviour.

10.0

v-

v' , 1.67 mor/i NOCI

t

+

E

Q

2

o

+

x v

+~ p p m ~ o * + + X K ) p p m CO++

\

E

t \ \

z

1 a

\

5

3.0

\ \

9

E

25ppmCo** 50pprn~a++

\ \ \

1.0

W

Hm

\

d 0.3

i

1

I

9.0

10.0 -pH

11.0

12.0

13.0

14.0

OF ausncsOulTloN

FIG.3: ILLUSTRATION OF INTERFACIAL TENSIONS AS A FUNCTION OF pH AT DIFFERENT CALCIUM CONCENTRATIONS (Acid number of crude uwd : 3.0)

578

Besides the emulsification phenomena, coalescence of the emulsion also contributes to the performance of a caustic flood. Since an emulsion is a thermodynamically unstable system, phase separation occurs through coalescence of the droplets. The rate of coalescence is dependent on temperature, flaw rate, interfacial properties and viscosity. In an effective caustic process the coalescence rate is balanced by the emulsification rate. Extra oil recovery by improved sweep efficiency and oil bank formation in relation to the caustic required for an effective process will determine the economic feasibility of a caustic flooding process.

2.3.

The effect of an increase in temperature An Increase in temperature will have a considerable impact.on the ease of

emulsification (the interaction of Wrangoni effects and external shear forces), the coalescence rate, the flow behaviour of the emulsion and the total caustic losses (see Fig. 2).

Emulsificati_on_aid_c_oalescence_ The reduced oil viscosity at higher temperatures promotes the diffusion of organic acids to the oilfwater interface. Thus the acid-caustic reaction is accelerated and the mixing process due to Marangoni effects is promoted. Aa a result, water droplets become more readily dispersed in the oil. In some cases, hawever, as will be shown in section 3, extra mixing energy is needed to further break up the water droplets to achieve a better emulsion stability. This energy is to some extent provided by the flow in the porous medim. If velocity gradients and ensuing shear forces are large enough, interfacial forces are no longer able to keep fluid particles intact, and they are broken up into smaller droplets. The theory of deformation and break-up of a droplet in a flaw field was first formulated by Taylor (16)and modified by e.g. Karam et al. (17).

001

01

0.1

FIG.4:BREAK-UP OF DROPLETS

10

10

VISCOSITY

IN A SIMPLE

R A T I O . vp;

SHEAR FIELD

579 Taylor showed that the drop behaviour only depends on the two dimensionless parameters u ’ / p and Gru/y, where p ’ is Khe viscosity of the discontinuous phase, u of the continuous phase, G the shear rate, r the diameter of the droplet and y the interfacial tension. In accordance with this, Karam et al. have plotted their results of droplet break-up of different fluids as a function of these two dimensionless parameters (see Fig. 4). Irrespective of the system studied, a single curve should be obtained by such 8 dimensionless plot. Droplet break-up occurs above this curve. In connection with the caustic process the following main conclusions can be drawn from this plot. If the interfacial tension is increased, for example by divalent ions present in the reservoir water, the shear rate in the porous medium needs to be increased by the same factor to cause similar droplet break-up (see Fig. 4). It is therefore very important that most of the divalent ions are precipitated using a suitable buffer solution. Secondly, the break-up of a liquid droplet occurs readily when the viscosity ratio between the water and oil phase ( p ’ / p ) is of the order of 0.2 to 1 (see Fig. 4). ’his implies that not only the acid number, but also the viscosity of the oil under consideration is an important criterion for the caustic process. By the application of heat the difference in viscosity between the oil and the water phase becomes less pronounced, resulting in easier emulsification. In a good caustic process a balance exists between emulsification and coalescence. Since an increase in temperature will enhance the coalescence rate, the temperature can affect the performance of a caustic flood in this way. El~w-b$h~v~our-of the - m - l ~ i ~ n The temperature effect on the flow behaviour of the emulsion is important in the following respect. The apparent viscosity of the emulsion should preferably be somewhat higher than that of the oil phase in order to provide mobility control, and it can be much higher in the case of diversion of the main flow from a water-flooded area (see also section 2.1). The strong dependence of apparent viscosity on temperature will be shown in section 3.

Caustic in the form of s o d i m hydroxide has been shown to strongly interact with the rock at elevated temperatures (14).On the positive side, the dissolution interaction generates in situ water-soluble silicates which may have a beneficial effect on oil recovery (15). In contrast to these high losses resulting from sodium hydroxide, we found considerably lower consumptions when using carbonate buffer solutions. ‘Ihis is probably due to the lower initial pH values required when a buffer solution is applied instead of sodium hydroxide.

3. EXPERIMENTAL RESULTS AND DISCUSSION The crude used for the caustic flooding and emulsification experiments was characterised by an acid number of 3.6 and a viscosity of 170 mPa.s(-cP) at reservoir t e m p e r a w (42OC). The reservoir brine contained 76115 ppm TDS, of which 3200 ppm Ca and 960 ppm Mg*. Optimum emulsion stability was found at a pH of 9.5 of the caustic solution. The caustic solution was a carbonate/bicarbonate buffer with sodium chloride added (total Na+ content: 1.25 mol/l). The effectiveness of such a caustic solution in recoversng the oil has been studied in Bentheim sandstone cores (permeabslity: 1.5 urn ) and in sandpacks of reservoir sand (permeability: 3-9 pm ). In the case of sand packs more divalent ion exchange can be expected, by which emulsification could be hampered.

580 The caustic flooding experiments were carried out at high initial oil Saturation at initiation of the caustic injection and at low oil saturations, 1.e. after a water drive. The effect of temperature, shear rate and permeability on the emulsification process and the corresponding oil recovery 18): has been studied. Shear rates have been calculated from (

G

-

4u/J ( 8 M )

(1)

where u is the flooding rate, k the permeability and 0 the porosity of the porous medium. Since the flooding experiments in the porous media used represented onedimensional floods, the oil recoveries observed only accounted for possible extra oil recovery because of slightly reduced residual oil saturation and/or oil bank formation (see Fig. 1) on account of the steep pressure gradients in the emulsion zone. A possible improvement in sweep efficiency for a real three-dimensional caustic flood can be expected when emulsion formation in combination with pressure build-up across the porous pack was observed. 3.1.

Caustic flooding experiments at high initial oil Saturations Caustic flooding experiments were carried out at elevated temperature, 80°C, and for comparisonat a reservoir temperature of 42OC. Caustic was injected after saturating the porous medium with synthetic reservoir brine and subsequent flooding with tank oil to irreducible water saturation. The experiments in Ben helm sandstone (see Table I) were performed at a flooding rate of 1.06 x lo-! m/s 3 ft/day). At a temperature of 42OC (exp.1) a considerable pressure build-up over the core length was registered during the caustic flood, indicating the formation of a viscous emulsion. The low mobility of this emulsion may explain why the oil recovery in this caustic drive was not significantly improved over that of a plain water drive (compare exp. 1 and 2). In a caustic drive experiment at 8OoC (exp. 3) the pressure initially increased, pointing to in-eitu emulsification, and afterwards decreased when most of the oil, followed by some emulsion, had been produced, indicating that the emulsion in this case did not have too low a mobility. The (0

TABLE 1 f loodlng rate:

Exp. No.

hustldwater drlve

1.06

Tenp.

[%I

-

0 I SPLACMENT EXPERIMENTS I N POROUS PAO(S

lo-'

m/s (= 5 ft/day).

Shear r a t e a t all

Enulslon formed

except ow. 7b: 0.55

l n l t l a l 011 satvatlon,

so I

m/s 011 recovered per cent of Sol

After 1 PV

Flnal

45 59 82 42

48 45 83 47

-----1

2 3 4

caustlc dr. a t e r dr. caustlc dr. a t e r dr.

42 42 80 80

27.4 27.4 27.4 27.4

xperlnwnts I n sand padts (poror1ty:O.l

5 6 7al

3

caustlc dr. a t e r dr. caustlc dr. court Ic dr. water dr.

42 42 80 80

80

7.8 7.8 7.8 4.2 27.4

-

YES YES

-

and pemsablllty:9.5

NO

-

YES YES

-

0.95 0.95 a 78 0.78

urn2,except 0.79 0.79 0.84 0.87 0.78

ew&and

40 48 64 63 40

8; Iengtk22 cm. 48 56 75 75 41

581 emulsion obviously a c t e d as a viscous phase, f o r c i n g t h e o i l o u t of t h e porous pack. The o i l recovery ( 8 3 % ) was f a r s u p e r i o r t o t h a t of t h e comparable waterd r i v e experiment ( 4 7 % , see exp. 4 ) . This l a r g e d i f f e r e n c e i n recovery and p r e s s u r e behaviour between a c a u s t i c d r i v e and a water d r i v e a t 80°C was confirmed i n d u p l i c a t e experiments. I n r e s e r v o i r sand a t 42OC t h e c a u s t i c d r i v e showed no p r e s s u r e build-up, and t h e o i l recovery w a s even lower than i n t h e corresponding water d r i v e (see exp. 5 and 6 i n Table I ) . t 80% t h e d r i v s were conducted a t two d i f f e r e n t lo-' m / s ( 1 f t / d a y and 3 f t / d a y , and 1.06 flooding rates: 0.35 resp.). Although s h e a r r a t e s ( s e e eq. 1 ) were d i f f e r e n t ( c f . exp. 7a with exp. 7b, Table I ) , both cases showed some pressure b u i l d u p , p o i n t i n g t o t h e ins i t u formation of a n emulsion bank. The o i l r e c o v e r i e s were i n both cases e q u a l l y high. The corresponding h o t water d r i v e (see exp. 8 ) y i e l d e d a 20% (of OIP) lower o i l recovery. A t h i g h e r p e r m e a b i l i t i e s , however, less d i f f e r e n c e i n recovery was found between t h e c a u s t i c and h o t water d r i v e s , probably because of t h e e f f e c t i v e n e s s of t h e v i s c o s i t y reduction of t h e o i l (from 170 mPa.s cP) a t 42OC t o 27 mPa.s a t 8OoC) i n porous media of high permeability. These experiments i n sandpacks i n d i c a t e t h a t a t higher temperatures (8OoC) mixing induced by Plarangoni e f f e c t s and a l s o d i f f u s i o n processes may be s u f f i c i e n t f o r t h e formation of a small emulsion bank, probably because of a l a r g e c o n t a c t area a t t h e i n t e r f a c e between t h e o i l and t h e c a u s t i c s l u g j u s t a f t e r i n j e c t i o n . So t h i s process a t high i n i t i a l o i l s a t u r a t i o n s was found not t o be dominated by e x t e r n a l s h e a r f o r c e s .

*

*

(9

Caustic f l o o d i n e eriments a f t e r a ( h o t ) water d r i v e The flooding e z e r z e n t s were performed a t r e s e r v o i r temperature (42OC) and a t e l e v a t e d temperatures. Crude and b r i n e were i n j e c t e d i n o r d e r t o bring t h e porous system a t connate water s a t u r a t i o n and subsequently reduce i t t o a low o i l s a t u r a t i o n . The water d r i v e s p r i o r t o t h e c a u s t i c i n j e c t i o n were performed a t t h e same temperatures as t h e c a u s t i c flood. The r e s u l t s of t h e s e tests a* given i n Table XI. They show t h a t i n - s i t u e m u l s i f i c a t i o n can indeed occur a t low o i l s a t u r a t i o n s , and t h a t t h i s process i s c r i t i c a l l y dependent on s h e a r rate, i n c o n t r a s t t o t h e process a t high i n i t i a l o i l s a t u r a t i o n s . Both t h e flooding rate using one p a r t i c u l a r type of porous material, and t h e permeability times p o r o s i t y of t h e c o r e are important 3.2.

TABLE I t Exp.

R r n s a q l l l t y Tenp. k lp f f%f

-

CAUSTIC FLOOOING EXPERIMENTS AFTER A HOT WATER DRIVE

Floodln rate" x lo-' n/s

Shear r a t e a t wall

Enulslon formed

01 I satwatton a f t e r water drlve. S OlP

1

2 3 4

5

6 7 8 9 10

1.5 1.5 1.5 1.5 1.5

88 80 80 60 42

3 x 0.35 3 x 0.35 a35 3 x 0.35 3 x 0.35

9.1 3.2

80 80 80 60 60

3 8 6 5 8

3.0 3.2 3.2

x x x x x

0.35 0.35 0.35 0.35 0.35

27.4 27.4

YES

0.40 0.50 0.38 0.40 a 39

7.6 3x4 27.1 2 24 35.8

NO YES YES YES YES

0.36 a41 0.37 o. 50 0.40

011 r e c o w e i a f t e r 1 PV fractlon of

64 51 20 44 11

7 41 42 10 12

582 parameters for emulsification (cf. exp. 2 and 3, and exp. 2 and 6). In the experiments where no emulsion is formed, the additional oil recovery is not higher than obtained by a prolonged water drive. Also in experiments at sufficiently high shear rates where an emulsion is formed, but which were run at lower temperatures, the additional oil recovery is poor (see exp. 5, 9 and 10). This is for the same reason as given for the experiments at high initial oil saturations, which were carried out at relatively low temperatures, i.e. the emulsion mobility is too low. The result is that at low temperatures most of the emulsion formed remains in the core, and that the caustic solution breaks through the emulsion bank. Improved caustic flood recoveries are obtained at higher temperatures, where an emulsion bank of higher mobility is formed; see Table 11. 'Ihis is supported by viscosity measurements. At 80°C the viscosity of the emulsion produced in the effluents during the caustic flood was found to be 200 mPa.s, in contrast with an emulsion viscosity of 2200 mPa.6 at 60°C. As a second effect of temperature, the amount of emulsion formed during flooding at one particular shear rate was found to decrease with increasing temperature. 'Ihis phenomenon may be caused by enhanced coalescence, which is common for emulsions at higher temperatures. Under optimal conditions for the formation of a stable and at the same time mobile emulsion bank, a sharp increase in oil saturation in front of the emulsion bank could be observed in both Bentheim sandstone and reservoir sand. This resulted in general in a decrease in water cut from about 100% to 60%, as is illustrated in Fig. 5 (exp. 1). After the emulsion bank had been produced, the o i l production stopped completely. In Bentheim sandstone the oil recovery was far superior to that of a comparable hot water drive (- 25% of OIP extra oil recovery at 8OoC). In reservoir sand the caustic flood performance at 80°C was similar to that in Bentheim sandstone in terms of pressure behaviour and oil bank formation, yielding an extra oil recovery after a waterflood of about 20% of OIP (- 18% PV), as illustrated in Fig. 6 (exp. 8 ) . For comparison, the production curve of a caustic flood at 42OC is given in the same figure. 1.0

0.9 0.8 0.7

o.6 0.5

5

0.4

'

0.3 0.2 0.I 0

FIG.5 :CAUSTIC FLOODINO EXPERIMENT IN A BENTHEIM SANDSTONE CORE FOLLOWING A WATERDRIVE.

s

583

0.8

-

HOT CAUSTIC(80"C) START CAUSTIC INJECTION

FIG.6:FLOODlNG EXPERIMENTS IN SANDPACKS.

4. COMPARISON OF THE EMULSIFICATION IN A COUETTE APPARATUS AND IN A POROUS MEDIUM Since the emulsification process at low initial oil saturations was found to be dependent on shear rate, we decided to study emulsion formation at different shear rates in more detail, using a thermostatted Couette apparatus. This apparatus (Pig. 7) consists of two concentric cylinders, the inner one of which can rotate. The Couette apparatus is particularly suitable for this investigation, since the shear rate is almost constant throughout the small gap between the inner and outer cylinder. The emulsification behaviour of a caustic solution in contact with crude in the Couette apparatus (see Table 111) has been compared with that in a porous medium at relatively low oil saturations (Table 11).

EMULSION

Dl EMULSION

NO EMULSIFICATION

PARTIAL EMULSIFICATION

COMPLETE EMULSIFICATION

FIG.7:EMULSION FORMATION IN A COUETTE APPARATUS

The emulsions formed in the porous medium and in the Couette apparatus were characterised by droplet size analysis (using a HIAC 520 particle-size analyser) and by microphotography. In general, a fairly good similarity between the emulsions was observed. In both cases peaks were found at a droplet size of 2.8 and 4 . 3 vm (see Fig. 8).

TABLE I I I

-

Shear r a t e 1s-1 I

EMJLSlFlCATlON I N COUElTE APPARATUS

b r m t l o n of W/O w l r l o n 40°C 68C YES (16% free a t e r )

28

YES

38

80%

YES OOS free a t e r )

No

YES (5s free a t e r )

No

46

KS

YES

KS

68

YES

YES

YES

113

KS

YES

TEES

-

Number distribution porous medium

COUeth r p p 8 d U S

I -

b a?

I'

2 2 5 3

L

5 6 1 8 9 1 0

I!

20

2 5 3 0

40

50

DROPLET

SIZE (pm)

---

Volume dislribullon porous medium couette 8pprretur

:

lo'

I0

t

b

5-

a? I 2

:

2.5

.

3

. .

A

5

. 7. 8. 9. 10.

6

I5

20

IS

30

LO

50

DROPLET

SIZE (pm)

FIG.8: DROPLET SIZE DISTRIBUTIONS OF EMULSIONS FORMED AT 60.C IN A POROUS MEDIUM (Exp.9,TablrE) AT A SHEAR RATE OF 22SII.AND IN A COUETTE APPARATUS AT A SHEAR RATE OF 4 6 9 (ToblrXU)

At the oneet of the emuleification proceee in the Couette apparatue, the development of inetabilitiee at the interface between the cauetic eolution and the oil wae observed, resulting in the formation of relatively large droplets. 'Iheee droplete only broke up further and f o m d a stable emuleion when the shear rate exceeded a critical value (eee Fig. 4, eection 2.3). Dependent on the shear rate applied, three eituatione could be dietinguiehed (see Fig. 7): (I) the two phaeee remained completely separated, (11) only part of the two phaeee wae emuleifled, (ill) complete emuleification.

585 The r e s u l t s of t h e Couette experiments performed a t d i f f e r e n t temperatures and s h e a r rates (see Table 111) i n d i c a t e t h a t t h e h i g h e r t h e temperatures, t h e h i g h e r are t h e s h e a r rates needed f o r e m u l s i f i c a t i o n . P a r a l l e l t o t h i s , i t w a s found t h a t i n t h e c o r e f l o o d s a n i n c r e a s e i n temperature a t a f i x e d s h e a r rate r e s u l t e d i n a decrease i n t h e amount of emulsion produced (see s e c t i o n 3.2). This phenomenon can be a t t r i b u t e d t o reduced s t a b i l i t y , which is in g e n e r a l observed with emulsions a t h i g h e r temperatures, probably due t o enhanced coalescence. In t h e c o r e flood tests (Ta l e 11) s t a b l e emulsions were formed when t h e whereas in t h e Cou t t e a p p a r a t u s t h i s s h e a r r a t e s exceeded about 20 ,'-s The lower threshold threshold value was somewhat higher, i.e. about 40 .'-s value in porous media may a r i s e from t h e f a c t t h a t , a p a r t from simple s h e a r flow, e x t r a v e l o c i t y changes involved in t h e flow through c o n s t r i c t i o n s and d i l a t a t i o n s a l s o c o n t r i b u t e t o t h e e m u l s i f i c a t i o n process.

5. CONCLUSIONS 1. The c a u s t i c process a t high s a l i n i t i e s is considered t o be most s u i t a b l e i n 2. 3. 4.

5.

6.

7.

t h e c a s e of a hot c a u s t i c d r i v e , s i n c e t h i s process provides i t s own m o b i l i t y c o n t r o l by t h e formation of a viscous water-in-oil emulsion. High temperatures can be favourable f o r t h e o n s e t of i n - s i t u emulsification. Apparent v i s c o s i t i e s of water-in-oil emulsions were found t o be very temperature-dependent (in our s p e c i f i c case .I 200 mPa.6 (- cP) a t 80°C, . I 2200 mPa.s a t 6OoC). In l a b o r a t o r y experiments on c a u s t i c flooding where a n emulsion bank was formed, but where t h e emulsions were t o o viscous, g e n e r a l l y no e x t r a o i l recovery was observed. This system may, however, be f e a s i b l e i n a waterflooded area t o decrease t h e permeability and consequently d i v e r t t h e main f l o v d i r e c t i o n t o areas of higher o i l s a t u r a t i o n . This would imply i n j e c t i n g a small s l u g of c a u s t i c , followed by (hot) water o r steam. A t low o i l s a t u r a t i o n , which implies a c a u s t i c flood a f t e r a water drive, t h e e m u l s i f i c a t i o n process w a s found t o be c r i t i c a l l y dependent on shear rate (a flooding r a t e , permeability, p o r o s i t y ) . The shear rate probably becomes less important i f a n oilbank has b u i l t up i n f r o n t of t h e emulsion bank, s i n c e from t h a t moment on a s i t u a t i o n resembling c a u s t i c flooding a t high i n i t i a l o i l s a t u r a t i o n is reached. An emulsion bank of s u f f i c i e n t m o b i l i t y was e f f e c t i v e i n d i s p l a c i n g t h e o i l , and r e s u l t e d a t low i n i t i a l o i l s a t u r a t i o n i n t h e formation of an oilbank. In one-dimensional packs of r e s e r v o i r sand e x t r a o i l recoveries of about 18% PV have been achieved as compared t o water floods of t h e same temperatures. Apart from a reduction i n Sor, i n a three-dimensional flood a s u f f i c i e n t l y mobile c a u s t i c emulsion is expected t o y i e l d a d d i t i o n a l recovery because of improved sweep e f f i c i e n c y over t h a t of a water drive.

REFERENCES 1.

2.

JENNINGS, R.Y.,

Jr.;

"A study of c a u s t i c solution-crude o i l i n t e r f a c i a l tensions", SOC. Pet. Eng. J. (June 19751, 197. COOKE, C.E., Jr., WILLIAMS, R.E. and KOLODZIE, P.A.; " O i l recovery by a l k a l i n e waterflooding", (12), 1365. J.Pet. Tech. (Dec. 1974) JOHNSON, C.E., Jr.; " S t a t u s of c a u s t i c and emulsion methods", J.Pet. Tech. (Jan. 1970), 85.

26

3.

586

Jr., JOHNSON, C.E., Jr., and McAULIFFE, C.D.; "A c a u s t i c w a t e r f l o o d i n g p r o c e s s f o r heavy o i l s " . J.Pet. Tech. (Dec. 1974); 1344. WAGNER, O.R. and LEACH, R.O.; "Improving o i l displacement by w e t t a b i l i t y adjustment", P e t r . Trans. AIME (1959) 216, 65. EHRLICH, R., HASIBA, H.H. and RAIMONDI, P.; Evaluation a "Alkaline waterflooding f o r w e t t a b i l i t y a l t e r a t i o n p o t e n t i a l f i e l d application", J.Pet. Tech. (Dec. 1974) 1335. MAYER, E.H., BERG, R.L., CARMICHAEL, J.D. and WEINBRANDT, R.M.; "Alkaline i n j e c t i o n f o r EOR A s t a t u s report", SPE 8848, ( A p r i l 1980). SCHULZ, W.; "Verfahren zur FMrderung von ErdMl", Deutsches Patentamt, A u s l e g e s c h r i f t 26.02.450, Bekanntmachungstag

4. JENNINGS, H.Y.,

5. 6.

7. 8.

-

-

(1.6.1978). 9.

REISBERG, J. and WSCHER, T.M.; " I n t e r f a c i a l phenomena i n crude o i l - w a t e r systems", no. 2, 43. Producers Monthly (Nov. 1956) CHANG, H.L.; " O i l recovery by micro-emulsion i n j e c t i o n " , US p a t e n t 4.008.769 (Feb. 22. 1977). . . SZABO, M.T.; I I A n e v a l u a t i o n of water-soluble polymers f o r secondary o i l recovery P a r t I", J.Pet. Tech. (May 1979) 553. DE ZABALA, E.F., VISLOCKY, J.M., RUBIN, E. and RADKE, C.J.; "A chemical t h e o r y f o r l i n e a r a l k a l i n e flooding", SPE 8997 (May 1980). MELROSE, J.C. and BRANDNER, C.F.; "Role of c a p i l l a r y f o r c e s i n determining microscopic displacement e f f i c i e n c y f o r o i l recovery by waterflooding", J.Can. P e t r . Techn. ( O c t . 1974) 1. SYDANSK, R.D.; "Elevated temperature c a u s t i c sandstone i n t e r a c t i o n implications f o r improving o i l recovery", SPE-DOE 9810 ( A p r i l 1981) 517. CAMPBELL, T.C.; "A comparison of sodium o r t h o s i l i c a t e and s o d i m hydroxide f o r a l k a l i n e waterflooding", SPE 6514, 47th Annual C a l i f . Reg. Meeting, B a k e r s f i e l d CA. April 13-15, 1977. TAYLOR, G.1.; "The i n f o r m a t i o n on emulsions i n d e f i n a b l e f i e l d s of flow", Proc. Roy. Soc. London (1934) 146A, 501. KARAM, H.J. and BELLINGER, J.C.; "Deformation and break-up of l i q u i d d r o p l e t s i n a simple s h e a r f i e l d " , I E C Fundamentals (1968) 3 no. 4, 577. KOZENY, J.; "Uber k a p i l l a r e Leitung d e s Wassers in Boden", B e r i c h t e Wien Akad., 136-U (1927) 271.

2,

10. 11.

12. 13.

14.

15.

16. 17. 18.

-

-

The a u t h o r s would l i k e t o express t h e i r thanks t o t h e i r c o l l e a g u e s i n KSEPL. who c a r r i e d o u t t h e experimental S p e c i a l thanks are due t o Mr. J.C.Stekelenburg, work.

UNITED STATES RESEARCH PROGRAMME

587

ENHANCED OIL RECOVERY R&D IN THE UNITED STATES AND IN THE U.S. DEPARTMENT OF ENERGY J. J. GEORGE STOSUR Office o f Oil, Gas and Shale Technology, U.S.Lkparfment of Energy

ABSTRACT The paper provides a g e n e r a l o u t l i n e of t h e s t a t u s of t h e enhanced o i l recovery technology i n t h e United S t a t e s w i t h emphasis on t e c h n i c a l problem and t h e s e a r c h f o r s o l u t i o n s . Upon t h i s background, t h e U.S. Department of Energy's e f f o r t and t h e r e s e a r c h p r i o r i t i e s i n enhanced o i l recovery a r e d e s c r i b e d i n c l u d i n g t h e new comprehensive d a t a c o l l e c t i o n system and a n a l y s i s on s e v e r a l hundred f i e l d p r o j e c t s .

INTRODUCTION There is u n i v e r s a l agreement t h a t enhanced o i l recovery (EOR) p r e s e n t s one of t h e b e s t o p t i o n s f o r l i q u i d f u e l s production i n t h e n e x t two decades. The U.S. r e s o u r c e t a r g e t f o r EOR is very l a r g e ; of t h e 450 b i l l i o n b a r r e l s of o i l t h a t have been discovered to-date, o n l y one-third, o r 150 b i l l i o n b a r r e l s W i l l be produced through primary and secondary methods, that is through d v l e t i o n and waterflooding. That l e a v e s a t a r g e t of over 300 b i l l i o n b a r r e l s of 011, t h e l o c a t i o n of which is known and i n r e s e r v o i r s which, though depleted a r e u s u a l l y reasonably w e l l d e f i n e d and o u t l i n e d .

Of t h e 450 b i l l i o n b a r r e l s found to-date i n U.S., 350 b i l l i o n b a r r e l s a r e considered as l i g h t o i l ( g e n e r a l l y w i t h g r a v i t i e s above 250 APT o r 0.91 g/cc). Even a f t e r waterflooding, 230 b i l l i o n b a r r e l s of t h i s l i g h t o i l remain i n the ground a w a i t i n g enhanced recovery t e c h n o l o g i e s , and even l a r g e r percentage f r a c t i o n of heavy oils remains unrecovered. While t h e r e is u n c e r t a i n t y a s t o e x a c t l y how much of t h i s o i l can be recovered by EOR p r o c e s s e s , a range of from 18 t o 52 b i l l i o n b a r r e l s is r e a s o n a b l e , depending on t e c h n o l o g i c a l successes and energy p r i c e s i n t h e f u t u r e . Here l i g h t o i l accounts f o r between 12 and 33 b i l l i o n b a r r e l s and heavy o i l f o r 6 t o 19 b i l l i o n b a r r e l s . By way of comparison, 52 b i l l i o n b a r r e l s is n e a r l y twice U.S. proved r e s e r v e s and equals t h e t o t a l o u t p u t from 7 1 s y n f u e l p l a n t s , each producing 100.000 b a r r e l s Per day over a 20-year p l a n t l i f e . While o i l production through EOR can be brought on l i n e f a r more quickly than s y n f u e l s , t h e r e are a number of c o n s t r a i n t s t h a t must be r e s o l v e d before t h i s can happen. Some of t h e more prominent are t e c h n i c a l c o n s t r a i n t s . The subject of t h i s paper is r e s e a r c h and development conducted a t U.S. Department of Energy t o m i t i g a t e t h e t e c h n i c a l C o n s t r a i n t s i n t h e a p p l i c a t i o n of EOR technologies. The views expressed i n t h i s paper are t h o s e o f t h e a u t h o r , and they do n o t n e c e s s a r i l y r e p r e s e n t t h o s e of t h e U.S. Department of Energy.

588

EOR TECHNIQUES

- AN

HISTORICAL OVERVIEW

There are three generic groups of EDR processes: chemical, gas (miscible and immiscible) and thermal. Each has several variants, but the processes which are most widely applied are: Chemical

- Polymer-augmented

waterflooding. It relies on the addition of "thickening" agents to water in order to increase displacement efficiency by reducing mobility of the displacing fluid.

- Alkaline

flooding. It is based on the addition of strong caustic substances to injection water in order to affect reduced surface tension between reservoir fluids, thus permitting easier fluid movement.

-

Surfactant polymer flooding. Surface active agents are injected to displace oil by reduced surface tension which allows building an oil bank that is subsequently pushed by polymers and water.

Gas (miscible and -

immiscible)

Hydrocarbon miscible. Miscibility is obtained by the injection of hydrocarbon gases which dissolve in oil, reduce viscosity and help the creation of an oil bank which can then be pushed to producing wells by water. Now that the cost of natural gas and LPG is high, the method is not much used.

- Carbon

dioxide flooding. It is based on injection of C02 t o strip the lighter components, swell the oil, partially mix with it and create an Oil bank which can then be displaced by additional gas or water.

- Nonhydrocarbon gas

drive. Inert gases can be used such as nitrogen or flue gas, primarily to add pressure to reservoir but also to attain miscibility (depending on pressure) and displace the oil in much the same way as Cop or natural gas.

Thermal processes Thermal processes apply largely to the recovery of heavy oils which are too viscous in their natural state to flow freely. Here, advantage is taken of the exponential decline of oil viscosity as temperature rises when reservoir is heated with steam injected from the surface or generated in the reservoir by in situ combustion.

-

Steam soak. The steam soak variety is typically used for stimulation to either accelerate or establish primary production in an otherwise unproductive heavy oil reservoir. Multi-cycle steam applications can be quite efficient under favorable conditions, but efficiency quickly

-

S t e m drive. Steam is injected COntinOUSly in one well, viscosity Of oil is reduced until it becomes mobile and can be displaced Or Produced by gravity drainage in surrounding wells.

- Pireflooding.

It uses energy derived from burning part of the oil in a reservoir to assist in the recovery o f the remaining unburnt oil. The combustion is supported by injected air and often water to increase efficiency of the process.

589 P o t e n t i a l EOR technologies

- Microbial

EOR. Microorganisms can be used t o generate s u r f a c t a n t s , t o produce C02 i n t h e r e s e r v o i r and t o otherwise change t h e composition of t h e o i l f o r improved recovery. This method is l a r g e l y i n research stage, though a few f i e l d tests were performed.

-

Combination mining. Several approaches have been proposed f o r t h e d i r e c t e x t r a c t i o n of crude o i l , including l a r g e diameter s h a f t s from which horiz o n t a l o r upwardly s l a n t e d w e l l s are d r i l l e d f o r drainage. Steam d r i v e i n l i g h t o i l . There is evidence that steam d r i v e could hold promise i n shallow l i g h t o i l r e s e r v o i r s where o t h e r methods f a i l e d .

- RF heating.

It is based on beaming r a d i o frequency energy i n t o a heavy o i l r e s e r v o i r . The method is c u r r e n t l y being f i e l d t e s t e d t o determine its potential.

An h i s t o r i c a l summary of EOR p r o j e c t s in t h e U.S. based on b i e n n i a l O i l and Gas Journal surveys (1) is shown i n Table 1. Table 1. United S t a t e s EOR p r o j e c t s i n perspective Method

1970

1973 -

1975 -

1977

1979 -

14 0 5

9 2 7

14 1 13

21 3 22

22 6 14

21 1 0

12 6 1

15 9 1

15 14 6

9 17 8

22 31 38

-

22 42 19

-

31 54 21

-

43 56 16

-

79 54 17

-

132

120

159

196

226

Chemical Polymer Flood Caustic Flood Mice1 l a r /Polymer Miscible Gas Hydrocarbon Miscible Carbon Dioxide Other Gases Thermal Steam Drive Cyclic Steam I n S i t u Combustion

Closer examination of t h e ten-year h i s t o r y of chemical EOR p r o j e c t s i n U.S. shows: steady i n c r e a s e i n t h e number of polymer p r o j e c t s s i n c e 1973; c a r e f u l experimentation with caustic floods, though s t e a d i l y i n c r e a s i n g over t i m e , and; steady i n c r e a s e i n new starts of t h e micellar/polymer p r o j e c t s u n t i l 1977 and then a sharp d e c l i n e i n response t o discouraging r e s u l t s . The miscible gas p r o j e c t s show a gradual phasing o u t of hydrocarbon miscible p r o j e c t s due t o r a p i d l y i n c r e a s i n g value of n a t u r a l gas; steady i n c r e a s e i n t h e number of carbon dioxide p r o j e c t s , which apparently replaced t h e increasingly c o s t l y n a t u r a l gas, and; a r e c e n t surge of i n t e r e s t i n nonhydrocarbon gases, even though most of t h e tests are very small.

590 The thermal recovery projects are most numerous, reflecting the relative maturity of the technology and show steady increase in the number of steam drive projects with a sharp increase in 1979 (even sharper increase is expected for 1981); gradual increase, then leveling off and slight decline in 1979 of steam soak projects in favor of the more efficient steam drive projects, and; a sharp decline of in situ combustion projects after 1970 when euphoria over the new technology gave way to the somber reflection that the technology I s a lot more difficult to apply than it appeared. These observations underline the tendency by the private sector to prefer the lower-risk, proven technologies such as cyclic steam and steam drive and to avoid the less certain and the less predictable but advanced approaches such as micellar/polymer floods, due to the high degree of risk and poor performance predictability. Equally interesting is the operators' own evaluations of their was compiled from the Oil and Gas Journal survey (l), Table 2. the projects judged technically and economically successful or those in the more or less established and less risky processes thermal recovery and polymer flooding.

Table 2. Operators'

METHOD

own

Tech. and Econ. Success

evaluation of project performance-March 1981 Tech. but Terminated Tco Total not Econ. or Early Success Promising Discouraging to Tell Eval. ~

~

57 7

6

26 1 4 1 2 5

Steam In Situ Comb. Polymer Caustic Micellar/Polymer Carbon Dioxide Other Gases

2 -

-

3 -

Total

77

11

42

2

10

-

-

2 1 1

2

projects which Again, most of promising are which include

5

1

-3 3 2

14

3 -

113 14 22 6 14 .17 8 -

48

194

19 3 5 3 8

7

The year 1981 will prove to be the year of a sharp increase of new EOR projects in the United States. To stimulate industry activity in U)R, a special incentive program was set forth by the Economic Regulatory Administration. Under this program an operator of a qualifying EOR project was permitted to realize b-orld oil price for controlled oil, provided that the difference was invested In the project. There were several limits: a project could recover no more than 75% of qualifying costs with a limit of $20 million per project. The purpose was to ameliorate the high front-end costs associated with EOR. The response was overwhelming, with as many as 4 2 3 FAIR projects by the time the program was concluded in March 1981, following total decontrol of crude oil prices. The incentive program for EOR was designed t o begin many.EOR projects that would lead to rapid oil production and, as expected, most of the projects proposed by industry involved the use of current technology, those processes that are less risky, better understood and requiring smaller capital investment. Table 3 shows the types and number of projects in various categories.

591 Table 3. New Enhanced Oil Recovery projects due to Energy Regulatory Administration's special incentive program Oil Recovery Technique Miscible Fluid Displacement (Less C02) CO2 Miscible Fluid Displacement Conventional Steam Drive Injection Unconventional Steam Drive Injection Microemulsion Flooding In Situ Combustion Polymer Augmented Waterflooding Cyclic Steam Injection Alkaline (Caustic) Flooding Immiscible Nan-hydrocarbon Gas Displacement Enhanced Heavy Oil Recovery (Other Than Thermal) Other Tertiary Enhanced Recovery Techniques Total

Number of Projects 13 95

93 34 37 35 48 16 32 11 3 6 -

423

The new EOR projects represent over $15 billion of private investment and are expected to recover nearly 3 billion barrels of crude oil, but as much as 80% of the total number use proven, less risky technology. The major promise of EOR is, however, with the newer, high risk "advanced" processes that have shown great promise in theory and in the laboratory, but .have not fared well in the transition to the field. The large number of new EOR field tests provide a unique opportunity for gathering and analyzing actual field data in a compressed period of time. The 423 incentive projects include a sufficient number of advanced technology applications that, when measurement and analyses are linked with oil production data, an excellent opportunity will present itself for scientific observation of their performance. Accordingly, a few of the more advanced field tests will be selected from among the cost-shared and incentive field tests for extensive preand post-test observation, diagnostics and analysis. It is hoped that these data coupled with the results from laboratory experiments and small nonproducing mini-tests, will be used to greatly improve the fundamental understanding of how and why the advanced EOR techniques behave as they do. The results should contribute towards more effective prediction of various processes under different reservoir conditions (2).

TECHNICAL CONSTRAINTS AND SEARCH FOR SOLUTIONS The high risks that deter operators from the advanced technologies are the principal focus of the goals of the DOE Enhanced Oil Recovery R&D program. R&D priorities among the processes directly reflect the degree of risk associated with each technology and the size of the potential of the respective processes. Research priorities have been developed to reduce or eliminate certain constraints. These priorities for the chemical, miscible gas and thermal EOR processes are reflected in the current R&D program, as follows:

592 Chemical

-

Basic studies on mechanism of displacement of bypassed oil. of surface and physical chemistry of microemulsions on displacement efficiency. Chemical degradation at high temperature, high connate water salinity and high clay content. More effective formulations of microemulsions and additives for mobility control, Fundamental R6D on rock/fluid interactions, which includes adsorption, wettability, ion exchange and formation damage. Quantitative determination of the effects of dispersion, relative permeability, apparent viscosity and inaccessible pore volume on mobility control under one-, two- and three-phase flow for the development of equations to be used for improving the precision of predictive reservoir simulators.

- Effect -

-

Gas Miscible Displacement (C02 Flooding)

A number of technical constraints to a wider application of gas miscible displacement are similar to those of chemical and even thermal recovery methods. One such generic problem is lack of adequate mobility control and the resultant low areal and vertical sweep efficiencies. Even when the displacing phase 1s fully miscible with crude oil under all conceivable reservoir conditions, an unfavorable mobility ratio leads to fingering which causes premature breakthrough and poor sweep efficiency. Other than the ever present problem of mobility control the R&D effort in miscible displacement processes includes:

- Fundamental studies on miscibility with reservoir oil, criteria for miscibility (single contact and multiple-contact miscibility). - Formation damage in carbonate reservoirs due to Cog flooding. - The effect of N2 and other gases on phase behavior and displacement efficiency.

- Static and dynamic laboratory -

investigations of phase behavior of C02crude oil systems. Studies of the effect of foams, polymers, graded-viscosity slugs and emulsifiers on the mobility ratio and displacement efficiency. Supply of natural C02 and its cost.

Thermal Recovery

- Development

of downhole steam generation capability at depths exceeding 2500 feet with the triple objective of substantially reducing transmission heat losses, overcoming flue gas emission probleme and increasing recovery efficiency due to the action of 0 2 with steam.

- Fundamental research on the effect of ancillary materials with steam on displacement and sweep efficiencies.

- Improved insulation of steam injection wells and the development of a metal-extrudable packer for high temperature wells.

- Development

of techniques for tracing the position of the high temperature front in steam flooding and in situ combustion methods (surface mapping of thermal fronts).

- Field

experimentation to determine the feasibility of bitumen recovery from tar sands using steam flooding, reverse in situ combustion and tk.e combination of both methods.

593 One of the more interesting EOR related projects sponsored by the Department of Energy is the development of a downhole steam generator at Sandia National Laboratories. The project was started 3 years ago and has recently attracted wide publicity in trade journals and some independent work by private interests. The downhole steam generator has indeed unique potential: it offers exceptionally high overall thermal efficiency (not only due to the elimination of heat lost in the transmission of steam from the surface to the bottom of the bed, but also due to the elimination of heat rejected and lost up the stack of a conventional steam generator); it can help overcome air pollution by injecting combustion products with steam into oil reservoirs, and; its economic benefits may be superior to the currently used steam generators. A prototype has already been tested under simulated conditions at the surface and a real downhole test of the high pressure system will be conducted in Long Beach, California, in the summer and fall of 1981. Another example of advanced technology brought to fruition and transferred to the private sector is in the area of faster, more efficient drilling. Sandia National Laboratory has developed a special bonding technique which permitted a new bit design with polycrystalline diamond cutters. One source quotes oil companies' reports that three synthetic-diamond bits can drill one 5000 ft.deep well section in 112 hours, while in the past, such a section would use up as many as 13 conventional bits (3). Far more important that the difference in hardware cost is the saving in time; synthetic-diamond bits can cut drilling time by several days for a saving of up to $1 million in the more expensive offshore wells. Worldwide, 13 companies now fabricate the synthetic diamond bits, with total capacity of the U . S . companies in the range of 2,800 bits per year and several of them have order backlogs extending for a year or more. A good example of the kind of long-term R6D pursued by the Department of Energy

is microbial EOR (4). There are currently five contracts with universities to determine whether microbial cells can be used to selectively plug highpermeability layers and thus improve sweep efficiency; to .examine the potential of using microorganisms for EOR by mechanisms other than selective plugging, such as in situ production of biosurfactants and biopolymers; to ecreen qualitatively and quantitatively for microbial organisms' ability to produce gases such as carbon dioxide, hydrogen and methane and; to determine the feasibility of bacteria to produce acids such as acetic acid, solvents such as alcohols and acetone as well as small molecules possessing surfactant properties. By most accounts microbial EOR is avant-garde, insufficiently pursued by private interests and yet, according to many scientists, offers exciting possibilities for brand new concepts in EOR. CONCLUSIONS Enhanced oil recovery has the highest probability of new-term impact on the production of liquid fuels, with lowest cost premium. However, a coordinated program of field experiments and supporting R6D is required to accelerate both the development of technology and early commercial implementation. TO this end, the U.S. Department of Energy has established a highly organized effort through its Energy Technology Centers, National Laboratories and nearly 30 universities to systematically attack the complex technical problems that have inhibited industry application of the potentially efficient but expensive and risky technologies. The U.S. Department of Energy R6D priorities reflect the new emphasis on highrisk, long-range, high potential EOR technologies. It is presumed that the industry will respond to the recent oil price decontrol with stepped-up development activities, including the economically marginal petroleum resources and increasing recovery efficiency. In all cases, the EOR program is closely coordinated with industry to avoid duplication of effort.

594 REFERENCES 1.

SHANNON, L. Matheny, Jr.; "EOR Methods Help Ultimate Recovery", Oil and Gas Journal (Mar 31, 1981) 79-124.

2.

"The DOE Light Oil Research-and-Development Program," Draft publication dated May 21, 1981.

3.

"Synthetic Diamonds Shake-up The Drill-Bit Market", Business Week, December 1, 1980, 98-99.

4.

"Contracts for Field Projects and Supporting Research on Enhanced Oil Recovery and Improved Drilling Technology", 26, WE/BETC-80/4, Sept 30, 1980.

595

AUTHOR INDEX

ACS, G.

,

299 H.,

ANDREWS, C . ,

63

43 395

APPLEYARD, J . R . ,

,

AZIZ, K.

367

, 299 , 441

BiRO, 2.

,

GHARIB, S. , 267

527

GHASSEMI, F . ,

549

HANDY, L . L . ,

149

, 299

BLACKWELL, R.

J . , 237

B R E I T , V.

223

S.,

81

BROWN, C. E . ,

CASINADER, P. C . , CHAUVETEAU, G.,

425

197

CHESHIRE, I. M . ,

395

CHESTERS,, D. A.,

563

CLARK, C.

HESSELINK,

F. TH.,

HUGHES, D.

S. , 247

JANSSEN-van

ROSMALEN, R.,

JENSEN, J. I., 329 JONES, T .

J., 135

J . , 563

135

CLINT, J. H.,

, N . , 63

LABASTIE, A.,

213

LANGLEY, G. 0. , 81

379

LEMONNIER, P., LOREW, P. DALEN, V., DAWE, R.A., D I E T Z , R.,

573

223

CARMICHAEL, J. D.,

COLLEY

543

R. L . ,

483

A.,

BARTHEL , R.

S., 409

FOULSER, R. W.

B A L ~ N T , v.

BANKS, D.

299

FARKAS, E . ,

FOX, BAILEY, N .

267

EL ARABI, M.,

AKSTINAT, M.

B.

,

123

329 161, 511 McCAFFERY , F. G.

499

DOLESCHALL, S . DOSCHER, T . X.,

I

299

MAHERS, E. G . ,

267, 549

MATTHEWS, J. D.,

, 285

511 241

573

596 R.,

MEYN, V.,

451

SHAH, D.

STOSUR, J . J. G., NEUSTADTER, E.

101

NOVOSAD, J . ,

543, 587

135

L.,

TAN, T .

C.,

THAVER, R.,

425 63

C., 313, 351 TOROK, J . , 299

TODD, A. OFFERINGA, J.,

299

POLLARD, R.

313

VAROTSIS, N . ,

K.,

PONTING, D.

351

TWEEDY, J. A . ,

267

OYEKAN, R.,

P A , T.,

527

K.,

395 441

VIO, L.,

213

VOGEL, P.,

179

179

PUSCH, G.,

527

WEIJDEMA, J . , RIDDIFORD, F. A.,

329

RISNES, R., ROBINSON,

563

D.

ROSS, G. D., ROWLAND, P .

WILSON,

D.

WRIGHT,

R. J.,

C.,

425 161, 511

483

P.,

351 R.,

483

ZAITOUN, A.,

J . , 467

313

STEWART, G.,

247

E.,

O., 1

SKILLERNE DE BRISTOWE, B.

M I N KWAN THAM, 123 MOTT, R.

285

SAYEGH, S. G.,

223

MAYER, E.

197