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THERI$AL RECOVERY OF OIL AND BITUNIEN
ROGERM. BUTLER Departmentof Chemical and PetroleumEngineering Universityof Calgary Calgary,Alberta, Canada
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PrenticeHall,EnglewoodCliffs,New Jersey07632
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Confenfs PREFACE xii Chapter 1. INTRODUCTIONTO THERMAL RECOVERY Enhanced Oil RecoveryMethods z SteamStimulation z Steamflooding 3 Hot Waterflooding 4 In Situ Combustion 4 World Fuel Resources 5 The Oil Sand Resource 7 VenezuelanHeavv Oil 8 g Canadian Heavy Oil and Bitumen Correlation of Canadian Tar Sand Deposits Il Size of Alberta Oil Sand Deposits 11 Comparisonof Heavy Oil and ConventionalCXIResources 12 Deposits of Heavy Oil and Bitumen in the United States 12 The Nature of Heavy Oil and Bitumen Deposits 14 Solid Mineral Matter 16 Kaolinite 16 Montmorillonite 17 Illite 17 Chlorites 18 Water 18 Oil and Bitumen 19 Gas 19 Units of Measurement Z0 Use of ProgrammableCalculatorsand Microcomputers 22 Radial Flow to a Vertical Well 22 The Problem of Economic Exploitation 25 Bitumen Transportation 25 Bibliography 27 General References 29 Chapter 2. CONDUCTIONOF HEAT WtTHtN SOLTDS 30 Introduction 30 Thermal Conductivity 30 Fourier's Equation 3L Flow of Heat into a Semi-Infinite Solid 32 Significanceof Solution 36 Heat Transfer from a Spreading Hot Zone 37 Constant Heat Injection Rate into a Fracture 3g conduction from a Spreadingchamber That Advances to a Limit and Then Stops 39 Numerical problem 40 Conduction Ahead of an Advancing Front 43
ql AlLr ot a[ rtovlnc|lu rtull Tnmll lil TII[8 47 llort Ab.d of Rilt In Ttanrlont Foriod 48 Cctlnurllon of tho Prsvlous Numcrical Example 50 Elfcst of Ctarylng Ffont Vclocity Tho Situation Whcrc the Front Advance Velocity Is Inversely 51 Proportional to the SquareRoot of Time 52 Radial Heat Flow from a Well 55 Cumulative Heat Flow from Well Bore 56 FactorsAffecting Well Bore Heat Loss 56 Insulation of Wells to Reduce Heat Loss The Equivalent Well Radius with Multiple Resistances 58 59 Direct Injection of SteamDown the Well Casing Injection of Steamin the Tirbing with the Annulus Full of Gas ConvectiveHeat Transfer Between Two Concentric Vertical 60 Cylinders 63 Background Material on Well Bore Heat Loss 63 Numerical Example of Well Bore Heat Loss Calculation 68 Radial Conductive Heat Loss from a Buried Heated Cylinder 71. Bibliography
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rr 3. CONVECTIVE HEATINGWITHIN RESERVOIRS 72 72 Introduction 73 Simple Convective Heat Transfer Without Conductive Heat Loss 74 Overall Heat Balance Approach 75 Steam Injection 75 Lauwerier's Equation 78 Numerical Example Thermal Efficiency for Constant-Displacement Rate Steam-Drive Fraction of Heat in Steam-SaturatedChamberAfter the Critical 85 Time 86 Asymptote for As/A if tp : o Thermal Efficiency for Constant Steam-Injection Rate: Marx and 86 Langenheim'sTheory 90 Numerical Problem Using Marx-Langenheim's Equation 93 Simple Formulasfor Estimation of the Oil-Steam Ratio 95 Convective Transfer of Heat Beyond the Condensation Front Size of Steam Zone for Time Greater than the Mandl and Volek's 96 Critical Time 98 Effect of Non-Vertical Front 99 Steam Injection into a Thin Channel or Fracture Comparison of Fracture Filled with Steam for Constant Injection Rate 100 and for.ConstantArea Areal Growth Rate Calculation of Mandl-Volek Critical Time for a Numerical 100 Example Extension of Numerical Example to Injection into a Very Thin 101 Horizontal Layer or Fracture 103 Bibliography 104 rr 4. STEAMFLOODING 104 Introduction A Qualitative Discussionof Steam-injectionProcesses lv
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Stcrmlloodlng 105 Suitability of Spccific Rcscrvoirufor Stcamflooding 107 The Propcrtiesof Stcam 110 TemperatureDistributioninSteamflooding 122 Fingering 124 Gravity Override 124 SteamfloodingMechanisms t26 Reduction of Oil Viscosity 126 Changesin Relative Permeability 127 Myhill and Stegemeier'sApproach to Steamflooding L29 Summary of Myhill and Stegemeier's Assumptions 130 Outline of Method 130 Limitations 131 Comparisonsof Theoretical Predictionswith Data L33 Ten-Pattern Steamflood at Kern River 135 San Ardo Steamflood and Infill Drilling 137 Comparisonof Steamflood and_SteamSoak 139 SteamfloodingMulti-LayerReservoirs 140 Jones'SteamDrive Model L4L Jones Empirical Adjustment Factors i+Z Injectivity t44 Steady-stateDisplacementBetweenan Isolated Pair of Vertical Wells L45 Time for Breakthrough 147 Isolated Injection Well Surrounded by a Circle of Equally Spaced Producefs 148 Confined Patterns 149 Confined Horizontal Well Pair 150 RepeatedFive-Spot 151 Repeated Seven-Spot 152 SteamZone Shape:van Lookeren'sEquations t52 Numerical Example of the Use of van Lookeren's Theory t57 FiarouqAli's Unified Approach I57 Gomaa's Correlations for Predicting Oil Recovery 158 Vogelb Simplified Heat Calculation for Steamfloods 162 Comparison of Vogel's Predictions with Myhill-Stegemeier 165 Numerical Example 166 The Fast Process 167 Other Mechanismsin Steamflooding 168 Conversion of Mature Steamfloods to Hot Waterflooding 173 t74 Qualitative Review of Steamflooding Bibliography 175 chapter 5. THE DTSPLACEMENT OF HEAVY OtL ' Introduction 179 FiactorsAffectingDisplacement 179 Displacement Concepts 180 Piston Displacgqt.ent-,..180 '- Breakthroush 180-
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t04 Contents
Contents
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lgl fttont.l sl.blllty l8l Thc Thoorctlcal Approrcho to Displaccmcnt 182 Flood Intcrfacc Stability-Muskat's Model 182 Darcy's Law and Interfacial Stability 184 Effect of Interfacial Tension 185 A Simple Theory for Stabilizationby Interfacial Tension 188 Stability upon Interfacial Effect of Condensation L9l Miller'sTemperatureGradientStabilization 192 Darcy's Law for Two-PhaseFlow 192 Relative PermeabilityCurves t93 The Fractional Flow Equation 196 Effect of the Gravity Term on Fractional Flow Effect of SegregatedFlow on Apparent Relative Permeability 197 and Fractional Flow 200 The Buckley-Leverett Displacement Theory 200 The Velocity ofthe Shock Front 201 The SaturationBehind the Front 203 The Upper Shock Front 205 Conditions at Breakthrough 205 Recovery at and After Breakthrough 207 Effect of Viscosity Ratio 208 PressureGradients During Displacement 210 Numerical Problem on Buckley-Leverett Theory Comparisonof Displacementwith Diffuse and Segregated 2I3 Flows 213 Conditions at Breakthrough 214 Conditions When Oil-Water Ratio Falls to 0.025 2L4 Comparison of Oil Recoveries 214 Water Saturation Profiles 216 C.W. Nutt's Capillary Bundle Model 220 Analysis of Steamflood Using the Buckley-Leverett Theory 222 Buckley-Leverett Theory Applied to the Steam Chamber 222 Calculation of Volume of Steam Within the Reservoir 223 Heat Balance. 224 Numerical Example 225 Heat Balance, Saturations, and Recovery 227 Displacement of Oil Ahead of the Condensation Front 228 Effect of Shapeof Relative Permeability Curves 229 PressureDrop'forSteamflooding 232 SteamOverride 234 Effect of SteamQuality 238 Effect of Vertical Heat Loss 238 Effect of Increasing Steam Viscosity 238 General Conclusions on Displacement 239 Bibliography tr
24r 0. CYCLIC STEAM STIMULATION 241 Introduction The Stimulation of Wells with AppreciableCold Flow 243 Well Bore Skin 243 Near-Well Bore Region vl
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244 Bobcrl and Llntzb Modcl 246 Effect of ProcessVariables 248 Scaling of Thermal Models 250 Niko and Troost'sCyclic Steam Stimulation Model Experiments 250 Effect of ProcessVariables Simplified Analysis of Production Rate Decline During Reservoir 259 Cooling The Problem of the First Cycle in the Cyclic SteamStimulation of Tar 266 Sands TIl Cyclic Steamingof Vacca Tar, Oxnard, California 272 Compaction Drive in Conventional Heavy Oil Reservoirs 274 Fracturing and Reservoir Expansion During Steam Injection 275 StressDue to Gravity in a Semi-Infinite Strain-Free Solid 276 In Situ Reservoir Stresses 277 Fracturing Pressure 277 Ground Heave 279 Effect of Fracture Orientation on Productivity from Stimulation Possible Production of Orthogonal Vertical Fractures 280 from the Fracturing of a Line of Wells 281 Bibliography 285 Chapter 7. STEAM-ASSISTEDGRAVITY DRAINAGE 285 Introduction 285 Concept 286 Relationship to Convention Steamflooding 287 Gravity Drainage Theory 289 Darcy's Law 291 Integrated Flow 291 Material Balance 292 Velocity of the Interface 293 Position of the Interface 294 The Exponent m-An Extended Definition 295 Change of Variable of Integration 296 Original Scaled Visual Model 297 Dimensional Similarity 300 Original Scaled,PressurizedModels 300 Calculated Drain4ge Rates for Field Conditions 302 Extension to the Original SAGD Theory TANDRAIN-An 303 Effect of No Flow Boundary 305 Further Experimental Data 307 Extrapolation of the Model Experiment to the Field 307 The Rising Steam Chamber 309 Value of Proportionality Constant in Height Equation 310 The Oil-Production Rate 311 Shapeof SteamChamber 312 Available Head 312 Finger Rise Theory Effect of Steam Temperature, Reservoir Temperature, and Oil 313 Properties on Drainage Rates 313 Steam and Reservoir Temperatures
242
Contents
Contents
vlpol tnsm Thc ZlmPm'AEC Stcam Ccncntor BibliograPhY 411
316 Nuncrlcrl Problomo Stoem-Arldcd Orrvlty Dnln4o 321 Stoam-InJoctionWclls 321 Horizontal Injection Wells 325 Vcrtical lnjcctors 328 Avoiding the Steady-StateHeat-Distribution Assumption 330 Valuesof the ParameterBg 331 Heat Penetrationas a Function of Distance Along Interface 333 Predicted Oil-SteamRatios 335 Effect of Steam Pressure SAGD Results from Scaled Laboratory Reservoir Models Operating at High and Low Pressures 336 343 Oil Production After Stopping Steam Injection 344 Recovery of Heavy Oil Above Water 3,+8 Effects of Reservoir Heterogeneities 353 Fbrmation of WO EmulsionsWithin the Reservoir Well Bore Flow Resistance 356 357 Conclusions Bibliography 358 rpter 8. STEAM RECOVERYEOUIPMENTAND FACILITIES 3ffi Introduction 360 Steam Generation 364 Effect of Water Impurities 366 Deaeration and Oxygen Control 368 Oil Field Steam Generators 371 SteamQuality 371 Convection Section Radiant Section 373 373 Vertical Steam Generators 373 SteamDistribution System 375 Cluster6d Deviated Wells Thermal Well-Completions 375 378 Temperature Logging 380 Control of Heat Loss in Steam-InjectionWells 381 SelectiveSteamInjection Artificial Lift 381 387 Improving Well Performance 388 Treating ProducedFluids 393 Production Treatmentwith High Sand Production 393 Makeup Water Supply 394 Recycling ProducedWater 395 Produced Water Analyses 396 Treating Recycled Water 402 WastewaterManagement 443 Esso'sThermal Softening Process 4.03 ReducingTotal DissolvedSolids 404 Alternate Steam Generators 404 Coal-fired Steam Generators 405 Downhole SteamGeneration 447 Fluidized Bed CombustionBoilers vlll
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41s Chaptcr 9. lN SITU COMBUSTION 415 Introduction 418 DrY Combustion bescriPtion of Phenomena 418 4t9 Combustion Tirbes 423 Alexander's Fireflood Pot 424 Fuel for Ratio otHlC Calculation Example of Stoichiometric Calculation for Combustion 425 Process 426 Fuel DePosition428 Oxidation LowjTemPerature 430 In Situ CombustionExperiments Using Oil Sands 432 Ignition 435 Temperature at the Combustion Front Combustion the upon Cooling Conductive of Effect 436 TemPerature 440 Examples o1 the Use of Ramey's Solutions 442 Oil Produced ProPerties of 442 Wet Combustion 445 LaboratorY Results 448 Water'to-Air Ratio 450 Sands Tar in In Situ Combustion 452 Use of OxYgenor Enriched Air 411 Potential Advantages for the Use of Oxygen . 454 Oxygen of Use the of Possible Disadvantages 455 The Cost of OxYgen The Effect of Pressureon Combustion Performance 457 with OxYgen 458 Design of In Situ Combustion Projects 459 Load Fuel Total 459 Air Requirement 4ffi Air Rate and Pressure 461 Oil DisPlaced per Volume Effect of Water-Air Ratio on Oil Recovery 464 Burned 466 Field Project Results 466 Lake Golden LloYdminster, 47L Ceityt Bellevue Field in Louisiana 473 Field ExPansionsat Bellevue 474 In Situ CombustionProjectsin Rumania 477 i BibliograPhY
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481 Appendix 1. SYMBOLS 481 Lower Case 482 UPPer Case 484 EnthalPies 484 Greek Contents
Contents
Unltr and Convcnlon Fhcttm
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dlx 2. D€NSITIESOF OtL RESERVOTR MATERTALS Watcr at Boiling Point 487 SaturatedSteam 487 Brine Solutions 48i ReservoirOil 488 Rocks 490 ConversionFactors 490 Bibliography 490
Apprndlx !. THERMAT IN8ULATION Bibliography 520
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OF STEAM Appendlx 9. THERMAL PROPERTIES 521 521 Saturation Pressureand Temperature Enthalpies of SaturatedLiquid and Vapor Bibliography 523
TNDEX
dlx3. THERMAL coNDucflvrry oF orL REsERvorR MATERTALS 49l UnconsolidatedOil Sands 49L Comparisonof MeasuredThermal Conductivity of Tar Sand with Prediction from Somerton'sFormula 4g3 ConsolidatedPorousRocks 494 Comparisonof Thermal Conductivities of Consolidated and UnconsolidatedSandstones 495 Thermal Conductivity of Hydrocarbon Liquids 4g5 Thermal Conductivity of Liquid Water 495 Thermal Conductivity of Over- and UnderburdenMaterials Thermal Conductivitiesof MiscellaneousMaterials 4g7 ConversionFactors 497 Bibliography 497
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llx 4. HEAT CAPACTTTES AND ENTHALPTES 499 Sandstones 499 Carbonate 499 Clays 499 Oils 500 Water 501 Heat Capacitiesof Common Gases 502 Average Heat Capacities Betweeen T1 and T2 S0Z Changein Enthalpy Between T1 and T2 SW Volumetric Heat Capacitiesof Reservoir Materials 503 ConversionFactors 503 Bibliography 503 ix 5. VISCOSITIES 504 Viscosity of Crude Oil 504 Viscosity of Water and Steam ConversionFactors 513 Bibliography 514 x 6. HEATS OF COMBUSTTON Hydrocarbon Liquids 515 Fuel Gases 516 Solid Fuels 5I7 ConversionFactors 5L7 Bibliography 517 x
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511
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Prefsce
This book describesthe recovery of heavy oils and bitumen by in situ thermal methods.It is basedon the lecture notes,which have been developedby the author for an annual thirteen-weekgraduatecourseat the University of Calgary,to classes drawn from full-time graduate students and to a greater extent from engineers whose work is directly related to the oil industry. The author has presentedthe courseeachyear since 1982and the book has been written during this period. The first chapter is an introduction to the subject.The heavy oil and, more importantly, the bitumen depositsin Canadaare an enormousresourcewhich will become of great economic importance. Production from these sourcesis already equivalentto a very significant fraction of the Canadianrequirementfor crude oil. Other countries as well as Canadahave vast depositsof these crude oils. The depositsin the Canadianprovince of Alberta and thosein Venezuelaare eachapproximately equalin quantity to thoseof conventionalcrudesin placein the Middle East reservoirs.The purposeof this book is to discussthe technicalfactorsand problems which are involved in their production by those in situ methodswhich involve the heating of the reservoir. Although the book discusses,in a logical development,the theory and much of the practice in this area,it is not intendedto be an encyclopediaon the subject. It describesthe main ideasof the subjectwith the purpose of providing the reader with tools which can be usedto make further advances.In places,the book summarizes well establishedthinking whereasin others,it describesoriginal ideasand approaches;some of these have been publishedpreviously in paperswritten by the author and his collehgueswhile others appearhere for the first time. Chapter2 dealswith the transfer of heatwithin the reservoirbulk and within the adjacentregionsby thermal conduction.Equationsare presented,and many are derived,which allow the analysisand prediction of quantities such as the heat loss from the boundariesof a heatedreservoir.Numerical examplesin this chapter,like those in other chapters,provide the readerwith the meansfor the practical understandingand applicationof the theoreticalmaterial. The interspersingof numerical exampleswithin the book and, in some cases,the use of the results from the examplesfor the further developmentof concepts,are intended to make this book interestingand useful to the practical engineer.The approachemployedis practical and fundamentalwith a minimum of academicsophistication.The author'saddress is now in an invory tower but he camewith tar on his boots. xii
One of the conclusionsto be drawn from Chapter 2 is that simple thermal conductionis, in most instances,an inadequatemeansfor heating substantialreservoir volumesfrom small diameterwells. It is too slow. The third chapterdiscusses convective heating achieved by the injection of hot fluids such as steam or hot water. This allows heat to be introduced much faster and over substantialvolumes. Again a practical approachinvolving the use of illustrative numerical examplesis employed.One of the conclusionswhich the readerwill draw from this chapter is that a very substantialquantity of heat is required simply to raise a volume of reservoir to the steam temperature and that this quantity has to be augmented,frequently several-fold,in order to also supply the lossesof heat from the reservoir boundaries.The material in the third chapterprovidesthe readerwith tools which allow the estimation of these quantities and with a grasp of how the heat is distributed in steamrecoveryprocesses. Steamflooding and results from steamflooding field projects are discussed further in the fourth chapter. The chapter also extendsthe theoretical ideas developedpreviously.For examplethe tendencyfor steamto override the oil during lateral steamflooding and the contribution of steam distillation to recovery are discussed. Chapter 5 is concernedwith the mechanismby which oil is displacedby injectedfluids. A factor of major importancehere is that the displacingfluid is usually much lessviscousthan the oil. This causesinterfacial instabilitiesand the fingering of the displacingfluid-particularly if it is water. The situation can be different with steamsince it condenseswhen it intrudes into colder oil and it is the resulting aqueouscondensaterather than the steamwhich fingers.Also steamtends to float abovethe adjacentoil and override becauseof its low density. One of the subjects which is discussedwith practically-orientednumerical examplesis the displacement of oil by steam within a steam-saturatedregion using the Buckley-Leverett approach. This mechanismis surprisingly effective despite the sharp contrast between the viscosity of the steamand the oil. It is shown that the reasonfor this is that the flow of steamin suchsituationsis, on a volumetric basis,much higher than that of the oil. Steamcontainsmuch lessheat per unit volume than doeshot water and much larger volumes are required to heat a volume of reservoir. These much larger volumesare much more effective in displacingoil from the heatedzone even though the dynamicviscosity of steamis lessthan that of water. The cyclic steamstimulation processis describedin Chapter 6. This process was discoveredby accidentin 1959and it provided the main thrust for the early developmentof thermal recoveryin California, although most of those projectshave now been convertedto steamflooding.Steamstimulation is still the major process for the in situ recoveryof Alberta bitumen although it is likely that it too will be surpassedeventuallyby steamdisplacementprocessesbecauseof their potential to achievehigher oil recoveries. The Steam-AssistedGravity Drainageprocessis describedin Chapter7. This involves steamfloodingto horizontal production wells which are located near the baseof the reservoir. Steamis injected from wells which are higher in the formazonesform and grow abovethe productionwells. The growth tion. Steam-saturated of these steam chambers can be both vertical and sideways.The oil near the Preface
xIl
boundary of eachchamberis heatedand it flows by gravity downwardsto the production well. An important feature of the processis that the displacedoil remains heatedasit flows to the productionwells.The processhasbeentestedin field pilots, particularly in AOSTRAs Underground Test Facility in the Athabasca tar sands near Mclvturray.The performanceof this pilot is promising and recent reviewsby AOSTRA concludethit the processshouldbe economicallycompetitivewith steam stimulation even for projectJrecoveringthe extremelyviscouscrude of Athabasca. The facilities which are usedfor thermal recoveryincluding steamgenerators, wells, lifting practices,treating, and recyclingwater are discussedand analyzedin Chapter 8. Heavy oil and bitumen recoveryusing in situ combustionis reviewedin Chapter 9. The main attraction to this process,as comparedto steaming,lies in the much lower cost of the heat for the reservoir.This advantagecontinuesto generate interest in the processalthough developmentactivity appearsto be declining. The chapter includesa discussionof the principles involved and describesseveralsuccessfuland economicfield applications. The final chaptersin the book are Appendiceswhich contain data and correlations useful in the analysisof thermal recoveryprojects' The author is grateful to many peoplefor the help and advice'theyhave given to him in developingthis work to its presentstate:Chi Tak Yee, Viera Oballa, and philip Bakesaswelias many other students,made important contributions in identifying inconsistencies,and errors, both substantialand typographical, in earlier veisionsof the text. Riza Konak of EssoResourcesCanadaand Ken Porter of Gulf ResourcesCanadareviewed the material of Chapter 8 and suggestedvaluableimprovementsand additions. Gordon Moore and Matthew Ursenbachof the Univeriity of Ca[ary reviewed the material on in situ combustionand made important The author is also indebtedto his former colleaguesof the and useful-suggestions. Heavy Oil ReiearchDivision of EssoResourcesCanadawho contributed ideas,advice, and enthusiasmwhich became embeddedin his experience.He has clear, vivid memoriesof many stimulating and productive disussionswith G. S. McNab, H.Y. Lo, D. J. Stephens,M. weiss, F. Greebe,D.A. Best, S. Bharatha,P. N. Troffimenkoff, p. J. Griffin, R. Leaute, and many others. For him they were exciting yearsand exciting people.The encouragementand supportwhich the author hasreceived from the- Alberta Oil Sands Technology and ResearchAuthority (AOSTRA), and particularly from its first Chairman Dr. C.W. Bowman and its first Vice-ChairrnanDr. M. A. Carrigy, is also acknowledged.The Authority employed the author as Director of Technical Programsduring 1983and it was in this period that its plans for the UndergroundTest Facility were finalized. In March 1984the author's proposal for the Sleam Assisted Gravity Drainage process as the first processio be demonstratedin the UTF was presentedat a review organizedby AOSTRA for potential industry participants. The successof the subsequenttest and the enthusiasmwhich this has generatedin industry has done much to bolster his confidencein presentingthe material of Chapter 7. The author is also indebted to the Calgary Seition of itre PetroleumSociety of CIM and to the industries of calgary lor ttreir endowmentof the chair of PetroleumEngineeringwhich he has o""ipi"a since 1983.This support has made the writing of this book possible' xrv
Preface
I wish to thank the following for permission to use and copy material for which they hold the copyright; in eachcase,credit is also give to the author where the material appears: (1982)' Alberta Energy provided the data for Fig. 1.3 from their publication EnergyHeritage A'2'1' print Fig' permission to The American PetroleumInstitute granted The Alberta Oil SandsResearchand Technology Authority (AOSTRA) for works published in theAostra Journalof Researcft,the proceedingsof the UNITAR/UNDP International conferences of Heavy Ciude and Tar Sands, and proceedings of the AOSTRA and CANPET thru 8.19,8'29,8'30' 8.1,7 seminars:rigs. 1.4,7.30thru 7.32,7.45thru 7.54,7.67,7.70,8.14, 8 . 3 3 ,9 . 5 ,9 . 2 2 , 9 . 2 3 a, n d9 . 4 4 . Babcock& wilcox, Barberton,ohio, for Figures8.1 thru 8.3 reproducedfrom their publication Steam. Business Information Services (BIS), copyright holders for PetroleumEngineerInternational magazine,for permissionto use Fig. 9.64. The Canadian Institute of Mining and Metallurgy, publishers of the Journal of Canadian .34,7.39,7.44,7.54thru for the following:Figs.4.7,7.I2, 7.15,7.16,7 Technolagy Petroleum ' 7.56,7.68,7.69,and8.2'1 The canadian Journal of chemical Engineering(cichE) for the following: Figs. 1.8, 7'1 thru 7 . 3 , 7 . 5 ,a n d7 . 7 . The CanadianSocietyof PetroleumGeologistsfor Figs. 1.2 and 1'5' Corod ManufacturingLtd. provided the original drawing for Fig' 8'21' Editions Technip, Paris,Francegrantedpermissionto reproduceFigs. 9'2 and 9.34. EssoResourcesCanadaLimited for permissionto useFigures8.23,8.24,8.25,8.35'and 8.38. Mr. W. H. Fairfield and Mr. P. D. White for permissionto publish Figures9.60 to 9.63 and Tables9.7 to 9.10. Foster Wheeler Fired HeatersLtd., Calgary,Alberta provided us with the illustrationsfor Figs. 8.10(a)and 8.10(b)' Dr. G.W. Govier for permissionto use his data in Table 1.2. McGraw-Hill, N.y., publishers of the 1st UNITAR/UNDP International Conferenceon Heavy crude and Tai sands.for the following: Fig. 1.1,Table 1.9, and Figs. 8.31and 8.32. Natco canada, calgary, Alberta provided the drawingsfor Figs. 8.7, 8.28' and 8.34. The National Research Council, publishers of. the Canadian Journal of Earth Science,for Fig.6.29. Professorc.w. Nutt, granted permission to publish Figs. 5.32 thru 5.35 and Figs. 5'40 and 5.41. Oxford University Press,Oxford, U.K., for Fig.2.l2. Used by permissionof the Oxford University Press. The petroleum Societyof the CanadianInstitute of Mining and Metallurgy (CIM)' Calgary Section,for Figs. ?.58 thru 7.66 published in the preprints of the 40th Annual Technical Meeting of the Petroleum Society of CIM. The society of Petfoleum Engineers holds the copyright for all material published in their SpE papers, theJournalof PetioleurnEngineering,the Societyof PetroleumEngineeringlournal, and transcripts of ttre Spb,of AIME. Permissionhas been received and acknowledgedfor the following:Figs. 1.9,4.g,4.11thru 4.1,4,4.17thru 4.2L,4.29thru 4.40,4.43thru 4.5t'5.1, 5.7,5.g,6.2thru6.13,6.I5,6.21,6.23,6.24,8'39,8.43thru8'45,9'6thru9'21,9'25thru9'32' 9.35thru g.3g,g.45thru 9.47,9.50thru 9.55,and 9.65;Tables3'3, 4.1thru 4.5,4'8,6.2'8'4' and 9.6. Dr. P. G. Saffmangrantedpermissionto reproduceFigs' 5'3 and 5'4'
TOTRAN ServicesLimited, calgary, Alberta provided the photograph for Fig. 8.8. Eugene F. Traverse supplied Figs. 4.15 and 4.16'
The first draft of the book was typed by Mrs. Margaret McAuslan in 1'984and the author is grateful to her for her hard work and interest. Since then the annual revisionsand ixtensions of the lecture notesand the manuscriptfor this book have been typed in a world-classmanner by Mn. Patricia Stuart-Bakes.The author wishes-tothank her for her perseverance,moral support, and enthusiasm. Finally, the authorwishesto recognizethe encouragementand patienceof his wife Joyce*ho hur understoodand supportedhim. Writing books is an interesting and worthwhile endeavorbut it is time consumingand hard on one'sfamily. Thank you, Joyce. Roger M. Butler Calgary,Alberta
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Preface
1 Introduction to Thermsl
Recovery
The efficient and economicrecovery of heavy oil and bitumen from reservoirsin Canada,Venezuela,and elsewhereis a majortechnicalchallengeand taskl As will be seenlater in this chapter,the quantitiesof heavyoil and, p-articularly, bitumen in place are as large as and probablyfar larger than thoseof conventionaicrude oil. The challengeis twofold: recovering the oils from the reservoir and converting them to useful petroleumproducts. Heavy oils and bitumen contain much largei proportions of nondistillableresidualmaterial than do conventionaloils. The residuescontain larger proportionsof asphaltenes, and this makesthem particularly viscous.It is their high naturalviscositythat makesthe recoveryof heivy oils ani bitumen difficult. The samefactors that determine the viscosity of theseoils also greatly affect their conversioninto conventional petroleum products. The high contents of asphaltic residue make them particularly suitable for asphalt maiufacture but also greatly reducetheir suitability for most other purposes.Their conversionto distillate boiling-rangematerial involvesresidualcrackingprocessessuchas coking and/ or hydrocracking.The high contentsof sulphur and niirogen in the distillatesireate the need for extensivehydrotreating.The aromaticcontent of the middle distillates obtained reducestheir value as dieseland aviation jet fuels. Improvementof these propertiesrequiresfurther extensivehydrotreating. The productionand utilization of heavyoils and bitumensasbasicraw materials for the manufactureof the conventionalproductsof petroleumthus involvesextensivetechnology;there are great incentivesfor the extensionand improvementof this technology.This book concentrateson the first of the two areasdescribed.the
recoveryphase.Although it may appearthat this phaseis the more straightforward of the two, neverthelessit aboundsin interestingfacetsand opportunitiesfor development and invention. ENHANCEDOIL RECOVERYMETHODS As the availability of conventionalcrude oil has declined, there has developedan increasedincentive for the improvementof the recovery from known reservoirs, and methodsfor "enhancedoil recovery" have been developed.The most important of these are as follows: . r . .
RECOVERY THERMAL Steamstimulation Steamflooding Hot waterflooding In situ combustion CHEMICALPROCESSES
o Surfactantfloods o Polymerfloods r Alkaline floods MISCIBLEDISPLACEMENT
o Light hydrocarbonfloods r Carbondioxidefloods This book is concernedwith the first of these, thermal recovery, a subject areathat includesthe techniqueswhich havefound the most extensiveuse.Most of the applicationsof thermal methodsare for the recoveryof heavyoils that are too viscois at the original reservoirconditions to flow with economicrates and recoveries.The effectivenessof thesetechniquesdependslargely upon the reduction in oil viscosity that accompaniesheating. Although heating the oil requires energy, this is, in lconomic applications,considerablyless than the energy that the producedoil is capableof providing. A flctor which promotesthe useof thermal recovery processesis that miny of the depositsof heavycrudesare large,rich, and often *"ti kno*n. Thermal recovery projects are usually profitable and are frequently quite large. ' Th; fo[owing introduces the sgliqnt characteristicsof the common thermal recovery approaches. Steam Stimulation Shell discoveredthe processof steamstimulation by accidentin Venezuelawhen it was producingheavycrude by steamfloodingthe Mene Grande field near the eastern shoreof Lake Maracaibo' During the flood, a breakthroughof steamto the surface of the ground occurred and, in order to reducethe steampressurein the reservoir,the injectionwell lntroductionto Thermal Recovery
Chap. 1
wasallowedto flow back. Copiousquantitiesof oil were produced;from this accidental discoveryin 1959(reported by de Haan and van Lookeren 1969)came the steamstimulationprocess,which also goesby the nameof steamsoak andhuff and puff' There was a very rapid growth in the use of steam stimulation in the next decade,particularlyin California.By 1967there were 408 steamgeneratorsin use in Californiaproducingabout 120kB/d of oit (Burns 1969). In the steamstimulationprocess,steamis injectedinto the reservoirat rates of the order of 1000B/dl for a period of weeks;the well is then allowed to flow back and is later pumped.In suitableapplications,the productionof oil is rapid and the processis efficient, at leastin the early cycles.The processis usedexiensivelyin California and Venezuela;if the steampressureis high enoughto fracture the reservoir and thus allow injection,it can alsobe usedto producethe very viscousoil of the oil sands.For this operation,a steampressureofibout 1 psi per ioot of depthis requiredto overcomethe in situ rock stresses to causefracturing. Imperial oil-and later its productionwing, Esso Resourcescanada-has been the leadingdeveloperof the cyclic steamstimulation processfor the production of bitumen from the oil sandsat Cold Lake. This developmentstartedwith small-scalepilot experimentsin the early 1960s.With -ote-or-lesscontinuousdevelopmenton an ever-increasingscale,Esso'sCold Lake field is now producingover 80'000B/d'of bitumen and this, togetherwith its proportionateshareof the production from the Syncrude operation, has now converted tmperial oil, which is Canada'slargestoil producer,to one that is dependentfor about half of its production on Canadianbitumen.It is reasonable to expectthat thesetrendswill continue. The main drawbackof the cyclicsteamstimulationprocessis that it often allows only about l5Vo of the oil to be recoveredbefore ihe oil-to-steamratio becomesprohibitivelylow. Steamflooding In this processsteamis forced'continuously into specificinjectionwells and oil is driven to separateproduction wells. The zonesaround the injection wells become heatedto the saturationtemperatureof the steam,and thesezonesexpand toward the production wells. oil and water from the condensationof steamare removedfrom the producers. With viscousoil there is a considerabletendencyfor the steamto override the reservoir,and this tends to limit the downward penetrationof the heat and hence the recovery. Steamflooding can allow higher steam injection rates than steam stiinulation; this advantageoften offsetsthe rather lower thermal efficiency.Steam stimulationusuallyrequiresless(and in favorablecasesfar less)steamthan llooding initially but is lessefficient as depletionproceeds.Often it is economicto switch to steamfloodingafter initial operation of a field by steamstimulation. The recovery from steamfloodingcan approach50Voor even more. lln the oil fields steamquantitiesare normally measuredas the volume of water at standard conditionscontainedin the steam;a barrel of steamis thus 350 lb and a cubic meter is 1 tonne. Burning bitumenasfuel in a conventionaloil field steamgeneratorwould produceabout 14 to " 15 m3of 70% quality steam per cubic meter of fuel burned (or 14 to 15 B/B).
EnhancedOil RecoveryMethods
It is usualand desirableto produceoil first by steamstimulationfrom both the injectorsand producersin a steamflood project. This providesrapid initial production and better economicsand also allows effective steamfloodingto be achieved more rapidly. Hot Waterflooding Hot waterfloodingis usuallylesseffectivethan steamfloodingbecauseof the lower heatcontentof hot water comparedwith steam.Also, it is found that the residual oil level that can be achievedwith a hot waterflood is markedlyhigher than that found with steam-even at the sametemperature. It is thoughtthat steamis more effectivethan hot water in displacingoil becauseof the following: l. The extra pressuredifferentialresultingfrom the higher kinematicviscosity of steam.A comparablemassflow of steamresultsin much hieher fluid veloc_ ities and pressuredifferentials 2. A relatively low tendencyfor steamto finger comparedwith water. 3. Steam distillation effects, which allow volatile fractions of the crude oil to evaporateinto the steam and be carried by it. There are, thus, some of the characteristicsof a miscible flood in displacementby steam. These factors are discussedin subsequentchaprers. There is some application of hot waterflooding as a follow-up rreatment to steamflooding;this is practicedin severalareas. In a later chapterit will be shownthat, during a steamflood,oil is largely,and effectively,displacedfrom the steam-saturated zone (the steamchamber)und irunrferred through the condensationfront. As the oil proceedsthrough the condensation front, it cools rapidly and its viscosityincreases.In tar sani reservoirswith high initial oil viscosity,this displacedoil can rapidly sealoff any communication passagesthat may exist (see,for example,sufi 19gg).In this reference,sufi shows that the injection of steaminto a permeablewater-saturatedzoneat the baseof a model reservoir containing tar sandsresulted in rapid blockage;bitumen carried into the fracture plugged it as it cooled. on the other hand, ihe injection of hot waterresultedin the gradualheatingof the tar sandmasswithout blockage;aswill be seenlater, the reasonfor this is that hot water effectsrelatively little transport of bitumenascomparedto steam.This differencemay be usefulif it is desiredio heat tar sandsby the injectionof heat-carryingfluids into a relativelythin permeable zone or fracture. Under thesecircumstances,hot water is superiorto steambecause the permeablezone doesnot becomeblocked. In Situ Combustion In situ combustioninvolvesthe generationof heat by combustionwithin the reservoir. Air or (in somerecent tests)oxygenis suppliedto the combustionzone by injection into wells drilled from the surface.fhe main attraction of theseprocessesis Introductionto Thermal Recovery
Chap. 1
.
that heat is producedmore cheaplythan by surfacesteamgenerators.Although the fuel for heating comes from the reservoir itself, there is a substantialenergy requirementfor driving the compressors and-if oxygenis used-for operatingthe oxygenseparationplant. I As the combustion2oneadvancesthrough the reservoir,the oil aheadof the front becomesheated.Volatilefractionsare distilledfrom the oil and then. as the temperaturerises,thermal crackingreactionsoccur. The residualoil eventuallv forms a coke residue In the successfulapplicationsof this process,it is, for the mostpart, this coke that burnsand suppliesthe fuel; becauseof the distillationand crackingthat occur, the producedcrudetendsto be lighter and somewhatmorevaluablethan the original crude oil. Emulsionsproducedby in situ combustionare often very difficult to separate. In situ combustiontends to be lessstable2than steamprocesses,and premature arrival of the combustionfront at the productionwells is common. Thii often causeswell failure. Problemsare alsocreatedsometimesby the bypassingof oxygen containinggasaround the front into coolerparts ofthe reservoir.This resultsin low temperatureoxidation (LTO) reactionsin which the oxygenis addedchemicallyto the oil. The oxygenated productshavehigherviscosities,and this makesthe oil jess easily recovered.Also, valuableoxygenis consumedwastefullyby IIIO reactions. The inherent thermal advantageof in situ combustionas comparedwith steamshouldbe greatestwhereheat lossesfor steamprocessesare greatest-in thin reservoirsand in deeplyburied reservoirs.In in situ combustion,only the reservoir at and beyondthe fire front needsto be at high temperature,particularlyif wateris injectedaswell as air (wet combustion).Waterinjectiongenerates steambehindthe combustionfront. This steampassesthrough the front and condenses aheadof it. In this way, heat that would otherwisebe left behind is utilized in steamflooding the oil aheadof the front. The verticalsegregation, due to gravity,of the water and airloxygenbehind the front can be a problem.
WORLD FUELRESOURCES Table1.1comparesestimatesof the world'sreservesof oil, gas,shaleoil, and heavy oil and tar sandsexpressed in exajoules(1 EJ : 1018 J = 169 x 106B of oil or 0.95 x 1012 SCFof gas).The columnsin the tableare not comparablebecausethe first two are for recoverable reserves, whereasthe secondtwo representthe resourcein place. Howeverit is very clear that the oil sandand shaleoil resourcesare enormous. TableI.2 comparesCanadianenergyresourcesof differenttypesusingboth a proven, recoverablereservebasis and also an "ultimate" (recoverable)resource basis.The productionin the year 1982is also shownfor comparison. 2The
reasons for the greater stability of steam fronts are discussed in later chapters. Here it is sufficient to note that if a finger of steam tends to advance before a broadly moving front, the steam will tend to condense, leaving only water to advance, and this will become rapidly cooled. Thus a stable advancing steam front can have in froirt of it fingers of cold condensate running toward the well. It is the water that fingers, not the steam.
World FuelResources
in Exajoules TABLE1.1 WorldFuelResources Resource in Place
Established Reserves
3970 3189
oil(t) Gas(t) Shaleoil(2) Heavy oil and oil sands(3)
100,000 22,000to 36,000 (16000 of abovein Canada)
(1)R. Enright (1982) J. (2)F. Hart'iey,J. M. Hopkins and H' C' Huffman (1980) L. (3)J. Janisch(1979)
comparison of the upper and lower parts of the table showsthat opportunities relatively limited' for findinj conventionatoii in Canadamay be consideredto be gas' for discovering potential more be On the oiher hand, there appearsto for conventional than higher much are oil The presentreservesior synthetic potential includesoil oil, and the potential is very -oth high".. This is becausethe mining' open-pit from in situ recoveryas well as that from
TABLE 1.2 Canadian
Resourcesin Exaioulesand Exajoules
Year FRONTIERS
RESOURCE
1982 PRODUCTION
NONFRONTIER
ARCTIC
OFFSHORE
TOTAL
Proved Resources Conventional oil Syntheticoil from tar sands Natural gas Coal Uranium (CANDU eff.) Hydro (30 yr)(l)
2.4 0.3 3.0 1.0 4.8 2.7
29 150 82 430 131 89
1 0
Total L4.2
911
9
7 0
0 8
)t
150 82 430 139 89 927
Ultimate Resources Conventional oil Synthetic oil from tar sands Natural gas Coal Uranium Hydro
2.4 0.3 3.0 1.0 4.8 2.7 Total 14.2
60 1,170 147 16,000
252 2'70
2r7 1,170 475 16,270
201
50
257
11,5'78
661
144
18,383
(r)Hvdroelectricpower is a renewable,"*.rra", and the reservesare, in principle, infinite' To achieve a y trt" q"antitv of energy thai woul-dbe produced from 30 of comparison,the quantitiesshown here t#;;;;1 opefation. (from Govier 1983)
lntroductionto Thermal Recovery
Chap' 1
The potential coal resourceis now seento be enormousand much higher than that for oil sands.The data indicate that there is sufficient coal to supplyCanada's presentproduction of energy resourcesfor over 1000years at the present rate of consumption-assumingthat the coal can be convertedinto the requiredforms. THE OIL SAND RESOURCE Table 1.3 lists estimatesof the volume of oil in place within the major known depositsof oil sand.There is considerable uncertaintyin thesefigures-particularly thosefor Venezuelaand for Alberta's CarbonateTriangle. Nevertheless,it is apparent that the heavy oil resourceis, for the major part, divided betweenCanadaand Venezuela. Canadais not endowedwith much "conventional"crude oil (at leastwith easily accessibleconventionalcrude oil that can be found) but it does have tremendous TABLE 1.3 Major Heavy Oil and Oil Sands Deposits Volume in Place (Billion Barrels) Venezuela Orinoco heavyoil belt Canada Athabasca Cold Lake Wabasca PeaceRiver Lloydminster CarbonateTriangle
700-3000
869 270 119 92 32 1350 Subtotal
U.S.S,R Melekess Siligir Olenek
U.S.A Tar Triangle Circle Cliffs Sunnyside P.R. Springs Hill Creek Asphalt Ridge Variousheavyoils
The Oil Sand Resource
Lower CretaceousSands Lower CretaceousSands Lower CretaceousSands Lower CretaceousSands Lower CretaceousSands PaleozoicCarbonates
PermianSands CambrianCarbonates PermianSands
r44 16 1 4
4 I I 110
Subtotal 137 Four-countrytotal 37134013 (from Janisch1979)
Tertiary and Lower CretaceousSands
2732
r23 13 8 Subtotal
GeologicalAge
PermianSands PermianSands EoceneSands EoceneSands EoceneSands EoceneSands Tertiary, Mesozoic
T
Caribbean Sea
Venezuela
Legend
i il,y;j*"
cotombia
C Eastl-ake D Barinas E Apure F SouthGuarico G SouthAnzoategui& Monogas H Delta I Guanoco J Gutfol Paria K N.W.Trinidad
Figure 1.1 Heavy Oil and Bitumen in Venezuelaand Trinidad (after Gutierrez 1979)
quantitiesof oil sandsand very substantialamountsof conventionalheavy oil. Canadacontainsabout one-sixthof the world'sdiscoveredoil in place,but about 95%of it is bitumen.The recoveryand utilizationof this bitumenis a challensefor engineersand scientists. VENEZUELANHEAVYOIL The Venezuelan heavyoil fieldsand the extensionsto them lie in a band acrossthe northern end of South America, as may be seenfrom Figure 1.1 (Gutierrez 1979). The easternend of this band lies in Trinidad (K), where asphalthas been a productfor manyyears.To the west lies the Gulf of Paria (J) and Guanoco(I). To the southand west lies the orinoco tar belt (E, F, G, and H), which contains the bulk of the materialshownin the previoustable.Up until now it has not beendeveloped,althoughthereare significantplansto do so.Area D is the Barinas subbasin. The reservoirsaroundLake Maracaibo(A, B, and C) are the mosthighly developed.It is here that Shellfirst experimentedwith steamfloodingand discovered steamstimulation.Productionfrom the Bolivar coastis discussedin Chapter6. CANADIAN HEAVY OIL AND BITUMEN Although the origin of the Alberta oil sand depositsis speculative,the following seemsto be a likely description. Figure 1.2(Jardine1974)showsAlberta asit is thoughtto havebeenin Cretaceoustime (120million yearsago).The climatewastropicaland giant rivers,fed by water from the Canadian Shield in the east and from mountains to the west. Introductionto Thermal Recovery
Chap. 1
%w'\"-8ASK.
LT S.
too Mil,E5
-
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+
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i
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\-5t',' \$ '''i
\,liil".i.x"'\r'..i,
H€AVY OII SANOS
ot t. MANNvil.tE
sED,MENT souRcE_ \ilii:iiiii,,r L*
Figure 1.2 Lower Mannville SedimentDeposition in WesternCanada (after Jardine 1974)
drainedinto what is now centralAlberta and then northwardto a sea.During the southwardas the land sank. period this seatransgressed One large delta formed the McMurray Sandsof Athabasca,and the other further, and the sand depositsformed similarly. Eventuallythe sea transgressed Upper Mannville period endedwith the depositionof the partly marine Grand RapidsSands.The depositionalenvironmentsunderwhich differentpartsof the oil sandswere laid down had a strongeffecton the natureof the sand.Depositsin the relatively still water of the seatended to be much finer than those in the channels where water motion kept the fine material suspended.Beach sand is finer than channelsand.Variationsin the seadepthwith time resultedin most depositshaving a layeredstructure. of the entire area.The seafrom Mannville time endedwith the subsidence the north joined the seafrom the south, and the Upper Cretaceoussedimentsand shaleswere deposited.The locationsof the major oil sandsdepositsare shownin Figure 1.3. The preceedingparagraphsdescribe how the large deposits of sand were formed from the sedimentscarried by the rivers from the mountains and high CanadianHeavy Oil and Bitumen
Figure 1.3 Heavy Oil and Bitumen in 'Vestern Canada (Courtesy Alberta Energy 1,982)
ground.How the oil was depositedin thesesedimentsand why it is so viscousare rather more obscure. Somehave argued that the tar sand oils have never been subjectedto suffi. ciently high temperatures and pressuresand that, becauseof this, the oils are immature.However,the view that the oil wasoriginallya conventionalcrudeoil that migratedto its presentposition and then becameoxidizedby bacteriathat consumedthe aliphaticchainsof the oil while utilizing oxygendissolvedin surfacewater percolatingthroughthe depositnow seemsmore likely. It is possible that the oil originated at a greater depth-possibly paleozoic limestonesourcebedsbeneaththe Mannville Sands.High vanadiumand sulphur contentshavebeensaid to indicate carbonatesourcerock rather than shale(Breger 1977)'Others(Demaison1977)think the sourcewas in downdip Lower Cretaceous shalesas far as 240 mi away. It is thought that the thermally mature crude could then have migrated upwards in the Late Cretaceousperiod until it was trappedin the Cretaceoussand under the shale cap. Support for this idea is found in the fact that oil is found in every.permeablezonewithin the reservoir.This oil becamebiodegradedby contact with oxygen-containingwater percolatingfrom the surfaceand through the shallow deposit. The flow of undergroundwater driven by gravity forces is well known. In supportof this conceptJardine (1974)points out that the densityof the Cretaceousoils in Alberta showsa definite correlationwith the salinity of the reservoirwater.Where there is high salinity,the densityof the oil is low. In Athabasca,wherethe water is of low salinity (indicatingthat the original seawaterhas 10
Introductionto Thermal Recovery
Chap. 1
r-------------- -1 tl |t - ---''
0.92 |
-1000
M
N ormalchromatogram
Figure 1.4 Origin of Heavy Oil from the West Slope in the SongliaoBasin, China (after Hu Jianyi 1986)
beenhighly diluted),the densityof the oil is relativelyhigh. Parallelingthis effect are the compositionsof the oils, asshownby a seriesof chromatograms. The heaviestoils havethe leastparaffin chainsand vice versa.This is consistentwith the idea that biodegradationattacksparaffinic materialspreferentially. A very interesting seriesof oil pools in the SongliaoBasin in northeastern China hasbeendescribedby Hu Jianyi (1986).Figure 1.4,which is taken from his paper,showsa seriesof oil poolscontainingoil of increasingspecificgravity and, as shownby the chromatograms, lessand lessaliphaticsidechainsin the hydrocarbon molecules.It is thought that the oil migratedupwardsthrough this seriesof traps and becamemore and more biodegradedas it encounteredmigrating surfacewaters containingoxygen. Correlation of CanadianTar Sand Deposits Figure 1.5 is Jardine's(1974)correlationchart of the CanadianTar Sanddeposits. The names of the reservoir structures employedin the various Canadian Lower Cretaceousheavyoil depositsare compared.Thus, for example,the D unit at Cold Lake, the McMurray Sandsin Athabascaand Wabasca,and the Gething and Bullhead Sandsat PeaceRiver were all depositedover the sameperiod. However,of these,only the Athabascaand PeaceRiver Sandscontainlargeoil saturations;the othersare water-saturated.
SIZE OF ALBERTAOIL SAND DEPOSITS Table 1.4 (Strom and Dunbar 1979)showsan estimateof the bitumen in place in the major oil sand depositsshown in Figure 1.5; Figure 1.6 showsa comparison from anothersource(Allen 1979)of the volumesof oil in thesedepositswith those of conventionaloil in SaudiArabia. Size of Alberta Oil Sand Deposits
11
o o o o o (D C) o
3
-3
[]-l
tuaintysano
I
HeavyOilsaturation
Figure 1.5 CorrelationChart of Lower CretaceousHeavy Oil and Bitumen oositsin WesternCanada(after Jardine 1974)
COMPARISONOF HEAVY OIL AND CONVENTIONALOII- RESOURCES Figure 1.7,which is basedupon a paperby A. Janisch(1979)comparesestimatesof the quantitiesof heavyoil plus tar sandswith thosefor conventionaloil. The quanThe Venezuelanand Canadian titieJ are shownas trillions of barrels(terabarrels). depositsare eachcomparablein quantityto the total of all of the known depositsof conventionalcrudeoils. uncerThe quantitiesshownin Figure1..7areestimatesthat haveconsiderable tainty associatedwith them. However,it is believedthat they are of the correct orderof magnitude.It shouldalsobe notedthat it is the oil in placethat is depictednot the recoverableoil. Little of the heavyoil and tar sandsbitumen is recoverable without thermal recoveryprocesses;even with these,much of the potential resourceis uneconomic.There is a tremendouschallengeto developimproved means for the production of heavy oil and bitumen. DEPOSITSOF HEAVY OIL AND BITUMEN IN THE UNITED STATES Although accumulationsof heavy petroleumare much smaller in total than the Venezuelanand Canadiandeposits,they are very substantialin the United States. Thesehavebeen classifiedas either 1. Heavy oil: petroleum heavier than 25'API but sufficiently fluid at reservoir conditionsto be producedcommerciallyby natural flow. 2. Tar sands:sandscontainingbitumen,asphalt,or oil that is too viscousto flow in commercialquantitiesat reservoirconditions. Table 1.5 showsestimatesof the sizeof the U.S. depositsusingthesedefinitions. 12
lntroductionto Thermal Recovery
Chap' 1
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Billions of CubicMetres 100 50 lr,r,l,,"l
s r
Lloydminster Gold Lake Athabasca(Mining) Athabasca(in Situ) SaudiArabia 0 Sourca EnorgyMlnat lnd Rrtouril,
Oll In Place RecoverableOll
400 600 200 Billions of Barrels
800
Cmldt
Figure 1.6 Comparisonof CanadianBitumen & Heavy Oil with Conventional Reservesin SaudiArabia (after Allen 1979)
HeavyOil and Oil Sands
i Vonszuela Canada
u.s.s.R.
!! !l tl
i
Othe|si ! I
ConventionalOil in Place
I
iMiddleEasti NorlhAmerica
iu.s.s.R. I
i Others
12
Oil in PlaceTrilllonsof Barrels Figure 1.7 Comparisonof Quantitiesof Heavy Oil and Tar Sandsto those for ConventionalCrude Oil in Place(order of magnitudeestimates)(after Janisch r979)
There is a total volume of heavyoil in placeof about 107billion barrels.About half of this occursin California,and most of the remainderis in Texas. Most of the tar sandsin the United Statesare in Utah; the total volume in place is about 24-30 billion barrels. THE NATUREOF HEAVY OIL AND BITUMEN DEPOSITS Although this sectionis written with the Cretaceousdepositsof heavyoil and bitumen in Alberta in mind, most of the conceptsare applicableto other deposits'Qll sand as it occurs in a reservoir is a multiphasemixture with a very definite struclntroductionto Thermal Recovery
Chap. 1
TABLE 1.5 Heavy Crudesand Tar Sandsin the U.S.A. HEAVY CRUDE OIL
Billions of Barrelsin Place
Alabama and Mississippi Arkansas California Louisiana Oklahoma Texas Utah Wyoming
J
5 54 6
z JI I
5 Total
r07
TAR SANDS Utah Other
23-29 1 Total 24-30
(basedon Whiting 1979)
salq or sometimesweakly cqnsoUqglgd ture. It consistslargelyof unconsolidated ',-----..fr within the pore spacebetweenthe containingfluids-oil, waterandsomdtimE3Sas gitini. In addition to the sandgrains, other finer solids are present:silt and clays. '-**A characteristicfeature of many of the tar sanddepositsis that most or all of layer of water is spreadover the solid surface, the solid-fitfAiiai;is1ygtgkd-A pore spacefrom contractingthe sag$,913i;r_s, bitumiffi the th6 Whre!319-y9nts . Figure 1.8 (Takamura 1982)shows the structure of typical Athabasca tar sand.Waterwithin the sandis shownas occurringin three forms: 1. At the grain-to-graincontacts,water is presentas pendular rings, which derive their shapefrom interfacial tension. 2. Along the surfaceof the solid materials,there is a thin (about 10 nm, or 0.01lcm) film of water. Although this is only a few tens of moleculesthick4,it is sufficient to protect the solid surfacefrom contact with the bitumen. 3. Water is associatedwith clay and other fine material. These solids occur as clustersof fine particleswithin the pore spaceand are often distributed as a layer on the main sand particles. 3Sometar sandssuchasthosein Utah are oil-wet rather than water-wet;the hot-waterprocess is not effectivein separatingthese.The solid matrix in someheavyoil and bitumen reservoirsis car'Alberta carbonatetriangle" bonate rather than sand.The Grosmont and other formations in the contain important Canadiandeposits.Theseformationsare frequentlykarstic and contain fractures and reservoirvolume.The RospoMare reservoir and voidsthat can provide important flow passages in the Adriatic Seais a very largeEuropeandepositthat-even thoughit containsa very heavyoilcan be producedby nonthermalmethods.The productivity is greatlyinfluencedby the fracturesand void volumes. uThe averagedistancebetweenmoleculesin liquid water is of the order of 0.3 nm.
The Nature of Heavy Oil and Bitumen Deposits
15
7
Figure 1.8 Diagram showing the Structure of AthabascaOil Sand (Courtesv Takamura1982)
Solid Mineral Matter Solid mineral matter is often a very complexmixture in itself. Usuallyit is unconsolidated.lhg large grains are called sand. In some cases,particularly in the Mc_\41rrBy format-ionof Athabasca,the sandgrains are almostentirely quartz.ln ,J other cases,such as the Clearwaterand Grand Rapids sandsof{tbeita (see Figure 1.5) the grains are a complexmixture of various mineral types: quartz, av7lchert, feldspars,and volcanicfragments. In additionthere are fine particles(lessthan 300mesh),which vary from less than 5 wtVoin high-gradesamplesto over 20 wtVoin low-grademateriaiThe fines containsubstantialproportionsof clays(e.g.,30-60 wtVo).The claysincludekaolinite, smectiteor montmorillonite,illite, and chlorite.The particlesizeof the claysis generallylessthan 2 pm. Clay mineralsare hydratedaluminum silicatesthat frequentlycontain other cations.They have a sheetstructuresimilar to that of mica. On an atomic scale, there are two kinds of layersthat occur in eachof the precedingclay minerals. l. Silica tetrahedra.Theseare tetrahedraof oxygenions with central silicon ions. Theseunits are linked togetherto form a hexagonalsheetof indefinite size. 2. Alumina or aluminum hydroxide layers. In these, oxygen ions or hydroxyl ions form two parallel sheetswith aluminum ions arrangedbetweenthe oxygen octahedra that constitute the structure; only two-thirds of the possibie aluminum sites are occupied, and the averagearea occupiedper aluminum ion is the sameas the area per silicon ion in the silica tetrahedrallayer. The main differencebetweenthe structure of the different clay mineralsarises from the relative proportions of the two types of layers. raoiinite Kaoliniteis basedon a 1:1 combinationof the two typesof layer.Its compositionis (oH)8Al4si4o1o 16
Introduction to ThermalRecovery Chap.1
Stoichiometrically,this may be looked on as follows: Silica layer 4 SiOz
Hydrated aluminalayer 2 AlrO(OH)4
It shouldbe realizedthat eachsilicon ion is, in fact, at the centerof an oxygentetrahedron, and the aluminum ions are each betweensix oxygenor hydroxyl ions (an octahedronhas six corners). When water is addedto kaolinite, the lattice doesnot expand(i.e., the distancebetweenadjacentlayersdoesnot increase).Another characteristicof kaolinite is that substitutionof iron or magnesiumfor aluminum is not observed;kaolinite is usuallywhite in color. It was named in 1867after a hill near JauchauFu in China (reportedin Grim 1968). Montmorillonite Montmorillonite (named after Montmorillon in France) is frequently used interchangeablywith the mineral name smectite.Someauthorsimply the broad class of expanding lattice clays by the term smectite and reservethe term montmorillonite for clay minerals of this type having only a small replacementof Al by Mg (Grim 1968). The mineral is basedupon a layer structure having one layer of alumina/ aluminum hydroxide sandwichedbetween two silica tetrahedrallayers. In the idealizedcasewith no substitutionof Al it has the composition (OH)4Al4Si8O2s. nH2O The Si/Al atomic ratio is now 2, as comparedto 1 for kaolinite. The structure may be visualizedas follows: Silica layer 4 SiO2
Hydrated Alumina 2 AI2O2(OH)2
Silica layer 4 SiO2
Water layer nH2O
The water is presentas a layer of water that penetratesthe lattice, between the silica layer of one threeJayer,silica-alumina-silica unit and the silica layer of the adjacentone.This quantityof water is variable.The additionof water to montmorillonitecausesthe lattice to expandand the clay to swell.This is an important characteristic of smectiteclays. The swellingof montmorilloniteclay is greatlyreducedif potassiumor magnesiumions are presentin the water layer,sincetheseare ableto bind the triplelayer sandwichestogetherand preventthe intrusion of water. This sensitivityof smectite clays to fresh water is of practical importance in petroleum engineering, since swollenclayscan plug reservoirs. lllite Illite (the "clay mica," namedafter lllinois (Grim 1968))is of a similar structureto montmorillonite except that some of the silicon ions are replaced by aluminum ions, and the resultingdeficiencyin charge(Al3* is trivalent, whereasSi4* is teThe Natureof HeavyOil and BitumenDeposits
17
F
-
travalent)is made upby the presenceof potassiumatoms.Theseappear at the out_ side flat surfaceof the three larger units and bind them together.This prevents swelling when water is added. Other substitutionsof metal]on, ur" found commonly within illites. Chlorites Chlorites have a threeJayerstructure similar to montmorillonite but are magnesiarich. The three-layerunits are held togetherby a magnesiumhydroxide layerl Chlorite claysare nonswelling. For more information on clays,the readeris referred to F. J. pettijohn (1957) and R. E. Grim (1963). Effect of clays on permeability clays, and particularlyswellingclaysof the smectitetype, can influence the per_ meabilityof a porous-solid.Swellingclayscan expandto utoct pores and particularly pore throats,and claysin generalcan alsobecomedetachedfrom the surfaces to which they adhere.They can then be carriedby the movingfluid and deposited so that they block the throats of pores.This is often not a ierious problem with high-permeability sands. In a recentstudy(M. Kwan 19gg)it wasshownthat repacked,extracted cores from Cold Lake had a muchlower permeabilityif they*"r"'L"fo*d to freshwater. Presumably -clays migrated and swelled and pluggei the coie. However, it was found that if extractedpreservedcoreswereemptoyed(i.e.,cores that had not been broken up and repackedbut were used in their originar mechanical form), then fresh water had little effect on the permeability.The iiff"r"n.. between the behavior of.repackedand preservedcoreswasvery large, and this shouldbe a concernto experimenters wishingto test permeabilityana ines migrationphenomenain core material. Water The sandgrainsin oil sandsusuallyhavefine clay materialadheringto them; this clay is wetted with the connatewater.sThis water is salineand often also contains calciumand magnesiumsalts,which make it hard. As has been mentionedprevi_ ously,the salinity of the watervariesconsiderably from areato area. The wetting of the mineral matter by water rather than by bitumen is a very importantcharacteristicof someoil sands,particularlythe deplsits in Athabasca; this makespossiblethe separationof mined tar sandby the blark hot-waterpro_ cess,which is usedby Suncorand by Syncrude.In this processthe tar sandis mixed with hot water and a little causticsoda.Most of the sandseparates cleanly,leaving the liberatedoil to rise to the surfaceas dropletsadheringio bubblesof gas. rhJ cleanseparationis possiblebecausethe bitumen doesnot wet the solid ini-tially. It is becomingapparentthat the natureof the wetting of the matrix alsoplaysan important role in the recoveryof heavy oils by steaminjection. In pariicular, it is 5Connate water is relatedto the residualwater left in the reservoirmatrix after the bulk of the original water was displacedby oil during the filling of the reservoir.
18
Introductionto Thermal Recovery
Chap. 1
found that a matrix that is wetted initially with connatewater greatly reducesthe water in oil emulsificationthat occurs on steamins. Oil and Bitumen The most important physicalproperty of crude oil in recoveryprocessesis its viscosity.Figure 1.9showsthe viscositiesof severaltypical heavycrudesas a function of temperature(Buckles1979). The viscosity of heavy crude oils correlates,at least approximately,with the density of the oil. Figure 1.10shows a correlation preparedby Farouq Ali (1983), which can be used to estimate the viscosity as a function of temperatureand the densityof the oil. However,becausesignificant anomaliesare found when the gravities and viscositiesof heavyoils are compared,Figure 1.10shouldbe usedonly for rough estimates. Gas Heavy oil reservoirsoften contain pocketswith gas saturationand most heavy oils and bitumenscontain dissolvednatural gas.Also, during heating,a gaqpt!As-g_qel-d"q* {gb" fqrmed.The mechanismsinvolvedin ihfulnclutle the-evolutionof dissolved naturalgas,the decompositionof inorganiccarbonatesto form carbondioxide,and the decarboxylationof organic acids. RCO2H -+ RH + CO2 Decarboxylationof acids
The gas produced from the steam recovery of bitumen frequently contains about 50Vocarbondioxide, with the remainderbeing mostly methane.Most of the carbon dioxide probably comes from the chemical transformation of carbonaterocks. It has been suggestedthat carbon dioxide comesfrom the thermal decompositionof siderite(ferrouscarbonate),which is lessstablethan other carbonates. FeCOg-+ FeO + CO2 Carbonatedecomposition
i 11 i 1,m0,q!0 l^\iril 100,q)0 i -- -\x- -- - -- - - - -----i----10,(n0 --'i- - -\\lAtnaoacca--i-i - - r - - - \
10(x)
i
- - - - i - - - - - - - .r
-r-\q.
- - - - i - - - - - - f- - -
L
i
I
-
&1m 6
8ro
p
3
.,
,
PiLon\j
i
in"""roi, ' Kernj River'A' \
iconditions, jU=.*-
i r!!!
0
i
i^cld Lake -i ':Y: ---
tReawdter i
i
'100 150 200 250 50 Temperatureo C
The Nature of Heavy Oil and Bitumen Deposits
Figure 1.9 Viscosity of Heavy Crudes as a Function of Temperature(Courtesy Buckles1979)
19
Temperature ln degreesCelslus io7 106
25 50 ttttlttl
75
100
125 150 175 200 225 250 ll
10-
o to4 o .9, o 3000 CL 1000 tr (, o 300
.E 100
.e o 0 o
en
lt,
10 3 2 100
150
200
250
300
350
400 450 5oO
TemperatureIn degrees Fahrenhelt
Figure 1.10 ApproximateRelationship between Oil Viscosity, Gravity, and Temperature(after FarouqAli 1983)
However,a more important sourceof carbon dioxide is probablythe reactionof inorganiccarbonateswith quartz (SiO) to yield silicatesand carbondioxide.Gunter and Bird (1989),in a review, describeseveralhydrothermalreactionsin which quartz reactswith carbonatesto liberatecarbondioxide.For example, calcite + quartz + kaolinite = Ca-smectite+ CO2 + H2O dolomite + quartz + kaolinite + H2o = ca-Mg-smectite+ calcite + co2 One way of interpreting these reactionsis to look on the SiOz as an acid which is displacingCO2 from the carbonate. UNITS OF MEASUREMENT Measurements in the field of petroleumproduction-as in other areas-are in some confusionbecausemany countrieshaveswitchedfrom a hodgepodge of old, traditional units to the new,more consistentSI (SystdmeInternational)units. However, the United Statescontinues,for the mostpart, to use customaryunits; as a result, mostof the literaturecontinuesto be written in theseunits. Evenin Canada.where the SI systemhas been adopted,the old units still prevail in many cases.For example,the Canadiangovernmentcontinuesto discussthe price of oil in dollars (US$)per barrel rather than per cubic meter.Even beforethe presenttrend to SI, there was confusionin the ranks of the reservoirengineers.Someauthorspresent equationsthat are dimensionallyconsistentand into which one may substitute numericalvaluesdrawn from any dimensionallyconsistentset of units of measurement, whereasothers write equationsthat involve dimensionedconstants.This latter classof equationrequiresthe use of specifiedunits in order to provide the correctresult. For example,Darcy'slaw for the flow of a fluid in a porousmediummay be written as the dimensionallyconsistentequation1.1.6 6,{ll symbolsare listed
20
in Appendix 1.
lntroductionto Thermal Recovery
Chap. 1
q=
T(E)
where ft is permeabilityI7 A is area # P is pressure MLlT-2 l.L is viscosityMrlT-1 x is distanceL q is flow fT-1
+
(1.1)
AX--.->
This equationwill give the correct answerproviding that any consistentset of units is employed.For example,it will work with SI units, with cgs.units, with fps units, and with any other setof units havinga consistentbasisfor mass,length,and time. In reservoir engineeringliterature, it has been (and still is in the United States) usualto measuretime in days,length in feet,viscositiesin centipoise,permeabilities in millidarcys, and volumes in barrels or sometimesin acre-feet.It has also beencustomaryto rewrite equationssuchas 1.1into forms in which the so-called field units can be substituteddirectly. Equation 1.2 is a frequently used dimensionalform of Darcy's equation. It is correct provided that the variablesare measuredin the particular units shown.
q = -0'0011'z|a(+\ p q,Bld
A, ft2;
k, mD
\AxI p, cp;
P, psi;
(1.2) x, ft
The numerical coefficient in equation 1.2 has the dimensions of (B cp ft)/ (daymD psi). Although lacking eleganceand sophistication,the field-unit systemhasprobably reducednumerical error by allowing the use of familiar and easily visualized quantities.However,the traditional field-unit systemhas the disadvantageof introducing awkward factors such as the 0.Nll27 of equation 1.2. It also requires that physicalpropertiesbe convertedto a rather rigid set of specific units. Conversion factors for various frequently employedquantities are shown in Tablesr.6 and 1.7. In this book, dimensionallyconsistentequationsare normally employed.In some cases,where dimensionalequationsare given, specificunits must be used.These are specifiedat the point wherethe equationis introduced.In descriptivematerial the authorhas employedthe units that are most familiar (to the author!). TABLE 1.6 ConsistentMeasurementUnits
Mass Length Time
SI
cgs
fps
Engineers
kg m s
gm cm s
lb ft
slug ft s
Units TABLE1.7 Oil Reservoir VOLUME 1 ac-ft : 7757.8B = 5.615ft3 : 0.159m3 1B PRESSURE I MPa = 145 psi = 106 Nm-2 where N : Newton I psi = 6.895kPa PERMEABILITY I D
: 1(cm3/s) (cp)(cm)(cm2)-'1atm;-' = 0.9869x 10-6cm2: 0.9869x 10-12m2 = 0.9869 r.r.m2
DYNAMIC VISCOSITY 1p lcP
: 1 g c m - l s - 1= 0 ' 1 k g m - r s - r o r 0 . 1P a ' s :0.01P:lmPa's
O : poise
KINEMATIC VISCOSITY 1st
I cm2 s-l : 0.0001 m2 s-t
I cst
I mm2 s-l
USE OF PROGRAMMABLECALCULATORSAND MICROCOMPUTERS Programmablecalculatorsand particularly microcomputersmake calculationsin this field much simpler.To usecomputerseffectively,it is important to have availablesimpleequationsthat allow the calculationof physicaland mathematicalquantities occurringin the problemat hand. For example,a microcomputercannotreadilyusea steamtable,but it can easily calculatethe desiredvaluefrom correlationequations.Justas engineersusedto use slide rules, so the modern engineerusescalculatorsand microcomputers.Often simplecorrelationsare sufficientlyaccurateto estimatephysicalquantitiesin view of the other uncertaintiesinvolvedin the problem.Slide-ruleaccuracyis sufficient for most engineeringcalculations. The practicing engineershould searchfor and collect equationsthat are of a suitableform to be includedin computercalculations.A selectionof usefulcorrelation equationsis given in the appendices. RADIAL FLOW TO A VERTICALWELL Figure 1.11showsthe plan view of a fully-perforatedwell that is producing oil in flow in a reservoirof height/2.It is assumedthat the boundary, radial,steady-state at radiusR", is at a constantpressureP, and that the well, of radiusR,, is at a constant lower pressureP,. The effective area for flow diminishesas the fluid approachesthe well; becauseof this, the absolutepressuregradientincreases. 22
Introductionto Thermal Recovery
Chap. 1
Figure 1.11
At someintermediateradiusR the pressuregradientto maintain the flow q is givenby substitutingthe area2rRh into Darcy'sequation(1.1).In this example,4 is consideredpositivefor flow to the well (i.e., in the oppositedirectionto R), so the minus sign in (1.1)is omitted. The resultis qp dPdR k(ZtrRh)
(1.3)
This equationmay be integratedto calculatethe flow arising from the pressuredifferenceA,P : P" - P-. D - D '-*[ * '-q P d R 'e J^.2trkh R
q:
Zrkh A'P
(1.4)
t,ln(R.lR.)
Equation1.4 is written for dimensionallyconsistentunits. If the dimensionalform of Darcy'sequation(equation1.2)is employed,the resultis equation1.5.This is the form found in many texts on reservoirengineering.
4=o.oo7o8;#h q,B/d; k, mD;
P, cP R", ft
h, ft;
R,, ft
(1.s)
AP, psi It is instructiveto substitutenumericalvaluesinto theseequationsto obtain an idea of the effect of viscosity on oil production rate. Table 1.8 showsvaluesof the production rate that havebeencalculatedfor a high-quality, thick reservoirthat is saturated with oils having viscositiesvarying from 1 cp (a low-viscosityconventional crude oil) up to 1,000,000cp, which correspondsto a material such as Athabasca bitumen. For a typical well bore radius of 0.3 ft, the production falls from 44,000B/d for the light crude to only 0.4B./dfor the bitumen.The first casecorresponds to a well of remarkableproductivity and the latter, to a well of little value. RadialFlow to a VerticalWell
TABLE 1.8 CalculatedWell Flow Rates Assumek = 1000mD (excellentsand);lr = 100ft; AP : 599 psi; R, : 1000ft. CALCULATED WELL FLOW RATES
10,000 100 R,,: 0.3fr 4.4 440 R, = 100ft 15.0 1,500
I
Oil viscosity(cP) Flow (B/d)
4.4 x 104
Flow (B/d)
1.5 x 105
100,000 0.4 l.)
using a largerwell bore will increasethe productivity.The lower line in the Altable showsthe iffect of using an imaginarywell having a radius of 100ft. by principle, in least at thoughsucha deviceis impractical,it maybe approximated' be might effect A similar the reservoirurorrnda well of normal dimensions. heati."ng in length. feet obtain;d by using a horizontalwell severalhundred Sucha strategymight, in the exampleshown,producea useful effect for the cp, but the productionwith the bitumenwould still oil having a viscosityotLO,gOO be too .-"ug", to be effective.A flow of 15 B/d is closeto the lower limit at which economicpioductioncould be anticipatedfor a practicalwell' Comparingthe resultsof calculationssuchasthis with the very sharpchanges of viscositywith temperature,which are shownby Figure 1.9,illustratesthe importancewhich reservoirtemperatureplaysin the recoveryof heavyoils. Figure 1.12showsthe oil recoveryachievablefor a number of Venezuelan (1979)' heavyoi fields as a function of the in situ viscosity,as given by Borregales for the viscosities the oil Also shown on the figure are points correspondingto Athabascaand Cold Lake fields' A majorreasonfor the higherviscosityof Canadianbitumensas comparedto Athathosein Venezuelais the loweireservoirtemperature'(Seedatafor Joboand
25 from'Physical
Fro
Principles
ol Oil Production"
by Muskal
.a'
'so- ^) \. .ra
o () o c15
_o
= o *10 J
t
Figure 1.12 APProximate Effect of
7 Viscosity on Oil Recoveryby Solution 6 5 "o 4 3 2 1 Gas Drive (after Borregales1979) Conditions) L;glO(Oil Viscosity in cp at Reservoir
24
lntroductionto Thermal Recovery
Chap' 1
bascacrudesin Figure 1.12.)The climateof Venezuelamakesthe ground surface by the temperaturemuchhigherthan in Canada,and this differenceis exaggerated deeperburial of the Venezuelanreservoirs.It is this differencein reservoirtemperature rather than intrinsic differencesbetweenthe crude oils that causesmuch of the differencebetweenthe productivityof the Venezuelanheavyoil wells and the Canadianones. Although the Canadianbitumensmust be heatedsomewhatmore than the Venezuelan onesfor satisfactoryproduction,the largestdifficulty that the high initial viscositypresentsis that of gaininginitial accessto the reservoirin order to be ableto contactthe materialwith heatingmedia.In many respects,the problemof the productionof bitumenin Canadais that of trying to heata remote,very thick, impermeable,immobile,asphalticconcrete! THE PROBLEMOF ECONOMICEXPLOITATION There are other practicalproblemswhich are encounteredin the exploitationof the problem heavyoil resourcessuchas thosein Canada.So far we havediscussed problem of movingit to the surfaceof the ground. of recoveringthe crude-i.e., the The concernof this book is moving it to the surfaceby the use of in situ heating. Another approachto the sameproblemis to removethe tar sandby mining methodsand then to separateit using processessuch as the hot-waterprocess. Large operationsof this type are carried out in Athabascaby Suncor (formerly Great CanadianOil Sands)and by Syncrudenear Fort McMurray,Alberta. These plants are successful.However,the approachis very demanding;it dependson brute force and is suitableonly for thosedepositsin Alberta that are relativelyshallow. Ninety percentof the bitumen in Alberta and most elsewhereis too deeply buried for this to be a practicalapproach. The publishedeconomicsof the large Cold Lake commercialplant that was onceproposedby Essoshowthat recoveryusingthe cyclicsteamprocessis competitive with mining (McMillan 1979).An EssoCold Lake commercialplant wasorigiproductionof bitumen nally proposedin the late 1970sthat involvedthe large-scale by cyclic steamingfollowedby the upgradingof the bitumen to syntheticcrudeby fluid bed coking and hydrotreating.The projectwas shelvedbecauseof the questionableeconomicsand the enormouscapital outlay which would have been required. However,since then, Esso has realizedthat the productionof bitumen without upgradingcan be economic.This approachinvolvesthe productionof bituin quantimen and pipelinetransportationof the bitumendiluted with condensate ties that will soonbe far above100kB/d. BITUMEN TRANSPORTATION Transportationof the product is a major problemfor the bitumen producersince it cannotbe pumpedthrough a conventionalpipeline.Possiblesolutionsare shown next. All havebeenput into practice. o Move the bitumen in trucks or trains e Convert the bitumen to a more fluid material bv chemical transformation
o Dilute the bitumenwith a solventsuchas condensate and transportit by pipeline o Pump the bitumenwith water through a pipelineunder conditionsthat allow the water to flow as an annulussurroundinga bitumen core o Emulsify the bitumenin water and transportthe mixture by pipeline For a number of yearsbitumen was moved from Cold Lake in road trucks as hot cargoes. Suncorand Syncrudeboth convertthe bitumento an overheadproductusing coking. Hydrogenationprocessesprovide an alternative method of conversionberecentexpansioninvolvesthe addition ing developedby severalgroups.Syncrude's process plant; to their Husky plans an H-oil Unit for their upgrader of an LC-fining processes These in Lloydminster. also find use for the conversionof the residual material from the distillation of conventionalcrude oils. Table1.9showsa comparisonbetweenthe propertiesof bitumenand thoseof a typical conventionallight crudeand the upgradedcrudeproductthat wasto have beenproducedby the Cold Lake commercialproject.The upgradingcracksthe bitumen, and the crackedproductsare treatedwith hydrogento removesulphurand nitrogenand to saturatesomeof the aromatics. The dilution of bitumen with a solvent such as condensateto make it pumpablehas been practicedfor yearsin the Lloydminster area and more recently, and on a much larger scale,at Cold Lake. The main problem is the availability of a suitable diluent; about 30 LY% (basedon bitumen volume) of a material such as condensateis required. In somecasesdoublepipelineshave been constructed,with the diluent being returned to the field from the remote refinery by a secondline. by Sloan,Ingham, The shipmentof heavyoils by pipelinehasbeendiscussed and Mann (1981).They concludethat the crude oil viscosityshouldbe lessthan 150cst and that the temperatureshould be maintained lessthan 200'F in order to TABLE 1.9 Cold Lake Project-YieldComparisons(LV%) Cold Lake Bitumen
Butane(Cn) Naphtha(C5-180"C) (c5-350"F) Distillate (180-345"C) (350-6so'F) Gas oil (345-565"C) (650-1050"F+) Residuum(565"C+) (1050"F+) Total sulphur-wt7o Gravity-kg/m3 -.API
Typical Alberta Light Crude
Upgraded Crude Objective
3-4 30
1,5-20
t7
30
45-50
40
30
28-30
7 0.5 834 38
0 <0.5 885-834 34-38
/1
4.5 992 11
(from Skrabec 1979)
26
Introductionto Thermal Recovery
Chap. 1
TABLE 1.10 Crude Oil Shipmentby Pipeline . Needsoil viscositylessthan about 150cst . Temperatureshouldbe lessthan about 200"Fto preventwater boiling under insulation
Temperature("F)(r)
Crude Viscosity (cst)
100 150 200
15,000 1,100 180
Approximate Barrels of Condensateper barrel of Crude to reduceviscosityto 150cst
0.3 0.15 0.02
(t)Approximatetemperatureto give indicatedviscosityfor Cold Lake crude oil. (from Sloan,Ingham, and Mann 1981)
prevent the boiling of trapped water beneaththe pipe insulation. Table 1.10shows how the viscosityof Cold Lake crude can be reducedto 150cst by variouscombinations of heating and dilution with condensate. Under some conditions it is possible to pump very viscous oils through a pipeline as a central core surroundedby an annularcylinder of water. The water actsas a lubricant,which facilitatesthe movementof the oil. A pipelineusingthis principle is being operatedby Shell in the United States,but the schemehas not found extensiveuse. The transportationof bitumen as an emulsionhas been studiedby several groups.Lagovenhas emulsifiedCerro Negrocrude (8.5'API) in laboratoryand pilot tests and by December 1986had produced more than 3 x 106B of emulsion that contained about30Vowater. The technicalwork hasbeencarried out in conjunction with British PetroleumCanada(BP). Extensiveplanshavebeenannouncedby Lagovento sell an emulsionof bitumen in water as a product ("Orimulsion") suitable for transportation in ocean tankers and for combustionas a substitutefor heavyfuel oil or coal. Technologyis also availableto producean emulsionthat is suitablefor breakingat the destination for use as a refinery feedstock. BP and Intervephavedevelopeda meansof emulsifyingbitumenin waterfor pipeline transportation.The emulsifiedbitumen is known as TRANSOIL, and a field trial involving the movementof 79 m3/d has been reported(Hardy, Sit, and Stockwell.1988). BIBLIOGRAPHY ALLeN,F. H., "The CanadianOil Sands:A RaceAgainstthe Clock" 1stUNITAR Conference,Edmonton,Alberta (Jwe 4-12,1979),reportedin TheFutureof HeavyOils and Tar Sands,New York: McGraw-Hill (1981),29-32. and Oil Recoveryin the Orinoco Oil Belt'l BonneceLes,C.J., "ProductionCharacteristics lst UNITAR Conference,Edmonton, Alberta (June 4-12, 1979),reported in The Future of HeavyOils and Tar Sands,New York: McGraw-Hill, (1981),498-509. Bnecen, I.A., "Geochemical ConsiderationsRegarding the Origin of Heavy Crude Oils: Suggestionsfor Exploration," 1.stUNITAR Conference,Edmonton, Alberta (June 4-12, Biblioqraphv
27
1979),reported in The Future of Heavy crude oils and Tar sands, New york: McGrawHill (1981),163_167. Bucrles, R.S., "Steam.Stimrlation Heavy oil Recovery at cold Lake, Alberta,,, preprint No. SPE 7,994, r979-car:!. Reg. Meeting of Soc. ret. eng. of AIME, ventura, ialif. (April 18-20, 1979).O 1979SpE. BunNs,J., 'A Review of SteamSoakoperations in californ ia,,,r. pet. Tech., 25_34(January, 1969). Gruu, R. E., Clay Mineralogy,2d Ed., McGraw Hill N.y., 196g. opHaau,H.J. and vaNLooxenEN,J.,"Early Resultsof the First Large-Scale SteamSoak Project in the Tia Juana Field, western venezuela," J. pet. kch. (J"anuary 1969),Trans. AIME,246 (t969). DeMersoN,G.T., "Tar Sandsand Supergiantoil Fields,"Am.Assoc. pet. Geol.,61: 1950_ 1961(November1977\. DEnoo,G., Trssor,B., McGnossaN,R.G., eNo DeR,F,, "Geochemistry of the Heavyoils of Alberta," in oil sands, Fuel of the Future, can. Soc. pet. Geol., Memoir 3, 14g-167 (1974). FanoueArr, s.M., Improvedoir Recovery,chapter 7,3r!-355,oklahoma city, okla: Interstate Oil CompactCommission,(19g3). Fanoue Ar-r, S.M., secondaryand rertiary oil Recovery processes, chapter 6, r27-rgz, oklahoma city, okla: Interstateoil compact commission, (Lglq;2d printing (197g). Fanoue Au, S.M., "SteamInjection Theories-A Unified Approach,,' spE L0746(rggz). GovtsR, G.w., "canada's Energy Resources",presentedbefore The Energy opportunities Conference,Edmonton, Alberta, 22 March $b$). GuurER, w.D. and Brnr, G.w., "Inorganicchemistry',,chapter 9 otAosrRA Technical Handbook on Oil Sands,Bitumen and Heavy Oils, AOSTRA Technical publication #6, Alberta oil SandsTechnologyand ResearchAuthority, Edmonton, Alberta (19g9). Gutlennez, F. J., "occurrenceof Heavycrudes and rar Sandsin Latin America,,, 1stUNITAR conference,Edmonton,Alberta (June4-12, 1979),reported in The Future of Heavy Crude Oils and Tar Sands,New york: McGraw_Hill (19g1),107_117. HeRoy, w. A., Srr, S.p. and Srocrwnlr-, A., "Field rrials of rransoil rechnology for Emulsion Pipeliningof Bitumen," 4th UNITAR/UNDP Conferenceon Heavy Crude and Tar Sands,Edmonton,Alberta (July 1988). JaNrscH,A., "oil Sandsand Heavy oil: can They Easethe Energy Shortage?"lst UNITAR conference,Edmonton,Alberta (June4-12, 1979),reported inihe Futu-reof Heavy Crude Oils and Tar Sands,New York: McGraw Hill (19g1),33_41. JAnDrruE, D., "cretaceous oil Sandsof western canada,', in oil sands, Fuel of the Future, Can. Soc.of Pet. Geologists,Memoir 3,50-67 (1974). JtaNvl, H., "Heavy Oil Asphalt and Oil SandResourcesand Their Distributionin China," Advancesin PetroleumRecoveryand upgrading Technology19g6,AosrRA (June 12-13, 1986). Kwau, M.Y. M., CuLLeN,M. p., Jarr.rrnsoN, p. R. and Fonrrnn, R. A., .A Study of FinesMi_ gration Related PermeabilityDamagein Extracted cold Lake Heavy oil cores,,, paper 88-39-59presentedat the 39th Annual Technical Meeting of the petroleum Society of C.I.M., Calgary,Alberta (June 12-16,19gg). McMrr-leN, J.c., "The challenge of Financing canadian oil Sands Development,,, 1stUNITAR Conference,Edmonton,Alberta (iune 4-12,1979),reportedin The Future of Heavy Crude oils and Tar sands, New york: McGraw-Hill (19s1);775-7g5.
28
Introductionto Thermal Recovery
Chap. 1
PErrrroHN,F.J., SedimentaryRocks,2dEd., New York: Harper and Row, (1957). PsrzecrsRlev, P. H. and Scorr, L. O., "Occurrenceand Prospectsof Tar Sands," 7th World Pet. Cong.,Mexico (1967),Vol. 3, London: Elsevier(1967),55L-571. Srnaeec, J., "ProcessSelectionConsiderationsin the Upgrading of Cold Lake Bitumen," 1stUNITAR Conference,Edmonton, Alberta (June 4-I2, 1.979),reported in The Future of HeavyCrude Oils and Tar Sands,New York: McGraw-Hill (1981),612-617. Sloen, A., INcualr, R., and MeNN, W.L., "Pipeline Transportationof Heavy Oils," lst UNITAR Conference,Edmonton, Alberta (June 4-!2, 1979),reported in The Future of Heavy Crude Oils and Tar Sands,New York: McGraw-Hill (1981),719-726. Srnou, N. A., and DuNneR,R. B., "Bitumen Resourcesof Alberta: ConvertingResourcesto Reserves,"1stUNITAR Conference,Edmonton, Alberta (June 4-t2, 1979), reported in The Future of Heavy Oils and Tar Sands,New York: McGraw Hill (1981),47-60. Sunr,A.H., "Injectivity Enhancementin Tar Sands-A PhysicalModel Study," PaperNo. 88-39-61presentedat the 39th Annual Technical Meeting of the Petroleum Society of C.I.M., Calgary,Alberta (June12-16,1988). Tereuunn, K., "Microscopic Structure of AthabascaOil Sand", Can. J. Chem. Eng., 60: 538-545(1982). WnrrrNc, R. L., "Heavy Crude Oil and Tar Sand Resourcesand Reservesof the United States.Emphasison Texas," 1st UNITAR Conference,Edmonton, Alberta (June 4-12, 1979)reported in The Future of Heavy Crude Oils and Tar Sands,"New York: McGrawHill (1981),90-96.
G E N E R A LR E F E R E N C E S '1.C., Thermal Methodsof Oil Recovery,New York: John Wiley (1988). Bonrnc, Ceur, F.W., The Tar Sandsof Alberta,Canada,2dEd. Denver,Colo.: CameronEngineers, Inc. (1974). Cennrcy, M. A., Historical Highlights of Major Events in the History of the AthabascaOil Sands,Alberta ResearchCouncil ContributionNo. 631(1973). Energy Heritage-Oil Sandsand Heavy Oils of Alberta, ENR ll19-1,p. 14, Alberta Energy (1e82). FrrzcEnaLo, J. J., Black Gold with Grit-The Alberta Oil Sands,Sidney,B. C.: Gray'sPublishing Co., (1978). Improved Oil Recovery,InterstateOil CompactCommission,Oklahoma City, Okla. (1983). Lanrl-,M., Enhanced Oil Recovery,Houston, Tex.: Gulf PublishingCo. (1980). OrRNoeN, E. (Ed.), Heavy Crude Oil Recovery,The Hague: Martinus Nijhoff (1984). (August Pners, M.,'A Current Appraisalof Thermal Recovery,"J. Pet. kch., 1129-1136
re78). Pnats, M., "Thermal recovery," SPE MonographVolume 7, Dallas, Tex: SPE (1982). Srolnooo, A. H., et al., "Pioneersof the AthabascaOil Sands".Edmonton,Alberta: Syncrude (1978). Thermal RecoveryProcesses, SPE Reprint SeriesNo. 7, Dallas, Tex.: SPE (1985). VeN Poor-r-eN,H.K., Fundamentalsof Enhanced Oil Recovery,Tulsa, Okla.: PennWell Books(1980). WurrE, P.D. and Moss, J.T., Thermal RecoveryMethods, Tulsa, Okla.: PennWellBooks (1983). GeneralReferences
29
Conductionof Hest within Sofids
INTRODUCTION The quantitative analysisof the transfer and movementof heatwithin the reservoir plays a central role in the subjectof thermal recovery.There are two major mechanismsby which heat is transferred:thermal conductionthrough relatively stationary materialsand convectivetransport by moving fluids. This chapteris concerned thermal conduction' with the first of thesemechanisms, The reservoir,.or adjoining strata, are consideredas a homogeneoussolid in which the transfer of heat is by conduction.Although this processis very important in thermal recovery,it is very slow.By itself, thermal conductionis an inadequate meansof transferring heat within large reservoirvolumes.However, it is effective in transferring heat over relatively short distances,as, for example,in the transfer of heat from a steam-saturatedregion to the adjacentcolder reservoir. It plays a particularly important (and undesirable)role by causingthe unwanted loss of heat io the overburdenand underburdenduring reservoir heating' When thermal recovery processesextend over large areas' the loss of heat from the reservoircan becomeintolerablylarge.This loss is relatively more important when the reservoiris thin. For example,a given vertical heat lossfrom a reservoir 10 ft thick might be intolerable,whereasthe same heat loss from a 150-ft reservoircould be aiceptablebecausea larger volume of oil would be recovered. THERMALCONDUCTIVITY The theory of heat conductionassumesthat the heat flux is in the direction of the temperaturegradient and is proportional to the magnitude of the gradient't The 'This statementis true only if the thermal conductivity is the samein each direction. The problemof variablethermal conductivityis not consideredhere'
30
proportionality constantis defined as the thermal conductivity of the material. For the one-dimensionalflow of heat by conduction, the heat flow is given by equation 2.1.,where Q is the flow, A is the cross-sectionalarea for flow, I is the temperature,andx is the distance. O = -KA:
dT dx
(2.1)
The negativesign arisesbecausethe heatflow is assumedto be positivein the direction of the x axis. For a positive flow of heat, a negativetemperaturegradient is required. Although in this chapterthe analysisis limited to one-dimensionalproblems, it is usefulto note the form of equation2.1,which arisesin the three-dimensional case.
rt = -K grad(T)
(2.2)
grad(r)=vr:t#*;#.i#
(2.3)
In equation2.2, i is the heat flux vector (i.e., the heat flow per unit area) and grad(T) is the temperaturegradientvector. FOURIER'SEOUATION heat conduction,the flow of heat is associExcept in the specialcaseof steady-state ated with a changein temperature.In a small element,such as that shown in Figure 2.1, the heat flow away from the elementwill usually not be equal to that flowing in. by a changinginventory The differencein theseflows will be accommodated of the heat within the element.The heat balanceis representedby equation2.4, and this may be reducedto (2.5),wherep is the densityand C is the heatcapacity; the group KlpC hasbeen combinedinto a singlevariable,a, which is known as the thermal diffusivitv with dimensionsof L2T-1.
#=-*n(#)=-*"(#)
(#)=*(#)
(2.4)
(2.s)
form of the more generalequation2.6' which Equation2.5 is the one-dimensional was first derived by Fourier in 1822.
. (Yr)=*(#) (#).(#) Fourier'sEquation
(2.6) 31
o 'lI F** 2'r Figure
I I
classes:2 Solutionsto this equationfall into two general is zero 1. Steady-statesolutions,where the term @flAt) changewith time-i'e'' 2. unsteady-statesolutions,where tempelatures zero not generally the term @Tlat)is
where
loss of such a.sthe steady-state The first classof solutionsis of interest in problems inmost of that is usually heat through insulation. It is the secondclais of solutions terestinthermalrecoveryproblems.Atypicalcaseisthatoftheheatlossfromthe which is initially at some upper surface of a heated'reservoirto lhe overburden, problem is consideredin the more-or-lessuniform low temperature.This particular next section. FLOW OF HEAT INTO A SEMI'INFINITESOLID solid body shown in Figure 2'?' kconsider the flow of heat into the semi-infinite ?h, that at time 1 = 0' tl" sumethat initially the solid is at a uniform temperature this temperatureis then mainsurfacex : 0 is raisedto a temperatureG; andihat is controlled by the onesolid the within tained at the surface.The temperature equation2'S' ^. dimensionalFourier heat-conduction ,----L^- ^c.,^ ' first reduce the number of varte simpremeirrodfor solvingthis problemis to is-useful to transform the temperature ablesby ,,,.unr of almensionalanalysis.[t substitution variable to a dimensionlessform by making the
,.=(H)
,solutionsof equation2.6 are also of interestin studyingthe transientflow around oil wells' (see'for analyzetraniieni pressuretestsof oil wells is The basicpartial differentiut equationusedto 1967) example,Matthews and Russell
a2P .azP . . - + , azP -+--6x'
dy"
0z'
$p.c dP
kat
w h e r e P i s t h e f l u i d p r e s s u f e a t t h e l o c a t i o n w i t h c o o r d i n a t e s . I , y , a n d z ,has $ i sthe - t h esame p o r oform s i t y ,as pisthe permeability.This equation viscosity,c is the compressibility,andk is the thermal to the equated diffusivity, tn" hydroili, .is equation2.6 if ther"r^ *1$pr,inrch is known_ai of solutionsof this equation'Solutionsof Fourier's diffusity, a. Well-testingtriiry i. rurg"ly a study For example' uppii.d to reservoirfluid-flow problems' equation in this chapter *n itrr, "[ot" a fracture maintained around distribution describingihe.pressure Figure 2.3 can be looked upon as kept the pressurearound a vertical well that is at a constantpressureuno'rigur" 2.!2, aso-erclltine pressure' reservoir initial the ai a constantpr"rrur" aboveor below
32
Conductionof Heat within Solids
Chap' 2
within T=TR everYwhere Surfacex=0 is mainain€d atT=TS aftert=0
solidat t=0
Figure 2.2 One Dimensional ConductiveHeating of Semi-infiniteSlab
x Coordinate
The desiredfinal solution will give the dimensionlesstemperatureZ* as a function of x, t, and a. Supposethis may be written as a power series,such as
(2.7)
T* =.-. * B;xotba'+..'
For sucha solution to be correct, it is necessaryfor the dimensionsof eachterm to The dimensionsof the be the sameas for 7*; in this example,7* is dimensionless. terms on the right-hand side are as follows: Bi x I d
dimensionless length 8 time E length2/time,i.e., L2T-1
For the right-hand side to be dimensionless,the exponentsin eachterm must satisfy c= and
8 dimension
2
,-a D=c=-;
;LOlmenston L
Hence, in general,the solution must be of the form: z*isafunction
'l
x \
"t \v;/
or, without loss of generality,3
T* = T*(x,La)= f*1r1,
wherez
x
(2.8)
2\/ at
The factor 2 is included for later convenience. Equation 2.8 enablesthe number of independentvariablesto be reducedby one and the partial differential equationto be convertedinto an ordinary one. The substitutionof z from (2.8) into equation2.5 results in equation2.9, with the boundaryconditionsthat Z* : L for z :0 and 7* : 0 for z : a. 3This approachis known as Boltzman'stransformation;seeCarslawand Jaeger(1959),p. 89.
Flow of Heat into a Semi-infiniteSolid
33
d2T*
^ dr* ---7-T = -zz---:clz' clz
(2.e
Equation2.9 may be integratedin two stages.First, letp = dT*/dz,with the result
(2.r0):
= -zrp 4 dz
(2.10
This is integratedto give equation2.LL,whereCr is an integrationconstant. P = CG-"
(2.r1)
Substitutionof dT*ldz for p in (2.11)gives equation2.12, which when integratedyieldsequation2.13. dr* ---az
=
Lt€
_,2 -
T*=Cz*Ct
(2.12)
I
-"2
,
(2.13)
e-dz
The first boundary condition leads to Cz - I and the second resultsin equation2.14.
o=1+ crfo-r-,'d,
(2.1.4
The value of the definite integralin equation2.14 can be determinedas follows; this derivationis basedon that given by Jensonand Jeffreys(1963). The volume of the solid of revolutionthat is formed by rotating the curve z : e " aboutthe z axis is given by v:
.
r-
| 2 r r R e - R ' d R = r r l e - o ' d ( R ' )= z r l - e - R ' | f f = n
J6
Jo
(2.I5)
The samevolume can also be found from the double inteeral
= q [ - a' r l - r - t , ' * , ' , 4 , v :41- [- r--'a ' rdx Jg Jo Js Jo (2.16)
4 l - r - , ' d' J, s[ * r - , ' 4 * = 4 1 , J6
where1 is the integralof equation2.14.Hence V=n=412
and I=!
2
(2.r7)
Substitutionof this value into equation2.I4leadsto C, : -Zl{; and the desired solution,equation2.18,whereerfc is the complementaryerror function.
T* = 1.- erf(z)= erfc(z)= ertu(:+) 34
\2Y at I Conduction of HeatwithinSolids
1r.ta; Chap.2
The error function and the complementaryerror function are defined by the following equations:
erf(z)=+r _,2,
(2,1e)
e-dz
erfc(z)=I-erf(z)
=+L-
(2.20)
e-t'dz
A graphof the complementary error function is given in Figure2.3. Numericalvalues of the error function and the complementaryerror function are given in Table2.1. TABLE 2.1 NumericalValuesof the ComplementaryError Function erfc(z)
erlc(z)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95
1.000000 0.943628 0.887537 0.832004 0.777298 0.723674 0.67t373 0.620618 0.571608 0.52451,8 0.479500
oltseot 0.396144 0.35797r 0.322199 0.288844 0.257899 0.229332 0.203092 0.r79t09
Forz > 3.
1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 t.45 1.50 1.55 1.60 1.65 1.70 r.75 1.80 1.85 1.90
r.95
0.157299 0.r37564 0.1t9'795 0.103876 0.089686 0.077100 0.065992 0.056238 0.047715 0.040305 0.033895 0.028377 0.023652 0.0t9624 0.016210 0.013328 0.010910 0.008889 0.007210 0.005821
erfc(z)
2.00 2.05 2.r0 2.L5 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95
0.004678 0.003742 0.002980 0.002362 0.001863 0.001463 0.001143 0.000889 0.000689 0.000531 0.000407 0.000311 0.000236 0.000179 0.000134 0.000101 0.000075 0.000056 0.000041 0.000030
erfc(d:4.___Le-,,
\/tr z+Yz'+2
Useful approximateformulasfor calculatingthis function usingmicrocomputers follow. RationalApproximationsfor the ComplementaryError Function Approximation1: erfc(x) = (ai + azt2+ a3t3'1e-"+ e1x! p = 0.47047
t = U0 + px) ar = 0.3480242
Flow of Heat into a Semi-infinite Solid
le(x)l< 2.5 x l0-5 az = -0.0958798
az = 0.7478556
35
for the ComplementaryError Function (continued)
Rational Approximation2:
erfc(x) = (a1 + a2t2+ a3t3+ aata+ a5ts)e-" + .1t; t = t/(1 + px) D = 0.327591L A 3 = 1.42t413741
le(x)ls 1.5 x t0-? az = -0.284496736 at = 0.254829592 aq = -1.453152027 as = L.061405429
Approximation3: erfc(x) = (L + ag + azx2+ a3x3+ a4x4)-4+ e(x) ar = 0.278393
l e ( x )
Approximation4: erfc(x) = (l + at
a+ = 0.078108
I a2x2+ a3x3'f aaxa* a 5 x s + a 6 x 6 ) - 1 6 + e ( x )
l e ( x )
nq
^
N
0.6
o 't-
n 0.4
o.2 '
O
2 1.5 1 0.5 ArgumentZ Volueof Dimensionless
Error 2.3 TheComplementary Fig,rre Function
Significanceof Solution The singlecurve in Figure 2.3 containswithin it all the informationrequiredto calculatetemperaturegradientcurveswithin the solid for varioustimes. It is a didistance.At later times heat plot of temperatureagainstdimensionless mensionless penetratesfarther into the solid. For a given temperature,the distanceis proporiional to the squareroot of the time. It takesfour times as longfor the heatto penetratetwice as far. The heat flux into the surfaceof the infinite solid is given by equation2.21'
* =-*(#)*,
36
Conductionof Heatwithin Solids
(2.21) Chap.2
Substituting(T - TillQs - zn) for z* in equation2.18givesequation2.22;where zs is the temperatureof the hot surfaceand zn is the reservoirtemperature.
r=Tn+(rs-nl ' ..r.f-t ) \2Vatl
(2.22)
The temperaturegradient at x : 0 may be calculatedfrom equation2.23.
/q\
- r, - r^(4!:\
\dx/,=o
\ dz l,=o
2\/at
(2.23)
Substitutionof dT*/dz from equation2.12and using the value that was calculated previouslyfor c1 resultsin equation2.24 for the heatflux at the surfaco.
- ,^rrlff ft : rr,- r-)i};=(rs
(2.24)
Equation2.24 showsthat the heatflux is inverselyproportionalto the squareroot of heat flux with time is an importantconsiderationin heat -gftime-.'Thisdecrease ffi;6 within solids such as the overburdenuuou" ,Lr"ruoi* ii ir interesting to note that the heat flux is equallydependenton the thermal conductivity,K, and, upon the volumetric heaLcapacity,pC. The cumulativeheatflux at time / maybe found by integratingequation2.24, to give equation2.25: t
1,1*=*=z(rs-rR)K
= 2(Ts- rfifkpA1,
llu
Q.25)
HEATTRANSFERFROMA SPREADINGHOT ZONE An important applicationof the theory developedin the previoussectionis to the caseof a flat h-e*ated areathat is increasingwith time. This conceptplaysan important role in theoriesdealingwith steamflooding.The heat loss to the overburden abovea spreadingsteamzone is an exampleof this situation. In the solution,it will be assumedthat the problemremainsone-dimensional. Heat is assumedto be transferredin a directionnormal to the surface:i.e.. transfer parallelto the surfaceis ignored.For the first casewhich will be considered,it is assumedthat the heatedareaincreaseslinearlywith time. A small elementof area dA = Adto is heated from Zn to fs between time /e and /o + dto;it is then maintainedat Zs.No restrictionsare placedon the shapeof the heated area.A.Also, althoughit is considereda constantfor the present,the spreadingrateA may vary with ro. At somelater time /, the cumulativeamountof heat,Q,, that hasbeentransferred through a particular area elementAdts may be found using equation2.25. The resultis given by:
- r^rrft-:-!!Aato de, = zK(Ts Y
HeatTransferfrom a SpreadingHot Zone
(2.26)
7fd
37
TABLE 2.2 Values of Factor 'y' *(n)
1.0000 0.9436 0.8955 0.8540 0.8176 0.7854= r/4 0.'7567 0.7309 0.7075 0.6862 0.6667
0 0.1000 0.2000 0.3000 0.4000 0.s000 0.6000 0.7000 0.8000 0.9000 1.0000
The total heat that has been transferredmay be found by integrating2.26 from /o = 0 to /6 = t. Equation2.27 is the result.
- T^)A e" = 1. 2K(Ts
t ,ffd.
(2.27)
Expandingthe heatedarea at a steadyrate rather than immediatelyexposingthe sametotal areato the high temperaturereducesthe cumulativeheat flux in time r by a factor of two-thirds(compareequation2.27 with2.25). The precedingderivationmay be made more generalby assumingthat the with the nth power of /s rather than linearly.An examplefor which areaincreases this is of interestoccurswhen a steamchamberriseswith the two-third power of time. The parametern is 0 for the casewhereA is constantand is 1 when the area increases at a constantrate. Using the sameapproach,it is found that the cumulativeflow is given by equation2.28, where the factor r/ is the function of the exponentn as defined below;atabulatedvaluesof.tlt aregiven in Table2.2.
- rilA,f Q,--zK(rs fifo
(2.28)
where
*(n)=ryi?r6 CONSTANT HEAT INJECTIONRATE INTO A FRACTURE A particularlyinterestingand useful applicationof equation2.28 occurswhen the exponentn is equalto 0.5. If ,4 is proportionalto the squareroot of time, then it is apparentfrom equation2.28that, for this specialcase,the rate of heatlosswill be constant. 4f(n) is the qammafunction of n.
38
Conductionof Heatwithin Solids
Chap.2
A practicalcasein which this occursis wheresteamis injectedat a constant flow rate into a fractureinitially at reservoirtemperature.The heat-lossratesunder this conditionto the materialeither side of the fracturewill eachbe equalto half the heat-injectionrate,and the heatedareaof the fracturewill grow proportionally to the squareroot of time.s Startingwith equation2.28,it is easyto showthat undertheseconditionsthe heatedarea of the fracture will be given by
^' = lQ,,\ l; /(tr,l- z^) \T )V;
(2.29)
where Q,i is the total cumulative heat injected into the fracture, becauseheat is lost from both sides of the fracture, Q"i = 2Q,. This equation is derived in ariother manner in Chapter 3 (see equation 3.59).
CONDUCTION FROMA SPREADING CHAMBER THATADVANCES TO A LIMITAND THENSTOPS In recoveryproblemsconnectedwith wells confined in a repeatedpattern, the heatedregionsof the reservoircan spreadlaterallyuntil they interferewith the hot regionsof neighboringwells. When this confinementtakes place, the hot zones ceaseto expand,and heat is lost to the overburdenat a decreasingrate. During the expansionthe hot zone is continually encounteringfresh cold overburden, and this requires considerableheat. Once confinement takes place, this drain stopsand the rate of heat lossstartsto decrease. Considerthe casewherethe heatedareais definedby A=)t
for0
A=)t,
fort>tt
In theseequationsr is looked uponas a variableand /1,the time requiredto reach the outer boundary,is a constant.,4is assumedconstant. Using (2.27)the cumulativeheat transferfor the period t < tl ma! be written as
-
r^)A ,,: ^ 4 _-._ lT = -4 K(rs ----:----:::-t: Q, = ; KlTt - TilA t/J Y itd.
J
(2.30)
VTd
lf t were greaterthan /1,then the value of Q. calculatedfrom the precedingequation would be too high becausethe heatedareastopsgrowingat time /1.The value of O. would be too high by the amountof heatthat would havebeensuppliedto the areagreaterthanAtt if the growth had carried on unchecked. The heatwhich would havebeensuppliedto the areabeyond)t1may be calculatedby settingt in (2.27)equalto the time after tt-i.e., to (t - rr). The resultis
4 K(Ts- rilA. Q,= J.-:(t VTTu
\1', - tr)t,,
(heatbeyond-4rr)
(2.31)
tThis exampleis also discussedin Chapter3, where it is shownthat the temperatureZs does , prevail not right to the end of the heatedzone. Conduction from a Spreading Chamber that Advances to a Limit and then Stops
39
The cumulative amount of heat supplied to the areaAt1 alone, for times greater than /1, can be calculatedfrom the differencebetweenthe heat for the total area calculatedfrom (2.30)and the heat for the excessareafrom (2.31).The resultis ().==
4 K(Ts- TilA. 3
l . t 3 t -2 ( t -
\./ra
tr)t,'f fort>
t1
(2.32)
The rate at which heatflows to the overburden,for / > /1,is found by differentiating (2.32),giving (2.33). lz.JJ )
Confinementreducesthe heat lost to the overburden;for this reasonconfined wells,particularlyin gravity drainageschemes,can be much more thermally efficient than isolatedones. Figure 2.4 showsthe effect on the heat-lossrate found when a spreadingzone encountersits neighbor.One reasonfor this is simplythat whenthe increasein area stops,it is no longernecessary to continueheatingcold overburden.Another factor is that as the overburdenbecomeshot, the heat flux per unit areadecreases. The overall effect is dramaticand sisnificant. NumericalProblem In a plannedsteamflooding project,it is estimatedthat the steamheatedzonewill, for eachinjection well, cover an areaof 4 ha after 10y of steaming(the spacingper injectionwell is 4 ha). Calculatethe quantityof steamin tonnesrequiredto supplythe heatlossesto the overburdenfor eachyear for the following three cases: i. The steam-heated zoneincreasesat a steadyrate of 0.4haly. ii. The steam-heatedzone grows at a rate of I ha/y for 4 y and then stops as it meetsits neighboringzones. iii. The steam-heated zone spreadsimmediatelyover the pattern. t.c q)
o
u
.n1 th,
o
J
to time
o o !
0,
Unconfined Areo proportionol-/
n q v's
o
(x
l'\
Confinement
Areo
T
E
1 DimensionlessTime
40
Figure 2.4 Effect of Confinement on Heat Loss to Overburden
Conductionof Heat within Solids
Chap.2
Assume the following : 5 MPa; Steampressure Quality :70Vo = 1.7Wlm"C Overburdenconductivity : 850/kg'C Overburdenheat capacity : z4N kg/m3 Overburdendensitv Initial overburdentemperature: 15'C Steamcondensateis produced at an averagetemperatureof
7n+O.zs1zi-z;1
For case (iii) plot the temperature,in degreesCelsius, as a function of distance abovethe top of the reservoirin metersat 2, 5 and L0years. Solution The problem will be solvedusing SI units. From steamtables:
Ts : Hs : H*: Zn: Tp= Hp :
264'C for 5 MPa 2794.3kJlkg 1154.2kUk9 15'C - 15)= 202"C 15 + 0.75(264 861.5kVkg
enthalpy of saturatedvapor enthalpyof boiling liquid production temperature enthalpy of water at 202"C
Net heat per I : (U.t x 2794.3+ 0.3 x 1154.2- 861.5)x 106 tonne oI steam
: 1.44tx I}e Jlt i. Steamrequiredassuming the steamzoneadvances at a steadyrateof 0.4ha/y. Useequation2.27:
e"=lx1rr-rilA
t
(2,27)
7fd
K _ 1.7W/m'C A _ 4000,8000,. . . m2 l=
1 , 2 , . . . Y : 1 x ( 3 . 1 5 3x 61 0 7 ) . s. . 11
*fu:8'333x10-7m2/s T_e cumulative heat to the overburdenafter 1 year is
trl*oo(#t#*)', e"= + x r.7(264-
= r,rrux1012 r
Tonnes of steam required for firstyear=
ffi
= 5438
The cumulative quantitiesof steamfor successiveyearsare calculatedin the same manner,and the yearly quantitiesare found by subtraction.The resultsare given in the secondcolumn of the following table. The annual heat requirementrises continuously as the heatedregion expands. from a Spreading Chamber Conduction that Advancesto a LimitandthenStops
4a
ANNUAL STEAM REQUIREMENT IN TONNES PER YEAR
YEAR
cAsE(i)
CASE (ii)
I
5,438 9,944 1,2,876 1,5,248 t7,296 19,r24 )n 10)
13,596 24,858 32,t91, 38,120 29,643 )) q<)
2 J
+
\ 6 7 8 9 10
19,790 1,7,719
22,336 23,779 25,140
TOTAL YEARLY AVERAGE kt/v
81,,576 33,790 25,928 21,858 19,257 t7,4rr 16,010 t4,90t 13,997 13,238
t6,zLr 15,038
I7t,973
230,rLg
17.2
257,966
23.0
ii. Steamrequired assumingthat the zone grows u, tG/u
25.8
una rhenstops.
For the first 4 years,the steamrequirementis calculatedin the samemanner as in (i), using: A = 10900,20,000,30,000 and 40.000m2 The results are shown in the first four rows of the third column of the preceding table. For the remaining years, the cumulative quantities of steam are calculated usingequation2.32:
(2.32) For year 5: a
=5x3.1536x107s
a1
=4x3.1536x107s
A
10,000 m, (3.1536 x 10') s - 15)10,000 1,.7(264 (rr8.333xl0-t1tr4.tt36 x 10-7 't(sx 3.1536x 10-\3t2- (3.1536x I0-\3t21
Q,=+.
= 1.994 x 1014J
= Cumulative steam requirement ffi 42
= 88,408t
Net steamfor 5 y = 138,408- 108,765= 2\643 t Conduction of Heatwithin Solids
Chap.2
Annual steamrequirementscalculatedin this mannerare given in rows 5 through 10 of the third column of the preceding table. The steam requirement rises to a maximum and then declinesafter the heatedarea stopsgrowing. iii. Steamrequired assumingheatedzone spreadsimmediately. The steamrequiredis calculatedusing equation2.25withA: 40,000m2and the remainingparametersas in (i). The resultsare given in the fourth column of the table. The steamrequirementstarts out very high (infinite at / : 0) and declines with time. The resultsof the three calculationsare shown in Figure 2.5. The average ratesare comparedin the followingtable.Theseresultsmay be put into a practical perspectiveby consideringthe relativecosts,with steamcostingsomewherein the range of $5 to $20 per tonne. Average Steam Requirement SPREADING TIME (y)
AVERAGE STEAM RATE (kt/y)
0
25.8 23.0 17.2
4
10
The temperatureabovethe top of the reservoiris calculatedusing equation2,22.
r = rn+(r, - ril *f"(*a)
(2.22\
In SI units.r is the distancein metersabovethe reservoir,/ is the time from the start of heatingin seconds,and a is the thermal diffusivity in squaremetersper second.6 The calculatedtemperaturesare shown as a function of depth for eachof the three times in Fisure 2.6. CONDUCTIONAHEAD OF AN ADVANCING FRONT ln previous sections,the unsteadystate conductionof heat into a solid from a stationary hot surfacewas considered.This was extendedto the casewhere the hot surfacewas expandingin area. Another one-dimensionalheat conductionsituation that is of interest in thermal recovery is that where a hot surface or front is advancingtlroug! the solid reservoir in a direction approximatelynormal to its surface. One situation where oForcalculationsof this type, it will often be more convenientto use the day as the unit of time rather than the secondofthe SI system.To do this it is necessaryto alsouse the day as the unit of time in eachof the other variables.In the presentexampleit would be necessaryto convert a to squaremetersper day; this is also a much more convenientunit. a = 8.333x 10-?m2/s= 0.072m2ld Conduction Ahead of an Advancing Front
43
40 -20
;oo
c c .o
Steamzonespreadsfor 4
!40 E20
fo .g J
cr
t
1oo 100
e 8 o 80 E 6 060
6 4 0 40
20 0 Figure 2.5 SteamRequirementskt/y
o ,6 o
o, zoo (,
o o, o t, qi
100 E (g o
CL
E o
10
DistanceaboveReservoir. m
20
Figure 2.6 Temperaturein OverburdenaboveReservoir
this can occur is at a more-or-less verticalsteamfront which is advancingas flooding steamis injected behind it. The steamcondensesat the front and the condensate.runswith the displacedoil through the front and aheadof it wherethey rapidly attain the temperatureof the reservoirmatrix. Heat is conductedaheadof theiondensationsurface and the heat for this preheatingmust also be supplied by the steam.If the processcontinueswith a steadystate of advancethe cumulative heat buildup aheadof the front reachesa steadyvalue. Another exampleof conductionaheadof an advancingfront occurs when oil drains downward acrossa steam front which is advancinghorizontally through a reservoir.This mechanismis important in thermal recoveryusinggravity drainage. Here the heatedoil and condensateare removedcontinuouslyby drainage,and the steam-saturatedchamber advancesinto the reservoir. I{ggt*is- g_o.-n-dlJclgd_-ahe of the advancingfront, and this mobilizes the oil. The situation is depicted in Figve 2.7. 44
Conductionof Heat within Solids
Chap.2
o L :t o L
o o-
E
|l, F
Distonce
/\ Front ot T5 i
Velocity U
t D r o i n o g eo f o i l downwords
Figure 2.7 Lateral Advance of SteamFront
The one-dimensionalFourier equation2.34 is applicable.
=+(# (-tt)
(2.34)'
norma-l..to. The distance.r is measured the advancingfro'4_t.In the analysisof this : '--*-' process,it is convenientto transform the distancevariable so that it is measured from the front rather than from a fixed origin. This is done by defining the new variablef as in equation2.35.
t=x-f,ro, or, if U is constant,
t=x-Ut
(2.3s)
In this equation,U is the velocity of the advancingfront. The elimination of x from the left-hand side of (2.34) may be accomplishedsimply by replacingxby t.
=(.u' e*)
(2.36) v,
Since T is a function of x and /, a generaldifferential may be written as follows:
or=({*),*.(#)"0,
(2.37)
If f is maintained constant duling the differential change representedby (2.37), then dx = IJ dt1, and (2.37)may be rearrangedto give equation2.38.
=ue\ *E t,q) \dtlt \drl, \dt
(238) j
tThis is true evenif U is not constant. ConductionAhead of an Advancing Front
45
Combining(2.36),(2.38),and (2.34)resultsin equation2.39. This representsthe temperatureZ as a function of the distancef aheadof a front advancingat a velocity U in a reservoir of thermal diffusivity a. It may be made dimensionlessby the use of the variablesdefined by equation2.40.
(2.3e) T -Tn Ts-T^
?*l -
.ut
c1
s-
(2.40)
-:
d.
,* -
Utt d.
equation2.4l results. When thesesubstitutionsare made,the dimensionless
(#). (#)=(#)
(2.4r)
Imagine a constanttemperatureheat front of temperatureZs being formed at time / : 0 and advancingat a constantvelocity U. The reservoir is initially at temperature ?n. Heat conductedaheadof the front warms the reservoir material. Initially there is no heat aheadof the front, but as the front advancesand time progresses, heat accumulatesaheadof the front. The processcan be imaginedin two parts.The first is the transientstage,in which the heat aheadof the front builds up asymptoticallyto reach an equilibrium level. After this there is a steadystate, in which heat ahead of the front is "run over" by the advanceof the front; a steady-state,dynamic equilibrium is achieved. In this steadystatethe temperatureat any distancef from the front is constantwith time. For this situation the right-hand side of equation2.4'J.canbe set equal to zero and the equationbecomes(2.42):
(#).(#)='
(2.42)
The boundary conditions are Z* = 0
forf = oo
T*=l
forf =g
and The solution that satisfiesthese boundary conditions is given by equation2.43 or, after substitutingthe original dimensionalvariables,by equation2.44.
(2.43)
T* = e-ET
-
Tn
= o-tJ{a -
p-(utd)(x-(Jt)
Ts-T* 46
Conductionof Heat within Solids
(2.44) Chap.2
The total heat stored aheadof the front per unit area can be found by integrating equation2.44, givingequation2.45: Q" A
Io cc{r r^)dt
=
^ (Ts - T^) = pto---U= Y(Ts tu
(2.4s)
- Ta)
Equation 2.45, since it is derived for the steadystate,representsthe asymptoteto the quantity of heat which can be storedaheadof the front. In many cases,the actual conditions are not far from this steadystate. The amount of heat storedaheadof the front varies inverselywith the velocity. Large quantities of heat can be stored aheadof slow-movingfronts and little heat aheadof fast-movingones.In gravity drainageprocessesthere is equilibrium. Heat storedaheadof the front mobilizesthe oil and allows it to drain away,and the oil draining awayallows the front to move.The drainageof oil controlsthe velocity of advance. TRANSIENTHEAT TRANSFERAHEAD OF AN ADVANCING FRONT The transientconditions that occur before the steadystateis reachedcan be calculated by solving equation2.41without neglectingthe time-dependentterm. The solution that correspondsto the boundary :onditions I*=0
when/=0
T*=l
whenf*=[
forallf
and and />0
is given by equation2.46 (Carslawand Jaeger1959).
r.=+f"""(ffi) *"-"**(
€*-t* ----------2 V t * )]
(2 46)
An alternateform of (2.46)is
#)l
(Note: T* -- e-€' as /* --+ oofor finite f*). The complementaryerror function employed in (2.46)hasbeen describedpreviously.Temperaturedistribution curvescalculatedfrom this equationare given in Figure 2.8 and in Table2.3. Heat Ahead of Front in Transient Period The integral of dimensionlesstemperaturewith respectto dimensionlessdistanceis given by equation2.47. Tabilated valuesof this integral are alsogiven in Table2.3, where it is referred to as the heat integral. 47 Transient HeatTransferAheadof an AdvancingFront
ol 5
E o.e o g
g 0.6 o o
E 0.4 .9 o
6 o.z
E o
oo' Dimensionless distancefromfront Figure 2.8 Transient Temperaturesbefore an Advancing Front
(,*i)*(Y)-; I,- yfi,-,',,* T*d{* =
(2.47)
The value of this integral rangesfrom 0 at time zero to 1 at time infinity. Multiplying the value of this integral by the heat accumulationfor the steadystategiven by equation2.45 givesthe net heat accumulationfor the transientcondition. Although the heatintegralcan be evaluatedaccuratelyfrom equation2.47,it is a cumbersomerelation and, for approximatedesign calculations,a simpler expressionis convenient.Equation 2.48 gives estimatesthat are within 0.03 of the quantitiescalculatedfrom equation2.47. [o-
,.0r.
- 1' -
"-.zz+t/F
(2.48)
Continuationof the PreviousNumericalExample Upon carrying out the steamflood describedin the earliernumericalexample,it is found that the steamspreadsrapidly over the reservoir,as in case(iii) of that example. It is thought that the production processthat occurs involves the downward growth of the steamchamber.Measurements indicatethat this occursdurine the 10-yperiod at an averagerate of 1.5 mly. iv. calculate how much steam,in tonnes, is required for eachyear to supply the heat that is stored ahead of the advancingfront, assumingthat this is the sameas if the front were stationary.8 v. Calculatethe cumulative tonnesof steamrequired to build up the heat ahead of the front in the steadystate. vi. Repeatthe calculationin case(iv), but this time allow for the forward movement of the front usingequation2.47. \his assumptionhasbeenproposedby Vogel(1982)as a basisfor the conservativedesignand analysisof steamfloodingprojects. 48
Conductionof Heat within Solids
Chap.2
TABLE 2.3 Dimensionless TemperaturesBeyondan AdvancingFront DIM. TIME
DIMENSIONLESS DISTANCE 4+
HEAT INTEGRAL
0.1
0.2
0.3
0.4
0.5
0.01 0.02 0.03 0.04 0.05
.456 .586 .648 .687 .7r3
.142 .286 .373 .432 .475
.029 .115 .189 .247 .293
.004 .037 .083 .r28 .167
.000 .010 .032 .060 .088
.000 .000 .000 .000 .001
.000 .000 .000 .000 .000
.000 .000 .000 .000 .000
.000 .000 .000 .000 .000 .000 .000 .000 .000 .000
0.10 0.20 0.30 0.40 0.50
.780 .82t .847 .859 .867
.588 .673 .1tl .733 .748
.428 .538 .590 .620 .641
.300 .423 .484 .52r .546
.202 .327 .392 .433 .462
.015 .06'7 .rr4 .151 .180
.000 .001 .003 .009 .015
.000 .000 .000 .000 .001
1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 10.00
.886 .893 .897 .899 .901 .902 .902 .903 .903 .904 .904 .904 .904 .904 .904 .905 .905 .90s .905
.783 .796 .804 .808 .811 .813 .814 .815 .816 .8r7 .8t7 .817 .818 .818 .818 .818 .818 .818 .818
.690 .709 .7t9 .726 .730 .732 .734 .'.136 .737 .738 .738 .739 .739 .739 .'140 .740 .740 .740 .740
.606 .63t .643 .651 .656 .660 .662 .664 .665 .666 .667 .668 .668 .669 .669 .669 .669 .670 .670
.531 .560 .s75 .584 .590 .594 .597 .599 .601 .602 .603 .603 .604 .605 .605 .605 .605 .606 .606
.263 .300 .32r .334 .343 .349 .353 .357 .359 .361 .362 .363 .364 .365 .365 .366 .366 .366 .367
.049 .074 .090 .t02 .110 .116 .120 .123 .126 .127 .t29 .130 .131 .132 .r32 .r33 .133 .t34 .r34
905
.819
.74r
.670 .607
.368
.135
.000 .000 .000 .000 .000
0.108 0.150 0.181 0.206 0.228
.000 .000 .000 .000 .000
.000 .000 .000 .000 .000 .000 .000 .000 .000 .000
0.310 0.413 0.483 0.537 0.581
.006 .014 .022 .027 .032 .036 .038 .041 .042 .044 .045 .046 .046 .047 .048 .048 .048 .048 .049
.001 .002 .004 .006 .008 .010 .012 .013 .014 .014 .015 .016 .016 .016 .017 .017 .017 .0I7 .018
.000 .000 .001 .001 .002 .003 .003 .004 .004 .005 .005 .005 .005 .006 .006 .006 .006 .006 .006
.000 .000 .000 .000 .000 .001 .001 .001 .001 .001 .001 .002 .002 .002 .002 .002 .002 .002 .002
0.720 0.799 0.849 0.884 0.910 0.929 0.943 0.954 0.963 0.970 0.975 0.980 0.983 0.986 0.988 0.991 0.992 0.993 0.99s
.050
.018
.007
.002
1.000
For the purposesof this exampleassumethat the physicalpropertiesof the oil sand are the sameas thoseof the overburden. Solution Steamrequirementfor the reservoirbelow the steamchamber: iv. The quantitiesof steamrequiredfor this caseare the sameasthosecalculated in (iii). v. The heataheadofa steadilyadvancingfront is calculatingusingequation2.45. In the presentcasethe frontal advancerate is U = 1..5m/y = 4.76 x 10-om/s Transient HeatTransfer Aheadof an AdvancingFront
49
The storedheat is thus KA(TS - TR)
U
1.7x40,000(264-15) = 3.56x 1014 J 4.76x l0-8
and the corresponding quantity of steamis 3.56x 1014 = 247 kt 1/4lt 1oq vi. The buildup of heat aheadof the advancingfront can be calculatedby multiplying the equilibriumvalue obtainedin (v) by the heat integralfactor calculated from equation 2.47 or read directly from Table 2.3. The yearly incrementsin theseheat requirementsare shown in the following table;the heat requirementdrops off toward zero as the heat accumulates. Steam Requiredto ProvideHeat Stored Beyondthe Front YEAR
CASE (iv) Fixed Front
CASE (vi) Moving Front
81,576 33,'790 25,928 21,858 19,257 17,4tl 16,010 14,901 13,997 13,238
71,583 24,268 16,714 12,89L 10,502 8,840 7,608 6,654 5,890 5,265
I
2 J
5 6 7 I 9 10
AverageRate, kt/y
Total 257,966 25.8
r70,2t5
r7.0
EFFECTOF CHANGINGFRONTVELOCITY In the precedingsection,the temperaturedistributionaheadof a front moving at constantvelocityUwas determined.It wasshownthat a dynamicsteadystateis approached.In practice,the front velocityis not constant;frequently,it tendsto decreasewith time. To study this effect, differential equation 2.41 was integrated numerically using the explicit finite differenceprocedure.The left-hand side of the equation wasevaluatedfor a giventime at equallyspaceddistancesand then the corresponding temperaturechangeat eachpoint wascalculatedfor a smalltime step,assuming that the right-handside of the equationdid not changesignificantly. The resultsof sucha calculation,in which-at a dimensionless time of 2-the front velocitywas reducedto half of the initial value (and the dimensionless time using the new value of U becameinstantaneously 0.5), are shown graphicallyin Figure2.9. 50 Conductionof Heat within Solids Chap.2
1.0
I
o o
ril 0.8
D c E
Response whenU changes from 200o/o to 100o/o at 0.5time
n- ' A -
o o
l-
E
Asymptot€ for U=200%
G 0.4 ctl
o
E o.z o o E
0
0
1 2 3 4 S Figure2.9EffectofReduced Dimensionless Timebasedon U=100% FrontVelocity
At the point at which the velocitywaschanged,the heat integralhad reached 85% of the initial steady-state value. With the decreasein velocity,the potential steady-statevalue doubled and the heat integral was then only 42.6Voof the new steadystate.With the reductionin velocity,the "run over" of heat by the interface decreased, and accumulationof heat beyondthe interfaceincreased.As a result, the responsecurve approachedthe new asymptote. Also shown in Figure 2.9 is the heat integral curve for the casewhere the interfacestartedout at the lower velocity.This curve is alwaysabovethe other,but it may be seenthat the differencebecomesquite small soon after the changein velocity. The Situation Where the Front Advance Velocity ls Inversely Proportional to the Square Root of Time lt happensthat a simplesolutionto equation2.38 canbe obtainedwhen the front advancevelocityis inverselyproportionalto the squareroot of time. It is of interest becauseit is a simpleexampleof the casewherethe front velocityfalls with time.e The variation of the front velocity u with time is assumedto be given by equation2.49,whereb is a dimensionless constantthat determinesthe rate atwhich the velocityfalls. The velocitystartsat infinity unlessb : 0.
U=b
d.
(2.4e)
The temperaturedistribution for this situation is given by the remarkably simpleequation2.50;this reducesto equation2.18it b is set equalto zero-i.e., if the front is stationary. 'A practical situationwhich correspondsapproximatelyto this condition is that wherea cylindrical steamzoneis growing radially about a vertical injectionwell. If the rate ofvolumetric growth of the chamberis constant,then the radius of the chamberincreasesat a rate proportional to the reciprocalof the squareroot of time, as is assumedabove. For this caseb:0.5R(at)-0s whereR is the radiusat time t. However,the situationis not identical to that describedabove,since the area is also increasins. Effect of Changing Front Velocity
-
1 s 0.8 o
ro 0.6 o o 0.4 ! G
> o.2 0r 0
Parameterb
Figure 2.10 Heat Integral Factors
erfc(z + b) n* '=-"rf.(b)
t wnerez=2{^
(2.s0)
The heat integralmay be calculatedfrom either equation2.51,which is similar in form to equation2.25 for the stationaryfront, or from equation2.53,which relates the heat integralto equation2.45 for,the steady.tut" foia constantvelocityfront.
o"t a^ = 2KQ,- ra tlLaall u1rd
(2.s1)
where
B(b) =
!
e"
erfc(b)
- b\f1r
(2.s2)
= oc{r,- riltcfu)
= where G(b)
#uru,
(2.s3)
The factorsB and G are shownasfunctionsof the parameterb in Figure2.10.It is interestingto note that the situationapproaches thi steady-state cas-efor largerb; i.e., G tendsto 1 as b increases. In many practicalcases,it will be found that the heat aheadof an advancing front is not very different from the steadystate level. For example,supposethat a front were advancingat a rate that is inverselyproportional to the .qrrur" root of time and that it had progresseda distanceof 100ft in 1 year.Then, usingthe formula in footnote9, and issuminga typical value of 0.7 ti'z/dfor a givesivalue of 0.5 x 100x (0.7 x 365;-os:3.73 forb. From Figure2.l0itcan be seenthat, for this valueof b, the factor G(b) would be nearlv 1.. RADIAL HEAT FLOW FROM A WELL When a fluid suchas steamor hot wateris injectedthrougha well, there is considerableheat loss from the well bore to the overburden.Fourier'sequationfor radial flow may be derived from equation2.6 by substitution. Howeve., it is simpler to start from first principles.The developmentis similar to that for linear flow eiven on page31. 52
Conductionof Heat within Solids
Chap.2
Consideran elementalcylinder about a vertical well such as that shown in Figure 2.11;the height of the cylinder measurednormal to the paper is L. Assumethat heat is flowing at a rate Q radially from the center. Then
e =-KAffi=-znnt*#
(2.s4)
_ a Q = zrnLpc#= zotK# + 2,RLK# AR
(2.ss)
and
A2T I AT dR' R AR
laT a0t
(2.s6)
We are interestedin the solution of this radial form of Fourier's equation for the casewherethe temperatureat the well bore (i.e.,whereR : R,) is suddenlyraised to the steamtemperature15 and the surroundingground is initially at zp. The temperaturedistributionwill be a function of time and radius.It will depend upon the radiusof the well bore,R,, and the thermal diffusivity, o.'It i, ,"uson_able to expect that the smaller the radius of the well-bo1,e,the les_s udfb.e lhe penetrationof heat into the surroundings.Also, the heat lossfrom a unit area of the well surfacewill be grgater than for a plane surface becauseof the divergent radial heat flow. The solution for these boundary conditions is developedby carslaw and Jaegerusingthe Laplacetransformationmethod.The resultis I I t R\ / p\
r - rn_,, 2 rr-7;='-;J--"
urr] ilr:::l ^r,-,1r,\, &)t dtn(w) [-,,", @ :l:\! (2.s7\
where,16and % are Besselfunctions of zero.ord,erand of the first and second kinds, respectively,and w is a dummyvariablethat dropsout when the integralis evaluated. Equation2.57 is of the form
#='(#,'*)
(2.s8)
Figure 2.11
RadialHeat Flow from a Well
53
The first parametermay be consideredto be the dimensionless time and the second, the dimensionless radius. Although the expressionfor F (the right-handside of equation2.57) is complex, it may be evaluatedreadilyusinga computer.A plot of F versuslog,o(R/R,) is given in Figure 2.12. For largevaluesof dimensionless time, the initial linear part of the curvesin Figure2.12is givenby a straightline drawn from (0, 1) to the point on the horizontal axiswhere
,.r,,(*) =
o.rlr"s,,(*) + o1u] '"t"(^+)- o'1so
(2.s8A)
This equationis basedupon an asymptoticexpansiongiven by carslaw and Jaeger -i!\
(1959).
The rate of heat lossfrom the well at time I is given by
e = -2trR*t.(+\ dR \
/o=*-
(z.ss)
The temperature gradient at the well may be obtained by differentiating equation2.57 with respectto R, with the result
-"^r'*, f-_" wllSw)+ Y\w)l
L'(g#) Q= (2,rR,
(2.60)
T-TR1.0
ffi
afterCarslawand Jaeger1g5g
0.8 0.6
Parametsr is dimensionless timedtl*
0.4 0.2 0
1
2
3
5
10
2030 so 100 R/Rw
Figure 2.12 TemperatureDistribution around a Circular Well Bore as a Function of Time
54
Conductionof Heatwithin Solids
Chap.2
The heat flow may be written in a dimensionless form as Q * = (2rrR,L) (Zr f^)
=
*
dW
# ['-'-a''ott*' wlr\w) + Y?,(w)l
o.=;vfu^="(#)
(2.61)
values of the integralin equation2.61 are tabulatedby Jaegerand clarke (Jaeger and Clarke 1942), and a plot of Q* versus the dimensionlesstime is given in Figure 2.13.The curve in Figure 2.13maybe represented by the following empirical cubic equation.
- 0.308x- 0.0150 ln(O*)= -0.000629x3 + 0.0203x2 where
'=t"(#) (2.62)
0 1. ( R q .) 1 0 ' Also shownin Figure2.13is the asymptotethat corresponds to the heatlossfrom a portion of a largeflat surfacehavingthe sameheatedareaas the cylinder. Cumulative Heat Flow from Well Bore The total heat lost from the well bore after time / may be found by integrating equation2.61. f' I' - & ) - rR ? ,If " F , d t * I edt =2rKL(Ts-rill JgFtdt=2rKL(75 "' q Jo
e,:
Js-
(2.63)
J
Solldcurveis theorelicalcurve. Triangularpointsare from correlallon.
Az o o tr1 o
6
E 0'5 ,9
E o'3
o) .E 0.2 o
0.1 0.1
Figure 2.13 Heat Loss from Well Bore. The Value ofR* usedin calculatingthe dimensionless time is 10,000 100,000 the equivalentradius of the well bore after allowing for insulationeffects.
Heatloss trom tlat surfacefor comDarison, 1
10
100
1,000
Dimensionless Time RadialHeatFlow from a Well
55
where . d- t-
t4
R'* This may be rewritten to give a dimensionless cumulativequantityof heatQ!:
QT 2rrKL(Ts- T^)R', = Q,O
o'o* fo.
(2.64)
A plot of pi versus/* is given in Figure2.14.The curve may be representedby the empiricalcubic equation ln(Q!) = -0.000629x3+ 0.0235x2+ 0.621x+ 0.472
(2.6s)
where
'"(*t) Factors Affecting Well Bore Heat Loss TLe_fateof heat loss from a well bore is proportional to the length of the well, to th,ethermalconductivityof the ground,and to the temperaturedifferencebetween the 1v_ell bore and the surroundings.The rate decreases with time, as shown in Figure 2.13.The decreasewith time is causedby the decreaseof the temperature gradientas the ground around the well bicomesheated. Although the heat loss falls initially at a rate inverselyproportionalto the squareroot of time, as it did for linear flow (seeequation2.24),the rate decreases more slowlyafter the initial periodbecauseof the divergingradial flow. A circular well is better cooledby the surroundingsthan is a portion of a largeflat planehaving the samearea. It is important to notice the effect of the well radiuson the rate of heat loss. For a given value of time in Figure 2.13,the rate of heat lossis lessfor a smaller radiusthan for a largerone;this is becauseits surfaceareais smaller.A well of zerc radiuslosesno heat! Insulation of Wells to ReduceHeat Loss Considerthe caseof a well havingan externalradiusR2 and supposethat the well is partly filled with an annulusof materialhavingan insideradiusof R r and an outside radiusof R2, aSin the crosssectionshownin Figure 2.15. If the insulationhas the samethermal propertiesl0as the surroundings,then the effect of the insulationis the sameas that of reducingthe radius of the well from Rz to Rr. The heatflow can be determinedby usingFigure2.13if Rr is substituted for the equivalentwell bore radiusR,. toonly the thermal conductivityis of importance,sincethe amountof heat storedin the insulation will be negligiblecomparedto the total quantitiesof heat involved.This is equivalentto saytransfer.This is the ing that the transferof heat through the annulusis equivalentto a steady-state reasonthat the plots of temperatureversuslogro(R/R,) becomestraightin the vicinity of the well in Fis.ure2.12.
56
Conductionof Heatwithin Solids
Chap.2
rO
o o o
105
6
104
3 o I o
Solld curve ls lheoretlcal llne. Trlangular polnts are from correlatlon.
to3
g E
o
l02 101
ll o
Brok€ncurve ls for flat surface,
-9 100 .9 o o E
i5
t o'1
1o'1
103 1ol ft2 Dimensionless Time
1oo
104
1os
Figure 2.14 CumulativeHeat Loss from Well Bore
lf the insulatingmaterial has a thermal conductivitydifferent from the surroundings,then an equivalentwell bore radiuscan be determinedby making the thermalresistance of the insulatingannulusequalto that of a hypotheticalannulus havingan internal radiusR, and the sameconductivityas the ground. The steady-state thermal resistanceof an annularinsulatoris given by Tt-Tz_ln(Rz/Rr)
2rLKr
O
(2.66)
whereKr is the thermal conductivityof the insulator.Let this be equivalentto the thermal resistanceof an annulushaving an internal radiusR, (the equivalentwell radius)and externalradiusof Rz and composedof materiallike the surroundings. Then ln(RzlRr)_ ln(RzlR,) 2trLKr 2rLK
(2.67)
which may be reducedto R*=
o,(fr)"''
(2.68)
WellBoreRadiusR 2 InsulationRadiusR ,
Figure 2.15
RadialHeat Flow from a Well
57
substitutionof this valueof R, in the abcissa of Figure2.13will make a properarlowancefor the effect of the annularinsulation. In mostcasesthe thermalresistanceof the_annurus, incrudingany insulation, will be defined by an overall heat-transfer coefficient rutrr", irrun uy tr," thermal conductivityof an insulatingmaterial.The estimationof this t coefficient is discussedlater. "ut+r"nrr"r If the transfer from the tubing of radiusR1 to the outer welr perimeter is determinedby a heat-transfer coefficientut (basedon the surfaceur"u or the tubing), then the heat-transferresistanceis givenby Tr-Tz
I
a
2rRrLUt
(2.6e
Equatingthis to the thermarresistanceof the annulusof internal radiusR, filled with materialof conductivityK leadsto ln(Rr/R") 2rLK
I 2rRtLUt
(2.70)
This reducesto the fo'owing expressionfor the effectivewell radius,R,: R. = ftrg-Ktu1a1
e,7t) substitutionof this value in the dimensionless time in the abcissaof Figure 2.13 will allow for the barrier to heat-transfer exertedby the annulus.Note that if ut = 6, then R. : R2; also,if u1 were zero, then R, would alsobe zero. The EquivalentWell Radiuswith Multiple t Resistances In most casesthe heat-transfercoefficient u1 representsthe combined effect of a numberof individual resistances to heat flow. A typical case vurv rr is rvl represented by the following diagram. Steam
Steam
Tubing
T=Ts
Film
Wall
Insulation if Present
Annulus
Casing Wall
Cement
Formation
The resistances of the steamfilm and of the metal walrs are relativelysmal and may be neglected.The heat-transferacross the annulus occurs by two parallel mechanisms-radiationand convection.The combinationof resistancesfor the overall situationmay be representedas follows: Convectlon
58
Conductionof Heat within Solids
Chap.2
In this diagram the resistancesto heat transfer are measuredin degreesCeloF siusper watt,'CW-1 (or in Englishunits, Btu-t h). ln(R2/R.u'1")
= lncement
z"LK*
"-
(2.72)
1.t l'conu
2rrRi
h,
where ft. is the convectiveheat-transfercoefficient for the annulus. Methods for predictingthis are discussedlater;R; is the inner radiusof the annulus. 1l lt l-^t
=
(2.73)
-
h, 2rrR, ln(R.",1.g/R;) 2rrLKinur
(2.74)
1
(2.7s)
The overallresistanceis *finsul
l"roral=In."..n,* I
1 -; t*
and the overallheat-transfercoefficient(basedon the tubing radiusR1)is givenby ZrRtUt
1
(2.76)
/total
or
u' -
1
(2.77)
2rRrrro,u,
The equivalentradiusof the well is given by R. = ftrg-z'K""t^t
(2.78)
Direct Injection of Steam Down the Well Casing Direct injectionof steamdown the well casingis the simplestway to operatean injectionwlll and is frequentlypracticed.For example,Esso,in its extensivecyclic steamstimulation project at Cold Lake in Alberta, injects steamdirectly down the packerto isolatethe annulus annulus.This avoidsthe needfor a high-temperature in cyclic wells bedifficulties presents packer a from the tubing. The use of such during the prothe anulus gases up venting causeof the problem in arrangingfor direct steam with operating of duction pu-ping period. A major disadvantage and temperature, steam the to raised injectionin tire annulusis that the casingis 'iery (e'g', casing High-strength high. mlchanical stressesdue to expansionare yield stressis usuallyexN80)is normallyemployed,and eventhen the compressive it is cooled' when stress ceeded,and thi casingdevelopsa residualtensile well radiusis that equivalent the because Heat lossesut" th" highestpossible projects the heatloss shallow oo). relatively in Nevertheless, of the casing(i.e.,u1: RadialHeat Flow from a Well
59
is acceptable.In the numerical examplethat is developedlater, the well bore heat lossfor a 17.8cm-diameterwell (7 in.) 460 m long delivering160m3/d of steamis about 5 to 10Voof the heat injection rate. Injection of Steam in the Tubing with the Annulus Full of Gas In this casethere are two mechanismsfor heat transferacrossthe annuluswhich operatein parallel: radiation and convection. Radiant heat transfer between two concentriccylinders The transfer of radiant energymay be calculatedfrom the following equation:
(2.7e) where i o T e Ai o
refers to the inner cylinder refers to the outer cylinder is the absolutetemperature is the surfaceemissivity is the areaof the inner cylinder is Stefan-Boltzmannconstant: o = 5.669x 10-8 Wm2 Ka or 1..714x 10-eBtu/h ft2 1.R;4
It is assumedthat the surfacesbehavelike "grey" bodies. The radiationheat-transfer coefficientftp,basedon the areaof the inner tube, is given by , Q =^
oQ?+ril(r,+r.)
-
flp
"
Ai(Ti -
T
T.)
;
*
R ,I I
- \ R,l; t/
(2.80)
The emissivityof typical oxidizedsteelis about0.8. A plot of /ra against4 from equation2.80is given in Figure 2.16for an emissivity of 0.8 and RifR, : 0.5. Curvesare shownfor a rangeof temperaturedifferences(I - [) and steamtemperature7]. Convective Heat Transfer between Two ConcentricVertical Cylinders The convectiveheat transferacrossthe annulusmay be written as 9conu =
,
" 60
=
2rrLK*LT
(2.81)
HR/&)
Keff Qronu -- I znR,r-LT & r"(R/R,
Conductionof Heatwithin Solids
Chap.2
E =
Eso o
:E t40 o
#c . 0 o l- 20 a!
o
Iot o a6-
E q iEl
tr
degreesCelsius SteamTemperature Figure 2.16 Tubing-CasingRadiant Heat Transfer
whereK"11,the ffictiue thermalconductivityof the gascontents,is higherthan the true thermal conductivity, Kg, of the gas becauseof the fluid motion causedby thermal convection.The ratio K*IK, has been studied for heat transfer acrossthe gap betweenvertical flat plates,but no studiesappearto havebeen madefor annuli betweenvertical cylinders.It is reasonable to assumethat the effectswill be similar. A mitigating factor is that for most steaminjection systems,the transferby convectionis significantlysmallerthan that for radiation. For the spacebetweenparallelverticalplates,the ratio K"u/Keis found to be a function of the Rayleighnumber,
Nnu= (YP)r,r,-r") whereg p p Cp tt K 6 Tt - T,
(2.82)
is the accelerationdue to gravity is the thermal coefficient of thermal expansionof the fluid equal to '1.f 1,/V@V/AI)(This is T^,",for an ideal gas.) is the fluid density is the fluid specificheat is the fluid viscosity is the fluid thermal conductivity is the gap betweenthe vertical surfaces is the temperaturedifference
In this expressionthe group within the bracketsis dependentupon the fluid and its temperatureand pressure.It is customaryto evaluatethesepropertiesat the averagetemperaturebetweenthe two surfaces.Numericalvaluesfor the group for air at pressures of 1, 10,and 100bar are shownin Figure 2.17. The value of the factor declineswith increasingtemperatureand increases with pressure.The pressureeffect is largely due to the changein the densityp; this
RadialHeat Flow from a Well
61
Ordinateis the groupwhichis in bracketsin equation2.82
'to12 'tott T
Y,oto ct
L rot
'l .'o' o C'
,[ to' 6 10
300
500 400 in degreesKelvin Temperature
600
Figure 2.17 Natural ConvectionFactorfor Air
I
is nearlyproportionalto pressure.Increasingthe pressureby a factorof L0increases the value of Nnuby a factor of approximately100.However, since the heat transfer is proportionalto the J or ] powerof Nn" (seethe following),the heattransferonly to 1001/3, or 3.2 to 4.6. inireises by a factor of approximately1001/a little effect on the transfer of heat. As has Nru, convection values of At low between106and 10i' at values increases; eventually, motion Nquis increased,fluid following equations(Holman the recommends Holman the flow becomesturbulent. 1981): K.,' Nn" < 6000 I\8
= r#(;)' fi o.rn
6000
x107
E
(2.83)
=oo',N#(;)
Theseequationsalso include the effect of the ratio of the height of the chamberto the width (L/6). The rangeof this variablecoveredby the correlationis 11to 42. It does not seemreasonablethat the effect of 6lL would increaseindefinitely up to the ratiosfound in injectionwells-e.g., valuesof Ll6 of severalthousand.[t is suggestedthat an arbitraryvalueofL/6 : 42be substitutedin the precedingequations for the prediction of convectiveheat loss in well annuli. That is, Ketr
6000
K8
= 0.13Nil1 (2.84)
2 x r o 5 ( N n u < 1 . x1 l o i
Z
= 0.048Nil;
Values of Ns" ma] be estimatedby multiplying the values of the ordinate from Figure2.I7 by 63(Ti- 4), as in equation2.82. 62
Conductionof Heatwithin Solids
Chap.2
BackgroundMaterial on Well Bore Heat Loss The classicpapersin this field are thoseof Ramey(1962,1965). As well as developing equationsfor the heat lossfrom a well at constanttemperature,which are similar to thosegiven in the previoussection,Rameyalso developedan approximate solution for the heat loss from a hot-water injection well. This solution allows for the decreasein temperatureas the injectedwater flows down the well. Satter(1965)extendedtheseideasto allow the calculationof heatlosseswhen superheated steamis injectedinto the well. Willwhite (1966)describedmethodsfor predicting the heat-transfercoefficientbetweenthe tubing and the well casing. Theseare basicallysimilar to the methodsdescribedhere,althoughthey do not use the conceptof the equivalentwell bore radius. FontanillaandAziz (1982)allowedfor the effectof two-phaseflow in the tubing of the injectionwell. FarouqAli (1981)describeda calculationmethodthat combines correlationsfor the two-phaseflow within the well bore and a rigorous treatment of heat loss to the surroundings.The resulting equationswere solvedby a numericalmethod.A recentpaper by Durrant and Thambynayagam (1986)describesa similar approachthat employsa somewhatdifferentcomputationmethod. NumericalExampleof Well Bore Heat Loss Calculation Steamis injectedinto a reservoirhaving a depth of 460 m using a well with a 17.8cm (7 in.) diametercasing.The conditionsare as follows: Reservoirtemperature: 10'C 10 MPa Steampressure: Steamquality: 70% Injectionrate: 160mr d I -t Assumethat the thermalconductivityof the overburdenis 1.7W m-t 'C and that its volumetricheatcapacityis 2410kJ m 3'C-r. Neglectthe effectof the cement aroundthe casing. (a) Calculatethe heat injection rate in megawatts. (b) Assumingthat the steamis injecteddirectly down the casing,calculatethe heatlossratein megawattsafter 1, 10,100,and 1000daysof injection.Express this lossas a percentageof the heat input. (c) Plot the temperatureas a function of distancefrom the casingsurfacefor each of the times in (b). (d) Calculatethe heat lqqsrate 14lryg!!qag1_sgg3l9-!Ir€*tgt*fg-{ ggchof the times in (b) and compare-tcthe heat loss that would be expectedfor a flat surfaceat the samesteamtemperature. (e) Assumethat the steamis injectedinto a 7.3 cm (21in.)-outside-diameter tubing and that this is isolatedfrom the casingby a thermalpackerat the bottom so that the annulusis filled with air at atmosphericpressure.Assumethat the emissivityof the facingtubing and casingsurfacesis 0.8. The internal diameter of the casingmay be takenas 16.5cm (6.5in.). For theseconditionsrepeat RadialHeat Flow from a Well
63
the calculationsin parts (b) and (d) and comparethe answers using a chart. calculate the heat-transfercoefficientr fo, u casing temperature 250"c and assumethat they do not vary with time. The theimal conductivit of air in the annulusmay be taken as 0.014gW m-1 oC-1.
(f) using the heat flows determinedin (e), calculate the casingtemperaturefor eachtime and make separateimproved estimatesof the helt+ranster coeffi_ cient U' Repeat the heat-flow cilculations of (e) and repeat until consistent valuesare obtained.Revisethe bar chart producedin (e) and atsoplot a graph showingthe casingtemperatureas a funciion of the sieaming time (use"alog scalefor time). Solution L : 460m; R?: trin. : 0.0gg9m; Zn = 10.C; ?s : 311.C steamquality : 70vo; injectionrate : 160m3d-1: 160,060kg 6-r K = 1.7W m-l 'C; vol heat cap : 2410kJ.-3 o6 -1. (a) Heat-injectionrate From steamtables: vapor enthalpy : 2724.7kJ kg-1 Liquid enthalpy = 1407.6kJ kg-1 Heat in 70Voquality steam : 2724.7x 0.7 + 1407.6x 0.3 : 2329.57kJ kg-1 above0.C : Heat above Zp 2 3 2 9 . 5 7 - 4 . 2 x I 0 : 2 2 g 7 . 6 k J k g - r Injection rate = 160,000 x 2297.6: 366 x 106kJ d-1 = 366 x 106x 1000/(24x 3600 x 106) : 4.24MW (b) Heat losswith injectiondown the casins
Dimensionlesstime (at/ R2*)(t) ln(dimenionlesstime) Heat lossin megawattsfrom (2.62) Heat loss as percentof input
(t)a: 1.7/(2410 x 1000)= 7.05x ffi
64
7.71 2.04 0.75 77.5
77.I 4.35 0.44 10.4
771, 6.65 0.29 6.8
Conductionof Heat within Solids
77I0 8.95 0.21 5.0
Chap.2
(c) Dimensionlesstemperaturesfrom Figure 2.12
DimensionlessTemperatures
Days of injection Heat lossW m-2 From well Flar surface(2.22)
2919 1169
10
100
1000
t726 370
rl44 lt7
810 JI
Correspondingradii and temperatures:
Radius in meters 0.09 0.16 0.28 0.50 0.89 1.58 2.81
s.00 8.89
Temperaturesin degreesCelsius 1d
r0d
100d
311 209 109 37 10 10 10 10 t0
311 251, 188 127 64 25 10 10 10
311 266 22r r76 127 85 52 22 10
Theseresultsare plotted in Figure 2.18. (d) Calculation of heat-lossrate External areaof well casing= 2rR*L = 256.9m2
Days of injection Heat lossW m-2 From well Flat surface(2.22)
RadialHeat Flow from a Well
2919 1,169
10
100
1000
1726 370
1144 1,1,7
810 37
65
o t '6
300
o
f;o zso q)
E,200 (,
! ,so o = loo G
Euo E
Po Distancefrom Centre,m Figure 2.18 TemperaturesAround InjectionWell
(e) Use equation2.80 to calculateftn. o = 5.669x 10-8W m-r K-a Ti=273+311=584K To=273*250:523K Emissivityfor both surfacesequals0.8. 4-' :':1t = 0.442; Ri = 0.442x 3.25 x 0.0254= 0.0365m Ro 6.5 hn: 28.41Y--2 og-t Use equations2.84 to calculateftc. $=
- 2.87s\2.54 0.5(6.s =
0.0460m
Averagegas temperature= 553.5L. Nnufactor from Figure 2.17 : 7.5 x 106 Nnu : 44,600; _ , = ,,
: 1.89 K"rrlKr: 0.13NR.25
1.89K
: n u' q '
RRRJ&) :
(J = hn * h6 : 29.3W --2 og-1 m R- : 0.01812 Calculationof Loss Rate Time in days Dimensionlesstime In(dimensionless time) Heat lossin megawatts
1 186 5.22 0.38
10 1,860 t.J3
0.26
100 18,600 9.83 0.18
1,000 186,000 12.13 0.13
(f) The precedingsolutionassumesa constantvalue for the casingtemperature. In practicethe casingtemperaturemust start initially at Zp and then increase asymptoticallytoward 7s. As it increases,the value of U also increasesand the value of R, increases.The problem can be approachedmore exactly by estimating the casing temperaturefor each time from the heat flows calculated earlier togetherwith the value of U. These temperaturesare then used to estimatenew valuesof U, and the calculationis repeated. 10
Time in days First iteration Heat flow (MW) Casingtemperature("C) Averageannual temperature('C)
ar ('c) ftr (W m-2'C-1) Np" factor x 10-7 Nn" hs N e wU ( W m t ' C t ) R, (m) dimensionlesstime ln(dimensionless time) Seconditeration New Heat flow (MW) Casingtemperature('C) Averageannual temperature("C)
ar ("c) l,R(W m-2 "C-t) Nn" factor x L0 7 Nn" hc u (w m-2 "C-1) R, (rn) dimensionlesstime ln(dimensionless time) New heat flow (MW)
0.375 190 250 61, )A)
r.4 82,925 2.2 26.4 0.0152 263 5.570
0.352 184 248 63 23.9 1.4 86,406 2.2 26.1 0.0149 zt5
5.611 0.350
100
1,000
0.256 228 270 4I 26.8 1 40,4'71 1.8 28.6 0.0175 2,001 7.601
0.184 252 281 30 28.5 0.65 18,864 1.5 30.0 0.0188 17,245 9.755
0.t32 268 290 2l 29.7 0.62 1,2,922 t.4 31.1 0.0199 154,030 11.945
0.253 22'1
0.186 252 282 29 28.5 0.65 18,619 1.5 30.0 0.0189 r7,151 9.750 0.186
0.136 270 290 2L 29.8 0.62 12,507 t.4 31,.2 0.0200 t52,638 tL.936 0.136
)AO
42 26.7 1 40,957 1.8 28.6 0.0174 2,016 7.609 0.253
The heat flows just calculatedare essentiallythe sameas thoseat the start of the seconditeration. Summaryof Calculations Heat Loss in MW No tubing With tubing last iteration With tubing first iteration Flat surface Casingtemperature(with tube) ('C) Casingtemperature(no tube) ('C)
0.75 0.350 0.375 0.300
0.44 0.253 0.256 0.095
0.29 0.186 0.184 0.030
0.21 0.136 0.132 0.010
184 311
227 311
252
270 3tl
Jll
The heat lossessummarizedin the upper part of the precedingtable are compared in Figure 2.19. The changeof casing temperaturewith time is shown in Figure 2.20. Note that the scalein this figure is logarithmic and that the linear rate of changeof temperaturebecomesvery small at the right-hand limit of the figure. //,/'\
(t-) \**,RADIAL
CONDUCTIVE HEATLOSSFROMA BURIEDHEATEDCYLINDER
Another thermalconductionproblernof practicalsignificanceis the radialheatloss from a verticalcylinderthat is initially at 7s and that is buriedwithin a mediumat a lower temperatureZn. For example,when steamis injectedinto a vertical steam stimulationwell, a vertical eylindrical region of the reservoir(radiusR7,)can become heated.The pioneeringpaper by Bobergand Lantz (1966)on cyclic steam stimulationassumesthat at the end of steaminjection,this situationprevailsand that during the steamsoakingperiod that follows,heat is conductedradially into the surroundingcolder reservoir.The temperatureof the surroundingreservoiris assumedto be uniform at 7n at the end of injection. The conditionsat the start of the soakingperiod (/ = 0) are thus
and
T=Ts
for0
T=Tn
forR>R,
also, for
t)0,
T=Tn
atR=o.
= 0.6 z
E
o.+ E o
J
6
f o.z 1
10 100 Steaming Time in days
1000
ffi natsurtace m Iniectintocasingffi tnpalntotubeffi tsriteration Well Figure 2.19 Heat Loss from Steam-Iniection
68
Conductionof Heat within Solids
Chap.2
.!
at,
I 35ol
I *01
SteaminsideCasing
9*,1 E,*l
Steaminsidetube
g{
F'*l
sl I '6
roo! 1
I
3
10 30 100 300 SteamlngTlme In Days
1,000
Figure2.20 Temperature of Well Casing
Two solutionsof the radial Fourier equation2.56 are availablewhich satisfy theseconditions. L. Volumetricheatcapacitiesand thermalconductivitiesof the cylinderand surroundingsare equal. T - r^ - t [- --r,,nltuz[t\lJ)d'[J 'Jo'
rr - k=
u
(2'85)
where7 is the volumeaveragetemperaturewithin the cylinder, is the first order "I1 Besselfunction of the first kind, and u is a dummy variable (Boberg and,Lantz 1e66). The precedingsolutionis basedupon an analysisgivenby carslaw and Jaeger (1959,346). The solutiongivenby theseauthorsis moregeneraland alsoallowssiiuationswherethe thermal propertiesof the cylinderand surroundingsdiffer. 2. The thermalconductivityof the cylinderis infinite. This casemay provide a more realisticrepresentation of a coolingsteamchamber. The reasonfor this is that the interior of a steamchambertendsto remainisothermal asit coolsbecauseof the transport of heat from hotter regionsto cooler onesby the evaporationand condensationof water. The solutionfor this casegiven by Carslawand Jaeger(L959,342)is T - To d[J = ! f* .-,ounl,pz (2.86) Tt-T^ r'JnULU where
6 = 2@e)tz -
(pC)^=^^ and 6s : IUJ"(U)- bJlU)1, + luyl(U) - by(U)12 where,16, Jb Ys,andY1are Besselfunctions. RadialConductiveHeat Loss from a Buried HeatedCylinder
69
T-t*
1.0
Ts TR
-
0.8
- -lo.s { .
Qylin6lsphas same properties as surroundings (Equation 2.85)
----
Infinite conductivity cylinder Parameteris b in eq. 2.86 b=2 for equal vol. h. cap.
0.6 0.4
o.2 0
-1
2
.ln.,o (d/Rfr ;
Figure 2.21 Radial Heat Loss from Hot Cylinder
Valuesof the dimensionless temperaturecalculatedfrom equations2.85 and 2.86 are given in Figure 2.21.The broken line is from equationi.ss for the case RadialHeat Loss from Hot Cylinder Equal thermal conductivitiesand heat capacities(equation2.85) d.t
Rl 0.0316 0.0562 0.1000 0.r778 0.3162 0.5623 1.0000 1,.7783 3.1623 5.6234 10.0000 17.7828 31.6228 56.234t 100.0000
70
'"r,,(#) - 1.50 -1.25 * 1.00 -0.75 -0.50 *0.25 0.00 0.25 0.50 0.75 1.00 t.25 1.50 1.75 2.00
T -T^ Ts-Tn
0.'7979 0.7363 0.6525 0.5473 0.425r 0.3023 0.1985 0.1229 0.0732 0.0426 0.0244 0.0139 0.0078 0.0044 0.0025
Conductionof Heatwithin Solids
Chap.2
where the thermal properties of the buried cylinder are the same as those of the surroundings.As would be expected,the heat lossfor this caseis lessthan that for the cylinder having the sameheat capacityas the surroundingsbut an infinite thermal conductivity(solidline with b : 2). The table on page 70 gives values of the dimensionlesstemperaturecalculations for a wider rangeof times than shownin Figure 2.21for equation2.85.
BIBLIOGRAPHY Bonenc, T. C. and LaNtz, R. B., "Calculation of the Productionof a Thermally Stimulated Well," JPT, 1613-1623(December1966). CarsLew, H.S. and Jaecen, J.C.: Conductionof Heat in Solids, Oxford: ClarendonPress (19s9). CLosueN,P.J. and SurrH, R.A., "TemperatureObservations and Steam-ZoneRise in the Vicinity of a Steam-HeatedFracture," SPEJ,575-586(August 1983). DunReNt, A. J. and THalrasvNavacau,R. K. M., "Wellbore Heat Transmissionand Pressure Drop for Steam/WaterInjection and Geothermal Production: A Simple Solution Technique," SPEReservoirEngineering, 148-t62 (March 1986). Fanouo Au, S.M., 'A ComprehensiveWellboreSteam/WaterFlow Model for SteamInjection and GeothermalApplications," SPEJ,527-534(October 1981). FoNtaNILLa,J. P. and Aztz, K.: "Prediction of Bottom-Hole Conditions for Wet SteamInjection Wells," JCPT, 8l-88 (March-April 1982). flasrtNcs, C., Jn., quoted by Annar"rowrrz,M. and SrecuN, l. A., Handbookof Mathematical Functions,National Bureau of Standardsrep. Dover (1965). Hor-laaN,J.P., Heat Transfer,5th Ed., New York: McGraw-Hill, (1981),286-292. Jarcen, J.C. and CLanKe,M.,A ShortTable...,Proc. Roy. Soc.Edinburgh,A6l,(1942) 229-230. JnNsott,V.G. and Jerrnevs, G.Y., MathematicalMethods in Chemical Engineering, New York: AcademicPress(1963),I49-15I. Manruews, C.S. and RusseLq D.G., "PressureBuildup and Flow Testsin Wells," SpE Monograph | (L967). RalaEy, H.J.: "Wellbore Heat Transmission,"IPT, 427-435(April 1962). Rauev, H. J., "How to CalculateHeat Transmissionin Hot Fluid Injection" in Fundamentals of Thermal Oil Recovery,Dallas, Tex.: PetroleumEngineeringPublishingCo. (1965). Serrrn, A., "Heat LossesDuring Flow of SteamDown a Wellbore,",IPl 845-851(July
1e6s).
VocEL, J.V., "Simplified Heat Calculationsfor Steamfloods,"SPE lI2l9, (1982);JPT, lI271136(July 1984). WtLLwuItE, G.P., "Overall Heat Transfer Coefficients in Steam and Hot Water Injection' Wells," SPE 1449(1966).
Bibliography
71
Convective Heating
Wilhin Reservoirs
INTRODUCTION
i ! f
I
t
Chapter 2 discussedthe transfer of heat by conduction;this is a slow process,and many yearsare required for heat to move only a few tens of feet. Approachessuch as the heatingof reservoirsusingwells containing electric or other heatersare ineffective for heating substantialvolumesof reservoirbecausethey, too, dependupon conduction.The transfer of significant quantities of heat to the reservoir by conduction through relatively small heating surfacesis simply too slow. In this chapterthe much more practical alternativeof heatingby the injection For practicalreasons of hot fluids (i.e., by forcedconvectiveheating)is discussed. the choiceof fluid is limited to water:either hot water or steam.Of these.steamis more popular becausemore heat can be transportedper pound and also because steamcan produce a much more stableand completedisplacementof the oil. Reasonsfor this secondadvantageare discussedin a later chapter. In the processesconsideredin this chapter,heat is movedinto the reservoiras latqrltreat in the injected fluid, and, as the fluid passesthrough the sensiblg_and reservoir,heat is given to the cooler surroundings.This transfer of heat produces temperaturegradientsin the surroundings,and these gradientscausethe conduction of heat from the boundariesof the flowing fluid. Thus, wh,i_le !!9 heat is transpg{tqd to the reservoir by fluid convection, thermif CbnduCti6naiso plays-a significant role..Qneimportant mechanismis the conductionof heat awayfrom the heatedreservoirinto the overburdenand underburden.Although conductiontends to be slow, the mechanismis of great importancqbecauseof the vast heatedareas that developas a resultof hot-fluid injection. ''
72
Most of this chapteris concernedwith the processof forced convectivetransport of heat to the reservoir coupled to the dissipationof this heat by conduction through the large heatedareasthat develop.
SIMPLECONVECTIVEHEATTRANSFERWITHOUT CONDUCTIVE HEAT LOSS Considerthe simple,one-dimensionalflow of hot water within the reservoirshown in Figure 3.1.It is assumed,in this section,that there is no heat lossfrom the upper and lower horizontal bounds of the reservoir and that temperatureis a function only of the distance,x, and time, /. It is assumedthat the fluid saturationsdo not changeduring the process;e.g., the oil saturation is at the residual oil level and the water saturation is constant. The fluid flowing out of the differential element,6x, shown in the figure will, in general,be at a different temperaturefrom that entering. The changein the heat flux will come from or go to the inventory of heatwithin the element.A balanceof the heat rates about the differential elementyields
-hnp,C,({ \dx
,6J
= hrrrr({),*
(3.1)
Heat in - Heat out = accumulation This may be rearrangedas
(q) .v.p._c,/{\ =o p r c r \ o xl ,
\ a tl ,
(3.2)
where p r C r = $ - 6 ) p ^ C p+ $ p " C , S , * 6 p . C o S o The term p1C1has the dimensionsof heatper unit volumeper degreeof temperature; it is the volumetric heat capacityof the reservoirand is nol equal to the average density multiplied by the averageheat capacity. Equation 3.2 showsthat for constantpositive valuesof the flow rate, the rate of rise of the temperatureat any particular point is of the oppositesign to the temperaturegradient if the volumetric heat capacityis constant,and is proportional to the temperaturegradient. Equation 3.3, which is the generalsolution of 3.2, describesa heat front that movesalongthe bed at a velocity given by V1.The solution is suchthat any existing temperatureprofile is moved unchangedalong the bed.
T=F(x:Vrt)
(3.3)
whereF is anyfunctionand 't
V.P.Cn PtCr
Simple ConvectiveHeat Transferwithout ConductiveHeat Loss
73
i V
'w
>
I I I
Figure 3.1 In this Figure Z. is equal to the total volumetricflow dividedby area the cross-seciional
+
Figure 3.2 depicts the movementof a heat front along the bed such as would be caised by suddenly raising the temperature of the incoming fluid--to a higher temperature. There are many simplificationsin the precedingderivation which will not be realistic in actual operations.The assumptionof neglectingthe vertical heat losses will be considerediater. Another assumptionis that the solid and fluid are at the sametemperatureat a particular location. This assumptionis sometimesreferredto as thermostaticequilibiium. It is realistic in reservoirscaleoperations,but it is ofbepackedbeds.If heat-transferresistances ten not realisticin small process-type in the included bed are the solids of the within tween the fluid and the bid and/or theory, sharp fronts tend to become spreadout with time' Another phenomenon in the directhat ciuseslongitudinaldispersionof heatis that of thermalc,onduction (seepage47 fronts moving for slow important tion of the fluid flow. This becomes in Figures3.1 shown situation the for example).Despitethesevariousassumptions, at reservoir a through moving front a heat and3.2 haswithin it the basicconceptof a rate which is lessthan the fluid velocity. Overall Heat BalanceAPProach Another insight into the precedingproblemcan be gainedby consideringan overall heatbalancefor the processdepictedby Figure3.2.In this processa quantityof hot fluid at In1 has passedinto the heat front from the left and has left to the right at temperature7n. The heat given up by this hot fluid has heatedthe reservoirin the distince intervalxt - xo.Thesetwo quantitiesof heat maybe equatedas follows: hV.p.C.(Ti':- Z^)(rr- /o) = hpvCl(Ti,1-Zp)(x1- xo) Equation 3.4 may be rearrangedto give (xt - .ro) vr= ur-tr)=
V*p.C, prc.
(3.4)
(3.5)
This is the sameexpressionfor the velocity that was derived previously. Another way of writing equation3.5 is
v,=m=Tffi=
Ho
p1C1(T^i- Tp)
xo
74
x1
x
(3.6)
Figure3.2
Convective Heating within RBservoirs
Chap' 3
In equation 3.6 the numerator, F10,iq the rate of heat iqjection pglurr,it" elosssectional area and the denominator is the heat content of a unit volume of the heatedreservoir above the initial temperatureZn. Steam lnjection Assumethat in Figure 3.1 wet steamhaving a qualityfi and a temperature7s is introduced into the reservoirrather than water. The steamflow rate is I{zskilograms per squaremeter per secondand the latent heat is ,\ kilojoules per kilogram. The water saturation in the steam-saturatedzone may be and probably will be lower than in the original reservoir.We will determine the velocity at which the condensation front will advance. As in the previoussectiona heat balancemay be written that equatesthe injected heat to that stored in the reservoir.As before, this heat balanceusesZn as the basistemperature. l41h(f,I + (7t - TR)C*)(I'- lo) = h(xt - xoX(prCrXZs- Z*) +,\dp"s") '
(xt - xo) (tt - to)
wu,I+(Ts-Tn)C,)
Ho
(ptCt),(Tt - fo) + ,\dp,S"
(A'Cr;,14 - fo) + ,\dp,S"
(3.7)
In the right-handside of equation3.7,the numeratoris the total rate of heat inje_gtion per unit area and the denominatoris the heat per unit volume of hot, steamsaturatedreservoir.This is similar to equation3.6. The term idpJ, is the latent heat of the steamremainingwithin a unit volume of steam-sweptreservoir;it is normally very small comparedto the sensibleheat term and can be neglectedwith little error. -For a given massrate of injection,,FIowill be larger for steaminjection than for hot-waterinjection. Consequentlythe rate of advanceof a steamcondensationfront be greaterthan that of a thermal front producedby the injection of hot water at ry!_l_l the sametemperature.The effect may be evenlarger if the volumetric heat capacity of the steamfloodedreservoir(prC,),is lessthan that of the waterfloodedreservoir becauseof the lower water saturation. An important conclusionwhich may be drawn from this analysisis that becausethe steamfront movesfaster than _awater front producedby the sa-mg*!q6s floy of water, heat is not carried beyond the condensationfront by the.conde4-safe from the steam;the steamcondensationfront catchesand keepspacewith the condensatehot-water front, and the two advancetogether. This phenomenonis discussedfurther later on. LAUWERIER'SEOUATION In many casesin thermal recoverywe are interestedin the lateral conduction of heat awayfrom a flowing streamof heatingfluid. One of the earliestrelationsthat was derived to describea processof this sort is due to H. A. Lauwerier. He considered the situationshownin Figure 3.3. Lauwerier considereda situation in which hot water is flowing in a layer of thickness /r within an oil sand reservoir. As the water flews through the waterLauwerier'sEquation
saturatedzone, heat is lost to the oil sand above and below. The derivation is also applicableto a permeablesand layer which is being heated by flowing water or other fluid and which is boundedaboveand below by impermeablerock. Figure 3.3 showsthe situation modeledby Lauwerier. The flowing water layer has a height ft. Vertical distancesare measuredfrom the centerline.It is assumedthat there is no vertical temperaturegradientwithin the water layer. Water is injected at a constant rate and temperature. A heatbalanceabout the regionof thickness6x gives equation3.8. This is the sameas equation 3.1 with the addition of the last term, which representsthe heat loss to the oil sand aboveand below.
-hnp-c,(#)*= h^r,(#)u'- ,*,(#),=^,,* (3.8 The term pr Cr representsthe volumetric heat capacityof the water layer, as given by
(3.e)
prCr = (I - 6)p^C^ +?p*CnS, * Qp.C"So
The conductionof heatwithin the oil sandis determinedby Fourier'sequation3.10, wherepzCz is the volumetric heat capacityof the oil sand determinedby an equation similar to (3.9).
"(#)=o,r,(#)
(3.10)
Substitutingthe dimensionlessvariablesof (3.11), I
4Kzx hrp.c*v.
I
'o =
t
Yo = 2Y/h
t I T a T
I I I I
I I
to =
(3.11)
4Kzt If P'c'
^ PrCt a= prc, resultsin the following systemof equations
Figure 33 Lauwerier's Problem Initial Boundary Conditions rf=Ti=0att=0 Ti : 1 forx = 0 at t > 0
ConvectiveHeatingwithin Reservoirs
Chap.3
For lypl > 1:
4#)=(#) -(#)=' (#).(#)
Forlyrl = 1'
(3.r2)
(3.13)
andTf = 7;
rr =rt =roll;;:3
For rp = 6;
(3.14)
These equationswere solved by Lauwerier to give equation 3.15,which expresses the temperaturewithin the oil sand layer as a function of time and location'
zi' = *"(ffi^ rrxo< to then
.)
(3.1s)
and if xo > to then ?| = g the temperaturewithin the water layer is found by substitutinglo: equation3.16.
I to live
If xo < to then ?i =
"rf.(--+) \2Y 0(to- xr)l and if xp 2 tp then ?i = g
(3.16)
Figure 3.4 showsthe temperatureas a function of distancewithin the water layer for variousvaluesof time plotted using the dimensionlessvariablesjust shown with 0=1. 1 g 0.8 E G o
CL
E 0.6 o o
8E 0.4 o
e o.2
.E oo 00.5
1 1.5 Posltion x D Dlmenslonless
Equation Lauwerier's
Figure 3.4 Reservoir Temperatures Calculatedfrom Lauwerier'sEquation 77
Numerical ExamPle Hot water at 200'C is injected into a water layer 4 m thick containedwithin an oil sandreservoirat a rate;f 10 m3/h. The flow from the well is radial.The following propertiesmaYbe used: Porosity0.30; Tr : 10'C Water laYer; S, : 1.0 Oil sand:S, : 0.3; S, : 0'71 K :1'2 Btu/h ft'F Rock: heat capacity0.2 Btu/lb "F: SG = 2.2 Oil: heat caPacitY0'5; SG : 0.95 Lauwerier'sequation, as derived before, can be employedfor a radial systemif the a dimensionaldistanceis redefined.Plot the temperaturewithin the water layer as and 100, 10, of for times well injection the from R distance function of the radial if 1000days.Also plot the temperaturedistribution that would have been obtained temperathe Plot underburden. and overburden the to there hid been no heat loss well located ture distribution that would be expectedin a temperature-observation and below above oil sand in the temperatures Include 10 m from the injection well. the water laYer. Solution 1. Lauwerier'sequationin radial coordinates
oR=o(nR2)=2nRdR
- o.o,r,(#) oo:, o,r,(#) dA- 2K,(Ty),=,,0n (3.r7) Heat stored
Heatfrom water
Heat loss
hv"' This is similar to equation 3.8. ,4 has been substitutedfor x and Qn teplaced i'e'' substitutions; these making The solution can thus be written immediatelyby
*o =
4Kzx
6;Ci,
becomes
=
4KztrR2
"o ip,c,e,
(3.18)
andyo, tp, ?nd 0 are unchanged. Calculation: The results are given in the following tables' a. Temperature in the water laYer ConvectiveHeatingwithin Reservoirs
Chap' 3
Column3
'o :
4K2rrRz
(h p *c,e,)
Kz = 1.2Btu/h ft oF = 28.8Btu/d ft .F h=4m=13.123ft p.C, = 62.4Bfifft3 'F Q* = ro m3f h = 847.4ft3ld Column 4 t^
=
-
4Kzt
h'prC,
p,C, = 62.4x 2.2 x 0.2:27.46 Btuft3 "F prCr = 6p,C* + (1 - 6)p,C, = 37.94Btu/ft3'F S, = 0.3; So = 0.7 poCo= 62.4x 0.95x 0.5 :29.64 Btufr3.F pzCz= 65,p,C, I gS',p,Co+ (1 - 6)p,C, = 31.10Btuft3'F
o=P'l'= 1.221 Pzvz
Xp, x ='j l 7 (ro _ *d l -',,
Temp (in col.2) = 10 + 190erfc(X)
Radius(ft)
Temperature('C)
XD
Time:10d to=0.176 0 10 20 30 40 50 60
200.0 198.8 194.9 r87.4 t73.6 t42.4 10.0
0.000 0.00s 0.02r 0.047 0.083 0.130 0.188
0.000 0.006 0.024 0.059 0.r24 0.275
Time= 100d tD -- 1.763 0 10 20 30
200.00 199.6 198.5 196.5
0.000 0.005 0.021 0.047
0.000 0.002 0.007 0.016
Lauwerier'sEquation
79
continued
Radius(ft)
40 50 60 80 100 L20 140 160 180 200 Time = 1000d tD -- L7.631 0 10 20 30 40 50 60 80 100 120 160 200 250 300 350 400 500 600
rature ('C) 193.8 190.1 185.5
l'73.r 155.3 130.3 95.0 46.4 10.0 10.0
200.0 199.9 199.5 198.9 198.1 r97.0 195.6 r92.2 187.8 t82.3 t68.2 r49.6 r20.6 86.7 ) 2.5
25.2 10.0 10.0
0.083 0.130 0.188 0.334 0.522 0.751 1,.022 1.335 1.690 2.086
0.029 0.046 0.068 0.126 0.2r2 0.338 0.537 0.923 2.822
0.000 0.005 0.021 0.04'l 0.083 0.130 0.188 0.334 0.522 0.751 1.335 2.086 3.259 4.694 6.389 8.344 13.038 18.774
0.000 0.001 0.002 0.005 0.009 0.014 0.020 0.036 0.057 0.083 0.150 0.239 0.389 0.590 0.862 1.239 2.7s2
The predicted temperaturesin the reservoir are plotted againstthe distancefrom the injection well in Figure 3.5 for 10, 100,and 1000days' b. Temperaturein observationwell at R : 32.8ft (10 m) Golumn 4 Height abovewater sand in feet
Golumn3 Vn-
80
height -"| = h/2
ConvectiveHeatingwithin Reservoirs
Chap' 3
oo tso
; J
6 100 o CI
-
o t50
600
Figure 3.5 Predicted Temperaturesin Reservoir as a Function of Distance from Injection Well
Column2 1=
xD+ yD-l
- *df''' 210(tD
The other columns are as before. TEMP'C
to-1
184.3 106.0 51.6 23.9 13.5 10.7
Tirne= 10d; to = 0.176; xa = 0.056 0.073 0.000 0.47r 0.305 0.869 0.610 r.267 0.914 1,.664 1.219 2.062 1.524
195.8 t51.4 111.1 77.6 52.2 34.4 23.1 16.5
Time = 100d; to = 1.763; ro : 0.056 0.019 0.000 0.231 0.610 0.442 t.2t9 0.653 t.829 2.438 0.864 1.075 3.048 t.286 3.658 t.497 4.267
r98.7 184.6 170.'7 157.0 r43.6 t30.7 118.5 106.8
Time = 1000d; to -- 17.631;xa = 0.056 0.006 0.000 0.072 0.610 0.138 t.219 0.203 1.829, 0.269 2.438 3.048 0.335 0.401 3.658 4.267 0.467
Height(ft)
0 2 4 6 8 10
0 4 8 t2 16 20 .A
28
0 4 8 t2 16 20 24 28
The calculatedtemperaturesin the observationwell are plotted in Figure 3.6. Equation Lauwerier's
81
oo 150
; E roo o c o F50
01020 Helght abov€ water sand In feet
Figure 3.6 Predicted Temperaturesin Observation Well
c. Temperaturedistribution for no loss Heat Balance Q,p*C,(Ts - Ta)t = nR2hprC t(Ts - Ta) p = (Q*P'c*t|n \ rhPrct I
This equationyieldsvaluesofR = 58.1,183.7,and 581.4ft for 10,100and 1000days. Thesevalueshave been plotted as dotted lines in Figure 3.5. Note that the noloss radiusoccurswhenxo : 1o. THERMAL EFFICIENCYFORCONSTANT.DISPLACEMENT RATE STEAM.DRIVE Considerthe steam-drivesituation shown in Figure 3.7. Steamis injectedfrom the left side at a rate sufficientto causethe heatfront to advanceat a constantrateA. The shapeof the heatedareaA is not specified. The specification of the problem requires that the steam-injectionrate be raisedcontinuouslyto compensatefor the increasingheat losses.It is assumedthat the temperatureZs in the steamchamberis constantup to the front, where it falls abruptly to Zn.This assumptionis reasonableuntil the time when all the latent heat in the steamis consumedby the heat lossesand only sensibleheat is hvailableto advancethe heated region. The time at *hich this situation occurs is calculated later on. Rateof heatloss
Steam -4_----->
Figure 3.7
82
Conductive Heating within Reservoirs
Chap. 3
reservoirsurfaceof area2A (A at fhe cqgplafiye-heailossjrom-the-heated the top_gflhe reservoirand,4below)maybe calculated from equation2.27.
etc=r(! *,nt,-rr/h)
(3.1e)
where the subscript2 refers to the over- and underburden. The cumulative heat required to raise the reservoir and its residual contents from the initial temperatureZn to Zs is
(3.20)
Qrc= prCthA(Ts-Tn) where pl Cr is the volumetric heat capacityof the steamedreservoir.l The total cumulative heat injected is thus
f'\ lq Q,c: Qrc* Qn = z\!' x,eC' - ril\,1,*)
* ,,cftA(rs - rR)
(3.2r)
The instantaneousrate of heat injection may be found by differentiating equation 3.2I with respectto t.
.l
L
Ho=A(Ts-TR)14K, \
,*
+ ercrh)
(3.22)
The heat-injectionrate is equal to the sum of the losses(which increasewith the squareroot of time) plus the constantheat rate to expand the steamchamber. At the critical time t", when latent heat is no longeravailableat the heal,ftlr{rJ, the lossesare all suppliedby the lltent heat. When this occurs, the ratio of heatlossrate to stored-heatrate will be equal to the ratio of the latent heat injection rate to the sensibleheat injectionrate; i.e., I l-,1
lo*'r,l**) -- H^
Ho- H^
[prcrh]
,,=no,(ffi^#)'
(3.23)
For times lessthan t", latent heat is availableat the heat front, and a sharp temperaturegradient is maintained. The critical time is proportional to the square of the reservoirthickness,and it is independentof the rate. The fraction of the injected heat that remainsin the reservoirmay be looked upon as a thermal efficiency. It is given by -
Qt'
"o= en \
PtCth
x
ptCrh+ ;' 5
f,
K, r/|
7Td2
1, = __________;_
(3.24)
4 1.I ----'=' X 3Yzr
lThe value of prCrused in this equationis for the steamedreservoir-i.e., with fluid saturations correspondingto the depletedreservoir.The displacedfluids are cooledto the reservoirtemperatureas they pa$ through the heat front. Thermal Efficiency for Constant-displacement Rate Steam-drive
83
where nv -- -
2K,
t
,rcrh
Qz
Thedimensionlessterr.rXinequation3,2!isthesamevariableusedbyMarxan section' i" the descriptionof their theory in the next Langenheim;it also "rir". Otherwrite,,of,-*-"-ploythedimensionlesstime/o,whichisthesquare of X. 4K2P2Czt 4KZt (3.25) = x-" =
to
( i- cr n) hr = hr ( pr ci
IfthevolumetricheatcapacityoftheoverburdenandunderburdenarethesameaS tor tDcan be simplified to equation3'26' that of the steamzone,then the expression accurate' This approximationis often sufficiently then fP =
lf.prCr = PzCz,
4q.rt
(3.26)
i
also be expressedas The simplified dimensionlesstime, tp, rfrz! 4ozA
ro= -Ftr
(3.264)
Thethermalefficiency,E;,isplottedagainstthedimensionlesstimeinFigure3.8 dearea,A,increases)the thermal efficiency As time increases(o, u, tt" flooded inthe supply to of tire steamis required creases;i.e., a larger and larger fraction creasingheat losses. Theheightofthereservoirisaparticularlyimportantvariableinthedimen. inherently is squared.rire ttrirmal efficiency is sionlesstime becaus" iirl"r"" to corresponding '4 of ones.Smallervalues hieher for thick reservoirsthan for thin by
;r5.;;ffi;"r"g,
for a givenrateasmeasured prt"iJ" nign"refficiencies
"r* alsogivebetterthermalefficiencies' l. Uigh", heatinjectio;;".1i.e.,iigtrer,,i) ue Jmployedas an approlimationif If ,,4is not consrant,Figure3.g can stitt ro' The critical riln" i. ruu?itutedinto (r:o in order-tocalculate the total steaming
0.8
E o.t .9
E o.o o.2 0
84
0 Log19(t9)
2
Fisure 3.8 Valuesof Thermal EfficiencYFactorEr, for Constant DisPlacementRate
Reservoirs Conductive Heating within
ChaP' 3
time, t", from equation 3.23 can also be expressedas an equivalent dimensionless time toc given by -
arl
H,
toc=Xi=il:l
\2
+ 1Hs- H;l
(3.27)
Fraction of Heat in Steam-Saturated Chamber After the Critical Time -
2K2(Ts- To) fo' Yrraz
2K2(Ts- 7h) [" ----)dto Jg Yt-to Yra2
dAs
Jo \/t-tn
where /6 is the birth time of dA andl
is constant. Hence,
- \/t - r,)
a^ '' =!!{{14(\,, lrqz
(3.28)
where/5 is the birth time of the limit of As ar time t.
+ p,c,h\ Ho= )(rs- 7^1(+x, rlt Ytrdz \ I H^ Ho
(3.2e)
(3.30)
T, \
"*-
. Prcth 4K"
which reducesto 1 -
Ht
-t
T1 A- - -"- : A
V'
Ho
1, 1 +2
t:
(3.31)
t;
where
,o=5!44 h'(P' C t)' If As : A (3.31)becomes(3'27). In general,if tD > toc then (3.31)can be manipulated to become
2='n-n' where
n=
'.+c 1
(3.32)
(3.33)
lr
r*z!,* Rate Steam-drive Thermal Efficiencyfor Constant-displacement
85
Asymptote lor AslA if fp = o' The ratio,4sfA approachesa constantvalue for large times. This can be calculated as follows. Ht ft.-
:
1+ and
I
(3.34)
Ho
t
c).=- (*o)' nH^
"H,
(3.3s)
RATE: FoRcONsTANTSTEAM-lNJEciioN EFFTCTENCY THERMAL THEORY MARXANDLANGENHEIM'S imporMarx and Langenheim(1959)developedtheoretical relations describingthe of tant caseof a growing steamzone tirat is limited in its growth rate by the loss introheat to the ovJrburden and underburdenand by the rate at which steam is for duced.Their theory is similar to that describedin the previoussectionexcept rate a the assumptionthai the steamis introducedat a constantrate rather than at has equation Langenheim's and Marx rate. advance frontal that providesa constant important it is and field, this in studies subsequent the formed a basisfor many of to gain an understandingof it. by Marx and Langenheimis shown in Figure 3.9' The situationcons-idered rate into a steamzone that is spreadinglaterally. constant Steamis introduced at a this zone is specifiedas input to the problem' into 110, The rate of heat injection, in the growing steamzone and the losses stored heat the The heat goesto intrease that no heat is transferredahead assumed It is to the overburdenand underburden. is realistic only when the laassumption this previously, of the front. As discussed supplyall the losses-i.e.' to is sufficient steam tent heat suppliedin the injected condition will usually This front. heat the at when there is still latent heit arriving obtained' is being ratio steam to oil be satisfiedif a reasonablyhigh The areal shapeof th" it"urn zone is not specified.In the original theory it can was assumedthat the condensationfront remainsvertical, but this assumption Rateof healloss
TH
6A formedat tO to t0 + 6tO
86
-. condensate
Figure 3.9 Conductive Heating within Reservoirs
Chap' 3
be relaxed;this is discussedlater in this chapter.within the steamzone,the temperatureis assumedconstantat rs. outside it is zn, as shownin Fieure 3.10.
A
Figure 3.10
At any intermediate time / the vertical heat loss rate per unit area will be larger near the front (seeequation2.24). Equation 3.36 gives the rate of heat loss from the area26A (61 aboveand 64 below),which was initially heatedat time /0. The time /s can b€ looked upon as the "birth time" of any particular heatedarea.
6- Q r = Z A I E W
(3.36)
Vrd2G - to)
The total rate of heat loss,Q1, is found by integrating(3.36)over the whole area,as in (3.37).The time at which the elementof areawas formed,/6, is a function of ,4; alternatively,A may be considereda function of /e, and the variable of integration may be changed,as shown: dA=
Or:tf
(#)",
K2(Ts - TR)
ftdr(t
-T,;r
Equation 3.38 definesQ,, the rate at which heat is being stored as sensibleheat in the reservoir.
(3.38)
Qs=PrC&(Ts-ri4 dt
The overall heat balancefor the processis given by equation3.39.It may be solved by Laplace transformation,solution of the resulting algebraicequation for -4, and inversionof the transform to give,4(r). The inversionof the transform may be carried out by comparisonwith a table of standardforms.2
Ho= 21,' {ffi4(#)", Injection=
loss
- ril# r p1c1h(rs +
(3.3e)
storage
The solutionof (3.39)leadsto'theresultshownin equation3.40.The theoryfor this problemis similar to that developedby Carter for the growth of a fracture with side zSeeCRC Standard MathemnticalTables(22nd Ed.), Transform 45, page 510. Thermal Efficiency for Constant Steam-injection Rate
g7
leakageand a constantinjection rate (Carter 1957),and the mathematicalform of the problem is identical. ' A(t) = -
H o p r Ct h (".' z p z C z ( T s- 7]R)
erfc(X)+ 4
Yr
- ')
(3.40)
where
x=
2K' p r C t h Yq z
tn
Equation 3.40 gives the heatedarea as a function of time and differentiation gives the rate of area growth: dA dt
Hsex'erfc(X) p(th(Ts - Tn)
(3.41)
The rate at which oil is displacedfrom the steamzone may be calculatedby multiplying the rate of increaseof the volumeof the steamchamberby its porosityand by the changein oil saturation:
q,=hQ(S"-t)#
(3.42)
The residualoil saturationSoain the steamzone is usually quite small; typical valestimateif no other data are availuesare 0.05-0.2.A valueof 0.1_5isa reasonable variableX is employed.This is dimensionless the and 3.41 able.In equations3.40 It is the samedimensionless Langenheim. and Marx by the variable that was used to as the dimensionless X2 is referred Frequently earlier. group that was described time /a.
^
4K1t
to=X-=Trp*=
(3.43)
If the volumetric heat capacityof the overburdenand underburdenare the sameas that of the steam zone, then the expressionfor to ca;ltbe simplified to equation 3.44. 4azt
. tD = --;'-
n-
(3.44)
The fraction of the injectedheat that remainsin the reservoircan be determinedas a function of the dimensionlesstime by meansof equation3.45 or from Figure 3.11.
. ,l-b - tf u,= Ilr'""rrc{t/-t"l
(3.45)
The curve in Figure 3.11showsthat the fraction of the heat lost from the reservoir varies over a large rangewith the variable /o; this is proportional to time. As time continues,the fraction of the total heat injectedthat is lost grows. It should also be noted that there is only a slight differencebetweenthe curve drawn for a constant 88
ConductiveHeatingwithin Reservoirs
Chap' 3
1
-
o.B
o o E I!
-'-
o
u.a
tr 0) !
a a
t-- u.z
Figure 3.11 Comparisonof Thermal Efficiency.Eafor Constant Heat-InjectionRate and for Constant Displacement Rate
-202 Lo91s (tp )
injectionrate (i.e., from equation3.45) and that for a constant displacementrate from the much simplerequation3.24. Numericalvaluesof the term e'o erfc(f tp) or e*'erfc(X) in (3.45)can be obtained from Table 3.1. In computerprogramsthe rational approximationsdeveloped by Hastingsgiven on page35 may be employed. A major factor is that as time goeson and more and more steamis introduced (recallthat it is assumedthat the injectionrate is constant),the steamzonecontin-
TABLE 3.1 Valuesof the Functionex'?erfc(X) X
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65
q19 0.75 0.80 0.85 0.90 0.95
ex'efic(X)
1.000000 0.945990 0.896457 0.850936 0.809020 0.770347 0.734599 0.701496 0.670788 0.642252 0.615690 0.590927 0.s67805 0.546181 0,5:259i0, 0.506938 0.489101 0.472327 0.456532 0.441641
X 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 L.45 1.50 1.55 1.60 1.65 L.7g 1,.75 1.80 1.85 1.90 1.95
ex'erfc(X)
0.427584 0.4L4299 0.40r73L 0.389826 0.378537 0.367822 0.357642 0.347960 0.338743 0.329960 0.321,s84 0.313590 0.305952 0.298650 0.291663 0.284973 0.278561 0.272413 0.266513 0.260847
Thermal Efficiencyfor ConstantSteam-injectionRate
ex'erfc(X)
2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 ?.70 2.75 2.80 2.85 2.90 2.95
0.255403 0.250L67 0.245130 0.240281 0.235610 0.231108 0.226766 0.222576 0.218532 0.?r462s 0.210850 0.207199 0.203668 0.2d02sr 0.196943 0.193738 0.190632 0.187622 0.184702 0.181869
89
uesto grow, and a larger and larger areaof overburdenis heated.Eventually,nearly all the injected heat iJ Ueinglost. The thicknessof the reservoir,/r, is the most significant iactor involved in the expressionfor /o, since its value is squared' As an exampleof the useof Figure 3.11,considerthe caseof a reservoir100ft thick. Assumethit the thermal diffusivity of the reservoirand the overburdenare both 0.9 ftzfi. fhe horizontal scalein the figure correspondsto valuesof rp varying The correspondingvaluesof real time in days,for this rangeare from 0.001io 10001 given by hztpf4a,or 2778to: 2.8 to 2J78,000d. For a reservoir10 ft rather than IOOft tiri.t, the correspondingtimes are smaller by a factor of 100.
r days for h : I00 I days for /l = 10
0.001
0.1
2.8 0.028
2',78 2.8
1000 27,780 278
2,'778,000 27,780
NumericalProblemUsing Marx'Langenheim'sEquations : PzCz:33 Btuft3 "F), For the two differentcases(h = 10 and 100ft and ptCt assume: 6 = 0'35 Tn: 75"F S, : 0'7 So,: 0.15 measuredat 75"F Seventy percent quality steam is injected at a tate of 800 Bld at a pressureof 500 psia. Calculatethe following for eachreservoir thickness: 1. The area of the steamzone is acresas a function of time 2. The radius of the steamzone, assumingthe steamzone is cylindrical 3. The volume of disPlacedoil 4. The ratio of displacedoil rate to steaminjection rate 5. The ratio of cumulative displacedoil to cumulative injected steam Plot thesevariablesagainsttime for eachof the reservoir thicknesses. ForX > 3, use 2t e''- erfqX) : ---F'
\/r X+\E+2
(3.46)
Solution The solution to this problem is given in Table 3'2' 90
ConductiveHeatingwithin Reservoirs
Chap' 3
TABLE3.2
YEARS
'D
Height= 100ft 0.00 0 0.50 0.07 1.00 0.r3 1.50 0.20 2.00 0.26 2.50 0.33 3.00 0.39 4.00 0.53 5.00 0.66 6.00 0.79 7.00 0.92 8.00 1.05 9.00 1.18 10.00 1.31 Height= 10ft 0.00 0 0.50 6.57 1.00 13.r4 1.50 t9.71 2.00 26.28 2.50 32.85 3.00 39.42 4.00 52.56 5.00 65.70 6.00 78.84 7.00 91.98 r05.t2 8.00 9.00 1,18.26 10.00 L31,.40
ACRES
RADIUS (ft)
CUMULAIIVE VOLUME (B)
0 99 136 162 183 201 217 245 268 288 305 322
0 0.71 1.33 1.89 ) a') 2.93 3.41 4.32 5.t7 5.97 6.73 7.46 8.16 8.83
JJt)
350
0 2.7r 4.t9 5.34 6.32 7.19 7.98 9.38 10.62 tt.74 12.77 t3.73 14.63 15.48
0 L94 241 272 296 3t6 333 361 384 403 ta1
436 450 463
BPD
osR
CUMULATIVE OSR
0 105,887 t97,965 282,630 362,0t1 437,267 509,139 644,675 771,442 891,128 1,004,989 1,1r3,876 1,218,450 t,319,229
694.20, 531.54 48152 448.18 422.96 402.66 385.68 358.39 336.99 319.48 304.74 292.07 28r.00 27r.20
0.868 0.664 0.602 0.560 0.529 0.503 0.482 0.448 0.421 0.399 0.381 0.365 0.351 0.339
0.868 0.725 0.678 0.645 0.620 0.599 0.581 0.552 0.528 0.509 0.492 0.477 0.464 0.452
0 40,495 62,547 79,786 94,433 107,393 rt9,t43 140,059 158,528 t75,249 190,640 204,97',| 2r8,449 23r,198
694.20 144.21 106.43 88.86 78.17 70.77 65.25 57.40 51.97 47.92 44.74 42.t5 39.99 38.15
0.868 0.180 0.133 0.111 0.098 0.088 0.082 0.072 0.065 0.060 0.056 0.053 0.050 0.048
0.868 0.277 0.214 0.182 0.162 0.t47 0.136 0.r20 0.109 0.100 0.093 0.088 0.083 0.079
Data: Thermal diffusivity: a : 0.9 ft2ld pC : 33 Btuft3 "F Heat capacity: Porosity: d : 0.35 Tn: 75'F Ts = 467'F from steamtable S" : 0.7 So.: 0.15 Steamrate : 800 BPD : 800 x 350 : 280,000lb/d Height h = 100ft
and 10 ft
ThermalEfficiency for ConstantSteam-injection Rate
two cases 91
1205Btu/lb 450 Btu/lb 43 Btu/lb
Enthalpy of vaPor Enthalpy of liquid at T5 Enthalpy of liquid at Tn Quality = 70Vo
from steamtables
Heat-injectionrate : 280,000(0'7x 1205+ 0'3 x 450 43) = 2.6194x 108Btu/d Column 1 in table:Time in Years Column 2: Dimensionlesstiine (equation3'44) to = 4 x0.9 x Yearsx 3651h2 Column 3: Area in acres(equation3'40) Areal(2.6194x 108h)/(4 x 2g.7 x 392 x 43,560)lf(tD) f(o) = (e*'erfc(X) .'l \Vzrl
- t\
(43,560ft2 = 1 acre)
and X = \/G
Colurnn 4: Radius in feet Radius = [(Col 3 x 43,560)lrrlos Column 5: Qumulativebarrelsdisplaced = A x 43,560x /t x 0.35 x 0.55/5.615 (5'615ft3 1 B) equation3'41) Column 6: Barrelsdisplacedper day (equation3'42 using 800' by 6 divided is column Column 7: Oil-steamratio 800 x years x 365' Column 8: Cumulative OSR is column 5 divided by
3.l2and the instantaThe heatedareasare shown as functionsof time in Figure 3.13.The heatedarea neousand cumulativeoil-steamratios are shown in Figure the thicknessis g.o*. onrv aboutT}Tofasterfor the thinner reservoir,even though lossesare a heat vertical ieduced by a factor of 10. For the thinner reservoir the muchlargerfractionoftheheatinput.ThisisShownclearlybythecurvesi 20 o
heightin ft' is reservoir Parameter
3ts 'S ,o
fo; s Tlme In Years
92
Figure 3.12 Heated Area as a Function of Time
ConductiveHeatingwithin Reservoirs
Chap' 3
1
t -- - - - - . loorl 10ft
0'8 .9 .E E 0.6 E (!
fino o
|
|
Cumulative
.r.
, o.2 \'...-
cumutative Gumulative I Instantaneous \-.:::::::::--=--=----a--y'_-;::::::::::::::
od*
46 Tlme In Years
Figure 3.13 DisplacedOilSteam Ratios
10
Figure 3.13.The point on the vertical axis marked "No Loss" correspondsto the maximum possibleoil-to-steamratio requiredby a heatbalancewith no heat losses. It can be calculatedby equation 3.47. While both setsof curves start at the same no-losspoint, the curves for the thinner reservoir drop very much more rapidly. OSR."" =
/{sd(s"- s,,) p1C{Ts - Tp)
(3.47)
In the equation,F/s is the net heat per unit volume of steammeasuredas water.
SIMPLEFORMULAS FOR ESTIMATIONOF THE OIL.STEAM RATIO Often the physicalpropertiesof reservoirsare known only approximately,and simpler formulas may suffice to provide initial estirnates.One approachis to basethe estimate upon equation 3.21,.The cumulative injected heat given by (3.21),correspondsto a cumulativequantity of displacedoil of @AS,hA.^fhe oil-steamratio is thus
(3.48)
If it is assumedthat the thermal propertiesof the reservoir and of the overburden are equal,then (3.48)becomes
oSR= or**"(
';l -\
l*;
8 1
Simple Formulasfor Estimationof the Oil-steamRatio
(3.4e)
-l
rrh2|
93
Ifnumericalvaluesforlls,pC,andaequaltothetypicalonesusedinthepreviou exampleare emPloYed,namelY, pC = 33 Btuft3'F Hs = 58,375Btuft3 a = 09 ft2/d then equation3.49maYbe written
oSR=ffi
17696LS"
(3.50)
where { and AS' are fractions Is and Tnare in degreesFarenheit t is in daYs h is in feet
equation3.50with h : 100ft for The following valueshave been calculatedusing valuestaken from Table3'2' the previousnumerical example;they are compalredto OSR from (3.42)
Years
OSR from Table3.2
0.868 0.581 0.492 0.452
0.868 0.590 0.504 0.466
0 J
7 10
A s w o u l d b e e x p e c t e d f r o m t h e c o m p a r i s o n o f t h e e f f i c i e ntoc ythose c u r vfrom e s s hthe own are quite close Figure 3.11,the resuttstiom the simple formulas Mirx-Langenheim equation' that heat vogel.is discussedin which he suggests In chapter + u ffi'uy immedispreads that the steamchamber lossesshouldbe calculatedby assumrng atelvacrossthetopofthereservoir.Thisresultsinanequationsimilarto(3.4 wtricir ttre factor B/3 is replacedby 4'
oSR= osn,""/--l--r
\ + * rl#, I \r
f"t immediatesteamspreading
(3'51)
[fthesamenumericalvaluesareusedforthephysicalproperties,thisbecom
I
osR=l-l
ttog'das,
I
(3.s2
L,n-r^)lt+2:41F)l sameas in equation3'50' where the units for the variablesmust be the 94
ConductiveHeatingwithin Reservoirs
Chap' 3
CONVECTIVETRANSFEROF HEAT BEYOND THE CONDENSATIONFRONT In the Marx-Langenheimtheory and in the previous numerical example,it is assumedthat no heat is transferredbeyond the heat front-i.e., that at the front the steamgives up all its heat, both latent and sensible.This idea is consistentwith the ideasdevelopedearlier,whereit wasshownthat the velocity of a condensationfront is greater than that of a thermal front carried forward by the sensibleheat of the condensatealone. Thus any heat carried before the condensationfront tends to be 'bverrun," and the two fronts remain combined.The assumptionof a single front madeby Marx and Langenheimis reasonableif there is still vapor left to condense at the front. However, the situation changesas the front becomesmore remote, since eventually all the steamis condensedby heat lossesbefore the heat front. Sincethe steamzon'eis at the steam-saturationtemperaturethroughout,3the only source of heat to supply the vertical lossesabove and below the zone is the latent heat of the steam.At the point where the latent heat has been completely consumedto supplylosses,the only remainingheat to be carried forward is the sensibleheat in the liquid water, and the processbecomesrather like that of Lauwerier, which was discussedearlier.It is not identical,however,becauseas the heatlosses are transferredto the overburdenand to the underburden,the rate atwhich steam mustbe condensedto supplytheselossesdecreases and excesssteambecomesavailableto advancethe condensationfront further. Thus eventhough essentiallyall the latent heat of the steamis being usedto supplythe vertical losses,the condensation front still advances;at the same time, substantialquantities of heat are carried beyond the condensationfront by the sensibleheat of the condensateand the heat front passesbeyond the condensationfront. Figure 3.14is a qualitative representation of the situation. Mandl and Volek (1969)and Hearn (1969)were the first to recognize this phenomenon;they each developedan equationthat predicts the time, /", at which it occurs. Let Hl be the rate at which latent heat is injectedinto the reservoir.The total heat-injectionrate is still taken as.F/0.AJ the critical time the latent heat-injection rate is just equal to the vertical heatJossrate. If this is so, then the rate at which heat is being stored must be equal to the rate at which sensibleheat is being injected-i.e., to FIo - I1r. This is shownby equation3.53,which reducesto equation 3.54.
= ptCth(Ts- Tn)Hyex'zerfc(X) -
Ho- H^ = Qs = p(ft(Ts - rf#
| -
prCth(Ts Ta)
*=
ex? efic(X")
(3.53)
(3.54)
'The steamtemperatureis assumedconstantin this chapter.In actual practicethere tendsto be a small reductionin steamsaturationtemperature,which is causedby the pressuredrop as the . steamflows awayfrom the injectionwell.
ConvectiveTransferof Heat beyondthe CondensationFront
95
_---_>
i Cond.i HeatFront i rtont i (fort > t.)
Latentheatis availableat AND STEAMOUALITYBEFOREtC TEMPERATURE
AND STEAMOUALITYAFTERI TEMPERATURE Steamcondensesbeforeit Figure 3.14
The critical time may be found by solvingequation3.54for the value of X" that correspondsto the particular value of.Htf Ho and then obtaining the time by the use of (3.43)or (3.44). equation ' Equation 3.54 was derived by Mandl and Volek (1969)and almost simultaneouslyby Hearn (1969).For given valuesof I{r and 110,the critical dimensionless time can be found by interpolation of Table 3'1' SIZE OF STEAM ZONE FOR TIME GREATERTHAN THE MANDL AND VOLEK'SCRITICALTIME Beyond the critical time, the vertical loss from the steamzone is given by equation 3.55,where-,4srefers to the area of the steamzone'
H", = fJsn " W a l
\/ rrazt - te)
(3.5s)
The time L at which the areadA of.the steamzonewas formed is found by calculating time as a functon of area from equation3.56. A(tn1=
96
HoptCth
4KzpzCz(Ts
^f(x)
ConductiveHeatingwithin Reservoirs
(3.s6) Chap' 3
where
x =
2K' p1C1h\/ a2
\/,
*4 r r l*'e rfc( X) f(X .)\=\ / (e
- t\
This time may then be substitutedinto (3.55)and I{ calculatedas a functon of ,45 by evaluatingthe integral. From this the value of,,45may be determinedfor specific valuesof I4. This procedurewas followed by Hearn, who expressedhis resultsby equation3.57. As=
As=
HoprCrh
4K\gs
'(.,ft)
(3.s7)
_ ?]R)
HsP1Cft 4K2p2C2(Ts- f^)
'(.,*)
Hearn'sfunction F is given by Table3.3. For times lessthan the critical, F is identical to f. TABLE 3.3 Values of flXl' andrk,L\ 'Hol \
Values ofF for various 111/116
X 0.2 0.4 0.6 0.8 1.0 r.2 1,.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0 10.0
f(X) 0.035 0.L22 0.245 0.392 0.556 0.733 0.918 1.111 1.310 1.512 2.032 2.566 3.105 3.650 4.200 4.753 5.863 6.978 8.097 9.218 10.340
0.6 0.035 0.103 0.r7r 0.240 0.309 0.378 0.448 0.517 0.586 0.656 0.829 1.003 1.t77 1.351 1.525 1.699 2.047 2.396 11AA
3.092 3.441
0.035 0.12L 0.22L 0.321 0.422 0.523 0.624 0.726 0.827 0.929 1.184 1.439 1.694 1.949 2.204 2.460 2.971 3.483 3.995 4.506 5.018
0.035 0.t22 0.243 0.372 0.502 0.632 0.762 0.894 1.025 1.156 1.485 1.814 2.1,44 2.475 2.805 3.136 3.798 4.460 5.L22 5.785 6.447
0.035 0.122 0.245 0.392 0.546 0.702 0.858 1.016 t.173 1.330 1.726 2.122 2.518 2.915 J.JIJ
3.710 4.506 5.303 6.099 6.896 7.693
0.035 0.122 0.245 0.392 0.556 0.732 0.910 1.089 t.268 1.448 1.899 2.352 2.806 3.260 3.714 4.169 5.079 5.990 6.902 7.8t4 8.726
0.7 0.035 0.122 0.245 0.392 0.556 0.733 0.918 1.111 1.308 1.506 2.002 2s01 2.999 3.499 3.999 4.500 s.503 6.506 7.510 8.514 9.518
0.8 0.035 0.122 0.245 0.392 0.556 0.733 0.918 1.111 1.310 r.5t2 2.032 2.563 3.094 3.628 4.1,62 4.696 s.766 6.837 7.908 8.980 10.052
(from Hearn 1969) Effect of a Nonvertical Front
97
The fraction of the total heat injectedthat remainswithin the steamzone may be calculatedby equation3.58. AshprC{Ts - TR) ^ un:
----------jj-l-
-
ITot
H')'(.,*)
(3.s8)
The resultsare shownin Table3'4 and plotted in Figure 3.L5. A similar figure has been derived by Myhill and Stegemeier(1978)basedon the theory of Mandl and Volek (1969)and modified by unpublishedwork of Prats and Vogiatzis.It is reproducedin Chapter 4 as Figure 4.10. EFFECTOF A NONVERTICALFRONT Myhill and Stegemeier(1978)point out that for the heat-lossequationusedby Marx and Langenheim(and the extensionsof it) to be applicable,it is not necessaryfor only that the total volumeof the steam the heatfront to be vertical.It is necessary the sum of by the expression(Ahlz), wherer4represents zonecan be represented the upper and lower surface areas. Exampleswherethis is true include 1. A sloped,but straight, front that is advancinglinearly, 2. An inclined front that is straight but advancingonly at the top, and 3. Cylindrical fronts. TABLE 3.4 ReservoirHeatingEfficiencyCalculatedfrom Hearn (1969) EFFTCIENCY FOR VARIOUS VALUES OF HtlHo X
X2
0.2 0.4 0.6 0.8 1.0 1".2 t.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0 10.0
0.04 0.16 0.36 0.64 1.00 r.44 r.96 2.56 3.24 4.00 6.25 9.00 12.25 16.00 20.25 25.00 36.00 49.00 64.00 81.00 100.00
98
^) 0.875 0.644 0.475 0.375 0.309 0.262 0.229 0.202 0.181 0.164 0.133 0.111 0.096 0.084 0.075 0.068 0.057 0.049 0.043 0.038 0.034
0.3 0.875 0.756 0.614 0.502 0.422 0.363 0.318 0.284 0.255 0.232 0.189 0.160 0.138 0.122 0.109 0.098 0.083 0.071 0.062 0.056 0.050
0.6
0.4 0.875 0.763 0.675 0.581 0.502 0.439 0.389 0.349 0.316 0.289 0.238 0.202 0.175 0.155 0.139 0.125 0.105 0.091 0.080 0.071 0.064
0.875 0.763 0.681 0.613 0.s46 0.487 0.438 0.397 0362 0.333 0.276 0.236 0.206 0.182 0.t64 0.148 0.125 0.108 0.095 0.085 0.0'17
0.875 0.763 0.681 0.613 0.556 0.508 0.464 0.425 0.391 0.362 0.304 0.26r 0.229 0.204 0.183 0.167 0.141 0.122 0.108 0.096 0.087
0.7 0.875 0.763 0.681 0.613 0.556 0.509 0.468 0.434 0.404 0.37',7 0.320 0.278 0.245 0.219 0.t97 0.180 0.153 0.133 0.tr'7 0.105 0.095
1.0
0.8 0.875 0;763 0.681 0.613 0.556 0.509 0.468 0.434 0.404 0.378 0.325 0.285 0.253 0.227 0.206 0.188 0.160 0.140 0.124 0.111 0.101
ConductiveHeatingwithin Reservoirs
0.875 0.763 0.681 0.613 0.556 0.s09 0.468 0.434 0.404 0.378 0.325 0.285 0.253 0.228 0.207 0.190 0.163 0.142 0.127 0.11 0.103
Chap.3
Parameteris H^/H
-g 0.8 UJ ,
\\
A0.6
\ o.e\
.9 ,9 o.a
o
e\
UJ 0.2
\
r-0.5
\
S
-ia
s.' S
0r0.03 0.03
0.1
0.3
1
10
3
30
100
Dimensionless Time tD Figure 3.1.5 ReservoirHeating Efficiency (basedon Hearn L969)
For conical fronts the volumevarieswith the degreeof truncation from an extreme otAhl3 toAhl2 asthe shapeapproachesa cylinder. Even this variation changesthe dimensionlesstime by a factor of only 4/9. As may be seenfrom the horizontal scale of Figure 3.15,changingtoby a factor of this magnitudedoesnot have a large effect on the predicted thermal efficiency. STEAM INJECTIONINTO A THIN CHANNELOR FRACTURE the limiting casewhereft is assumedto apIn his paper,Hearn (1969)discusses proach zero. His result may be obtained by allowing ft, in the right-hand side of equation 3.40, to approachzero. If the multiplier & is combined with each of the terms inside the bracketsof equation3.40, only the central term remains as ft approacheszero and the equationbecomes A(t) =
Ho\/ a2t
(3.se)
Kz(Ts- T){rr
Substitutingtt for t in equation3.59, solving the resulting equationfar L, substituting the result into equation3.55, and rearrangingleadsto H^=2Ho ["' n J6
ll
,
oo,= Ho
(3.60)
Y or.t
V\",rn-al);-"
.)
This may be integratedto give Ht=
-zH'l. lsln 1rl
Kz(Ts- 7h)\l"
H, )1,
(3.61)
which leadsto . ,t'=
Ho\/drt
.lr
H^\
*--o, _ nrrsntit\i'ar:/
(3'62)
This remarkablysimpleexpressionindicatesthat the steamzone remainsa constant fraction of the total with the fraction being a sine function involving the ratio SteamInjectioninto a Thin Channel or Fracture
99
2.29.lts use is disH^lHo.Equation 3.59was also derived in chapter 2 as equation cussedin a later numerical example' Comparison of Fracture Filleil with Steam for Constant Injection Rate and for Gonstant Areal Growth Rate be seen from equaFor a constant steam injection rate into a fraction it can to the total heated area saturated steam the tions 3.59 and 3.62 that ihe ratio of area is given bY, _,-l n_.H^\ = s''\T' HoJ 7
As
(3.63)
injection times the same For a constant injection rate it was shown that, for long ratio is given bY,
(3.64
- )ryt/4\ = f4\' ' uo \H'l \e l. These two valuesare quite similar'
Valuesof 15ft Ht
Constant Injection
Constant DisPlacementf = o
Ho
1 0.8 0.6 0.4 0.2 0
1 0.96 0.84 0.64 0.36 0
I
0.95 0.81 0.59 0.31 0
Example calculation of the Mandl-volek critical Time for a Numerical theory ignoredt The solution to the numerical exampleof the Marx-Langenheim by the vertical heat losses. possibility of the steambeing completelyco_ndensed critical time. Mandl-Volek the after this occurs tu, U"r" "*pfained, later' calculated &tQ tes, time, X, andthe dimensionless /{i : 800 x 350 x 755 x 0J = 148 x 106Btu/d Ho: Ht + 800 x 350 x 407 :262 x L06Btu/d Find X. from Table 3.i.
' 100
*=
o'435= exP(x3)erfc(X") ConductiveHeatingwithin Reservoirs
Chap'
The root is X" : 0.973;this is obtainedby interpolationof Table3.1' toc:X?=0.947 The correspondingactual times are calculatedas follows:
,"=*=26d
forh=roft
t" = 2630d
for&=100ft
For the thinner reservoirthe critical time correspondsto only 26 days(0.07years); for the thicker reservoir the time is 2630 days, or 7.2 years.At times later than thesethe condensationfront lagsbehind the heat front. This will tend to reducethe quantity of oil displacedbelow that calculatedpreviouslybecausethe residualoil in the waterfloodedregionwill be larger than in the steamfloodedzone.The displacement of oil by steamis comparedto that by water in Chapter 5. The sizeof the steamzone (asdistinct from the larger heatedzone)can be obtained by calculatingthe volume (and hencethe area)of the steamzone that would be obtained if there were no heat lossesat all and then multiplying this by the efficiency read from Figure 3.15.This is done for the previous numerical examplein Table3.5. Extension of Numerical Example to Injection Into a Very Thin Horizontal Layer or Fracture In the previouscalculation, it was seenthat the heatedarea increasedmore rapidly for the thinner reservoir.The reasonfor this is, of course,that lessheat is neededto heat a given area of reservoirwhen it is not as thick. The limiting casecorresponds to that of a very thin reservoiror fracture.This casemay be viewed in two ways: l. The limiting situation for the injection of steam into progressivelythinner reservoirs,or 2. The injection of steaminto a narrow fracture within a thick reservoir. In the first casethe injected heat is essentiallylost, whereasin the secondit heats the adjacenttar sands.The total heatedareaand the steamzone area can be calculated ior the data of the previous exampleusing Hearn'sequations3.59 and 3'62, respectively. Ho:262 x 106Btu/d t : 365tr"^, d2 : 0.9 ft2ld Kz:
29.7Btuft d'F
Ts : 467"F;Tn : 75"F or Fracture SteamInjectioninto a Thin Channel
101
TABLE 3.5 Calculationof Steam Zone Area Allowing for Mandl-VolekEffect Time Years
SteamZone
Dimension
Efficiency(2)
Reservoirthickness: 10 ft: 113 226 J
n
5 6 7
8 9 10
0.20 0.L4 0.t2 0.10 0.09 0.08
39 53 66 79 92 105 118 r3l
HeatedArea in Acres No Loss(l)
1a
34 51 68 85 102 119 t36 153
o'rt
r70
Reservoir thickness= 100ft: 1 0.13 2 0.26 3 0.39 4 0.53 5 0.66 6 0.79 7 0.92
With Loss
u./o
t.t
0.71
3.4
0.67
).1
0.63 0.61 0.59 0.56
6.8 8.5 10.2 11.9
SteamZone
ta
6.3 8.0 9.4 10.6 11.7 12.8 13.7 14.6 15.5
J.+
4.8 6.1 6.8 7.6 8.2 9.3
1.3 2.4 3.4 4.3 5.2 6.0 6.7
3.4 4.3 5.2 6.0 6.7
7.5 8.2 8.8
7.9 8.4
1.3 z.+
Critical time -- 7.2 y 8 9 10
1.05 1.18 1.31
0.535 0.515 0.495
t3.6 l).J
r'7.0
t.5
',t.)!1tt/lorC',h{ft- Tp))convertedto acres. *''FromFisure 3.1.5.
Area in acres= Ht:
Ho{drt
43,5601[rKz(Zs- r^)
= 5.283!G,
148 x 10"Btu/d
= 0.775of the total heatedarea As=A"{(;)e)] The resultsare given in Table3.6. Also shownin Table3.6 are calculatedaverage valuesfor the total thicknessof the heatedzoneaboveand belowthe heatedzone. Thesewereobtainedby dividing the total volumeof the heatedzonecorresponding to the quantityof steaminjectedby the total heatedarea.[t will be noted that the heat penetratesabout 50 tt (10212)on either side of the heatedzone in 10 years. With heat-penetration distancesof this order, it is easyto seewhy steamingthin reservoirsfor long periods is inefficient. 102
ConductiveHeatingwithin Reservoirs
Chap.3
TABLE 3.6 CalculatedHeatedArea and Steam Zone Area for Injectioninto a Very Thin Layer Years
10
Hot zone in acres ).J
t -J
Steamzone in acres 4.1 5.8
9.t
10.6
11.8
7.r
8.2
9.2
12.9
10.8
r4.9
15.8
16.7
11.6
t2.3
12.9
Averageheatedzone thicknessin feet(l) 32 45 56 64 72 79 85 91 96 t02 (t)Assuming that all of the injectedheat remainsin a zoneof uniform thicknesshavingthe samearea as that calculatedfor the hot zone.
BIBLIOGRAPHY CentEn, R. D., Appendixl of.Optimum Fluid Characteristics for FractureExtensionby G. C. Howard and G. R. Fast,Drill. and Prod. Prac.,API (1957),267-268. HernN, C.L., "Effect of Latent Heat Content of Injected Steam in a Steam Drive," JPT, 374-375 (April 1969).o 1969SPE. I-euweruen, H. A., "The Transport of Heat in an Oil Layer Causedby the Injection of Hot Fluid," Appl. Scl. Res.A, 5: 145-150(1955). MeNoq G. and VoLnr, C.W., "Heat and MassTransportin SteamDrive Processes,"SPEI, 59-79 (March 1969). Menx, J.W., and LeNceuuuu, R. N., "Reservoir Heating by Hot Fluid Injection," Pet. Trans.AIME, 216:3I2-3I5 (1959). MvHrLL, N.A., and SrecuraerrR,G.L., "Steam-DriveCorrelationand Prediction," "IPI l7 3 -182 (February 1978). RAMEv,H. J., "How to CalculateHeat Transmissionin Hot Fluid Injection," in Fundamentals of Thermal Oil Recovery,Dallas, Tex.: Petroleum Engineer Publishing Company.
(1e6s).
VoceL, J. H., "Simplified Heat Calculationsfor Steamfloods," SPE lt2l9, (1982);IPT, tl271136(July 1984).
Bibliography
103
Steqmflooding
INTRODUCTION In this chapterthe ideasintroducedin Chapter3 are expanded,and it is shown how they may be used as the basisfor the analysisof field projects.The chapter also discussesimportant factors that were not included in the developmentof the ideasin Chapter3. Theseinclude the effect of gravity in causingoverrideof the steam,the effect of steamingupon the permeabilityof the matrix, depletion,and steamdistillation. A OUALITATIVEDISCUSSIONOF STEAM.INJECTIONPROCESSES i
Steam-injectionprocessesfor the recovery of heavy oils are divided into two categories: L. Cyclic stimulation 2. Steamflooding Cyclic Stimulation In stimulation,steamis injectedinto the reservoiratafate of up to about1000B/d (160tld or m3/d)for a period rangingfrom one to severalweeks,and then the well is producedby allowingfluids to flow back.When the pressureat the bottom of the well drops, the well is pumped. During the pumping period, the well temperature continuesto fall. Over a peiiod that can rangefrom severalmonths to a year or more, the oilproduction rate falls to the point where it is no longer advantageousto continue, 104
and the well is restimulatedby injectingmore steam.This cyclic processis continued until the quantity of oil recovered is no longer sufficient to justify further steaming.At this time the recoveryis typically of the order of I5%; the recovery dependson the natureof the reservoir,the economicvalueof the producedoil, the well spacing,and other variables. Steamflooding In the flooding process,steamis injectedcontinuouslyinto one or more wells and oil is driven to separateproductionwells. Usually the wells are placedin regular patterns.The steamfloodingprocessis alsoreferredto assteamdrive. In the examplesdescribedin this chapter,the objectiveis to drive the oil sidewaystoward productionwells.If the reservoirdips, it is advantageous to drive the oil downwardin order to utilize gravity to keep the steamfrom bypassingthe oil.l Frequentlythe two methodsof steaminjectionarecombinedandwellsareproducedby stimulationbeforeflooding is started.When it is desiredto producevery viscousoils suchasfrom oil sands,stimulationbeforeflooding is almostessentialin order to achieveflow communicationbetweenthe injectionand productionwells. Communicationcan be establishedbetweenpairs of wells even in cold tar sandby creatinga fracturebetweenthem. This can be doneby injectingsteamat a sufficientlyhigh pressure.In tar sandsdeeperthan about1000ft, suchfracturesare usuallyvertical, and they tend to have a definite azimuthal(compass) orientation. In much of Alberta this is approximatelySWNE. At shallowerdepths,horizontal fracturestend to be formed. lf steamis injectedinto a verticalfracturein cold tar sand,heatingwill occur and condensate will flow to the connectingproductionwell. There is a tendencyfor the steamto override,and the fracture can becomeheatedalongthe top without much heat penetratingto the lower parts. The pressuregradientalong a steamed communicatingfracturetendsto be smallbecauseof the needto preventexcessive steambypassing.As a result,while heat is transferredto the adjacentreservoir,oil productionis slowbecausethere is little driving force availableto movethe heated oil. Becauseof thesedifficulties and becauseof the attractiveness of early oil production, the preheatingof the reservoirbefore steamflooding appearsto be the preferableroute to achievingconventionalsteamfloodingin bitumen reservoirs. Although little practicalfield experienceis available,vertical steamflooding gravitydrainageapproach,which is describedin Chapter7, usingthe steam-assisted may be preferablein many circumstances-particularly for projectsinvolving thick reservoirs.In many cases,steamflood projectsthat were startedwith the idea of driving oil horizontally have endedup with more and more attention being paid to the importanceof gravity in providingdrive. It is recognizedthat downwardsteam drive in dippingreservoirsis a practicalmeansof achievinghigh injectionand productionrates.In commercialoperations,steamstimulationis often economicallyattlt is being realizedmore and more that downwardsteamfloodingoffers considerableadvantages.One way of accomplishingthis is to use horizontal productionwells locatednear the baseof the reservoir,with the steamintroducedabove.This approach,which has becomeknown ass/eamassistedgravity drainage,is discussedin Chapter 7.
A OualitativeDiscussionof Steam-injectionProcesses
105
tractive becauseit enablesrapid production of oil with acceptableand sometimes very high oil-to-steamratios. While the short-term economicsof stimulation are frequently satisfactory, only about 15 to 20% of the oil can be producedeconomically.After this, the oilsteamratio becomesrelativelypoor. At this stageit is common,at leastin fields containingmobileoil (particularlythosein California),to convertthe steamstimulation operationto a steamflood. Steamfloodscan produce recoveriesof the order of 50Voof the original oil in placewith oil-steamratios of the order of.0.2. Volumesof steamare traditionally measuredin terms of the volume of the equivalentwater; a barrel of steamis thus with the steam)and 1 m3is 1 t. 350lb of steam(includinganyliquid waterassociated nature upon the of the reservoir.Very deep ratio is dependent The oil-steam most) are uneconomic for conventional (deeper ft the very than 5000 at reservoirs pressures and correthe very high steam flooding because of and steamstimulation quantity steam reHeat losses and the of required. high temperatures spondingly Another factor become excessive. temperature quired to raisethe reservoir-to-steam the overburden. from the well bore to is the excessiveheat loss that can occur There is an increasein the well bore heat lossesas the depth of the reservoiris increased.As was discussedin Chapter2, this increaseis causedby the extra length of the well and also by the higher steamtemperatureassociatedwith the higher pressures. Thermal insulationcan be usedto extendthe practicaldepth for steam injection,but this tendsto be expensive. The next most important criterion for a successfulsteamrecovery project is that the reservoirshouldbe thick-certainly at least10 ft thick and preferablymuch thicker. The reasonfor this is that the heat lossesto the overburdenand underburden representan excessiveproportion of the total heat requirementfor thin reservoirs.This ideawas discussedin the last chapter. Typical successfulsteam-driveprojectsare in relativelyshallow,fairly thick reservoirs-e.g.,1000to 2000ft in depth and 100ft thick. Usuallythesereservoirs or looselyconsolidatedsandhavingreasonablyhigh perconsistof unconsolidated meability and porosity (e.g., 1 D and 30Voporosity) and high oil saturation. [t is usual to produceoil by stimulationfrom both the injection and the productionwells Stimulationis often continued,evenduring the drive, beforethe drive commences. if the temperatureof the producedfluids tendsto fall. It is alsobecomingcommon, as steamfloodedfields become depleted,to recover some of the remaining oil by waterflooding.In this situationit is still desirableto stimulatethe producersperiodically if the production tends to fall in temperature. Very shallowreservoirsare usuallynot suitablefor steamflooding(or for stimulation, either). The reasonfor this is that the steampressurethat can be utilized would have to be kept low to avoid fracturing to the surface of the ground above the reservoir. With the lower temperaturesthat correspondto the lower-pressure steam, the oil (particularly if it is bitumen) may not become sufficiently fluid to make recoverypracticable.Fracture pressureis, to a first approximation,equal to 1 psift of depth from the surface. The use of horizontal wells in place of conventionalones makes the use of steamfloodingprocessesin shallow reservoirsmore practical. Their greatercontact 106
Steamflooding
Chap.4
kB/d
,_
M//.4
l-l lffi t-l II
--- ---1 Sreamsoak1 SteamfloodI
rot"t
I
1968 1970 't972 1974 1976 1978 1980 1982 1984 1986 1988
Year Figure 4.1 Heavy Oil Recoverywith Steam in the United States(Sourceof Data Oil and Gaslournal\
with the reservoirallows more viscousoils to be producedat a useful rate. This ls discussedin Chapter7. During recentyearsthe trend in the heavyoil fieldsin Californiahasbeento switch from steam stimulation to flooding, and most heavy oil from there is now producedby steamflooding.Ihe main reasonfor this is the economicincentiveto improve the recovery.Figure 4.1.comparesthe historical recovery of oil by steam stimulationwith that by steamfloodingin California. In additionto providing a higher recovery,steamflooding-with its continuous injectionof heat-can produceoil significantlyfasterthan can the cyclicstimulation process.This, too, can have a significant economic impact. The main disadvantages of steamfloodingcomparedto stimulationare the following: o There is a lower oil-steamratio. In steamfloodingit is necessaryto heat a larger part of the reservoir,whereasin stimulation, at least in the early cycles,the heating is confined to a smaller region around the well. o There is a longerperiod of time before significant production starts. o Often flooding is not possibleinitially becauseof the lack of flow communication. FORSTEAMFLOODING SUITABILITY OF SPECIFICRESERVOIRS The choiceof steamfloodingas a meansfor the recoveryof petroleumhasbeendiscussedby a number of authors(including Farouq Ali 1974,FarouqAli and Meldau 1979,Geffen 1973,Matthews 1983,and Chu 1985).Whereas the suitability of a reservoir for production by steam stimulation can be determined relatively simply Suitabilityof SpecificReservoirsfor Steamflooding
107
and the nell ued until th steaming-Al dependsm rl well spriq; SteanrflooC
Sfeqmflooding
INTRODUCTION In this chapterthe ideasintroducedin Chapter3 are expanded,and it is shown how they may be used as the basisfor the analysisof field projects.The chapter also discusses important factorsthat were not includedin the developmentof the ideasin Chapter3. Theseincludethe effect of gravity in causingoverrideof the steam,the effect of steamingupon the permeabilityof the matrix, depletion,and steamdistillation. A OUALITATIVEDISCUSSIONOF STEAM.INJECTIONPROCESSES Steam-injectionprocessesfor the recoveryof heavy oils are divided into two categories: 1. Cyclic stimulation 2. Steamflooding Gyclic Stimulation
In the floodil oil is driren t patterns.Tb ples describa duction q-ellr order to utilil Fregrs duced bl srir viscousoib I order to rhi Comm sandbv creti sufficientl;*hi usuallvverth In much of A fracturested If sear and condens the steamto much heat pt communicdil steamblpasc productiut b oil. Becauscr duction.thc 1 preferableru Althqt usingthe srce may be prcfa reservoirs-lin driving cil h the impotal drive in di6i duction ratcs
In stimulation,steamis injectedinto the reservoiratarate of up to about1000B/d (160t/d or mt/d) for a period rangingfrom one to severalweeks,and then the well is producedby allowingfluids to flow back.When the pressureat the bottom of the well drops,the well is pumped.During the pumpingperiod, the well temperature continuesto fall. Over a period that can range from severalmonths to a year or more, the oilproduction rate falls to the point where it is no longer advantageousto continue,
'It is tri tages.One rryt the reservoir,ri assistedgranty I
104
A Oualitatiw I
and the well is restimulatedby injectingmore steam.This cyclic processis continued until the quantity of oil recoveredis no longer sufficient to justify further steaming.At this time the recoveryis typically of the order of I5Va;the recovery dependson the natureof the reservoir,the economicvalueof the producedoil, the well spacing,and other variables. Steamflooding
ded, and it is shown projects.The chapter l developmentof the usingoverrideof the ratrix.depletion,and
ES .i
re divided into two
up to about 1000B/d ks, and then the well 3 at the bottomof the the well temperature iear or more,the oilltageousto continue,
In the flooding process,steamis injectedcontinuouslyinto one or more wells and productionwells. Usually the wells are placedin regular oil is driven to s-eparate patterns.The steamfloodingprocessis alsoreferredto assteamdrive. In the examplesdescribedin this chapter,the objectiveis to drive the oil sidewaystoward productionwells.If the reservoirdips, it is advantageous to drive the oil downwardin order to utilize gravity to keep the steamfrom bypassingthe oil.1 Frequentlythe two methodsof steaminjectionare combinedandwellsareproducedby stimulationbeforeflooding is started.When it is desiredto producevery viscousoils suchasfrom oil sands,stimulationbeforeflooding is almostessentialin order to achieveflow communicationbetweenthe injectionand productionwells. Communicationcan be establishedbetweenpairs of wells even in cold tar sandby creatinga fracturebetweenthem. This can be doneby injectingsteamat a sufficientlyhigh pressure.In tar sandsdeeperthan about1000ft, suchfracturesare usuallyvertical, and they tend to have a definite azimuthal(compass) orientation. In much of Alberta this is approximatelySWNE. At shallowerdepths,horizontal fracturestend to be formed. lf steamis injectedinto a verticalfracturein cold tar sand,heatingwill occur and condensate will flow to the connectingproductionwell. There is a tendencyfor the steamto override,and the fracture can becomeheatedalongthe top without much heat penetratingto the lower parts. The pressuregradientalonga steamed communicatingfracturetendsto be smallbecauseof the needto preventexcessive steambypassing.As a result,while heat is transferredto the adjacentreservoir,oil productionis slowbecausethereis little driving force availableto movethe heated of early oil prooil. Becauseof thesedifficulties and becauseof the attractiveness duction, the preheatingof the reservoir before steam flooding appearsto be the preferableroute to achievingconventionalsteamfloodingin bitumen reservoirs. Although little practicalfield experienceis available,vertical steamflooding gravitydrainageapproach,which is describedin Chapter7, usingthe steam-assisted may be preferablein many circumstances-particularly for projectsinvolving thick reservoirs.[n many cases,steamflood projectsthat were startedwith the idea of driving oil horizontally have endedup with more and more attention being paid to the importanceof gravity in providingdrive. It is recognizedthat downwardsteam drive in dippingreservoirsis a practicalmeansof achievinghigh injectionand production rates.In commercialoperations,steamstimulation is often economicallyattlt is being realizedmore and more that downwardsteamfloodingoffers considerableadvantages.One way of accomplishingthis is to use horizontal productionwells locatednear the baseof the reservoir,with the steamintroducedabove.This approach,which has becomeknown as srearnassistedgravity drainage,is discussedin Chapter 7.
A OualitativeDiscussionof Steam-injectionProcesses
105
tractive becauseit enablesrapid production of oil with acceptableand sometimes very high oil-to-steamratios. While the short-term economicsof stimulation are frequently satisfactory, only about 15 to 20Voof the oil can be producedeconomically.After this, the oilsteamratio becomesrelativelypoor. At this stageit is common,at leastin fields containingmobileoil (particularlythosein California),to convertthe steamstimulation operationto a steamflood. Steamfloodscan produce recoveriesof the order of 50Voof the original oil in placewith oil-steamratios of the order of 0.2. Volumesof steamare traditionally measuredin terms of the volume of the equivalentwater; a barrel of steamis thus 350lb of steam(includinganyliquid waterassociated with the steam)and 1 m3is 1 t. The oil-steamratio is dependentupon the nature of the reservoir.very deep reservoirs(deeperthan 5CI0 ft at the very most) are uneconomicfor conventional steamstimulationand flooding becauseof the very high steampressures and correspondinglyhigh temperaturesrequired. Heat lossesand the quantity of steam required to raisethe reservoir-to-steam temperaturebecomeexcessive.Another factor is the excessiveheat loss that can occur from the well bore to the overburden. There is an increasein the well bore heat lossesas the depth of the reservoiris increased.As was discussedin Chapter2, this increaseis causedby the extra length of the well and also by the higher steamtemperatureassociatedwith the higher pressures. Thermal insulationcan be usedto extendthe practicaldepth for steam injection,but this tendsto be expensive. The next most important criterion for a successfulsteamrecovery project is that the reservoirshouldbe thick-certainly at least10ft thick and preferablymuch thicker.The reasonfor this is that the heatlossesto the overburdenand underburden representan excessiveproportion of the total heat requirementfor thin reservoirs.This idea was discussedin the last chapter. Typical successfulsteam-driveprojectsare in relativelyshallow,fairly thick reservoirs-e.g.,1000to 2000ft in depth and 100ft thick. Usuallythesereservoirs consistof unconsolidated or looselyconsolidatedsandhavingreasonablyhigh permeability and porosity (e.g., 1 D and 30vo porosity) and high oil saturation. It is usual to produceoil by stimulationfrom both the injection and the productionwells beforethe drive commences. Stimulationis often continued,evenduring the drive, if the temperatureof the producedfluids tendsto fall. It is alsobecomingcommon, as steamfloodedfields become depleted,to recover some of the remaining oil by waterflooding.In this situationit is still desirableto stimulatethe producersperiodicallyif the productiontendsto fall in temperature. Very shallowreservoirsare usuallynot suitablefor steamflooding(or for stimulation, either). The reasonfor this is that the steampressurethat can be utilized would have to be kept low to avoid fracturing to the surfaceof the ground above the reservoir. With the lower temperaturesthat correspondto the lower-pressure steam,the oil (particularlyif it is bitumen)may not becomesufficientlyfluid to make recovery practicable.Fracture pressureis, to a first approximation,equal to 1 psift of depth from the surface. The use of horizontal wells in place of conventionalones makes the use of steamfloodingprocessesin shallow reservoirsmore practical. Their greatercontact 106
Steamflooding
Chap.4
E' 50
3XD
FitDate O
with the rescr discussedin O During n switch from sf producedby c improve the rr stimulationwl In additi ous injectim d lation process disadvantager
e There b i largerpa cycles.th o Thereis, o Often fh commun
SUITABILITY OF SPC
The choiceof r cussedby a nu 1979, Geffen I reservoirfor p
Suitabilityof 59
rbleand sometimes uently satisfactory, After this, the oiln. at leastin fields rt the steamstimuf the original oil in m are traditionally rel of steamis thus am) and 1 m3is 1 t. :servoir.Very deep ic for conventional rressures and correantity of steamreive.Another factor lo the overburden. the reservoiris inb;-the extra length rd with the higher ;al depth for steam recoveryprojectis nd preferablymuch 'denand underburnentfor thin resertallow, fairly thick lly'thesereservoirs rasonably high peroil saturation.It is re productionwells n during the drive, rccomingcommon, e remainingoil by .he producerspericding (or for stimurat can be utilized the ground above the lower-pressure ufficiently fluid to ,ximation,equalto
kB/d
,_
--- --- -1
lV////,
Steamsoak I
IKffi
Steamflood
II
rotut
t_ l*
I
1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 t988
Year Figure 4.1 Heavy Oil Recovery with Steam in the United States (Source of Data Oil and Gas lournal)
with the reservoirallowsmoreviscousoils to be producedat a usefulrate. This is discussedin Chapter7. During recentyearsthe trend in the heavyoil fieldsin Californiahasbeento switch from steamstimulationto flooding, and most heavyoil from there is now producedby steamflooding.The main reasonfor this is the economicincentiveto improvethe recovery.Figure 4.1.comparesthe historicalrecoveryof oil by steam stimulationwith that by steamfloodingin California. In addition to providing a higher recovery,steamflooding-with its continuousinjectionof heat-can produceoil significantlyfasterthan can the cyclicstimulation process.This, too, can have a significant economic impact. The main disadvantages of steamfloodingcomparedto stimulation are the following: o There is a lower oil-steamratio. In steamfloodingit is necessaryto heat a largerpart of the reservoir,whereasin stimulation,at leastin the early cycles,the heatingis confinedto a smallerregionaroundthe well. r There is a longerperiod of time beforesignificantproductionstarts. o Often flooding is not possibleinitially becauseof the lack of flow communication. SUITABILITY OF SPECIFICRESERVOIRS FORSTEAMFLOODING
makesthe use of reir greatercontact
The choiceof steamfloodingas a meansfor the recoveryof petroleumhasbeen discussedby a number of authors(including Farouq Ali 1974,FarouqAli and Meldau 1979,Geffen 1973,Matthews L983,and Chu 1985).Whereasthe suitability of a reservoir for production by steamstimulation can be determined relatively simply
fboding
Suitabilityof SpecificReservoirs for Steamflooding
Chap.4
107
by meansof singlewell tests,field experimentationto determineits suitabilityfor steamfloodingis much more costly. Even the simplesttest must involve multiple wells and long periodsof operation. Severalquantitativeguidelineshave been developedto indicate whether a reservoirpropertymight respondfavorablyto steamfloods.Table4.1 is a summary of suchscreeningguides;it is taken from Chu (1985). Matthewslists the followingfactorsthat are unfavorablefor steamflooding. 1. 2. 3. 4. 5. 6.
Oil saturationlessthan 40% Porosity less than 20Vo Oil-zonethicknesslessthan 30 ft Permeabilitylessthan 100mD Ratio of net to grosspay lessthan 50% Layersof very low oil saturationand high permeabilityin the oil zonethat act as thief zones 7. Extremelyhigh viscosity 8. Fractures2 9. Large permeabilityvariationsin the oil zone 10. Poor reservoircontinuity betweeninjectorsand producers 11. Deep high-pressurereservoirsand shallowreservoirswith insufficientoverburdento permit steaminjectionwithout fracturing He points out that steamfloodsmay be successfuleven if one or two of the above conditionsare not met, providedthat the remainingfactorsare highly favorable. Chu (1985)describesan empiricalcorrelationthat predictsthe oil-steamratio (osR) or its reciprocal,the steam-oilratio (soR). His correlationequationsare givennext; note that the units employedare,in somecases,not the customaryones. tf soR < 5.0(osR> 0.201: Englishunits (asdefinedshortly): - 14J95" SOR = 18.744+ 0.001453D- 0.05088h- 0.0008864k- 0.0005915p. - 0.0002%8L! l.L
Metric units (asdefinedshortly): -14.795. SOR = 18.744+0.004767D-0.I6693h - 0.8981k- 0.5915pr
- 0.000s767LL l.L 2Fractures may be undesirablebecausethey promote bypassingof the steam.In the steamassistedgravity drainageprocess,however,which is operatedbelow the critical steam-coningrate, fracturesenhancethe processif they are vertical and have little effect if they are not.
108
Steamflooding
Chap.4
nine its suitability for nust involve multiple
<S
OOa
Nqi6
o indicate whether a Dle 4.1 is a summary I for steamflooding.
=
x-
orQ o -o
Vo N
'= 3u.? trv o
ln
t the oil zone that act
FoP A
8883= 338s+ \/\/\/on
c.l
ls ith insufficient over-
o
*
.s.i
o o Clo 9C'.1 o ci
F
or two of the above re highly favorable. ts the oil-steamratio lation equations are I the customarvones.
rJ) @ gt
^
i
AA-n o
'i ar E
6S
ho
i^^Nr^ Oni
Od)
d/\/\oY
C) o
nv?n
o) '6'
oON
G
- 14.795. Itr59151^c
E o
ot a
N
c.l a,
o) p
o
q
s
-vi oo €O€O6 hi-ii-i oAAAA
9l5p - 14.795,
.E o o
()
(t) t tI|
thc steam. In the steamitical steam-coningrate, lcy are not. rflooding
Chap. 4
@
r vx€=ir\FF
Ov
9H I* E .s; Y xai
109
tf soR > 5.0(osR< 0.201: Englishunits (asdefinedshortly):
where I
- 0.00t3570+ 0.000007232p. oSR = -0.011253+ 0.0N02779D+ 0.0001579h
+ o.oo001o4z4 + o.5t2oos" l.L
Metric units (asdefinedshortly): - 0.077i50+ 0.007232p" OSR = -0.011253+ 0.00009117D + 0.0005180h
+ 0.0000346tU + 0.st20ds, p
English D = ft : I = S, : Soi= So,= I = d= p : 4 :
depth thickness permeability oil saturationat start initial oil saturation residualoil saturation temperature dip angle viscosity porosity
Metric
ftm ftm mD
mD
fraction of pore volume fraction of pore volume fraction of pore volume r
The term FY done per uni systemopctl equivalentI tem operatiq
"c
degree rad cp Pas fraction of bulk volume
These equationsmay be used quite simply becauseall they require are fairly basicmeasurements or estimatesof the reservoirproperties.Two formsof the equations are given,one for Englishunits and one for metric.Chu'spapercontainssummary data for 28 different steamflood field projects, including references.The equationsjust given were found to correlatewell with the data. Chu recommends that the equationfor SOR < 5 be tried first and that the secondequationbe used only if the answerfrom the first indicatesthe SOR to be greaterthan 5. Tables4.2, 4.3, 4.4, and 4.5 reproducethe field projectdata summariescollected by Chu. Referencesto the sourcesof the data are listed in Chu'spaper. It is interesting to note that of the 28 projects studied by Chu, only 7 gave oil-steam ratioshigher than 0.2.
where the lct ing the qrlcr For ert Wr(Hp - IJrl ing formulai tial energy,t the PV terme caseswhercd tional terms i At any 1 increaseste{ further heat i amount of hc is added,thc water vapor i mation. If fir The s plantssucha oil fields,wa that definest the weight fn thus liquid. I numericalfn The erl Table 4.6 as
THE PROPERTIES OF STEAM The most important properties of steamfor thermal recovery processesare those involvingenthalpy.Enthalpy is defined as
or, since
H:U*PV 110
Steamflooding
Chap.4
The Propertie
whereH
is the enthalpyin units of energyper unit mass,e.g.,kykg (or Btu/lb) U is the internal energy,k/kg (or Btu/lb) P is the pressure,kPa (or Btuft3) V is the specificvolume, m'lkg (lbft3)
i78 + 0.000007232p.
t7* + 0.007232pt
The term PV hasthe dimensionsof energyper unit mass;it is the work that mustbe done per unit massof material to introduce it at pressureP into a continuousflow systemoperatedin a steadystate.Similarly, material leaving the systemcan do an equivalentamount of work. The total heat effect in a continuous-flow,isolatedsystem operatingin a steadystate is thus Heat added= ) H" Wp- ZHrWr
Metric m m mD : r'olume : r'olume : volume
'c
rad Pas ; r'olume
:heyrequireare fairly '\r'o forms of the equa's papercontainssumrding references.The ata. Chu recommends ond equationbe used ater than 5. t data summariescold in Chu'spaper.It is only 7 gave oil-steam
where the terms Hp and Wprefer to the enthalpiesand massesof the productsleaving the systemand Hr and W are the correspondingterms for the feed. For example,the heat addedin a boiler to convert the feedwaterto steamis Wr(Hp - Hr) if the massof steamproductis equalto the massof feed.The preceding formulation of the law of conservationof energyneglectsterms such as potential energy,kinetic energy,electrical energy,and work other than that included in the PV terms;this is justifiablein the calculationsdescribedin this book. In other caseswhere theseother energyterms are significant, they must be included as additional terms in the energybalance. At any particular pressure,the temperatureand the enthalpyof liquid water increasesteadilyas heat is addeduntil the boiling point of the water is reached.If further heatis added,the waterboils at a constanttemperatureuntil an additional amountof heatequalto the latentheatof evaporationhasbeenadded.As this heat is added,the liquid is continuouslytransformedinto vapor until eventuallyonly water vapor is present;a very large increasein volume accompanies this transformation. [f further heat is added,the steambecomessuperheated. The steamemployedfor processheating and power generationin process plantssuchas refineriesand power stationsis usuallydry and superheated. In the oil fields,wet steam(i.e., a mixture of waterandvapor)is employed.The parameter that definesthe conditionof sucha mixture is the steamquality,/5;it is definedas the weightfractionof the steammixture that is vapor.A weightfraction (1 - /5) is thus liquid. The steamquality is often expressedas a percentagerather than as a numerical fraction. The enthalpy of steam of quality /s can be calculatedfrom the data of Table4.6 as IIs=(1 -/r)H"*fsH,
(4.1)
T DTOCeSSeS are those
or, since IIv=Hrl
amflooding
Chap.4
The Propertiesof Steam
tr 111
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TABLE 4.6 Enthalpyof Water and Steam at SaturationConditions
T
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P (MPa)
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Water
Evap.
0.006 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.r7 0 .l 8 0.19 0.20 0.21 0.22 0.23 o.24 0.25 0.26 0.27 0.28 0.29 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.70 0.80 0.90 r.00 1.10 r.20 1.30 1.40
0.0 99.6 102.3 104.8 t07.1 109.3 rtt.4 113.3 rr5.2 116.9 118.6 120.2 rzr.8 123.3 t24.7 126.1 127.4 128.7 130.0 13r.2 132.4 133.5 138.9 143.6 t47.9 151.8 155.5 158.8 165.0 170.4 t75.4 179.9 184.1 188.0 191.6 195.0
0.0 417.5 428.8 439.4 449.2 458.4 467.1 475.4 483.2 490.7 497.9 504.7 511.3 5t7.6 523.7 529.6 535.4 540.9 546.2 551.5 556.5 561.4 584.3 604.7 623.2 640.1 655.8 670.4 697.1 720.9 742.6 762.6 781.1 ',198.4
2501,.6 2257.9 2250.8 2244.L 2237.8 2231,.9 2226.3 2220.8 2215.8 22t0.8 2206.t 2201.6 21,97.2 2193.0 2188.9 2t84.9 2181.0 21,77.3 2173.7 2170.0 2166.6 2163.2 2147.3 2132.9 21t9.7 2107.4 2095.9 2085.0 2064.9 2046.5 2029.5 2013.6 1998.6 L984.3 1970.7 1957.7
814.7 830.1
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T
P (MPa)
("c)
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198.3 20r.4 204.3 207.1 209.8 212.4 223.9 233.8 242.5 250.3 257.4 263.9 269.9 275.6 280.8 285.8 290.5 295.0 299.2 303.3 30'7.2 311.0 318.0 324.6 330.8 336.6 342.1 347.3 352.3 357.0 361.4 365.7 369.8 373.7 374.2
Enthalpyk/kg
844.6 858.5 871.8 884.5 896.8 908.6 961.9 1008.3 t049.7 1087.4 Lt22.r 1154.5 1184.9 r2r3.7 t241.2 L267.5 1292.7 1317.2 1340.8 1363.8 1386.2 1408.1 1450.6 149L.7 1531.9 r57L.5 1610.9 1650.4 1691.6 1734.8 1778.7 1826.6 1886.3 2010.3 2107.4
t945.3 1933.2 192r.6 1910.3 1899.3 1888.7 1839.0 t794.0 1752.2 t7t2.9 1675.6 1639.7 1605.0 1571.3 1538.3 1506.0 1474.]. 1442.7 14rr.6 1380.8 1350.2 1319.7 1258.8 rr97.5 1135.1 1070.9 1004.2 934.5 860.0 '779.0
2789.9 2791.7 2793.4 2794.8 2796.r 2797.2 2800.9 2802.3 2801.9 2800.3 2797.7 2794.2 2789.9 2785.0 2779.5 2773.5 2766.8 2759.9 2752.4 2744.6 2736.4 2727.8 2709.4 2689.2 2667.0 2642.4 2615.1 2584.9 255t.6 2513.8 691.8 2470.5 591.6 2418.2 461.2 2347.5 186.3 2196.6 0.0 2101.4
Table {-( of evaporatkr temperature. The ralu unitsbv the ft
Simplerelatic tions of tempc Specific1 The latenthcr the criticalpo erating pressu 706'F), none i 2802kl/kg at In the fr is usual to ggr Typicallya gl than dry or sr water for the I Oil field the combustiq of about 70 to containshigh residualliquid
Abstractedfrom "U.K. SteamTablesin SI Units 1970",United Kingdom Committeeon Properties of Steam,Edward Arnold, London 1970.
Hs can also be expressed as
(4.2)
Hs=Hr*/sr\
where i is the latent heat of evaporationand the subscripts,S, L, and V refer to the steammixture, boiling liquid, and saturatedvapor,respectively. 120
Steamflooding
Chap.4
The Propertiesr
Table 4.6 and Figure 4.2 give the enthalpy of boiling water, the latent heat of evaporation,and the enthalpy of saturatedsteam as a function of pressureand temperature. The valuesin Table4.6 are in S.I. units. They may be convertedto Enelish units by the followingconversions:
Enthalpyk/kg bter '44.6 5E.5 i71.8 i{i4.5 iqt-8 oE.6 61.9 oE.3 49.'t E7.4 22.r 54.5 u.9 r3.7 1t.2 '67.5 92.7 t7.2 if0.E 63.8 ,t6.2 08.l 50.6 9r.7 31.9 71.5 I0.9 50.4 91.6 34.E 7E.7 26.6 E5.3 r0.3 0i.4
Evap.
Steam
1945.3 1933.2 1921.6 1910.3 1899.3 1888.7 1839.0 1794.0 t752.2 1712.9 1675.6 1639.7 1605.0 1571.3 1538.3 1506.0 1474.1 1442.7 14ll.6 1380.8 t350.2 t3t9.7 1258.8 rr97.5 1135.1 1070.9 1N4.2 934.5 860.0 779.0 691.8 59L.6 46t.2 186.3
2789.9 279t.7 2793.4 2794.8 2796.1 2797.2 2800.9 2802.3 280I.9 2800.3 2797.7 2794.2 2789.9 2785.0 2779.5 2773.5 2766.8 2759.9 2752.4 2744.6 2736.4 2727.8 2709.4 2689.2 2667.0 2642.4 2615.1 2s84.9 255t.6 25t3.8 2470.5 24t8.2 2347.5 2t96.6
0.0
2107.4
dom Committeeon Prop-
(Pressurein psia) : 145(pressure in MPa) (Temperaturein "F) = l.8(temperaturein 'C) + 32 (Enthalpy in Btu/lb) : (enthalpyin kJlkg)/2.326 Simplerelationsfor calculatingthe enthalpiesof saturatedliquid and vapor as functions of temperatureand pressureare given in Appendix 9. Specific points that should be noted with respectto Table 4.6 are as follows: The latent heat of evaporationdecreasesas the pressureis raised and disappearsat the critical point. Lesslatent heatis availableper unit massof steamwhen the operatingpressureis higher.Above the critical point (22.7MPa,374"C or 3208psia, 706"F), none is available.The enthalpy of saturatedsteamreachesa maximum of 2802kJlkg at 236'C and 3 MPa (1205Btu/lb at 457'F and 435 psia). ln the field, steamis generatedat pressuresup to about 15 MPa (2200psi). It is usualto generatewet steam-i.e., a mixture of saturatedsteamvapor and water. Typically a quality of 70 to 80Vois employed.The main reasonfor using wet rather than dry or superheatedsteamis to reduce the purity requirementsfor the feedwater for the steamgenerators. Oil field steamgeneratorsusually contain a single boiler tube coiled around the combustionzone.Water is pumped at high pressureinto one end and a mixture of about 70 to 80% vapor and 20 to 30Voliquid leavesthe other. The water usually containshigh concentrationsof dissolvedsolids.These remain dissolvedin the residual liquid water and are removedcontinuouslywith the steamproduct. More
IE
a15 -, o
06+ Quality
| o lzs I so I zs \ roo
J
810
o
o-
(4.2) l, andZ referto the ly. mflooding
Chap.4
2000 1000 EnthalpykJ/kg The Propertiesof Steam
3000
Figure4.2 Pressure-Enthalpy Diagram for Steam-Water
121
informationon water treating,steamgeneration,and steamdistributionis given in Chapter8. TEMPERATURE DISTRIBUTIONIN STEAMFLOODING Figure 4'3 shows,in an idealizedway, one conceptof the conditionsaround a steam-injection well. The temperaturein the vicinity of the well is nearlyconstant and is equalto the saturationtemperatureof the steam.This temperatuieprevails to the point wherethe last of the steamcondenses. Beyondthe condensation front thereis a hot-waterzonein which the temperature falls. The temperaturegradientjust beyond the front may be relatively ubrup, or moregentle,dependingupon the conditions.This wasdiscussed in the list chapter in connectionwith the works of Mandl and volek and of Hearn. Much of the heat introducedwith the steamis lost to the overburdenand to the underburdenby thermal conductionin the mannerdiscussedearlier. In the situation shown in the figure it is assumedthat the hot zone has reachedthe overburdenand underburden.In practice,it is possiblethat conditions may existin which the steamzonehasnot yet extendedto the upperand lower limits of the reservoir. A particularlycommonand importantsituationis that wherethe steamzone has risen, becauseof gravity effects,to the top of the reservoirbut has extended only part of the way to the bottom.Under theseconditionsthe oil belowthe steam zoneis beingheatedbut is producedslowly,and the potentialthermaladvantageof havinga thick reservoirto heatmay not be realized.lt is a challengeof thermil recoveryengineeringto devisesystemsby which the maximumavailablethicknessof reservoirmaterialis producedin orderto minimize the areaof over-and underburden to which heat is beinglost. Steamstimulationtendsto do this initially. In any case,as time goeson the steamzoneexpands,and the areatfiat is being heatedaboveand belowincreases. As a resultthe heatlossesalsoincrease,and lnjector
producerl
I i-->
.--->
Steam zone
warer flowtng lnrough
slow-moving oil bank___1,-
i->
Water
.9
E
Steam
E o
oil
n ------\
$ |
i
a smallerpod heating.The ited by inrerf The spr mining the u and underbu it takeslonga is greater. The dcs mal efficiency wells involrrcd the difficultv i in maintainiq when cold rig fingeringin C Tl.pical r of 2to 6 rres patternin Fgr seven-spotpea Figure4.5).At three prodrrc equal-the'ior from the -si& t ha : 10.m A featurt the project mr producersas e the bypassedo in this chaper Whenrh downdipin cr ment front. Th
---__..\
|
122
Figure 4.3 Diagram showingthe Distribution of Temperature,Pressure, and Saturationsin a Hypothetical One-DimensionalSteamflood
Steamflooding
Chap.4
l'!
TemperatureCIc
listributionis eivenin
conditionsaround a rell is nearlyconstant t temperatureprevails in w'hichthe temperarv be relatively abrupt ussedin the lastchapHearn. he overburdenand to ssedearlier. hat the hot zone has xsible that conditions : upp€rand lower limwherethe steamzone yoir but has extended te oil belowthe steam thermaladvantageof rallengeof thermalreavailablethicknessof rf over-and underburo this initially. nd the areathat is be;sesalsoincrease,and
a smaller portion of the heat in the injected steamis employedin useful reservoir heating.The heat lossesincreaseup to the point wherearealgrowth becomeslimited by interferencewith the neighboringpatterns(seeFigure 2.4). The spacingbetweeninjectorsand producersis an important factor in determining the utilization of heat. Large spacingsresult in large areasof overburden and underburdenhaving to be kept hot for longerperiods of time. For a given flow it takes longer to drain the oil betweenthe injector and the producer if the spacing is greater. The designof a steamfloodinvolves an economicbalancebetweenthe thermal efficiency of closespacingand the lower well investmentrequired for the fewer wells involvedwith larger spacings.Another factor, particularlywith tar sands,is the difficulty in establishing communication.Sometimesthere is alsothe difficulty in maintainingcommunication,sinceinterconnectingflow pathsmay tend to block when cold viscousoil drains into them by gravity drainage.(Seethe discussionon fingeringin Chapter5). Typical commercialsteamfloodprojectshave productionwells with spacings of 2 to 6 acreswith either one injection well per productionwell (inverted five-spot pattern in Figure 4.4) or one injection well for every two production wells (inverted seven-spotpattern in Figure 4.5). Line-drive configurationsare also common(see Figure4.5).Another popularconfigurationis the invertednine-spot;this resultsin three producersper injector.In this arrangement,the producingwells are not all equal-the "corner"wells (2, 4,6, and 8 in Figure4.4) havedifferent surroundings from the "side"wells (3,5,7, and 9). (Note:I acre= 43,560ft2 = 0.405ha and t ha : 10,000m2.) A featurethat is commonin manysteamfloodsis the additionof infill wellsas the projectmatures.Theseare frequentlyaddedwhen steambreaksthrough to the producersas a resultof gravity override.Infill wells allow the recoveryof someof the bypassedoil which lies belowthe steamzone.This is discussedfurther later on in this chapter. When there is a dip in the reservoirit is usuallyadvantageous to drive the oil downdip in order to make use of the gravitationalforce to stabilizethe displacement front. This is discussedin the next chapter. Injectionwellsareshownwithdiagonallinesthroughthem
d
(/
d
,g
a-,,--------a
aaooooao aaQaaaS0
o
O----------t
d
d
d
o
o a
e?e9oao ;^ ]"?'a'z
o
o
o o
o.-
ii
//,od INVERTEDFIVE SPOT PATTERN
)iagramshowingthe of Temperature,Pressure, rnsin a Hypothetical onal Steamflood
amflooding
Chap.4
producer 1 injector and1 (4quarters) perpattern
o
i9.-ez.-,a6oo
o.
INVERTED NINESPOTPATTERN 1 injectorand3 producers (4quarters+4halves) per panern
Figure 4.4 Inverted Five- and Nine-SpotWell Patterns Temperature Distribution in Steamflooding
123
Inloctlonwells ar6 shownwlth dlagonalllnesthroughthem.
i
fr q )J
V) i
@ i
3
a a
o
'12
/
i
iz
,at
164 ''r ac
6% oil satur.:: a steamf lft.i
i
o
STAGGEREDLINE DRME
II,IUER TEDSEVENSPOTPATTER N 1 Injeclor and two producers (slx one-thlrds)per pattern Figure4,5 InvertedSeven-Spot and Staggered-Line Drive patterns
1 Inlectorperproducer
FINGERING In the displacement processshown in Figure 4.3, the condensedwater runs more rapidly than the oil to the productionwell becauseit is much lessviscousthan the oil that it is displacing.Frequentlythe water runs as separaterivulets, or fingers, through the oil; the flow pattern can be visualizedas oil and water running togetheralongseparateflow paths,with the water velocitybeing much higherthan that of the oil. Thus, rather than dry oil, a mixture containingvery substantial quantitiesof water is produced.The fingeringof water through the oil may alsobe promotedby heterogeneities within the reservoir,including those createdby the fracturingthat resultsfrom steaminjectionat pressures abovethe minimum in situ stress.Passage of the water mustoccur if steamis to continueto supplyheatto the reservoir.If the removalof condensateis not possiblewith the availablepressure drops,then the processwill be slowedgreatly. Even if therewere no fingeringdue to the formationof unstablewater/oildisplacementfronts, the water would still run through the oil layer, with an early breakthroughbecauseof the adverseviscosityratio. It is shownin the next chapter that when an attemptis madeto displacea viscousoil with water,breakthroughof the water occursrapidly,becauseof the relativepermeabilityand viscositycharacteristics-even if the flow is diffuse rather than segregated (i.e., even if the water doesnot run as fingers). GRAVITYOVERRIDE A major difference between the practical situation and the flow depicted in Figure4.3 is that the differencein densitybetweenthe steamand the liquidsin the reservoircausesthe steamto override-i.e., to flow abovethe oil; the situationis as depictedin Figure 4.6. Eventuallysteambreaksthrough at the productionwell. The upper steam-swept regionhas a much lower residualoil saturationthan the lowerwater-floodedregion.For example,Blevinsand Billingsley(1975)report a 124
Steamflooding
Chap.4
:l
this project rcp ZOnerepre\':'l:( sure gradien: :r tion rate in o:J A sien::: w i l l r e s t r i c t: : e sure drop :rJ flooded zr.nu s t e a m ,u h r ; : ; . : 1 9 8 2 ,A l - K ; : : ; to be effectire ture and tha: t required. Foam meabilitrstr.:. Promisint the Midu ar-Su the injected rtci that the pro!-c: Friedman flooding of Bcr tant. Thel frrun oil saturationrt formed at high terial at lo* r el s a m el o \ . \ ' e l $ Mohamm test involr ine ir in California. t resulted in thc pounds of AOS R e s u l t sl r ' field in Califtrrr The test inrtrlr s t e a m .P o s i t i re causeof the un was reported c* The addit lated approach
GravityOverrrd
1a
lgh them.
Injection
CTPATTENN 0 Pfoducers Per Pattern 'rvePatterns
enseowater runs more 'h lessviscousthan the ate rivulets,or fingers, and water running toeing muchhigherthan ainingvery substantial rgh the oil may alsobe I thosecreatedby the 'e the minimum in situ re to supplyheatto the the availablepressure i unstable water/oildisil layer, with an early wn in the next chapter water,breakthroughof r and viscositycharac(r.e.,evenif the water
the flow depicted in t and the liquids in the he oil; the situation is at the production well. ual oil saturation than lingsley (1975)report a aamflooding
Chap.4
Production
Figure 4.6 Gravity Override of Steam
6Vooil saturationin the steam-swept zoneversus23Vofor the water-sweptzonefor a steamfloodin the Kern River field in California.The upper Steam-swept zonein this project representedabout one-third of the sweptvolume and the waterfloodetl zone representedtwo-thirds.Once steamhas broken through, there is little pressuregradientto removethe oil, particularlysinceit is necessary to reducethe injection rate in order to control steambypassing(i.e. steam"coning"). A significanteffort is being made currently to developsteamadditivesthat will restrict the flow of steamwithin the steamzone,therebyincreasingthe pressure drop and causingmore rapid encroachmentof the steam into the waterflooded zpne.A popular approachis the addition of surfactantmaterialsto the steam,which causethe formationof foamwithin the steamzone(e.g.,Dilgren et al. 1982,Al-Kahaafji et al. !982, and Eson and O'Nesky1982).For foamingmaterials to be effective,it is necessarythat they be chemicallystableat the steamtemperature and that their cost be low enoughfor them to be economicin the quantities required)'Foamadditivescan alsoreducethe bypassingof steamthroughhigh permeabilitystratain heterogeneous reservoirs. " Promisingresultswere obtainedby Ploegand Duerksen(1985)in field testsin the Midway-Sunset field in Californiain which sulphonatesolutionswere addedto the injectedsteam.Theseauthorsconcludedthat incrementaloil wasproducedand that the processwas economical. Friedmann and Jensen(1986)have reported an experimentalstudy of the flooding of Bereacoreswith foamspreparedusingChevronChaserSD1000surfactant. They found that the surfactantreducedthe relativepermeabilityto gas.High oil saturationsreducedthe degreeof foam formationand propagation.Foams,preformed at high velocitiesin sandpacks, could be propagatedthrough reservoirmaterial at low velocities.However,it wasnot possibleto generatefoamsin situ at the samelow velocities. Mohammadi,van Slyke,and Ganong(1989)reportedthat in a steamflooding test involving four five-spot patterns in the Potter sand in the Midway-Sunsetfield in California, the addition of NaCl, alpha olefin sodium sulphonate,and nitrogen resultedin the incrementalproductionof 207 kB of oil in 2 years.Four million pounds of AOS were injected. Resultsfrom a surfactant/steam-injection field test in the Guadalupeheavyoil field in Californiahavebeenreportedby Mohammadiand McCallumin California. The test involved the addition of alkyl toluene sulphonateand nitrogen to the steam.Positiveresultswere obtained,althoughthe test was stoppedabruptlybecauseof the unavailability of steam.An incrementalproduction of 29,400B of oil was reportedas the resultof the injectionof 257,0001bof activeAIS. The addition of thin film spreadingagents(TFSA) to the steamis another related approachin which there is interest.Thesematerialsare madeby treatingpheGravityOverride
125
nol with formaldehydeand then reactingthe resultingpolyolswith ethyleneoxide or propyleneoxide. Productsof this type are frequentlyusedasdemulsifiersto treat heavycrudes. In this applicationthey are thought to work by being adsorbedat the water-oilinmaterialsthat stabilizethe water terfaceand displacingthe bulky asphaltene-type in the oil emulsion.With the thinner demulsifiermoleculesat the interface,water dropletsare thought to approacheachother more closelyand then to coalesce.It is thoughtthat the effect of the TFSA in steamrecoveryis to promotethe waterwetting of the rock-i.e., to detachoil from oil-wet portionsof the surface. Blair, Scribner,and Stout (1982)describetestsin California in which indications of significantly improved performancewere obtained for such a chemical in cyclicsteamstimulationoperations.Further results(Stout,Blair, and Scribner1983) have shown that the effects of the TFSA appear to persist into subsequentcycles eventhough additionis stopped. STEAMFLOODINGMECHANISMS Reductionof Oil Viscosity The main physicaleffectof steamthat promotesthe recoveryof heavyoil is the reversiblereductionin viscositythat resultsfrom increasingthe temperature.This reduction in viscosityis very dramatic;with oil sand bitumen, it is almost of the nature of the meltingof a solid to form a fluid liquid. relationshipsfor a varietyof biFigure 1.9showstypicalviscosity-temperature tumensand heavyoils and alsofor lighter oils. Figure 4.7 showsthe effect of temperatureon the ratio of the viscosityof variousoils to that of water.The reduction in the viscosityof the oil makesit easierto push the oil at appreciablerateswith the pressuregradientsavailable.There are also other effects that promote the mobility of the oil. The first of theseeffectsis due to the improvementin the ratio of the viscosity of the oil to that of the water.This makeswaterpercolationableto dragoil at a 1,000,000
fasterrate tct thc waterfloodednq Even after mobility ratio. ll tendencvfor gee the steamcm& exceptwhenit is manner.the co fingers. This mech allowsfurther ct movedis largeri volume of rescrr (measuredas rz The calcu! from a reservtir I The quantitl of r ume of resentir the table repnesc steamtemp€ratu losses.In relatir doublingthe gce Changesin R*
Another phenoo floodsis that th thereis not a coo temperatureche tive permeabilit reduced.Anotha to be lower und
in cp at 100o C Parameter is oilviscosity
o
TABLE 4.7 Ouatl
1O0,000
G
TE '6 o o o
10,000
1,000
Stcr 100
10
0
100
300
200
in DegreesCelsius TemPerature Figure 4.7 The Effect of Temperatureon the Ratio of Oil Viscosity to Water Viscosity
126
Steamflooding
(t)or
Chap.4
in B/B.
Steamfloodirg lle
rls with ethyleneoxide ) to treat heavycrudes. led at the water-oilinhat stabilizethe water at the interface,water I then to coalesce. It is )romotethe waterwetthe surface. ornia in which indicafor sucha chemicalin air. and Scribner1983) into subsequent cycles
i of heavyoil is the rel temperature.This rern, it is almost of the hipsfor a varietyof biows the effect of temf water.The reduction appreciablerateswith that promotethe mothe ratio of the viscoson able to drag oil at a
fasterrate to the productionwell, which resultsin more effectivedepletionin the waterfloodedregionfor a givenvolumeof water (condensate). Even after heating,water still fingersthrough the oil becauseof the adverse mobility ratio. However,aswill be discussed in the next chapter,there is muchless tendencyfor steamto do so. It seemslikely that in most steamfloodcircumstances, the steamcondensationfront advancesin a stablemanner (i.e., without fingers) exceptwhenit is movingupward.While the condensation front advances in a stable manner, the condensatedrains through the oil to the productionwell, often in fingers. This mechanismremovesthe relativelylargevolumesof condensate and thus allows further condensationof the steam.Often the condensatethat must be removedis largerin volumethan the volumeof the oil produced.In order to heat a volume of reservoir to steam temperature,more than one pore volume of steam (measuredas water) is required. The calculatedquantity of steamrequired to raise a high-qualityreservoir from a reservoirtemperatureof 10'C to the steamtemperatureis given in Table4.7. The quantityof steamis expressed as the volumeof steamrequiredto heatthat volume of reservoirwhich containsa unit volumeof oil. The calculatedquantitiesin the table representthe heat required solelyto raise the reservoirand its contentsto steamtemperature.It is necessary, in addition,to provide steamto supplythe heat losses.In relativelyefficient situations,this will have the effect of approximately doublingthe steamrequirementsshown. Changesin Relative Permeability Another phenomenonthat plays a role in increasingthe effectivenessof steamfloods is that the relativepermeabilityeurveschangewith temper4tqre.Although thereis not a consensus on this, experimenters havegenerallyfound that raisingthe temperaturechangesrelativepermeabilitycurves.The main effect is that the relative permeabilityfor oil flow tendsto be increased,and the residualoil saturationis reduced.Another factoris that the relativepermeabilityfor liquid waterflow seems to be lower under steamfloodingconditionsthan it is with ordinary oils having TABLE a.7 Otlantityof Steam Requiredto Raisea High-QualityReservoirto Steam Temperature Basis: Porosity Oil Saturation Reservoir Temperature SteamQuality SteamTemperature
us iscosityto Water
32% 80% 10'c 70%
('c)
Ratio of Steam to oil (m3/m3f1)
100 150 200 250
0.52 0.86 t.2'1 1.81
(t)orin B7B. amflooding
Chap.4
Steamflooding Mechanisms
127
viscositiesat room temperaturesimilar to that of the heavy oil at steamflood conditions. A possiblepartial explanationfor theseeffectsis that waterhasa tendencyto form water-oilemulsions,within the reservoir,with bituminousoils under steaming conditions.This can explain the lower residualoil, since the residualoil droplets are "diluted" with micron-sizedropletsof water.In a way, a steamfloodcan be visualizedas beingpartially miscible.Another reasonfor a lower residualoil saturation which is applicablewhen there is steamsaturationis the steamdistillation effect;this is consideredlater.Emulsificationalsohasthe effectof reducingthe apparentwater-relativepermeabilitybecausesomeof the water is tied up with the slow movingoil phase. If in situ emulsificationdoesplay a role in the displacementof heavy oils, then it seemslikely that the conditionsof the experiment-such as thoseinvolved in the preconditioningof the core or sandpack-as well as the measuredsaturations,will play an important role. For example,changesthat affect the wettability of the core, the prefloodingconditions,and whether steamhas contactedthe oil may be expectedto have important influences.Experiments(Chungand Butler 1988,Jamaluddinand Butler 1988)have shown that water in oil emulsificationis promotedby the direct condensation of steamon colderbitumenand alsoby an oilwetted reservoirmatrix. There is less emulsionproduction,if any, when oil and phases.The effectof emulsificationupon the relawaterflow togetherascondensed tive permeabilityof the oil and wateris thus intertwinedwith the conditionsin the steam-saturated regionsof the reservoir,particularlyat the condensation interface. Although oil and water flowing together probably do not emulsify, water in oil emulsionformed at the condensationinterfacecan be pushedaheadof the steam chamberand then flow in the absenceof steam. Resultsfrom somepublishedstudiesof the effect of temperatureon relative permeabilityare given in Figures4.8 and 4.9.
100 -80
; = lt (E60
o
E o o40 o 620 E 020
u!
.{ paper I relativepcrE vent and tbeo I them. It appc very'deperdc follor*ed furrl Th€ sfr complicatedr effect an irry MYHILL AND STB(-
1.O Cetus oil, 22 o API Midway Sunset Unconsolidated sand
tr
.9 0.8 a) (u
*'o
r.
l!
I o.o
i\
E b o.c o. (, 2
74 o F \ r r
lt o o
..\ 2osoF
6 0.2 IE Knv
06
128
---.'
20 40 60 80 Water Saturation, 7o Pore volume
Figure 4.8 The Effect of Temperature on Relative Permeability(Data of Montgomeryreportedin Wu 1977)
Steamflooding
Chap.4
The paper by field. It usestl to providera, The be{ sizeof th€ $a (1959)apprd the possitility Thesemetbod The otf,r heatinjectedit to the saturali The rul ity of usinga t isee
aln d
Myhill and Stag
rvv oil at steamflood ater hasa tendencyto usoils under steaming e residual oil droplets steamfloodcan be vi'er residualoil saturathe steamdistillation :ct of reducingthe ap:r is tied up with the cementof heavy oils, ;uch as those involved the measuredsatura, affect the wettability has contactedthe oil ts (Chung and Butler n oil emulsification is ren and alsoby an oilif any, when oil and fication upon the relar the conditionsin the ondensation interface. emulsify,water in oil d aheadof the steam
tH
s.o
A--A
g
77 oF 340 oF
kro
t
(E60 o
l\
E o e+o
\
o .E
r,
?620
.|
G
20
40
60
.^ kr* 80
l(X)
Water Saturation,"/oPV
Figure 4.9 RelativePermeability Curves for BereaSandstoneCore (from Lo and Mungan 1973)
A paper by Bennion, Moore, and Thomas(1983)indicatesthat vastly different relative permeabilitycurves are obtainedif heavyoil coresare extractedwith a solvent and then restoredthan if they are preservedwith the originalreservoirfluid in them. It appearsthat the relativepermeabilitiesof corescontainingheavyoils are very dependentupon the state of wetting of the porous solid. This lead should be followedfurther.3 The effect of steam treatment and temperatureon relative permeabilitiesis complicatedand not understood.Overall, however,it appearsthat steamingdoes effect an improvement.
mperatureon relative MYHILL AND STEGEMEIER'S APPROACHTO STEAMFLOODING
'he Effect of Temperature 'ermeability(Data of reportedin Wu 1977)
rnflooding
Chap.4
The paper by Myhill and Stegemeier(1978)should be read by all workers in this field. It usesthe heat conductionand heat convectionideasof the previouschapter to provide an estimateof the efficiency of a steamflood. The basic idea used by Myhill and Stegemeierinvolvesthe calculationof the size of the steamzone from a simple energybalance using the Marx-Langenheim (1959)approachmodified by the ideasof Mandl and Volek (1969)in order to include the possibility of all the steambeing condensedbefore it reachesthe heat front. These methodswere discussedin the previouschapter. The objectiveis to calculatethe volume of the steamzonefrom the amount of heatinjectedinto the reservoir,the heat neededto raisea unit volume of steamzone to the saturationtemperature,and the heat lost to the overburdenand underburden. The method is simpleto use, is rapid, and gives a useful idea of the practicality of usinga steamflood in a particular situation. sSeealso the discussionof the work by M. Kwan (1988)in Chapter 1, page 18.
Myhill and Stegemeier's Approach to Steamflooding
129
Summary of Myhill and Stegemeier'sAssumptions
This p
The basicassumptions for the calculationare as follows: 1. The reservoircontainsa uniform amountof oil per unit bulk volume as defined by the productof porosity,net to grossthickness,and oil saturationin the net pay. Grossthicknessand areaper injectorare alsoconstantthroughout the reservoir2. Thermal properties,includinginitial formationtemperature,heat capacityof reservoirrock, and heat capacityand conductivityof cap and baserock are assumedconstantthroughoutthe zone. 3. Steamis injectedat a constantpressure,quality, and rate per injector. 4. Verticaltemperaturegradientsin the reservoirare zero. 5. Heat lossesfrom the steamzoneare by conductiononly and occur normal to the reservoirinto the cap and baserock. Heat is transferredin the reservoir by convectiononly, and heatpassesthroughthe condensation front only after Mandl and Volek'scritical time. 6. The quantity of residualoil remainingin the steamedchambercan be representedby an average,assumedresidualoil saturation.
u'here
f, f,.
Oncethe th culatedfs t capacitl'of r
or
q'here I I tpc
Outline of Method The heart of the methodis Figure4.10.It allowsthe thermalefficiencyof the heating to be obtainedfrom a knowledgeof the variablesin the dimensionless time numberand the steam-condition parameter,which is calledfi".
Myhill and S displacedfro saturationri
G
U Li
Z^6 N
u'hercq (
=
,s
U
'o L
0.t
L
t
o o z !! o
The rate of < rewritten fc
0.4
L
r
lrJ J
0.2 = G U
-
F
The valueof Limitatkrc D T M E N S T O N L ETSI M S E ,t D Figure 4.10 Fractionof Heat Injectedin Steamfloodthat Remainsin SteamZone (from Prats 1982)
130
Steamflooding
Chap.4
This approa aqueouscood
MyhillandSE
This parameteris the ratio of injected latent heat to injected total heat: H^ f'i In' = ,1, - 1a,= 110 bulk volume as dernd oil saturationin ;o constantthroughure,heatcapacityof p and baserock are , per injector.
wherefi I H, H*,
is the injected steamquality measuredat the bottom of the injection well is the latent heat of evaporationof water is the enthalpy of the injected steam is the enthalpy of liquid water at reservoir temperature
Oncethe thermalefficiencyis known, the volumeof the steamchambercan be calculated for the injection of a given amount of steam and a knowledgeof the heat capacityof a unit volumeof the chamber. Heat in steamchamber= HotEn,= VcbC)c(Ts- Tn)
rnd occur normal to ned in the reservoir rtion front only after amber can be repre-
lficiencyof the heatdimensionless time
Vc=
HotEn, (pC)c(Ts - Tn)
(4.3)
where Vc is the volume of the steamchamber Ho is the averageheat injection rate (pC), is the volumetric heat capacityof the steamchamberafter the oil has been displaced Myhill and Stegemeierrelate the volume of the steamchamberto the volume of oil displacedfrom the steamzone.To do this, they assumea value for the residualoil saturationwithin the steamzone: Q"=
Vc0(5" - 5",) Ho6(5. - So,)E6,t (pC)c(Ts- Tn)
(4.4)
where 4, is the cumulativevolume of oil displaced - 6 is the porosity otS, is the initial oil saturation {S,, is the residualoil saturation The rate of oil displacementat time / is obtainedfrom equation3.42, which may be rewritten for times before /" as
n = ffie'o
erfc(\/tp)
(4.s)
The value of the function of tp mal be obtained from Table 3.1. Limitations This approachneglectsthe oil removed ahead of the steam zone by the flowing aqueouscondensate.This amount is often quite small, but it can become signifimflooding
Chap.4
Approachto Steamflooding MyhillandStegemeier's
131
cant, particularlywheresignificantheat is carriedpast the condensation front, for injectiontimes greaterthan the Mandl-Volekcritical time. Unlessan allowanceis madefor it in choosingthe value of so.,the approach alsoneglectsthe smalloil bank (seeFigure4.3 and chapter 5) that buildsup behind the condensate front. The oil saturationin the steamzonetendsto be reducedfurther by the actionof the flowing steambehindthe front. The effect is due both to the sweepingaction of the steamin moving the oil and also to steamdistillation. The latter mechanismremovesthe lighter fractionof the oil selectively,leavingbehind a reducedsaturationof oil which is heavierthan the original crude. Figure 4.11(FarouqAli 1982)showsexperimentalvaluesfor the residualoil saturationtakenfrom a numberof experimentsand literaturedata.The meanvalue appearsto lie in the range70to ISVo.a There is a trend for lower residualoil saturation to be obtainedwith lower initial oil viscositiesand with highersreamtemperatures (pressures). The data are scattered,probablybecauseof the variationof other factorssuchas the propertiesof the reservoirmatrix. Myhill and Stegemeierassumethat the volume of the oil displacedis also equalto that produced.This is a weak part of their method,particularlyif an attempt is madeto predictthe oil productionduringthe earlypart of the flood. Also, 9.tlmay be displacedelsewherethan to the production*"it, particularlyin unconfined or only partially confinedpilots.It may alsobe left behlnd in the chamberas bypassedoil. The strict applicationof the Myhilr-Stegemeier approachwould predict the highestrate of production(for a constantsteaminjectionrate) at the start of the Figure 4.11 SteamfloodResidualOit as a Function of Temperatureand Oil Viscosity (from FarouqAli 1982).Some of the data (the solid circles)in this figure are from literature references and some(the open circles)from work reportedfor the first time in Farouq Ali (1982).The numbersin brackets are the steamtemperaturesin degrees Fahrenheit.The numberswithout bracketsare literature referencesas follows:
25 >20 o. * j15
o
Ero so
31 Blevinset al. (1969) 32 Bursellc. c. (1979) 33 Bursell,G. G. and Pitmann,G. M.
o E5
(Le7s) 100
ro1 fi2 103 104 Oil Viscosityai Tp in cp
105
34 Ozen,A. S. and FarouqAli, S. M. (1969) 35 Valleroy,V.V. et al. (1967)
"The tendencyof the steam to override introducesa difficulty in applying the Myhill and Stegemeiertheory, particularly in thick reservoirs.At the point of steambreakthrough,the average steamzonethicknessis lessthan the height of the reservoir.After breakthrough,there is a tendency for heatedoil to be bypassedbecauseof insufficient pressuregradientto move it to the production well. In this circumstance,the averageresidualoil saturationwithin the heatedregionis higher than that found in one-dimensionalsteamdisplacement.
132
Steamflooding
Chap.4
flood sirrc predicred suppll rhc Artq not predic speciflin r pracrice.rl impossibl the ecorn Th€ rates are ! overburdc high rares end of gea simpleapg useful.ft b rate of inF
Comparbo
Figure{-l? numberof r Each of ttr ment is g€D Figun fields.trr'or ditionalpm sent the tot obtaineds-i
Ff
F" 2l-
F" 0
Myhilland Sre
:nsationfront, for 5* the approach tbuildsup behind o be reducedfurect is due both to *eam distillation. tively, leavingbeil crude. lr the residualoil r. The meanvalue esidualoil saturaer steamtemperavariationof other displacedis also :ticularlyif an atrf the flood. Also, icularly in unconin the chamberas rould predict the I the start of the nflood ResidualOil emp€ratureand Oil rrouqAli 1982).Some ,lid circles)in this eraturereferences n circles)from work rst time in Farouq mbersin brackets peraturesin degrees umberswithout ture referencesas r%9) 1979) and Pitmann,G. M. d FarouqAli, S. M.
flood sincethe predictedthermal efficiency is highestthen. The rate would then be predicted to fall with time due to the increasingproportion of the heat neededto supplythe lossesabove and below the growing chamber. Another weaknessin the Myhill-Stegemeierapproachis that the theory does not predict what the experimental conditions will be. For example, one has to specifyin the calculationboth the steampressureand the injection rate,whereas,in practice,the injection pressureis dependentupon the rate. [n many cases,it may be impossibleto inject steamat the desiredrate without fracturing the reservoir.Often the economicswill dependupon the rate at which the processcan be conducted. The Myhill-Stegemeiermethod leads to the conclusion that high injection rates are most efficient becausethey allow production with less heat loss to the overburdenand underburden.However there are practical limitations to the use of high rates.Nevertheless,the method doesrationalize the resultsfound toward the end of steamfloodswhen most of the displacedoil has been recovered;for such a simple approach,the agreementbetween the predictions and the results make it useful. [t is also useful for prediction if someexperimentaldata are availablefor the rate of injection that may be achieved. Comparisonsof Theoretical Predictionswith Data Figure 4.12showsthe oil-to-steamratios predicted by Myhill and Stegemeierfor a number of scaledlaboratory steamfloodscomparedwith the experimentalvalues. Each of these points representsconditions well on into the flood, and the agreement is generallygood. Figure 4.13showsa similar comparisonfor field steamdrives. For many of the fields, two experimentalpoints are shown. The lower circlescorrespondto the additional production ascribedto the useof steam,whereasthe upper trianglesrepresent the total production;i.e., they include the productionthat would have been obtainedwithout steam. tt
afterMyhlllandStegemeler 1978
tr o
E o o. x ul 6 tt o
Mt.Poso (lowpressure)D,;
; 0.s o tr Midway-Sunset
E
o
tr SchoonEbeck Mt. Poso (highpressure)
o
et al. (1967)
c
rlying the Myhill and Ithrough, the average 3.h.there is a tendency rc it to the production d regionis higher than
looding
Chap. 4
.E (!
.Tatums Coalinga
.z t (t IIJ
0
00.5
1 CalculatedequivalentOSR
Myhill and Stegemeier'sApproach to Steamflooding
Figure 4.12 Comparisonof ExperimentalModel Resultswith CalculatedValues
133
Overril Another*av ( thicknessTh loss,eventhd is later hearcd becauseit hr availableto r Anolhcr age residualo spondingto tl one can cqri lower valued
1978 alterMyhlllandSt€gemeler o AdditionalOiusteamRatio(OSR) A TotalOSR
tr o o g
70% ol
(!
.u
6
f
cr
3G o.s tr
,9
A
d{
E9br
68,8
{EF/y #;EA"ti
It ll
I .9
€.-:Ad u-^Y
5
:^'cY'z'E-E 6
tt
Dl .60
l/ o (! c
-
J
6
F
{EP
Ten-Pattrn t
1 0.5 Calculated Addltlonal Equlvalent OSR
Figure 4.13 Comparisonof Field Steam-DriveResultswith Calculations
In general,the experimentalfield projectdatain Figure4.13tend to fall below the solid theoreticalline and lie mostlyin the rangeof 70 to I00% of the theoreti70Voof the theoreticalprediction.Myhill and Stegecal. The brokenline represents meierpoint out that there are severalreasonswhy field data might be expectedto be below the theoretical,includingthe fact that much of the field data comefrom patternsthat are unconfined.In suchpatterns,someof the mobilizedoil may be driven outsideof the pattern.Another reasonis that steamoverridemay resultin the averagethicknessof the steamzonebeinglessthan the reservoirthickness. As was shownin Chapter3, the followingequationpredictsalmostthe same OSR as doesthe more complicatedMarx-Langenheimexpression. OSR =
osR-", l---f-----
(3.4e)
r'7696 LS" ( T s- Z ^ ) ( 1+ L $ \ / W )
(3.s0)
1' -, 8 -\tll " t |.' J 'n'
ReservoirChra
ry
od1 :ir ' tt
T, 5, o t (Oglesbr et al ll
The resen'cirr 3.02x lff Bd FigureJ.l{. The cil il
?s and Za in "F, / in d, and h in ft. lt predictshigheroil-steamratiosfor the followingconditions: o o r o
As an exampl of the Kern I Billingslel-tl9'l in a patternc( spot averaged producenand given in the fr
Higher valuesof ASo-i.e., higher,.S,or lower S,, Higher porosity More rapid recovery,lower / Thicker reservoirs,high h
The lower oil-steamratiosfound in practiceas comparedto thosethat may be expectedfrom equation3.49 result from the mechanismbeing different from that postulated.
The recoven'r oil saturatiqr r m a i n i n gu i t h i n steam-s\r'epta
Chap.4
Myhill and Steg
134
Steamflooding
Override of the steamresultsin undisplacedoil remainingin the reservoir. Another way of looking at this is to saythat ft (in practice)is lessthan the reservoir thickness.The heatthat haspenetratedbelowthe steamchamberis equivalentto a loss,even thoughit resultsin heatingthe oil below.Even if much of this lower oil is later heatedto the steamtemperature,it tendsto staywithin the steamchamber becauseit has beenbypassedby the advancingfront and little pressuregradientis availableto move it. Another way of looking at the problem of bypassedoil is to saythat the average residualoil saturationin the steam-heated region is greaterthan that correspondingto the value for a one-dimensional steamflood.From this point of view, one can considerthe reservoirheightto be the appropriatevalue for ft, but a much lower value of AS" is requiredto allow for the bypassedoil. Ten-Pattern Steamflood As an exampleof this idea,we will considerthe Chevron"Ten-PatternSteamflood" of the Kern River Field in california, which has been discussedby Blevin and Billingsley(1975)and by Oglesbyet al. (1982).The projectconsistedof a steamflood in a pattern consistingof ten contiguousinvertedseven-spots. The areaper sevenspot averaged6.1 acresto give an averagespacingof 320 ft between injectorsand producersand alsobetweenadjacentproducers.Characteristics of the reservoirare given in the following table.
mparisonof Field sultswith Calculations
t3 tend to fall below Wc of the theoretir. Myhill and Stegeight be expectedto eld data come from obilized oil may be rrride may resultin ;€rvoirthickness. cts almostthe same on.
(3.4e)
I ReservoirCharacteristics: Ten-PatternFlood, Kern River
I
Depth Oil gravity Net sandthickness Tn r.s
s, q
(3.s0)
700-797 ft 14'API 97 ft 90"F Approx. 310'F 0.52 (after primary production) 0.34 4000mD
(Oglesbyet al. 1982)
The reservoirwassteamedfor 7 y; 18.58x 106B of steamwere injectedto produce 3.02 x 10"B of oil (i.e., OSR = 0.16;SOR : 6.15).Performancedata are shownin Figure4.14. The oil in placein the reservoirinitially is given by 6S,Ah=0.34x0.52x61 x 43560x97 = 45.6x 106ft3 or 8.1 x 106B rosethat may be exdifferent from that
The recoverywasthus 37Voof the oil at the end of the steamflood,and the average oil saturationremainingwas 0.52 x 0.63 = 0.328.This oil was madeup of oil remainingwithin the steam-swept zoneand of bypassedoil, suchas that beneaththe steam-sweDt zone.
nflooding
Myhill and Stegemeier'sApproach to Steamflooding
Chap,4
135
9.n
FE
6
o
F =
It is clea passedin this project,and m: that has beeno of the producti tion has beenr 4 by the endd 1000B/d (abqr will have beco
10
6 2
20,000 10,000
'$ S u,ooo =q
2'ooo
10,000 o 5,000 * cE _ 2,000
.EE t,o* I I .L
Ten-PatternStrr
5oo
100
| 6 S | 6 6 | 6 Z t 6 8 | 6 9 | Z OI t 1 t Z 2 t Z g t Z q t Z ' t Z 6 t Z t | 7 8 t 7 9 t g g I
Prrmer_ Stearofh \Aarcrfb
Years Figure 4.14 Performanceof Ten-PatternSteamflood(from Oglesbyet al. 1982)
Calculatingthe expectedOSR using equation3.50 and a residualoil saturation of 0.328leadsto OSR =
1769x 0.34x (0.52- 0.328)
San Ardo Str
(310- eo)(1 + r.43fi x 365m = 0.30
This value is much higher than the value of 0.16found in the field and, of course,very much higher than would be found if a lower residualoil fraction had been substitutedin the equation.Part of the reasonfor the high predictionis that someof the injectedheatbypasseddirectlyto the productionwells.[t wasestimated by_Blevinsand Billingsleythat this would reachl8Vo of the injectedheat.sIf allowance is made for this bypassedheat, then the expected OSR would be 0.82 x 0.30 = 0.246.This is still significantlyhigher than the value of 0.16 observedin the field. It is possiblethat the injectedsteammay have had a lower quality than was assumedin derivingequation3.50;steamquality data are not availablein the published information.Another similar factor is that no allowanceis made for heat lossesin the well bore in the precedingcalculation.However,it is unlikely that thesefactorswill accountfor the whole discrepancy. Another possibilityis that the spreadingof the heatedzone acrossthe patterns may have been much more rapid and that the heat lossesare underestimated. Equation3.52 is similar to equation3.50but is basedon the assumptionthat the steamzone spreadsimmediatelyacrossthe flooded area.Using equation3.52 insteadof 3.50for the precedingexampleleadsto a calculatedoil-steamratio of 0.225 or 0.184if allowanceis madefor the bypassedheat.This is muchcloserto the observedrates. tlt will be notedfrom Figure 4.14that the steam-injectionrate wasloweredfrom about 10,000 to 6000B/d during the period 1970to 1975in order to conservesteamafter breakthrough.
136
Steamflooding
Chap.4
Another largr. achievedis thc 1983).Most of t characteristict can be injected Properties of Arri
( T r a v e r s ee t a l l 9
The field has b pattern areaof with this sprin ductionrate.a0 pattern,as sbor Theseinfi zone,as shown MyhillandSteg
It is clear from the precedingcalculations that considerablehot oil was bypassedin this steamflood. This has been recognizedin the Chevron Kern River project, and muchof the remainingheatedoil hasbeenrecoveredby the waterflood that has been operatedsince 1975.During this waterflood, cyclic steamstimulation of the productionwells has beenused.As will be seenfrom Figure 4.14,this operation has beenvery successful,and the cumulative SOR has fallen from 6 to almost 4 by the end of 1980.During this period, the oil production rate remainedat about 1000B/d (about 50 B/d per production well). It is estimatedthat 78Voof.the OOIP will have been recoveredbv the end of the flood. Ten-PatternSteamflood-Oil Recovery 7o Recovery OOIP Primary Production Steamflood Waterflood
iby et al. 1982)
10 J+
34 (20 by end of 1980) 78
t residualoil satura-
San Ardo Steamflood and lnfill Drilling
in the field and, of lual oil fraction had gh prediction is that alls.It wasestimated injectedheat.sIf al:ed OSR would be re value of 0.16 ob-
Another large, successfulCalifornia steamflood in which a high recovery is being achievedis the Texacoproject in the SanArdo field (Traverse,Deibert, and Sustek 1983).Most of the steamfloodrecoveryhas been from the Aurignac zone.This has characteristicssimilar to the Kern River field. Although it is much deeper,steam can be injectedwith a bottom hole pressureof only 125 psig at 1300B/d per well. Propertiesof AurignacZone-San Ardo Area h Depth
ver quality than was availablein the pubae is made for heat r, it is unlikely that zoneacrossthe patare underestimated. assumptionthat the ng equation3.52 in-steamratio of 0.225 uchcloserto the ob-
a K
Tn Oil gravity
1755acres 97ft 2300ft 0.349 1000-3000 mD 100'F 13'API
(Traverseet al. 1982)
,rered from about 10,000 r breakthrough.
The field has been developedusing repeated,inverted nine-spot patterns with a pattern area of 20 acres.It has been concludedthat a 50Vorccovery is achievable with this spacing.In order to achievea higher recovery and to maintain the production rate, an infill drilling has been initiated. Four infill wells are addedto each pattern,as shownin Figure 4.15. Theseinfill wells have the objectiveof removing the oil from below the steam zone, as shown in the cross-sectionaldrawing at the right of Figure 4.15.
mflooding
Myhill and Stegemeier'sApproach to Steamflooding
Chap. 4
137
S A N A R D OF I E L D INTERVAL WITHINFILLS 9.SPOTSTEAM
C R O S S- F L O (
CURRENTFLOODPATTERN
o
d
ao
o
o
o
o
INJECTION
O-lNFlLL
o o + X - SECTION
o
t'igrrr
With furrl the use of foas patesthat a rcc INFILLS
COMPARISONOF SN
An interesting p switchingfrom Figure.l.l' 2.S-acrespacir
* BOP
;'P;'1
|
I
I
I
PRoDUCTION .IPRIMARY I WITHOUT STEAMFLOOD 70 7t 72 73 74 75 76 77 78 79 80 8t 82 Figure 4.15 Addition of Infill Wellsto SanArdo 9-SpotPattern(from Traverse et al. 1983)
In a nine-spotpattern there are three producersper injectionwell. [n the infilled pattern shown in Figure 4.15,there are sevenproducersper injectionwell. Texacoplans to reduce this ratio and to promote recoveryof additional oil by the conversionof the cornerwells of the original nine-spotpatternfrom producers to injectors.This idea is shownin Figure 4.16;it hasbeencalledcross-floodingby Texaco.Also shownin this figure is the conceptof how this conversionwill recover additionaloil from the bank which has accumulatedaround theseproducers.The conversionof the cornerwellswill resultin two injectorsper original 20-acre,ninespotpatternand six producers,or a ratio of three producersper injector.This convertsthe patternto a repeated10-acreinvertednine-spotpattern.Texacoestimates that the recoveryfrom their projectwill increasefrom 50Vofor the original pattern to 60% for the patternwith infill drilling. An important economicconsiderationis that the productionrate is maintained. 138
Steamflooding
Chap.4
;0.8 o o o
s-o.s E o o
6 o.q o
-g = 0.2 E
=
o
0
1
Comparison of St
SAN ARDO FIELD g-SPOTSTEAM INTERVAL IYITHINFILLSANDCROSS.FLOODING
C R O S S- F L O O D I N G
o
d ORIGINAL INJECTOR
INFILL WELL
F CORNER VT,ELL
CONVERTED TO INJECTOR
x-sEcTroN
O
.
.
ADDITIONALAREA TO BE SWEPTBY STEAM THROUGH CROSS-FLOODING Figure 4.16 Cross-Floodingat SanArdo Pattern(from Traverseet al. 1983) O
O
With further operationalchangessuch as waterflooding after steamflooding, the use of foam additives, and the selectiverecompletionof wells, Texaco anticipatesthat a recoveryof 79Vowill be achievableat San Ardo. COMPARISONOF STEAMFLOODAND STEAM SOAK An interestingpart of Myhill and Stegemeier's paper is concernedwith the effect of switching from steamstimulation to a steamflood. Figure 4.17showsthe injection rates,from a scaledmodel,for a steamsoakon 2.S-acrespacingthat was converted to a steam drive after 4.5 years comparedto 82
afier Myhllland Sl€gem€lar1978
| (from Traverse
rtion well. In the in:rs per injection well. of additional oil by ftern from producers lbd cross-flooding by nversion will recover these producers.The lriginal 20-acre,ninercr injector. This conErn.Texacoestimates n the original pattern omic considerationis
rnflooding
Chap.4
t o.s
.9 (t
o
s-o.e E IE
ffi
o
6 o.+ o .= -g 0.2 ? E I
o
o
0
05101520
"*"o"*t
Timein Years
Comparisonof Steamfloodand Steam Soak
Figure 4.17 Cumulative Steam Injection-Midway-Sunset Model Experiments
139
0.5 afierMyhilland Stegemeior1978
o.
5 0.4 o
G q,
g 0.3 o.
.z
5
o
o
g 2 0.4 E f
0.2
o
'F
s=
E 0.1 =
o
0.6
;
0,2
s,*ry4 51015 Time in Years
20
Figure 4.18 Cumulative Oil Productionin Midway-SunsetModel Experiments
Tin!r
JONES'STEAM Df,fY thosefor steamsoakingand to thosefor a soakprojectwith closerspacing.It was possibleto inject more steamwith the flood than with the steamsoak evenwith infilling. Figure4.18showsa comparisonof the cumulativeoil productionfor the same experiments;the parallelwith the injectioncurvesis very striking. Higher injection ratesgive higherproductionrates.The convergence of the cumulativeoil-to-steam ratio curves shown in Figure 4.19is also very interesting.One can seefrom this studywhy therehasbeena generaltrend to switchfrom steamstimulationto flooding in Californiaas a field matures.One may presumethat the sametendencywill developin the Canadianbitumenfieldsasthe projectsmature,asvirgin high-quality tar sandreservoirsbecomemore scarce,and as practicalexperienceis obtainedin the recoveryof tar sandoil by flooding. It is probablydesirableto extendthe cyclic steamstimulationphasein Alberta becauseof the generallyhigher initial oil viscosity.Also, the use of vertical steamfloodingwith horizontalwells (steam-assisted gravity drainage;seeChapter7) will probablyprove to be a superioralternativeto conventionalhorizontalsteamfloodingin many projects.
Therehasbec
clude factorsr Jonestl9 Figure 4.10 fro field with tha modelis alsosl The \trt earlyin the fb rateswhich are periodsin a Ee from one stag Stage 1 During this fin and, in somee 10 0 0
STEAMFLOODING MULTILAYERRESERVOIRS In somecases,multiple reservoirsseparated by impermeable barriersmaybe steamflooded sequentially.In thesecases,someof the heat lost during the flooding of one layer may be presentin the layer above(or below)when it is flooded.A study by Restine(1983)for two such operationsin Getty's Kern River Field shows,as might be expected,considerableimprovementsin the oil-steamratio and higher production ratesfor the preheatedoil sand.This effect affords greatereconomyfor the production of oil from stackedreservoirsthan from single ones. One wonders,for example,whether the extensivesteamingof the Clearwater sandsin the Cold Lake field will result in more economicproductionfrom the higher Grand Rapidsformation,perhapsusing the samewells that were drilled to exploit the Clearwaterformation. 140
Steamflooding
Chap.4
o
(L
E o
,' -n-n
E. c
.9 O I -c,
1n lv
(L
Jones' Steam Dri
1.0
afterMyhilland Stegem6ier1978
tr o
o.u ? .=
SteamSoak
G
o.+ E E f
o
SteamDrive
0.2
Figure 4.19 Cumulative Oil-Steam Ratio as a Function of Time from Start of Steam-Drivefor Midway-Sunset Experiments
05101s TlmeInYears,startlngat 4.5y
Cumulative Oil r Midway-SunsetModel
JONESSTEAMDRIVEMODEL closer spacing.It was seam soak even with oduction for the same king. Higher injection rmulativeoil-to-steam )ne can see from this t stimulation to floodhe sametendencywill , asvirgin high-quality erience is obtained in le to extend the cyclic higher initial oil visI wells(steam-assisted ;uperior alternative to
There has been progressin modifying the Myhill-Stegemeierapproachso as to include factorswhich were ignored in the original treatment. Jones (1981)describesan empirical approach that is simple and realistic. Figure 4.20 from his paper comparesthe reported recovery from the Kern River field with that predicted using the Myhill-Stegemeiertheory. A curve for Joned model is also shown. - The Myhill-Stegemeiermethod gives unrealistically high production rates early in the flood, reasonable onesin the middle,and as the flood reachesits end, rates which are severaltimes too high. Jonesconsidersthat there are three major periodsin a steamfloodand that the dominant factorschangeas the processmoves from one stageto the next. Stage 1 During this first stagethe dominant factor is the very high viscosity of the cold oil and, in somecases,the need to build an oil bank-i.e., to fill gas saturationwith 1000
rarriersmay be steamluring the flooding of it is flooded.A study River Field shows,as reamratio and higher ls greatereconomyfor le Ones. ring of the Clearwater r production from the tlsthat were drilled to
o (L rn
;
Myhilt-Stegemeier :-j ----- -- ---- --f ___.
100
o
E.
o
3 -o o
10
/
L
(L
1'
1968
1969
't970
1971
Yeor
amflooding Chap.4
Jones' Steam Drive Model
1972
1973
Figure 4.20 Comparison for Kern River, California, Steamflood Field Data with TheoreticalPredictions (after Jones198L)
141
oil. During this period, water channelsthrough the oil, and there is little production until warm oil can approachthe productionwell. It is during this period that steamstimulationof the producer(s)can be particularlyvaluableand with heavybitumens,almostessential.(Seelater discussionof tar sandflooding.) Stage 2 where r{
In the secondstagehot oil is movedto the productionwell relativelyeasily,and the productionrate is about equal to the rate of growth of the steamchamber.The Myhill-Stegemeier assumptionsare reasonablyvalid. The peak productionoccurs early in this stage. Stage 3 The Myhill-Stegemeiertheory would allow the secondstageto continue indefinitely, with the production rate dropping asymptoticallyto zero as the area for vertical heatlossesgraduallyincreased.In practicethe drainageareais finite, and the productionrate becomeslimited becauseof the depletionof the reservoir.No allowanceis madefor depletionin the Myhill-Stegemeier theory. Jones' EmpiricalAdjustment Factors
F'
Equatir doesnot l'ani viscosities. O flood. A visc sands;this is A concc volumetricba steamchamh must imagirr bypassed-ut Voo is tl tion 4.9.
Jonesallows for the effectsjust describedby multiplying the production rates predicted from the Myhill-Stegemeiertheory by three empirical factors: Vpo,Aco, and V6p. q-
VpoAcortrm
- S::),r,o erfc({G) - Z^)
(4.6)
Vpoallowsfor the effect of the initial gassaturation.It is given by equation4.7.
Jt
\43,560Ah"65s1
where-4 h^ 6 Ss 4,ini
orelse Wo-l
is effective pattern area in acres is net zone thicknessin feet is porosity is initial gassaturation is injectedsteamin barrels
(4.7)
Zp6,is equal to the squareof the injected steamvolume, measuredas liquid water,dividedby the initial volumeof free gasin the reservoir.When this ratio becomesunity, then Zrp is forced to be 1. ,4co allows for the effect of the initial oil viscosity.It is calculatedfrom equation4.8. It will be noted that the higher the value of poi, the lower is -,462.As the steamzone increasesin area,the value of A6p increases up to the forcedlimit of 1. For an initial oil viscosityof L06cp, the squareroot term is just equalto unity. 142
t
s
,* = ('^"-:tl,ut,=\' 0
where .\'1
Steamflooding
Chap.4
Equatio tion, but this r transactions. The effq particular ere Jones'paperfactors,whicb Jonej u applied to a rl
oAn extrtt jection pressurt.I is heatedeither ri is available. Under lcl ratedwith los-c
Jones'Stean D
there is little producuring this period that rle and with heavybioding.)
(4.8)
0
e to continue indefiro as the area for verarea is finite. and the 'the reservoir.No al.
where-4, is steam zone areain acres A is effective pattern area in acres poi is initial reservoiroil viscosityin cp Equation4.8 predictsthat for an initial viscosityof L06cp, the viscosityeffect doesnot vanish until the steamchamberoccupiesthe entire pattern area.For lower viscosities,the influence is predicted to disappearpart of the way through the flood. A viscosityof 106cp is about equalto the value found in the Athabascatar sands;this is a very high value. A conceptuaiproblemthat ariseswith Jonesfr4cofactor is that of the overall volumetric balancein the reservoir.It is not clear where the displacedoil from the steamchamberhas gone, if it has not been pushed to the production well(s). one must imagine the oil as still remainingwithin the steamchamber-i.e., as being bypassed-until the oil beyondbecomessufficiently fluid to allow it to flow out.6 Voo is the factor that allows for the depletion effect. It is given by equation 4.9.
_& s",
production rates precal factors: Vpo,Aco,
N AS,
0
9.6)
en by equation4.7.
(4.7)
€, measuredas liquid ir. When this ratio be:ffect of the initial oil d that the higher the area,the value of Aco ttof 106cp, the squarenrnflooding Chap,4
orelse Aco=1
(4.e)
orelse Voo=l
whereNr
is cumulative oil production in barrels 43'56944'6s"t N is equalto ooIP t 5.62 Sor is initial oil saturation AS, is equal to ,Soi- S,,
Equation 4.9 appearedwith No in place of Np in the original JPT publication, but this was changedin the version of the paper which was bound in the SpE transactions. The effect of theseempirical factorson the predictedoil production rate for a particular example is shown by the curves of Figure 4.21, which is taken from Jones'paper. This figure also shows the value of the three individual correction factors,which were calculatedasjust described. Jones'method is a very practical one; in his paper,Jonesshowshow it fnay be applied to a wide range of field exampleswith considerablesuccess,althoughjudg6An extremeexampleof
this is where the reservoirfracturesas a result of the high steaminjection pressure.In this case,condensatefollowed by steampassesdown the fracture.The reservoir is heatedeither sideof the fracture but the heatedoil remainsbecauseof the low driving forcewhich is available. Under lessextremeconditions,steamfingers.maygrow into the cold reservoirwhich is saturated with low-mobility,viscousoil. In either caseheatedoil is bypassedrather than produced.
Jones' Steam Drive Model
143
150 -stosr 1-
'c;
100
v. c
.9 o3u
l-
stoso2-
f
proved inject allowingthc When r jeetedstearnr quantitvof st balance:thb much more d ume of stean equalto seru tanceto the f displacedcil, than calcula calculatedinf the effective
stog.
-t5'j":":-";)
{N
Adjusted using Jones' foctors
o (L
0
o !L
q) a
12 Timein Yeors
0.8
Steady-stat of Vertbd t
u.o 0.4 o.2
oo-
Figure 4.21 Predictionof Recovery rate using Jones'Method (after Jones 1981)
The radial fk was discusse lated usingq
ment is requiredin the interpretationof the field conditions.The methodmay be usedeasilywith programmablecalculatorsor personalcomputers. INJECTIVITY The rate at which steamcan be injectedinto the reservoiris not predictedby Myhill and Stegemeier's theorynor by its modifications.Nevertheless, it is of prime importance.The economicsof a steamfloodingprojectare largelydependentupon the ratesat which steamis injected and oil is recovered.Low injection ratesimply slow productionratesand low cashflows. Also, aswasdiscussed in Chapter3 and in the earlierparts of this chapter,the terminal efficiencyof steamfloodingis determined largelyby the rate at which it can be conducted.Slow injection ratesresult in a large proportionof the injectedheat beinglost becauseof the longertimes required. Much of the value of precommercialfield-pilot experimentationlies in the determinationof the practicalsteam-injection ratesthat are achievable. Oncetheseare known, the Myhill-Stegemeierapproachand its modifications can yield reasonable estimatesof the performancewhich is to be expected. In this section,the rate at which injectioncan be achievedin reservoirsis approached by considering the steady-stateflow between injection and production wells,for variousgeometries,assumingthat the injectedfluid hasthe sameproperties as the displacedoil. At the start of the processthis is a reasonablerepresentation, provided that the oil is the only'mobile phase.Assumingthat the injected fluid is more mobile than the displacedone, one would expectthat the injectivity would improve as the displacementproceeded.Advantagecan be taken of this im144
Steamflooding
Chap.4
whereP is thc a productianr Consida are separate and that the I equationssim producer.
The plus sign two equation eratingin a st and vice r.eru Eachof
Injectivity
proved injectivity by increasingthe injection rate for a given injection pressureor by allowing the pressureto fall for a given injection rate. When steamis injected, the volume displacedis related to the volume of injected steamand to the thermal propertiesof the fluids and reservoirmaterial.The quantity of steamrequired to displacea unit volume of oil is determinedby a heat balance; this heat balance has been consideredin Chapter 3 and is discussedin much more detail in Chapter5. For the present,it is sufficient to note that the volume of steam(measuredasthe equivalentvolume of liquid water) injectedis usually equal to severaltimes the volume of oil displaced.Sincethere is usually little resistance to the flow of steamin the steamchamberor to the flow of water through the displacedoil, the injectivity for steam may be expectedto be considerablylarger than calculatedfor simple oil flow. A reasonableapproximationis to multiply the calculatedinjectivity by the estimatedSOR and by a factor of about 1.5 to allow for the effective increaseof the injector well bore radius due to heating. Steady-state Displacement Between an lsolated Pair of Vertical Wells rediction of Recovery :s' Method (after Jones
The radial flow of oil to an isolatedvertical producer or from an isolatedinjector was discussedin Chapter 1, where it was shown that the pressurecould be calculated using equationssuch as
The method may be ters.
x predictedby Myhill , it is of prime impordependentupon the :tion ratesimply slow Chapter3 and in the ooding is determined ratesresult in a large er times required. ntation lies in the devable.Oncetheseare ; can yield reasonable ed in reservoirsis apction and production has the samepropereasonablerepresentaring that the injected ct that the injectivity n be taken of this imrnflooding
Chap.4
P=Pq-ffinn
(4.10)
whereP is the pressureat a radiusR from a well in which the injection rate is 4. For a production well, q is negative. Consider a well pair consistingof an injector and a producer whose centers are separatedby a distanceL. Assumethat the systemis operatingin a steadystate and that the flow of injection fluid, q, is equal to the flow of producedfluid. Two equationssimilar to 4.10can be written, one for the injector and the secondfor the producer.
I n j e c t o r P i= P o-i
ffin
Producer Pp= Pop +
ffin
n,
(4.11)
no
(4.r2)
The plus sign appearsin equation4.12becausethe flow is toward the well. These two equationsrepresentthe reservoirpressuresfor the caseswherethe wells are operating in a steadystate and individually (i.e., there is injection without production and vice versa). Each of these equationsis a solution of Laplace'sequation. a2P ----= * 0x' 6y'
4=o
Injectivity
(4.13) 145
A combinedsolution that representsthe combinedpressuresfor the caseswhere the two wells are operating togetheris obtained by adding the two solutions(4.11)and (4.12)to give
P=pi*po=,,-#,^*
gJ4)
At the midpoint b_etween the wells, Ri = Rp and the pressurebecomesp,. At the injector well bore,7 Ri = R,i,
Rp:
L
and
P n= i P o+ : + l n + lrrth
T
(4.1s)
R,,
ity to refer a centipois€.I units are dl given b1' (ti
Equation4.1 normalizedr It can t however.thc tion. Calcuh
At the producerwell bore, Ro = Rrr,
Ri:
L
and
P,p= Po-
(4.16)
#h*
The differencein pressurebetweenthe injectionandproductionwellsis givenby
AP=P*i_p,P=h^(#,) If R,, : R,,, this becomes:
AP=P-i-P,p=#,^*
(4.r7)
If R,; + R,o, then the geometricmean,R* : \/R.,R.', can be usedin (4.17). This maybe rearrangedto give the normalizedinjectivity(in consistentunits).
Normalized injectivity=
#O,
=
:h
(4.18)
'n\n--i
Equationsfor the normalizedinjectivityfor a varietyof geometricarrangements are given by Morel-Seytoux(1966).8 In his paper,Morel-Seytouxdescribesihe normalized injectivity just given as the conductivity andusesthe term normalizedinjectivTEquation 4.14 is an exact solution of the Laplaceequationfor a line sourceand sink. It is, however,only an approximationfor the flow betweencylindrical wells, sincethe constantpressure lines are only approximatelycircles near the line sourcesand sinks. However, for practical situations whereL > R", it is an accurateapproximation. sAnalytical equationsfor the flows betweenwells have been discussedby a number of authors.The generalschemeof superimposingthe pressuredistributionof a numberof wellswasdeveloped by Muskat (1937)and subsequent work is basedto a large extent on this pioneeringeffort.
146
Steamflooding
Chap.4
Most of the bores,and tf, this meanstl the invasion creaseconsi< tive radiusol L/R" willchr 6.91to-1.61 of the prodr this too r.ill r
Time for Err
Considerthc sure gradied equation-l.l{
The average usingDarcyi Injectivity
)r the caseswherethe o solutions(4.11)and
(4.r4) E becomesP,. At the
(4.1s)
ity to refer to a dimensionalvalue in which q is measuredin barrels per day, pcin centipoise,ft in millidarcies,ft in feet, and AP in poundsper squareinch (these units are often termedfield units). Morel-Seytouxnormalizedinjectivity is thus given by (q inB/d)(p in cp)
(k in mD) (h in ft) (AP in psi)
100 200 500 1000 2000 5000
(4.16) ion wells is given by
e usedin (4.17). (in consistentunits). _
(4.18)
I ric arrangementsare escribesthe normalt normalizedinjectivre sourceand sink. It is, rcethe constantpressure ever, for practical situa-
(4'19)
Equation4.I9 may be usedto calculatethe injectivity in barrelsper day from the normalizedvaluesgiven here. It can be seenfrom equation4.18that the injectivitydecreases asl, increases; however,the effect is not very great becauseof the nature of the logarithmic function. Calculatedvaluesare shownin the followingtable.
L R"
(4.r7)
: l'127x 1o-3 (#)."",,,,"", "
NormalizedInjectivity in Consistent Units 0.682 0.593 0.506 0.455 0.413 0.369
Most of the resistanceto flow occursin the immediatevicinities of the two well bores,and the resistanceaddedby increasingl, is not very great.In steamflooding, this meansthat oncethe resistance aroundthe injectionwell decreases as a resultof the invasionof the low-viscositysteam,then the injectivitymay be expectedto increaseconsiderably.For example,supposethat steamflow has increasedthe effective radiusof the injectionwell from 0.1 to L0m. For a casewhereL is L00m, then L/R,willchange from 1000to 100/V10 x 0l = 100and ln(LlR*) will changefrom 6.91to 4.61;Ihe injectivitywill increaseby a factor of 6.9114.6I= 1.5.Stimulation of the productionwell can also result in an effectivelargerwell bore radius,and this too will increasethe injectivity. Time for Breakthrough, Considerthe straightstreamlinethat joins the two wellsjust discussed.The pressure gradient along this streamlinecan be obtained by setting Rp : L - R; in equation4.I4 and differentiatingP with respectto R;.
=- #("-' ., - *--L (**).=, )
(4.20)
ised by a number of aurmberof wellswasdevelhis pioneeringeffort.
The averagefluid velocity alongthe central streamlineis given by q/A$AS. and, usingDarcy'sequation,is
nflooding
Injectivity
Chap. 4
147
fr
4!=v==---g--dt
/aP\ -
q
._L
pr6LS,\aR,/"=o 2trhgAS, S(f -
A6LS"
S)-
g'21)
In this equation,S is the distancethat a particle of the fluid movesfrom the injection well in time /. The time for breakthroughcan be obtainedby integratingequation 4.21.with the result ThL26 LS,
LBT _
(4.22)
3q
Substitutingfor the value of q from equation4.18leadsto the expression .
6 AS"rtL2ln\lR*)
@'23)
"r:tftF-
The volumeof oil that is displacedduring the breakthroughperiod is givenby rearranging equation4.22: Qtar =
ThL26 AS"
(4.24)
3
This volumeof oil is independentof the rate of injection.It is equalto one-thirdof the volume of mobile oil containedwithin a cylinder of reservoirof heiehth and radiusL.
The dim circle of profi breakthroueh
It is a functiq Confined hl
lsolated Injection Well Surroundedby a Circle of Equally Spaced Producers The generalprocedurejust describedcan be extendedto the caseof an injectorsurroundedby a circle containingequallyspacedproducers,as shownin the left part of Figve 4.22. Resultsof this analysisare tabulatednext (Morel-Seytoux1966): qLL
-
kh LP
.
.RT
2nN (N + 1) ''(*)
(4.2s) - h(N)
: o
/r\ I | * ') r"(;il - rn(N)l 'LS.pL'?L(N
g E o
(4.26)
_
2(N + 2)kAP
N
(!
Qtnr= {TtnhL26LS"
E o
z
(4.27)
In these equations,N representsthe number of wells surroundingthe injector. Thus, for example,for an isolatedfive-spot there is one injector with four producers arrangedaroundit and N is equalto 4. The radiusof the surroundingcircle,.L, in this caseis half of the diagonallengthof the squarepattern.The injectivitiesfor a number of valuesof N are shown in Fisure 4.23. 148
In a repeated boundaries.Tl tern indefinitc infinite series example,the
Steamflooding
Chap.4
Figrr: Spacc
Injectivity
s(r - s)
(4.2r)
/
v
N equallyspacedwells of radiusRw
9r
/ --'*------
lr. io ! AI
t,'?
AO
novesfrom the injecl by integratingequa-
I
I
g)9*-t'
I i J.
_ _ . _ _ . { r ) _ _x_ _ I I I I
(4.22)
A v I
: expression
i I I
A v
(4.23)
I
"N+1 Spot"Pattern
Partof infiniterow of wells
Figure 4,22 Typical IsolatedWell Patterns
rriodis givenby rear-
(4.24) equalto one-thirdof 'voir of height h and
The dimensionless breakthroughtime for N = 1,. . . ,6 and for a continuous circle of productionwells is shownin Figure 4.24.In this figure the dimensionless breakthroughtime is definedas
Dimensionless breakthrough time = !-^o!'u' q c.sop,L2
(4.28)
It is a function of the systemgeometry-in this case,of N andLfR,. Gonfined Patterns
se of an injector surrown in the left part
In a repeatedregularpattern, planesof symmetrybetweenwells becomeno-flow boundaries.The flow in suchpatternscan be computedby extendingthe well pattern indefinitely and summing up the pressureterms for eachwell as one or more infinite series.[n somecasesthe resultinganswerscan be surprisinglysimple.For example,the pressureproducedby the seriesof equal injectionwells uniformly
rx 1966): Parameteris the numberof producersin the
(4.2s)
circle around the isolatediniector
:> 69
I
9C
..1
:;
)l I
8 8'E .N
(4.26)
(!0 Fo
5.E z
(4,27) unding the injector. 'with four producers oundingcircle,L, in 'he iniectivitiesfor a
mflooding
Chap.4
otot Radlueof clrcleAfVellbore radlus Figure 4.23 Injectivity of Isolated Well Surroundedby a Circle of Equally. SpacedProducers
Injectivity
149
Continuous
\,,,
..."2
No flow bo..rn
T-
---h I Parameter isthenumber of producing wells whichsurround theinjec,tor 100
1000
Distance to ProducerAltellbore Radius
10000 Figure 4.24 BreakthrouehTime for Isolatedpatterns
spa:edalonga straightline, which is shown in the right hand part of Figure4.22 and also in Figure 4.25,is given by (Muskat 1937)
P=Po-ffiLnfcorr,+-*'Tl
(4.2e)
Extendingth verticalu'elb
Repeated Fh
In equations4.29 and 4.30 the flow, q, is per unit length of well. Equation 4.29 canbe usedto predictthe flows betweena horizontalinjictor and a horizontal producer,asshownin the smalldiagramin Figure4.26.To do this it is necessary to write equationsfor the contributionof four seriesof regularlyspacedwellsand t-hen to combinethesewith the result shownin equation4.30. Gonfined Horizontal Well Pair qp_ kLP
(4.30)
The dimensionless injectivity from equation4.30hasbeenplotted againstthe logarithm of C/L in Figure4.26for a constantratio of R*fL:0.002.hhe injectivlty risesfrom a low value of 0.3 to the asymptotecorrespondingto a pair of isolatei wells (i.e., the injectivity given by equation4.18). c is equalto R, for the casewherethe two wells are immediatelybelow and above the reservoirboundaries.In this case,if it is also assumedtiat L ) R,, equation4.30 can be reducedto qp 0.5r -k^P: GF,r* 150
(4.3r)
Figrn Horra
Steamflooding
Chap.4
Injectivity
| )tmoge wetts No flow boundories .l'-/
9\
I )lmoge wells
{
rcatthrough Time for li
I part of Figure 4.22
(4.2e)
i
Figure 4.25 Infinite Vertical Column of Horizontal Wells to RepresentWell within HorizontalBoundaries
Extending this approachto repeatedinverted five-spot and seven-spotpatterns of vertical wells resultsin the injectivities given by the following two equations. Repeated Five-spot
3h of well. Equation stor and a horizontal this it is necessaryto pacedwells and then
qp kh AP
- 0'6174 r"(^fr)
(4.32)
L = distancefrom injector to producer
=)]l
(4.30) Asymplote- no effectol boundades Equation4.18
)ll
E
E o.o E
ao
ted againstthe logat.ffi2. The injectivity to a pair of isolated
.g E 6 -o O.2 tr o
.E o
mediatelybelow and nrmed that L > R.,
0
-3-2-101234 tog.,o(C/L)
(4.31)
Figure 4.26 Effect of Proximity to Reservoir Boundaries on Injectivity for Horizontal Wells
rnflooding
Chap. 4
Inje.ctivity
151
RepeatedSeven-spot
o E
qP khAP
tr3
4r
ct
1 ^1. lt\ - os6elj ,L',(fr)
tc z
Theseare plotted in Figure 4.27.eAlso shown in this figure is a curve for an injection well locatedwithin a continuousrow of producersa1the sameradius.comiar_ ing Figure 4.27 with Figure 4.23 showsthat the injector in the repeatedpattern has a significantly lower injectivity than that in an isolated pattern. A considerable fraction of the oil in the iso.latedpattern flows outsideof the pattern and then back toward the production wells. The quantity of oil that is producedat breakthroughis also considerablylarger for the isolatedpattern; much oi the producedoil has come from outside the pattern. This is shown in the following tabie. Volumeof oil Producedrtjlglth*g!
Initial mobile oil Fraction produced at breakthroueh
glyid"g
Isolated Repeated
!y Vorumeof oir Initiailywithin partern 2+ AS,L2 1.0472
2.5986 LS.L2 0.9069
0.7178
0.7437
o a a c gt
-
7
c E
-
0
(flow norm tions for ttr lar; onll-th Aba be characle tion 4.3-ial within the s
wherethe p The dimensionlessbreakthroughtimes (as defined by equation4.28) areplotted in Figure 4.28 for isolated and repeated5- and 7_spotpatterns. STEAM ZONE SHAPE: VAN LOOKERETVS EOUATTONS
and where y
W
.l/ I I k
Van Lookeren (197.7)developedequationsthat describethe degree of override that may be expectedin a steamflood. These equationsare based upon fundamental principles such as Darcy's law and make use of the assumption oi segregatedflow
v: (osR 3
.: Eg .gg EE o6 N . =
E E Fo E.E z Figwe 4,27 Injectivity in Confined Patterns
The ps ize the stati faces,u'here developmen In man it has been1 comparedto cousoil *'ith fingerinewil
equationsare given by Deppe (1961),who alsogives equationsfor the inverted ninespot pattern and for patternsat the boundary of a field development.
'oThis ir a n i n i t i a l h i g hr becauseof b1-p
152
Injectivity
esimilar
Steamflooding
Chap.4
o i:g C')
o 6a
a curve for an injecame radius.Comparrepeatedpattern has tern. A considerable lattern and then back ed at breakthroughis roducedoil has come
Within Pattern Seven-Spot 25986L5"L2 0.9069
o o o o o
El
o o
i5
0
10
100
1000
10ooo
Dlstanceto Producer/Wellbore Radius
Figure 4.28 BreakthroughTimes for Confined and IsolatedPatterns
(flow normal to bedding plane of the reservoir is neglected).He developedequations for the caseof linear flow and alsothe caseof radial flow. The two are similar; only the radial flow equationsare describedhere. A basic finding in van Lookeren'spaper is that the degreeof override may be characterized by a dimensionless number,which he termsz44;it is givenby equation 4.33 and is proportional to the squareroot of the ratio of the viscousforces within the steamzoneto the gravity forces.
o^=ffi'$-14*y
0.7437
(4.33)
where the pseudomobility
pt!,p,. (osR), tr4*_
n 4.28)are plotted in
l L ,k o P o
and where z" is kinematicviscosityof steam,m2/s IV,i is steaminjection rate, kg/s gree of override that d upon fundamental n of segregatedflow
njectivityin Confined
ros for the inverted nine-
rnflooding
Chap. 4
ap i fuksl^' g is graVity, m/s2
h k, p: (OSR)r
is thickness,m is permeability of steamzone to steam,pm2 is effectiveviscosityof oil, Pa . s is instantaneousoil-steamratio The pseudomobilityratio is analogousto the mobility ratio usedto characterize the stability of water floods. Valuesof M* lessthan unity lead to stableinterfaces,whereasthose greaterthan unity tend to lead to unstableinterfacesand the developmentof steamtongues. ln many cases,where the oil in the reservoiris not extremelyviscousor where it has been preheatedby stimulation before flooding, M* may be relatively small comparedto unity. On the other hand, whereattemptsare madeto drive cold viscousoil with steamdirectly,M* will be high and it will control the situation;steam fingeringwill then occur.'o loThisis relatedto the situationwhere,in Jones'method,the value of lco is lower becauseof an initial high oil viscosity.In both cases,oil that is heateddoesnot flow readily to the producer becauseof bypassing.
Injectivity
153
If M* is relativelysmall,then the value of -4n is controlledby the square-root term in equation4.33.Ot the variablesin this term, the only one that is in the direct control of the operator is the injection rate W,i.Higher rates give higher1ai.e., the viscousforcesincreasewhile the gravity forcesremain the same. Lower valuesof the permeabilityto steamwill alsogive highervaluesof Ap; aswill be seen,this leadsto steeperfronts and thicker steamzones.Accompanying this will be an increasein the oil recoveryand in the oil-steamratio. There is considerableresearchand developmentactivity that has the objectiveof reducingthe permeabilityof the steamzone to steamin order to increasethe pressuregradient belowthe steamzone.11 A promisingmethodinvolvesthe additionof surfactantsto causethe formationof foams. The effect of-4a on the predictedshapeof the steaminterfacecan be seen from Figure4.29.With low valuesof ,4p,the steamtendsto be confinedto the top of the reservoir,and the front is inclined at a low angle.As,4a increases, the front approaches the vertical. With a situationsuch as that shown in the top drawing in Figure 4.29, it is apparentthat steamwill break through early and that, for the amount of oil that will be produced,the heat lossesto the overburdenand to the unsweptreservoir belowthe steamzonemay be excessive. In this casethe advantagethat would have beenexpectedfor a thick reservoirfrom Myhill and Stegemeier's modelwill not be obtained.The productionrate and oil-to-steamratio will be almostindependentof Valueof A p
hst/h
^v - RadiuS +
t
-T'
Practical Range in Field
_l: -+,,
Rangeof Experiments Modelsin Laboratory
.-1,0
aftervanLookeren
Figure 4.29 Interface Profile during Injection (after vanlookeren) ttNot only doesthis increasethe recoveryof oil from below the steamzone but it also improvesthe recoverywithin the steamzone.The apparentviscosityof the steamis increasedand it is better able to displaceoil from the steamzone; this aspectis discussedfurther towardsthe end of Chapter5.
154
Steamflooding
Chap.4
reservoirthic the squarem height of re* evenif the n Doscbc considertbd thick resenti voir is renxru thicknessof t
Anothcr agramsof Fir to have to p|! helpingthe u the oil is allor assistedgrarit With rh ing force thl tween the ini At the starrtb voir. Once btt comesrelatiw steamdecreas below. For los'r not extendto I well or, if the , the formation .a particularlr light, tendsto I allowsone to a The parr the well bore n decreasing R. r move lower do In order t be able to cah in Figure{.31 cases,1 and J. fall in bet*'eeo that the avera Low valu reachor onll't Injectivity
I by.thesquare-root ne that is in the dirs give higher-46the same. righervaluesof .4p; nes.Accompanying ratio. There is con:ive of reducingthe re pressuregradient on of surfactantsto terfacecan be seen confinedto the top increases, the front in Figure4.29,it is amountof oil that 3 unsweptreservoir €e that would have 's modelwill not be nostindependentof
r'aciical Range 'Feid
:i &periments ^ ilboratory
okeren) am zone but it also ima m i s i n c r e a s e da n d i t i s ther towards the end of
rf looding
Chap.4
reservoirthickness.It is of interestto note (equation4.33)thatAp is proportionalto the squareroot of the ratio (Wtlh)lh-i.e., to the rate of steaminjectionper unit height of reservoirdivided by h.In thicker reservoirsthe overrideis thus greater evenif the rate of steaminjectionper unit heightis maintained. Doscherand Ghassemi(1981)and Doscher,omoregie,and Ghassemi(19g2), considerthat, in many practicalcases,the high oil-to-steamratios expectedfor thick reservoirsare never obtained becauseonly the oil from the top of the reservoir is removed.[n thesecases,accordingto van Lookeren'stheory, the average thicknessof the steamzonewill be hn=Q.Jl11*=Q.5
""'fir Lpgk,''
M*)
(4.34)
Another problem,which is apparentfrom the overrideshownin the upperdiagramsof Figure 4.29,is that after breakthroughthere is a tendencyfor the steam to have to push remainingoil up the slope.Gravity is playinga role, but it is not helpingthe movementof the oil. What would be moredesirableis a systemwhereby the oil is allowedto drain downwards.This is oneof the thoughtsbehindthe steamassistedgravity drainageprocessto horizontalwells discussedin chapter 7. with the situationshownin the upperdrawingsin Figure4.29,the only driving force that is moving oil to the productionwell comesfrom the differencebetween the injectionpressureof the steamand the pressureat the productionwell. At the start this is very large,but so is the resistingforce of the oil-saturatedreservoir. Once breakthroughoccurs,the resistanceto flow throughthe steamzonebecomesrelativelylow, and the driving force requiredto maintain a given flow of steamdecreases. Under theseconditionsmuchlessdrive is availableto movethe oil below. For low valuesof ,4a, Figure 4.29 showsthat the steam-liquidinterfacedoes not extendto the baseof the injectionwell. The steamescapes from the top of the welltr, if the well is perforatedonlyat the bottom, risesvery rapidly to thi top of the formation.The reasonfor this is not, as might be assumedat first, that theie is a particularly favorableopen streak at the top but simply that the steam,being light, tendsto float to the surface.Figure4.30,which is from van Lookeren'spaper, allowsone to estimatethe liquid level within the well. The parameterLNTM dependsupon the valuesof the drainageradius,R,, the well bore radius,R,, and the skin factorfor the well, s. For a givenvalueof ,4a, decreasing R, or increasingS hasthe effectof causingthe steam-water interfaceto move lower down the well. In order to estimatethe vertical conformanceof a steamflood,it is useful to be able to calculatethe average,area-weighted steamzone thickness;this is given in Figure 4.31.The curves in this figure are drawn for two extremetheoretical cases,1 and2, which are developedbyvan Lookeren.Actual casesare expectedto fall in betweenthesetwo theoreticalcurves,and it is suggested by van Lookeren that the averagecurve shouldbe used. Low valuesofr4p correspondto caseswhere the steamzone either doesnot reachor only barelyreachesthe baserock; seeFigure 4.29.when,4p is lessthan Injectivity
155
-til-
1.0 !
steam a F
Parameteris LNTNterm
.c 0.8 o o = 0.6 ,= ' E 0.4 = o
Sincc t for low valu thicknessal Altbq by Figure4given by Fg of the injecti fect the thirl
<jt>
LNTM=3 LNTM=gfor plugged --.->
:
nearwelboia
Numericel t
H
AS an ex2rilt
River steam culate,,{pan
.E 0.2 (, (!
il
llo
0
0.8 0.2 0.4 0.6 SteamZoneShapeFactorA p
Figure 4.30
SteaminF
1.0 Rate pcf
Predicted Water Level in Injection Well utl
L N r M = r n ( R , / R .-) t l 2 - R l / z R :+ S S is skinfactor;seeChapter6 (aftervanLookeren) 1.0, the mean steam zone thickness, as a fraction of the total thickness, is simply equal to half the -4n. This is also equal to the vertical conformance.
1.0
Aa
\.c r' O
Case1
z 0 . 5A n
l-c
g 0.8
The average
Averaoe Curve'
o
N
E o I 0.6 o
Case2
Using this tx an expected
5
o 6 th
o 0.4 E v .9
This is lesst that the pro< included.
F
o 0.2 C'I G L
afiervanLookeren
o
0 -
0
0.5
2.O 1.5 1.0 ShaPeParameterA R
FAROUOALI'S I..|II
2.5
FarouqAli ( many of the simplifiedag
Figure 4.31 RelativeAverageSteam-ZoneThicknessas a Functionof,4n (after van Lookeren)
156
Steamflooding
Chap.4
Farouq Ali'sU
ll tl
since the reservoir height occurs in the denominatorof ,4p, this meansthat, for low values of Ap, the mean steam zone height is independentof the reservoir thicknessand alsoof time. Although the steamheight within the well dependsupon R, and s, as shown by Figure 4.30, theseparametersdo not affect the averagesteamzone thicknessas given by Figure 4.31.The effect of R, and S is confined to the immediatevicinity of the injection well. Injecting steamonly at the bottom of the reservoirtendsto affect the thicknessof the steamzone only in the region closeto the injection well.
t-l J . .l ll -
*r>
v
Fii
tl tl tl
-ii
Numerical Example of the Use of van Lookeren'sTheory As an exampleof the use of van Lookeren'stheory, considerthe ten-patternKern River steamflooddiscussedpreviously.The valuesof the variablesrequired to calculateAp are as follows:
tl tl tl tl tl t_t
Steaminjection rate: 18.58x 106B of steamwere injected over a period of7 y, or 727 B/d per injection well average Rate per injector W,i = 727 x 350 x 0.4536/86,400= 1.3kg/s z, at 310oF= 5.0 x 10-6m2/s
I
-s
A^p= 960 kg/^, thickness,is simply ance.
I = 9.81m/s2 h = 97 x 0.3048= 29.6m k, = 0.4 x L0-12m2(assumingkn = 0.4) A^=(
Case1
5 x 10*6x 1,.3 \ r/2 = o''n' r r x 9 6 0 x 9S1,nR X 0.4 x 10-12 )
The averagesteamchamberheight would thus be
Averaqe Curve-
En = 0.5Anh = l'i..1m, or 38.5 ft
Case2
Using this height and an expectedresidualoil saturationof about 0.15would give an expectedrecoveryof 0.52- 0.15 38..s Ug "dx100Vo=28.27o This is less than the reported recovery of 37Vo.One reasonfor this difference is that the production of oil by waterflooding beneath the steamzone has not been included.
t 5
FAROUOALI'S UNIFIEDAPPROACH Farouq Ali (1982)has presenteda description of an approach that encompasses many of the conceptsdescribedpreviously in this chapter and unites thpm into a simplified approximatemodel.
on of,4p (after
nflooding
Chap. 4
FarouqAli's Unified Approach
157
His procedureinvolvesthe calculationof the steamzone thicknessft,, from van Lookeren'stheory and then, using the Mandl-Volekmethod,the calculationof the steamchambervolumefor successive time steps.At eachtime step,the flow of oil and waterfrom the regionbelowthe steamzoneis estimatedassumingthat the temperatureis uniform at a value determinedby the heat contentfor the heat loss calculated.Relativepermeabilities from Gomaa'scorrelationare used(Figure4.31). The procedureis repeateduntil the steamchambervolume grows to the breakthroughvolumecalculatedat the start.At this point the steaminjectionrate can be adjustedto control the amountof steambypass.FarouqAli providesan encouraging comparisonin his paperof the resultsof his calculationfor the Kern River data with the samecurvesdrawn by Jones.
tr,,-..
function ,.: reserroir Ft thick*a:,:rt were fou::i1! portion \': :l \ \ . a -. ,.1
C O I I C C I c ' Ci , x
then the c:-, w a s a l s o: ' : ; s u l t si f t n r . stant.There neither inr e'
GOMAAS CORRELATIONS FORPREDICTING OIL RECOVERY
'\ n
Gomaa(1980)developeda setof correlationchartsfor the predictionof steamflood oil recoveryand oil-to-steamratio as a function of reservoircharacteristics and operatingconditions.The correlationsare basedupon a seriesof numericalsimulation studies. Although Gomaa'sstudyis limited to a particularsetof fluid and rock properties and is dependenton the assumptionsinherent in the numerical simulation methodemployed,it developsinterestingconclusionsand ideas.The studyconsiders a reservoirwith the relativepermeabilitycurvesshown in Figure 4.32.These curveswere found to give a satisfactoryhistory match for an actual Kern River steamflood.Comparedto the valueswhich are commonlyfound for conventional oils, the relativepermeabilityof water is very low. It has been found necessaryto employrelativepermeabilitycurvesof this type to simulateheavyoil steamfloods in numericalsimulators.If conventionalcurvesare employedit is found that water is producedmuchtoo quickly.The distortedrelativepermeabilitiesemployedcompensatefor other problemswhich are involvedin the simulationsuch as the extremelylargetemperatureand viscositygradientswhich occur in the vicinity of the condensation front. The gravity of the oil in the studywas 14oAPI and the reservoirtemperature was 90"F. 1.0
'-.,
( 4 0 % 1u a . : o a given pr,rJ Dec:ca floodine rfi" through 'Fig this increa.< tion of thc n
a. o o |e \ F S*
g 0.8
o p ql
6
t
o
\J
3 o.o
?c-
.g 0.4 6
0q n
E e 0.2 Water note soecial scale 0.2
158
0.4 0.6 0.8 ( S s - S * 1 ) / ( 1 - S 1-aS; 6 1 )
Figure 4.32 NormalizedOil-Water RelativePermeabilities(from Gomaa 1980) Steamflooding
Chap. 4
Figun G.':.
Gomaa'sCo''e
e thickness8,, from d. the calculationof Lmestep,the flow of rd assumingthat the ent for the heat loss e used(Figure4.31). grows to the breakin|:ction ratecan be ovidesan encouragthe Kern River data
iction of steamflood aracteristics and oprumericalsimulation uid and rock properumerical simulation s. The studyconsidFigure4.32.These r actual Kern River rnd for conventional r found necessaryto :avv oil steamfloods t is found that water ities employedcomtion such as the exin the vicinityof the
Figure 4.33 showsthe oil recoveryfor reservoirsof variousthicknessesas a function of time with a constantsteam-injection rate of 1.7 B/d per acre foot of reservoir.For example,the steam-injectionrate for the caseof the reservoir 300 ft thick was30 timesgreaterthan that for the reservoir10ft thick. Higher recoveries werefound for thick reservoirs.This might be expectedbecauseof the smallerproportion of the total injectedheat that would be expectedto be lost vertically. A significantfinding from this studywas that if the heat injectionratesare correctedfor the vertical heat lossesto give the net heat injectedto the reservoir, then the diversecurvesof Figure4.33 all fall on the singlecurve of Figure 4.34.It was also found that neither the pattern shapenor the pattern size affectedthe results if the steam-injection rate per unit volume of reservoirwas maintainedconstant. There was a small effect of the rate per unit volume parameterthat was neither investigatednor includedin the correlation. interestingfeatureof thesestudiesis that an intermediatesteamquality (40Vo)wasfound to give the highestthermal efficiency.More heat was requirid for a given productionwith steamof lower or higher quality. Decreasingthe steamquality from l00Vaincreasesthe amount of hot waterflooding that occursbeneaththe steamzone and delaysthe time of steambreakthrough (Figure4.35);with the assumptions made in the simulationcalculations, this increases the recovery.Figure4.36showsthe calculatedoil recoveryas a function of the net heat injectedfor varioussteamqualities.
fttJECTION RATE : t.? B/O/Act. Fl
srEAileuaLrry:06 uoElLE olL saruRAror{ = o .la
q.
:servoirtemperature
I --J------=i
I RESERVoIR THICKNESS'Ft
60
a o le -40 \ e
so $
!zo { o
o ormalizedOil-Water abilities(from Gomaa
nflooding
Chap. 4
TtME , YEARS Figure4.33 Effectof Reservoir (from Thickness on Steamflood Oil Recoverv Gomaa1980) Gomaa'sCorrelationsfor PredictingOil Recovery
159
roo I
ft{JECTIOtR { ATE: l.? 8/Ollc?.F1. s T E A I Q U A L I T Y: 0 . 6 I O S I L E O I L s A T U R A T I O N: O . 4 2
x o
xo
60
a. o o ta .40 \ t \ s
q
INJECTil
o
t
300 too 40 20 to
o o
d o ^a oqcx
200
400
NEf
In using( reservoiruP ut heat loss read the effectof c Usingttr ageof the or[ the estimatedt the reservoiri initial oil satu stimulationbc Figure4. of reservoirth
RESERVOIR T H T C K N E SFSr,,
ax
b t{ 20 t
;:: .a *
x
600
HEAT INJEC\E?
800 MMBtu./Auc
1200
rooo Ft.
Figure 4.34 Oil Recoveryas a Functionof Net Heat Injectedfor VariousReservoir Thickness(from Gomaa 1980)
too OUALITY. % O 20 +r ++ ++ ++ 40 60 oooo 80
-+
Sol'5O7. Qlnj' 395 t{H8tu/AcrcFt. s .F
{ o
\ t\ +
l{J
_ooo oo-
{ deo o I { q
J(.
\
roo
T x
PROOUCER
INJECTOR
(A): 50% OIL SATURATION PROFILES (DISPLACEDOIL BANK)
++++ o ooo _H INJECTOR
\ o x40 \
+ + +
Sol. 507o Oini . 395 MMBtu/AcrrFt.
*
s
s
o sl{J 2 0
t_..' I
e
r
-J
PROOUCER
(B}: I5O"F ISOTHERMS (UNIFORMITY OF WELLBOREHEATING)
Steamflooding
s o
(fromGomaa Figure4.35 Effectof SteamQualityon Displacement Parameters 1980) 160
Qro
E
QUALITY. 7C
0 20 40 60 80 IOO
t
F€'
Chap.4
Vogel's Simdffi
,----
+ +-t.t r:I Sol. 5096 Svi.O Qlnl ' 390 MMBtU/Act Fl.
o o oo
60 go PROO{JCER
It{J€CTOR
(C): IO% VAPORSATURATIONPROFILES (STEAU ZONEGROWTHA BREAKTHROUGH) (continued)
Figure4.35
ln using Gomaa'scorrelation,one first calculatesthe net heat injectedinto the reservoirup until the end of the current time step.This is correctedfor the vertical heat loss read from Figure 4.37, and this net heat injection is adjustedto allow for thq effect of steamquality using the factor read from Figure 4.38. Using the effectiveheat injectionjust calculated,the oil recoveryas a percentageof the originalmobileoil (i.e., the oil saturationat the start of the flood minus the estimatedresidualoil saturationafter steaming)is obtainedusingFigure4.39.If the reservoir has been producedby steamstimulation prior to the flood, then the initial oil saturation should be adjustedfor the oil production during the steam stimulation before using Gomaa'scorrelation. Figure 4.40 showssometypical results from the correlation; the importance of reservoir thickness,oil saturationand the net-grosspay ratio are quite evident.
ERVOIR xltEss, Ft. 300 too 40 20 to
/ariousReser-
roo {
s
IOSIL
lrJ
O I L S A T I RATlON
,o oflf
Geo
.42
-l
PRODUCER
I
G60
b
s l{
o tQ40 \
s S
o sr{.12 0 t {
PROOUCER
tt
.t
s o
,r'
4
.\
3x :x
o
,fl r 200
400
STEAM OUALITY
t.o o.8 o.6 o.4 o.2 I 600
800
looo
1200
NET HEAT NJECTEO , llll&tu. /Acrc Ft.
,(fromGomaa
nflooding
t
{
(fromGomaa1980) Figure4.36 Effectof SteamQualityon Oil Recovery Chap.4
VogelisSimplifiedHeat Calculationsfor Steamfloods
161
\
\ao
d
.N
:i 80
\
=
b
6
N\
\
t60
\
I o
\
$ \
loo
T rtttl
$
\
--' HEAT IilJECTPil RATE un&u. /o/Acr. Fl. -).or lllrl
*,o
tb
\'l
_.2 \ \.4
s20
t40 \'
\
$
.b
lr
$ o
Bto a o
40
80
t20
t6o
200
240
ZAO
320
RESERVOIR THEKIIESS, FEET Figure 4.37 Heat Loss to Overlying and UnderlyingStrata(from Gomaa 1980)
{ o
o t
VOGETSSIMPLIFIEDHEATCALCULATIONFORSTEAMFLOODS
Figrn { N{obrlc I
Vogel(1984)haspresentedan approachto the calculationof the steamrequirements for a steamfloodthat is simple,practical,and conservative.The casethat Vogel considersis the one in which overrideof the steamchamberoccursrapidlyand the productionof oil is by gravity drainage,assistedby "steamdrag." As production proceeds,the steamchamberthickens.The generalconceptis shownin Figure 4.41.
I
s
Roo
H,O
No.
Fot
d
I
\
t-
!r)
\ oz
I N \
R \
s
I
t-
I
So'
L 0.6
$
I
t
I
o
o.2 0.4 0.6 0.8 INJECTEO STEATIOUALITY
l.o
o
Figure 4.38 Heat-Utilization Factor as a Function of Steam Quality (from Gomaa 1980)
162
o.5
Steamflooding
Figurc{ on Cum
Chap.4
Vogel's Simplif-n
roo
d
4
IIOBt ILE 5eo - tMtl.IAL ,IRAT, otL SATr i
K*
* <60
_]sg: ,/
b 40 l40 \'
/t
s
'/t
S
8 z20o
t
/t
{ s
o 2
om Gomaa 1980)
7
to
s
280
z
t/
2
,/ /
/
/ ro_
/
ry
.5'
/
800
rooo
1200
EFFECTIVE HEAT NJECTEO, tlll8tu./Gross Acro Ft Figure4.39 Steamflood Recovery asa Functionof EffectiveHeatInjectedand (fromGomaa1980) MobileOil Saturation
D
le steamrequirements The casethat Vogel xcurs rapidly and the drag." As production shownin Figure4.41.
Ro o
t \
POROSITY : 537. S T E A M Q U A L I T Y: 6 0 7 0 I t { J E C T I O NR A T E : 1 . 5 B / 0 / c n O S S A C R EF r N ET / G R O S S LOO --o.73
No. q { o
S oz R \
s
lo,
RESERVOIR THICKNESS,
l.o 0ro2030405060 NI4AL HOE|LE OtL SATURATTOT'|, X Figure4.40 Effectof Oil Saturation, Reservoir Thickness, andNet-Gross Ratio on Cumulative Oil-Steam Ratio(fromGomaa1980)
Quality (from
amflooding
Chap.4
Vogel'sSimplifiedHeat Calculationsfor Steamfloods
163
HEAI
fLOIV
TO
CA'
The heat causethe hot i tend to resultir Vogel p
U
ROCK
at U F
. a
Comparisand
J
STEAT ZO'{E -AP
o
+
By combiningI thermalefficicr the steamchas HIAT
t
FLOW
TO
UNOERLVING ZONE
COLD OIL
where
I
tf,JCCTOn
RE@VERY IECHANIS-GRAVITY ORAII'AGE OF HOr OIL ANO SLIGHT STEAT ORAG ?ROOUCES
The heat loss to the overburden,calculatedin this way, is conservativebecause the whole upper surfaceof the reservoircannot heat up immediately(seeequations 2.25 and 2.27).
This equationi front (equatio the vertical he surfacesof thc tion 4.37 it is heatedimmedi Vogelsho lower than tbc and which arc Figure 4.42 cq the Marx-Larg Also sho ciency.Recall t ratios were gec ' cal efficiencl-. the range of ru Vogel s.qg rate initialll"a heatflux. He r steamhas rert dependentof th reservoirwith I
164
Vogel'sSim6*fie
Figure 4.41 SchematicCross Sectionof ContinuousSteam-InjectionRecovery Process (from Vogel 1982)
In Vogel'sapproachthere is no way of predicting how rapidly the drainage from the reservoirwill occur,and it is necessary to assumea lifetime for the steamflood. The methodcan also be usedto analyzethe statusof an ongoingflood. In either caseit is necessaryto estimatefor the time of interest(i.e., for time t) the correspondingaverageheightof the steamchamber,ft. The heatstoredwithin the drainagesteamchamberis given by equation4.35.
(4.3s)
Q,=Ahp1C'(fs-fn)
Vogelassumesthat the steamchamberspreadsimmediatelyacrossthe top of the wholereservoirpattern.He then calculatesthe verticalheatlossesto the overburden and alsoto the materialbelowthe steamchamber(this may be underburdenand/or undrainedreservoir).To calculatetheseheatlosses,he usesequation4.36(sameas equation2.25) for the heat lossupward and also for the heat lossdownward.
Qr = ZKzA(Zs- Z^)tE Trdz
(4.36)
Y
Steamflooding
Chap.4
The heat loss to the underburdentendsto be overestimatedeven more becausethe hot interfaceadvancesduring the drainageprocess.Both these errors tend to resultin a pessimisticestimateof the steamrequirements. Vogel points out that if it is found for a field steamflood that more heat is beingconsumedduring the processthan would be calculatedby his approach,then it is likely that thereare additionalheatlosses,suchasto other regionsor to a water layer.This is a very useful featureof his approach. In comparingthe resultscalculatedby adding the heat storedin the steam zonefrom (4.35)and the vertical heat lossesfrom (4.36)to the heat injectedin the steam,one also has to make allowancesfor heat lossfrom surfacelines. heat loss from the well bore, and the heat in the producedfluids.
G
3 a
Comparison of Vogel'sPredictionswith Myhill-Stegemeier
o
By combiningEquations4.35 and 4.36,it is simpleto derive an expressionfor the thermalefficiency,E,1,, which is the fractionof the net injectedheatthat remainsin the steamchamber;this is shownby equation4.37. -1 rth =
)
(4.37)
1+ _-:__X Yrr
where X =fto (seeequation3.25)
rapidly the drainage ifetimefor the steaman ongoingflood. In t (i.e.,for time r) the ven by equation4.35.
(4.3s) acrossthe top of the ;sesto the overburden e underburdenand/or quation4.36(sameas lossdownward. (4.36) conservativebecause mediately(seeequa-
rnflooding Chap.4
This equationis similar to that derivedin Chapter3 for a steadilyadvancingsteam front (equation3.24). The differencelies in the factor of J in the expressionfor the vertical heat losses.In equation3.24 it was assumedthat the area of the hot surfacesof the overburdenand underburdenincreasedat a constantrate. In equation 4.37 it is assumedthat the surfaceof the overburdenand underburdenis heatedimmediately. Vogelshowsthat this simpleexpressionpredictsthermal efficienciesthat are lower than thosepredictedby the Myhill-Stegemeier frontal displacement approach and which are in close agreementwith the field results given in their paper. Figure 4.42 comparesthe efficiencycalculatedfrom equation4.3'l with that from the Marx-Langenheimapproach. Also shown in the figure is a curve for 70Vaof the Marx-Langenheimefficiency.Recall that the Myhill-Stegemeier analysisshowedthat the field oil-steam ratioswere generallyin the rangeof 70 to 100Vo of the Marx-Langenheimtheoretical efficiency. They are in agreementwith the much simpler Vogel equation over the rangeof mostpracticalinterest. Vogel suggeststhat in a steamflood it is desirableto inject steamat a higher rate initially and then to reduce the rate to compensatefor the reducedvertical heat flux. He also makesthe point that in a mature steamflood-i.e., where the steamhas reachedthe breakthroughpoint-the rate of productionis essentiallyindependentof the rate of steaminjection; additional steamtendsto blow through the reservoirwith little incrementalproduction of oil. Vogel'sSimplifiedHeatCalculations for Steamfloods
165
1
THE FAST PROCESS
s r! 0.8
A someuhatd scribedbi Cm SanMiguel tar posit is of a ts
C'
0.. .E o lu o.+ (E
constant disPlacementrate \.
r, . \
\.
,-Maaand
Langenheim
Specific Viscosir. Sulphurc CCR utQ
70%ot Marxand Langenheim's E;,
o
T o.z
Rangeof results from Myhill-Stegemeier
0.001
0.01
0.1
10
100
1,000
Dimensionless Time Figure 4,42 Comparisonof CalculatedHeat Efficiencies
The simpleapproachsuggested by Vogelis practicaland useful.Its weakness is that it doesnot give meansfor the estimationof the rate at which oil will drain. In Chapter7 the calculationof the rate at which oil drains from around a steam chamberto a horizontalwell is described.Sucha systemis a logicalextensionof the processshownin Figure 4.41. The precedingequationsdue to Vogel have been previouslydescribedin a form that allowsthe direct calculationof the oSR. (Seeequations3.51and 3.52.) NumericalExample Following the discussionof van Lookeren'sequations,a numericalexamplewas givenon page157in which it waspredictedthat for the conditionsof the ten-pattern Kern River steamflood,the averagedepth of the steamchamberwould be 38.5 ft. At steambreakthroughfor the 61.-acre, ten-patternproject, the oil displaced from the steamchamberwould have a volumeof
It is thoughrtb of degradation scribedon pag The Sanl zontallyb1-au (8.3m) in thid The four to producehc this particula pected.Nexttl jector was frtl and steaminia the horizontal Performr first 174d of o Comparisonol timeshighertl the reservoirb
tt Aso r-. 61x 43,560x 0.34x (0.52-0.15) x 38.5 Joitil =
AQ
I
= 2.29 x 106B
3 l60
if it is assumedthat the residualoil saturationwithin the steamchamberwas 0.15. In the field productionit was found that the productionwas 3.02 x 106B. The OSR for the projectis predictedby equation3.52as OSR =
1769x 0.34x (0.52- 0.15)
= 0.26 (310- e0)(1 + 2.r4\h x 36s/3s9)
3 t40 ,,1, rZO
iYr m EEO
Blevinsand Billingsleyrepgrt that 18%of the injectedheatappearedin the production. This would reducethe expectedOSR to 0.26 x 0.82 = 0.21.This is still higherthan the experimentalratio of 0.16.The discrepancyis really largerthan it appearsbecausethe actualproductionwaslargerthan that just calculated,and the 0.16ratio from the field includesthis effect. A possibleexplanationis the indication in the paperthat steamwaslost to uppersandlevelsin part of the projectarea. Steamflooding
@
Chap.4
!so =40 t20
0
I
I
f
The Fast Procel
THE FAST PROCESS
tacementrate
I I I
I 3 LanSenheim I
I
I
I
>=J 0o 1,000 ncies
J useful.Its weakness t whichoil will drain. from around a steam gical extension of the iously describedin a rtions3.51and3.52.) mericalexamplewas onsof the ten-pattern rberwouldbe 38.5ft. Bct. the oil displaced
A somewhat different and interesting approach to steamflooding has been describedby Conoco(Britton et al. 1983)for the recoveryofvery viscoustar from the SanMiguel tar sanddepositin the StreetRanchin SouthTexas.The tar in this deposit is of a very low quality: Specificgravity(60"F) Viscosityat 175'Fcs Sulphurcontentwt. Vo CCR wtTo
1.080-1.093 520,000 9.5-11.0 24.5'
It is thoughtthat this very viscousand denseoil resultsfrom the extensivebacterial degradationof a lighteroriginalcrudeoil-presumably like the processthat wasdescribed on page 10 for Athabascabut more severe. The SanMiguel tar sandis at a depth of 1500ft (457m) and is divided horizontallyby a nonpermeable limestonebarrier.The testwasconfinedto alayer 26 ft (8.3m) in thickness.A five-spot,5-acre(2 ha) patternwas used. The four producerswere fractured using cold water under conditions thought to producehorizontalfractures.This was possiblebecauseof the in situ stressin this particular reservoir.In many other reservoirs,vertical fractureswould be expected.Next they weresteamstimulated,perforated,and resteamed. The centerinjector was fractured hydraulicallywith fresh water. This was followed by hot water and steaminjectionat avery high rate and with an injectionpressurethat exceeded the horizontal fracture pressure. Performancedatafor the pilot are shownin Figures4.43 and4.44.During the first 174d of operation,the averageinjectionrate was about 3000Bld (477m'/d). Comparisonof this rate with the data in Table4.4 showsthat this rate is several times higher than conventionalpractice-particularly when the small thicknessof the reservoiris considered.This drastictreatmentresultedin the productionof oil,
I x 38.5 pf,EHEAT | |
rm chamberwas0.15. 3.02x 106B. s = 0.26 pearedin the produc= 0.21.This is still s really largerthan it st calculated,and the rnationis the indicart of the projectarea. rnflooding Chap.4
160 3 (D g t40 ,.i,f ZO
- lrcT |ATER
rATRrxrr{JECTIOil
Lrrortr*
-'--
a
i= roo
6 -
r.r 80
at,
5ro RATE---+
= 40 D t20
U
-2rr,
, 77Zi
0
.D I I ll, E
Figure 4.43 StreetRanch Tar Production(from Britton et al. 1983) The Fast Process
167
I
EIIOOFIATRIX ITUECTfr P'IASE
s,,160
tsslcn-__)t-'
J cEt
independent d distillatestbt Distilhi heavyones-ll nificant disril
lgry:5
= t40 I
g r20
60
E,oo ;80
gs0
F
E+o
o
-60
o
3oo = 20 o 0 0
-22.850 ELS r _EiO OFPNEHEA PHASE tttl
F.o o
AI IIJECTIOI{ '€R INJECIIOI
, ,-,ti
500 t000 1500 2000 - TBELS FLUID CUTULATIVE II{JECTED
2500
o20 I o F10
Figure 4.44 StreetRanch Pilot PerformanceData (from Britton et al. 1983)
and it was demonstratedthat eachof the four producerscould flow tar at a rate greaterthan 100barrels per day. Steaminjectionwasstoppedat I74 d to allow the reservoirpressureto drop so that additionalobservationwells could be drilled. Followingthis, a prolongedperiod of steaminjection at a pressurejust below the fracture pressurewas carried out, and considerableoil was produced. In the final stageof the project, a waterflooding operationwas carried out and little additionaloil was removed. Overall, about 170,000B of tar were producedfrom the injectionof 1.8 million barrelsof steam.On a cumulativebasis,the steam-to-tarratio wasreportedas 10.9.Even thoughthis figure is very high, it is remarkablein view of the very viscousnatureof the oil, the relativelythin reservoir,and the low initial tar saturation of the reservoir(abolt 55%). OTHERMECHANISMSIN STEAMFLOODING The materialdiscussed previouslyconcentrates on the effectof heatin loweringthe viscosityof the oil and thus making it moremobile.Other mechanisms that play an importantrole in steamfloodingincludesteamdistillationof the lightercomponents from the residualoil within the steamchamberand also the thermal expansionof the oil.12 wu and Brown (1975;also reportedin wu 1977)havemeasuredthe yield of hydrocarbondistillatesproducedby contactingsteamwith a seriesof crude oils. They found that the volumeof distillatewasa functionof the quantityof steamemployed (measuredas the correspondingvolume of liquid water) but was essentially r2Thethermal expansionof the oil is largelyignoredin this book. Its effect is, however,includedindirectly becausethe residualoil saturationsare measuredat ambienttemperature.At steam conditionsSo,would be larger by as much as l\Vo.
168
Steamflooding
Chap.4
.; O.2 6
lr ttr g
0.6
o ut > 2
0.4
9 k o, J
9 o.s o =
0.. H o 0.1 10'|
ctl Figrn{ Viscodt Other Mechanb
independentof the steampressure(or temperature).Figure 4.45 showsthe yields of distillatesthat they obtained. Distillation occurs to a much larger extent with light crude oils than with heavyones.However,with even the heaviestoil shown in Figure 4.45, there is significant distillateproduced. 60 *50 o
E+o .l!, trl
3so 6
rufciloi
00
2500
psiglSezor1 2OO - 500psig(471oFl
o20 p o
Fro
t
ionet al.1983) uld flow Iar aI a rate fr pressureto drop so this, a prolongedpepressurewas carried I the project, a wateras removed. e injectionof 1.8 mil'ratio wasreportedas t view of the very visw initial tar saturation
0.6
o.4
()
d
! lt
6
lr jlto
-J
measuredthe yield of I seriesof crude oils. quantityof steamemrr) but was essentially Irs effect is, however,inEnt temperature.At steam
rnflooding
Chap. 4
0.1 NE
o g
lrJ
z 9
z o
o
F
f heat in lowering the chanismsthat play an he lightercomponents thermal expansionof
Figure 4.45 SteamDistillation of Heavy Crude Oils (after Wu and Brown 1975and Wu 1977)
51015 InjectedSteamto Oit Ratio
0.3
0.1 F
t2 0.0 o o.4 =
9, o = ut o
UJ
o
CRUDE OIL API GRAVITY
0.0 100 3510 1000 5000 OIL VISCOSITY (cr, al 100" F)
Figure 4.46 Correlation of SteamDistillation Yields with API Gravity and Oil Viscosity (from Wu and Elder 1983)
Other Mechanismsin Steamflooding
169
The effectof steamdistillationon the recoveryprocessis greaterthan that of the simpleproductionof the distillatethat is removedfrom the residualoil, because the distillateis an effectivesolventthat reducesthe viscosityof the oil beyondthe steamzone as it condenses and mixeswith the reservoiroil. Wu and Elder reportedsteamdistillationresultson a rangeof 16 crude oils and correlatedthe hydrocarbondistillateyieldsagainstthe gravity of the crude oil and the volume of steamused(left-handside of Figure 4.46) and againstthe viscosity of the crude oil measuredat 100"F(right-handside of Figure 4.46). In the left side of Figure 4.47 the distillateyields are correlatedagainstthe simulateddistillationtemperatures of the crudeoils for 20 volumepercentoverhead. The correlationon the right-handsideof this figure showsthe steamdistillateyield as a function of the yieldsat variouscut points for the simulateddistillationof the variouscrudeoils. Eachof thesecorrelationsallowsthe predictionof the steamdistillate yield of crude oil as a function of the propertiesof the crude oil and the quantityof steamemployed. Hsueh,Hong, and Duerksen(198a)showedhow steamdistillationcurvessuch as thosein Figure 4.45 can be predictedaccuratelyusinga simulatedtrue boilingpoint curve obtainedby gaschromatographic analysisof the crudeand a thermodynamic calculationbasedon the Peng-Robinson equationof state.
In a pro (Willmanet a found that src coveredmore seriesof expc \4'ith bo tivelyquickll til about1.3 p In anotl tained bi usi versus77.6cct be due largel The irrr heavyoils.Tb for the oils.F floods comes
For bodr I o Reductk o Thermal For stcr o Remova
o Exhaugi r A solvet front of'
ct
c; o
6
l!0
rli
0.1
^.'- 0 . 0 j]t"
o0 g
o
t!
()
0.5
J
_uj
z0
o
z o
JU
J
tr .20
t2 o = uJ 3n
on = ur o0
tz
0.3
GJ
9 6 Or
0 .1
Y< u.cF .2
0.0
6p z
t! (J
0.3
(r lrJ
o
0
300
400
500
600
700
SIMULATED DISTILLATIONTEIIPERATURE AT 20oloYIELO ('F)
0.0 1.0 0.4 0.2 0.6 0.8 0.0 SIMULATED DISTILLATIONYIELD (FRACTION OF Voi)
Figure4.47 Correlationof SteamDistillation Yields with Data from Simulated Distillations(from Wu and Elder 1983)
170
Steamflooding
Chap.4
(:
Figurc terfloo ter. Co
Other Mechan
is greaterthan that of e residualoil, because of the oil beyondthe ange of 16 crude oils avity of the crude oil ) and againstthe visFigure 4.46). :orrelated againstthe ,mepercentoverhead. : steamdistillateyield ned distillationof the tion of the steamdishe crude oil and the isillation curvessuch mulatedtrue boilingrude and a thermodyate.
In a pioneering,experimentallaboratory study, willman and his co-workers (Willman et al. 1961)carriedout a seriesof linear hot-waterand steamfloods.They found that steamfloodsrecoveredmore oil than hot waterfloods,which, in turn, recoveredmore oil than cold waterfloods.Figure 4.48showsthe resultsof one of their seriesof experiments. With both waterfloods and steamfloods,water breakthrough occurred relatively quickly in eachexperiment.However, steambreakthroughdid not occur until about 2.3 pore volumesof total fluids were produced. ln another experiment it was found that a still higher recoverycould be obtained by using high-pressuresteam (84Vorecoverywith steam at 520'F, 800 psig versus77.6Vowith steamat 327"F,84psig).This additionalrecoverywasthoughtto 'be due largely to the lower oil viscosity that resultedfrom the higher temperature. The increasedrecoveryfound with steamwasgreaterwith light oils than with heavyoils. The differencescould be explainedapproximatelyfrom distillation data for the oils. From the studiesit was concludedthat the extra recoveryfrom thermal floods comesfrom severalfactors. For both hot water and steam
o Reduction in oil viscosity becauseof higher temperatures o Thermal swellingof the oil For steam drive, the preceding plus
o Removalof additional material from the residualoil by steamdistillation o Exhaustivegas drive resulting from the steamflush o A solvent dilution effect causedby the condensationof the light ends in front of the steamzone
y',._, o
v",
(IN CORE9) STEAMINJECTION lrl
o J
otz
Vt ="
(AT COREOUTLET) STEAMBREAKTHROUGH (IN HOT WATERFLOOD COREIO)
GJ
y6
(IN COREIO) COLDWATERFLO@
o,
3sGr
RECOVERY450lo AT 16 PV
.2
5r z lrl
o
tr
Yt=t"
v",
UJ C
(WATERFLOODS) WATERBREAKTHROUGH
600'F f-.-J--.J--J
.a 0.6 1.0 0.8 DISTILLATION YIELD ;TtoN oF voi) Simulated
rnflooding
(STEAM INJECT|ON) WATETR BREAKTHROUGH
Chap. 4
TOTALPRODUCED PORE VOLUMES FLUIDS - PORE FLUIDS VOLUMES (STEAMCONSIDERED AS EOUIVALENT VOLUMECONDENSATE) Figure4.48 Oil Recoveries by SteamInjection,Hot Waterfloodand ColdWaterflood,in Corescontaining 12.2"APlBachaquero WaCrudeOil andConnate ter. Coldwater80'F;Hot water330"F:Steam327'F(fromWillmanet al. 1961) Other Mechanismsin Steamflooding
Table 4.8 showsthe magnitude of these effects as evaluatedby Willman et al. for experimentswith three oils having different amountsof volatile material. Theseoils were blendsof a very low volatility white oil and a heavy naphtha. The recoveriesshown on the first line of the table are for a hot waterflood. The secondline showsthe additionalrecoverythat wasobtainedwith the "nondistillable" oil using a hot nitrogen flood; this representsthe additional recoverythat would be obtained by the gas-water-driveeffect during the steamflood.Added to this are the steamdistillation effectsof line 3. Thus, for example,for the 25Vodistillableoil, the residualoil without distillationwould be 42.2%(100- 54.8 - 3.0)of the original oil in place. It would be expected that 25vo of this residual oil, or 10.58o, would be recoveredby distillation.The total of the first three lines is somewhat lessthan the recoveryby steamflooding(line 5). The difference(line 6) is the unexplainedrecovery. It is thought that much of the recoverydescribedas unexplainedin the table was the result of the solvent-extractioneffect mentionedpreviously.In the caseof the nonvolatileoil, this differencewas very small, as might be expected.Although the extra recoverywas smaller for the oil with 50Vovolatilesthan that for the oil with25Vo,the levelof recoverywasmuchlargerin this caseand the opportunityfor recoveringadditional oil was smaller. Willman's paper was one of the first in this field and must be regardedas a major contribution to the subject. The production of a 24'API crude from the Brea Field in California by means of a downwardsteamfloodwas describedby volek and Pryor (1972).They describe both laboratory recovery experiments and the field project. The reservoir was 4600ft deep, and very high steamtemperatureswere involved becauseof the pressure; reservoir temperaturesas high as 623"F were recorded in observationwells. Initially, the high temperaturesresultedin excessivewell bore heat lossesand mechanical problems.These were largely overcomeby employinginsulatedtubing. The reservoir was steeply dipping (66" from the horizontal). Steamwas injected near the top of the formation, and a stablecondensationfront formed, which advanceddownward.As a result of the steamdistillation effect, a residualoil saturation of lessthan 8Vowasobtained,and it wasfound that the product oil contained TABLE 4.8 Actual Steam RecoveriesComparedwith PredictedRecoverieswithout Solvent Extraction Recovery-Percentof Oil in Place Nondistillable 1. Hot waterflood recovery(includesviscosity reductionand swelling) 54.8 2. Extra recoverydue to gas-driveeffects J.U 3. Extra recoverydue to distillationr 4. Predictedrecoverybasedon abovemechanisms 57.8 5. Actual recoveryby steam 59.0 1a 6. Unexplainedrecovery(line 5 minus line 4) '(Percent of oil that is steam-distillable)x [100 - (line 1 + line 2)] (Willman et al. 1961) 172
25 Percent Distillable
50 Percent Distillable
54.8 3.0 10.5 68.3 76.0 7.7
58.0 3.0 19.5 80.5 83.9 3.4
Steamflooding
Chap.4
300 o : i o (.t J
tt
o o.
200
o o 100 .: -g =
E :
o
significantlyhi The quantityo basedon estir proach.A cr In later y the steamchl steamcondeof sation front. CONVERSIONOF M'
During a stear to a maximun high, falls to a mum. and ther Predicted are shownin I It is fouu verting from h later stagesof1 River ten-pattc with the sarnc In a reh steamflood pn should have p WOR (water
by Willman et al. for e material.Theseoils htha. for a hot waterflood. red with the "nondislitional recoverythat teamflood.Added to ile, for the 25% distil(100- s4.8 - 3.0)of 'this residualoil, or ;t three lines is someference(line 6) is the
o 300
5
c
.9 (,
3 tt 200
o o 100
ies without Solvent :rcentof Oil in Place 25 Percent Distillable
50 Percent Distillable
54.8 3.0 10.5 68.3 76.0 '7.7
58.0 3.0 19.5 80.5 83.9 3.4
rnflooding
Chap.4
Actual--r,:
E
g f
E 3
rxplainedin the table 'iously.In the caseof : expected.Although than that for the oil rdthe opportunityfor ne of the first in this iect. r Californiaby means (1972).They describe l. The reservoir was I becauseof the presin observationwells. e heat lossesand meg insulatedtubing. mtal). Steamwas inr front formed, which ct. a residualoil satuproduct oil contained
Calculated
o o.
o
J
64
65
66
67
Year
68
69
70
Figure 4.49 Comparison of Actual Oil Productionwith that Calculatedfrom EstirnatedSteamChamberVolume (from Volek andPryor 1972\
significantly higher proportions of light componentsthan did the original crude. The quantity of oil producedagreedquite well with that calculatedto be displaced basedon estimatesof the steam chambervolume using the Mandl and Volek approach.A comparisonis shown in Figure 4.49. In later years, the actual production tended to exceedthat calculated from the steamchambervolume. It was thought that this was due to the effect of hot steamcondensateproducingoil by waterflooding aheadof the descendingcondensation front. CONVERSIONOF MATURE STEAMFLOODSTO HOT WATERFLOODING During a steamfloodit is found that the rate of production of oil increasesinitially to a maximum and then declines.At the sametime, the steamoil ratio startsvery high, falls to a minimum near to the time when the oil production reachesits maximum, and then graduallyrises as the reservoirbecomesdepleted. Predictedsimulation data for the Kern River ten-patternproject (Hong 1985) are shownin Figures4.50 and 4.5L. It is found that considerableeconomycan be achievedin suchprojectsby converting from high-quality steaminjection to low-quality steamor hot water in the later stagesof production.Ault, Johnson,and Kamilas (1985)show that in the Kern River ten-patternsteamfloodthis procedureresultedin considerableenergysavings with the sameproductionof oil (seeFigure 4.14). ln a related paper, Hong lists a number of guidelines to indicate when a steamflood project should be converted to a waterflood. The oil-production rate should have passedits peak and be in a decline.The SOR (steam-oilratio) and WOR (water-oil ratio) may be expectedto be rising steadily.The reservoirpressure will also have peakedand be closeto its initial value.Total fluid productionwill likely be 85 to 95Voof the steam injection rate. The cumulative heat injection (injectedminus produced)will be about 450 to 500 million Btu per grossac-ft. Alternatively,the calculatedheat storedin the reservoir(asdistinct from that lost verConversion of MatureSteamfloods to Hot Waterflooding
173
$ +oo .E
fi aoo
E
c
e(, 200 f
E
i 100
o
Optimumtime of conversion
0
0
1000 2000 Time in Days
3000
Figure 4.50 Predicted Oil Production Rate, Kern River Ten-Patternproiect (from Hong 1985)
tically and that produced)will have reached280 to 300 million Btu per grossac-ft (240 to 260 MJlm3). OUALITATIVEREVIEWOF STEAMFLOODING The themeof this chapteris the quantitativeanalysisand predictbn of steamflooding performanceusingthe conductiveand convectiveheattransfeiequationsdeveloped in Chapters2 and 3. [n approachessuch as that of Myhill and Stegemeierthe volume of steam-saturated reservoiris calculatedfrom the heat contentof the injectedsteamand the volumetricheatcapacityof the reservoirwith an allowancefor the heat that is lost by conduction,verticallyto the overburdenand underburden. A major problem is found in applying this method becausefrequently, and probably usually, the steam-saturatedzone does not grow around the injector as a continuousregionwith a near vertical condensation surface. 120
Often. ir employingiri cumstancesti driving forcc I In reser continuousfa and the cood nouncedin tl voirswhichnr systembehaw steam chambc than would h approachbece Anorhcr through at th oil is largell h of gasconingr cap. In con\-G producingat r and steamthi Chapter7, rhi Useful q prematurestcl i) ii) iii) iv)
The usc r Waterfh Using lon Foamirg
The use of hq method which Chapter7.
E
o o
Pso
E o be 40 tr o a
Optimumtime of conversion
0
1000 2000 Time in Days 174
3000
Figure 4.51 PredictedSteam-Oil Ratio and Optimum Time of Conversion(from Hong 1985) Steamflooding
Chap. 4
Ar-KHeralr. A- | Systemsat Rc Aurr, J.W..Jot Low Qualitv! CaliforniaRq BENNrox,D.\l'.. Numerical Sil CIM, 34th AO Ble,rn,C. M.. Sc by Cyclic Stea Bibliography
-Pattern Project
on Btu per grossac-ft
dictbn of steamfloodnsfer equationsdevelill and Stegemeierthe €at content of the inwith an allowancefor bn and underburden. cause frequently, and ound the injector as a
often, in cold bitumen-containing reservoirssteam can be injected only by employing injection pressureshigh enough to fracture the reservoir. In these ciicumstancesthe steamheatsthe reservoiradjacentto the fracturesbut there is little driving force to move the oil. Heated oil is bypassed. In reservoirscontaining more mobile oil the steamchamber does grow in a continuousfashion but, as describedby van Lookeren, the steamtends to override and the condensationsurface becomesrelatively flat. This effect is more pronouncedin thicker reservoirs.As a result much of the advantagefor thicker reservoirs which would be predictedfrom the Marx-Langenheimtheory is not found; the systembehavesas if the reservoir height were no more than that of the overriding steam chamber. The heat lossesfor a given volume of steam chamber are larger than would be expectedfrom the simple Marx-Langenheimor Myhill-St"g"-"-i", approachbecauseof the greatly extendedsurfaceof the steamzone. Another problem which accompaniessteam override is that steam breaks through at the production wells and the pressuredifferential that was driving the oil is largely lost. Again heatedoil is bypassed.This is rather similar to the problem of gasconing which occursin the production of conventionaloil from beneaiha gas cap. In conventionaloil production the problem can sometimesbe controlled by producing at a rate low enoughto prevent drawing gas to the well. with heavy oil and steam this rate is often too low to be economic although, as will be seen in Chapter 7, this limitation can be improved by using horizontal wells. Useful approaches,which have been discussed,to overcomethe problem of prematuresteambreakthroughwith conventionalsteamfloodsinclude i) ii) iii) iv)
The use of infill wells Waterflooding after breakthrough Using low quality steam Foaming additiveswhich will increasethe apparentviscosity of the steam
The use of horizontal wells as an alternative to conventionalwells is a production method which is becoming increasingly attractive and which is discussed in Chapter 7.
BIBLIOGRAPHY
PredictedSteam-Oil timum Time of rom Hong 1985)
AL-KHAEAJI, A. H., WeNc, P. F., Cesretren, L. M., and BnrGHarr,r, W E., ,.SteamSurfactant Systemsat ReservoirConditions," SPE L0777(1982). Aulr, J.W., JoHNsor.r, WM., and KavrLes, G.N., "Conversionof Mature Steamfloodsto Low Quality Steamand/or Hot-WaterInjection Projects," SPE 13604,Bakersfield,Calif.: California RegionalMeeting, (March 1985),149-166. BENNtor.t, D.W., Moonr, R.G., and THorraas, F.8., "Effect of RelativePermeabilityon the Numerical Simulation of the Steam Stimulation Process," Paper 83-34-46,Pet. Soc. of CIM, 34th Annual Technical Meeting, Banff, Alberta (1983). BlaIR, C. M., ScnrnNrn,R. E., and Srour, C. A. "ChemicalEnhancementof Oil Production by Cyclic StearnInjection," SPE 10700(1982).
rnflooding
Bibliography
Chap. 4
BLEvrNs,T. R., AsnrrrNr, R. J., and KrRr, R. S.: 'Analysisof a SteamDrive project,Inglewood Field, California," IPT, tl4I-t150 (September1969). BI-evtNs,T. R. and BrLtINcsrnv, R. H., "The Ten Pattern Steamflood, Kern River Field. California," JPT, I505-L514(December1975). BnrrroN, M.W., IWrn"rrN, W.L., LrrnnecHr, R.J., and HanuoN, R.A.,..The StreetRanch Pilot Test of Fracture-AssistedSteamflood rechnology," Jpr, 5lr-s22 (March 19g3). o 1983SPE. BucrLes, R. S., "SteamStimulation Heavy oil Recoveryat cold Lake, Alberta," spE 7gg4 (1e79). BuRcrn, J. and cHeurLoN, D., "How to EstimateProductioncost by SteamDrive," pef. Eng. Intl.,56-70 (June 1983).(This referenceis not mentionedin the text but is a very practicalapproachto the use of the Marx-Langenheimmethod.) Bunser-qc.G.: "SteamDisplacement-KernRiver Field",JPT 1225-1231(october 1970). BunsELL,c.G. and PrrrvreN, G.M.: "Performanceof SteamDisplacementin the Kern River Field," IPT 997-In4 (August 1975). cHu, c., "State-of-the-ArtReviewof SteamfloodField projects,'Ipr, l8B7-1902(october 1985).O 1985SPE. CttuNG,K. H. and BurLEn, R. M., "GeometricalEffect of SteamInjectionon the Formation of Emulsionsin the Steam-Assisted Gravity DrainageProcess,"JCpr, 27, no. l:36-42 (January-February1988). Dertr, J. c., "Injection Rates{he Effect of Mobility Ratio, Area Swept and pattern," SPE"I,81-91 (June 1961). DrLcnrN, R.E., DnerueR,A.R., and OweNs,K.B., "The LaboratoryDevelopmentand Field Testingof Steam/Noncondensible Gas Foamsfor Mobility Control in Heavy Oil Recovery," SPE 10774, 1982. DoscHen,T. M. and GHassruI,F., "The Effect of ReservoirThicknessand Low Viscosity Fluid on the SteamDrag Process,"SPE9897(1981). Doscuen, T.M., Ouonecre, O.S., and Guessrur, F., "SteamDrive Definition and Enhancement,"JPT, 1543-1545(July 1982). EsoN,R. L., and O'Nesry, S.K., "Evaluationof a ConventionalSteamDrive with Ancillarv Materials: North Kern Front Field," SPE 10775,1982. FenoueAtl, S.M., "Current Statusof SteamInjectionas a Heavy Oil RecoveryMethod,,' JCPT (Jantary-March 1974). Fanoue Arr, S. M., "Steam Injection Theories A Unified Approach," spB r0i46 (L982). @ 1982SPE. FenoueAr-r, S.M. and Melonu, R.F., "Current SteamfloodTechnology,"JpT, t332-42, (Oct. 1979). FRIEDMaNN, F. and Jer.rsrN,J, A., "SomeFactorsInfluencing the Formation and Propogation of Foams in Porous Media," sPE 15087,56th california Regional Meeting of the SpE, Oakland,Calif. (April 2*4,1986). GerreN, T.M., "Oil Productionto Expect from Known Technology,"OiI Gas J.,66-76, May 7,1973. GorvtAA,E.E., "correlations for Predictingoil Recoveryby Steamflood,'Jpr,325-332 (February1980).@ 1980SPE. HoNc, K. C., "Guidelines for Converting Steamflood to Waterflood," SPE 13605,Bakersfield, Calif.: CaliforniaRegionalMeeting(March 1985),167-179. O 1985SPE. 176
Steamflooding
Chap.4
HoNc, K. C.. (Ma1 l9tlt. Hsuen.L.. Hcr perature9ce ture o.f fkm'. McGrarr-Hr I Jenaer-uoprx. Oil Emulsiq 'Stce JoNes,J.. (Septemberl' Lo, H.Y. and I Oil-Wet and I MaNol. G. aod 59-79 (\tarcl
Mar.x, J.\\. ad AIME. }16.3 MArri{e*s. C. I MoHe,vrr.-rorS Dome Tumtr MoH,A,i\,rrteD S California.-l MonEl-SerrcrHomogeneo Musrar, \1.. Il Hill (19ilr:F Mvsrll. \..{173-182tFeh Oct-ese"'.K. DSteamflood.I OzeN,A. S. an Crudeb1'Sta Plorc, J. F. arx and 26C. \ti (March 27-2 Pnars,M.. *Tb ResrrNe,J. L.. (March 1S3t Srour, C. A.. B Film Spread Annual Tech Tnavpnsr. E. F cessfulSteam Vellenor'. \. V of Recovery.I veNLooxener, voirs," SPEJ 6788.@ 19" Bibliography
am Drive Project, Inglelood, Kern River Field, " A-, "The StreetRanch 5lr-522 (March 1983). tte, Alberta," SPE 7994 t by Steam Drive," Pet. n the text but is a very 5-l?31 (October 1970). placement in the Kern PT, 1887-7902(October rction on the Formation rcPT, 27, no. l:36-42 a Swept and Pattern," ttory Development and ontrol in Heavy Oil Reoessand Low Viscosity ve Definition and Enrm Drive with Ancillary Oil RecoveryMethod," ;h," SPE t0746 (1982). Dolq;y," JPT, 1332-42, mationand Propogation al Meeting of the SPE, W," Oil Gas 1., 66-76, nflood," lPT,325-332 t," SPE 13605,Bakers€ 1985SPE. rnflooding
Chap.4
Hor.rc,K.C., "SteamfloodStrategiesfor a SteeplyDipping Reservoir," SPERE,43l-439 (May 1988). Hsuen, L., HoNc,K. C., and DunnrseN,J. H., "Simulationof High Pressureand High TemperatureSteamDistillation of Crude Oils," 2d UNITAR Conference,reported in The Future of Heavy Crudesand Tar Sands,Caracas,Venezuela,Feb.T-L7,1982 New York: McGraw-Hill (1984),924-935. JRuaLuoorN,A. K. M. and BurLER, R. M., "FactorsAffecting the Formation of Water-inOil EmulsionsDuring Thermal Recovery,"AOSTRA I. of Research,4, no. 2: 109(1988). JoNes,J., "SteamDrive Model for Hand-Held ProgrammableCalculators,"IPT, 1583-1598 (September1981).@ 1981SPE. Lo, H.Y. and MuNcarv,N., "Effect of Temperatureon Water-Oil Relative Permeabilitiesin Oil-Wet and Water-WetSystems,"SPE 4505(1973).@ 1973SPE. MaNot, G. and Vot-er, C.W., "Heat and MassTransport in SteamDrive Processes,"SPEJ, 59-79 (March 1969). Manx, J.W. and LeNGeNuuu, R. N., "ReservoirHeatingby Hot Fluid Injection," Pet. Trans. AIM E, 216: 312-3t5 (1959). (March 1983). ManrHews,C. S., "Steamflooding,"JPT, 465-471, MoHnuueor, S.S., veNSLyre, D.C., and GaNoNc,B.L., "Steam-Foam Pilot Projectin Dome Tumbador,Midway-Sunset Field," SPE Res.Eng.,7-16 (February1989). Mouerraueol,S.S. and McCellurra, T.J., "Steam-FoamPilot Projectin GuadalupeField, California,"SPE Res.Eng., 17-23 (February1989). Monpl-Spvroux, H. J., "Unit Mobility DisplacementCalculationsfor Pattern Floods in HomogeneousMedium," SPEJ,.2f7-227 (September1966). Musrer, M., The Flow of Homogeneous Fluids ThroughPorousMedia, New York: McGrawHill (1937);Reprintedby IHRDC, Boston(1982). MvHIt-1, N. A. and Srnceueten, G. L., "Steam-DriveCorrelationand Prediction,"./PI 173-182(February 1978).O 1978SPE. W. M., "Statusof the lO-Pattern Ocusnv, K. D., BrnvrNS,T. R., Rocnns,E. E. andJoHNsoN, Steamflood,Kern River Field, California,"IPT,225l-2257 (October1982).O 1982SPE. OzrN, A.S. and F.lloueArr, S.M.:'An Investigationof the Recoveryof the Bradford Crude by SteamInjection," JPT 692-698(June 1969). Pr-oec,J. F. and DuenrsrN, J. H., "Two SuccessfulSteam/FoamField Tests,Sections15A and 26C, Midway-SunsetField," SPE 13609,California Regional Meeting, Bakersfield (March 27-29, t985). PnArs, M., "Thermal Recovery," SPE Monograph Volume Z SPE, Dallas (1982). RrstrNE, J.L., "Effect of Preheatingon Kern River Field SteamDrive," JPT,523-529 (March 1983). R.E., "ContinuingBeneficialAction of Thin Srour, C. A., BlerR, C. M., Jn., and ScRIBNER, Film SpreadingAgents Injected during Cyclic Steam Simulation," Paper 83-34-31,34th Annual Technical Meeting, PetroleumSocietyof CIM, Banff, Alberta (1983). Tnevrnse, E. F., DernEnr,A.D. and Susrnr, A. J., "San Ardo-A CaseHistory of a SuccessfulSteamflood," SPE t1737,Ventura, Calif.: California RegionalMeeting (1983). L.W.: "Deerfield Pilot Test V^LLLenoy,V.V., WrlluaN, 8.T., CarrarnnLL, J. B., and PowERS, of Recoveryby Steam-Drive,"JPT 956-964(July 1967). vANI-ooKEREN,J., "Calculation Methods for Linear and Radial SteamFlow in Oil Reservoirs," SPE[ 427-439 (June 1983).The paper was presentedoriginally in 1977 as SPE 6788.O 1977SPE. Bibliography
177
vocer, J.v., "Simplified Heat calculations for Steamfloods,"Ipr, lr27-L136 (July 19g4). voLrr, c.w. and PRyoR,J. A., "SteamDistitlation Drive-Brea Field california.,' Jpr. g99906 (August 1972).@ i972 SPE. WrLLruAN, B.T., Velr-enov, V.V., RuNnEnc,G.W., ConNer-rus, A.J., and powens.L.W.. "Laboratory studies of oil Recovery by Steam Injection," Jpr, 681-690 (July 1961). o 1961SPE. wu, c. H., 'A critical Reviewof SteamfloodMechanisms,"spE 6550,1977.@ 1977spE. wu, c. H. and BnowN,A., 'A Laboratorystudy on SteamDistillation in porousMedia,,' sPE 5569(197s).O 1975SPE. Wu, C. H. and ELonR,R. B., "Correlationof Crude Oil SteamDistillationYieldswith Basic Crude Oil Properties,"SPEJ,937-945(December1983).@ 1983SpE.
The E
of He
INTRODUCTION
The material l by which heari steamzonewt the chambera It was al specifiedrates low fracture p reservoir b.v-st volve reservci The heat only part of ti the displacem by which this r
FACTORSAFFECTT
There are mal displacedfron PROPSTI
178
Steamflooding
Chap.4
Permeat Fracturin situatiqr injection
r l - - 1 1 3 6( J u l y1 9 8 4 ) . Cali fornia," "/PT,899. and PowEns,L.W., 6.sl-690(July 1961). ; r t . 1 9 7 7 .O 1 9 7 7S p E . rrrn in Porous Media," rtlon Yields with Basic PE.
The Displqcemenf of Hedvy Oil
INTRODUCTION i
The materialpresentedin the previouschaptersis concernedwith the mechanism by which heatis transferredin the reservoirand it concentrates upon the sizeof the steamzonewhich is formed.It was assumedthat the heatedoil was displacedfrom the chamberand that mostof it found its way in somemannerto productionwells. It was also assumedthat it was possibleto inject fluids into the reservoirat specifiedratesand pressures. In actualpractice,injectionat appreciable ratesat below fracture pressuremay not even be possiblewithout previousheating of the reservoirby steamstimulationor otherwise.Frequentlysteamstimulationmay involve reservoirexpansionby fracturing. The heatbalanceand heattransferconsiderations of the previouschaptersare only part of the problem.In this chapterconsiderationis given to the problemof the displacement of oil by water,by hot water and by steamand to the mechanisms by which this displacement occurs. FACTORSAFFECTINGDISPLACEMENT There are many factorswhich influence the efficiency and rate at which oil may be displacedfrom the reservoirby water and steam.The most importantof theseare: PROPERTIES OF THE RESERVOIR MATRIX
rflooding
Chap. 4
Permeability,wetting, homogeneity,capillarity Fracturing-either natural or, more importantly, in many thermal recovery situations, fracturing or reservoir expansioncreated by high pressurefluid iniection 179
DISPLACEDFLUID PROPERTIES
Particularlyviscosity DISPLACINGFLUID PROPERTIES
Viscosity Tendencyto changephase(both condensationand evaporation) Potential to transfer heat CONDITIONSAND GEOMETRY
Flood velocity (injection & production rates) Geometricparameterssuchas dip, spacingand pattern DISPLACEMENT CONCEPTS Piston Displacement This is an idealconceptin which the displacingfluid flows throughthe reservoirin a directionwhich is normal to the front and movesreservoirfluids to the production well at an equalrate. The conceptis that of "pushing" the oil by the injected fluid. Breakthrough The arrival of the displacingfluid at the productionwell is termedbreakthrough. For pistondisplacement, this is the end of the process.However,in reality,further oil in admixture with the displacingfluid is often producedlong after breakthrough.with very heavyoils nearly all the productionfrom waterfloodingoperations containsa preponderance of water and may be consideredto occur following breakthrough. Override When steamis injected,it tendsto rise and advancealongthe top of the reservoir. Thus the interfacebetweenthe steamand reservoirliquids becomesinclined, and steamwill arrive at the productionwell before the reservoiris completelyswept. This effect reducesthe vertical conformanceand tendsto wastesteamby bypassing. The "short circuit" of the steamto the productionwell reducesthe pressure gradientavailableto move the oil.
ment carried two closelr 1 Provide a tT c In stean stable and adr However. the displaced.
THE THEORETICAL
In the sectitx oped from thr
Frontal Stability Under someconditions,particularlywhen a viscousoil is displacedby pushingit with a fluid of lower viscosity(e.g.,heavyoil with water),the front betweenthe fluids becomesunstable,and fingersof the low viscositymaterialpenetrateinto the fluid being displaced.There are a numberof factorsthat affect frontal stability: the viscositiesof the fluids, the direction of displacementrelative to gravity,veIocity,condensation of steamand imbibitionof water.Figure5.1showsfingersthat developedduringthe displacement of a viscousoil with waterin a laboratoryexperi180
The Displacement of HeavyOil
Chap.5
1. Displac p l a c i n eI p l a c e d .r is knon I s t a bIii t r
2. The Buc bilitr lh change
The Theoretic
oration)
ough the reservoirin fluids to the producre oil by the injected
ermedbreakthrough. er. in reality,further :d long after break*aterfloodingopera:d to occur following
top of the reservoir. rcomesinclined,and is completelyswept. ste steamby bypassreducesthe pressure
placedby pushingit rc front betweenthe ial penetrateinto the lect frontal stability: lative to gravity,ve.l showsfingersthat r a laboratoryexperiFteavyOil
Chap.5
Figure 5.1 ViscousFingering.PhotographsShowingthe Developmentof ViscousFingersResultingfrom the Displacementof Oil by Water in a Hele ShawCell. Velocity is 1.8Times the Critical One (from Chuokeet al. 1959)
ment carried out in a glassHele Shaw cell. A Hele Shaw cell is constructedfrom two closelyspacedglassplateswith the fluids in between.It has been used to provide a two-dimensionalmodel of flow within a poroussolid. In steamflooding,the interface at which the steam condensesis frequently stableand advancesregularly-particularly if the advancedirection is downwards. However, the condensatethat is formed flows as fingers through the oil being displaced. THE THEORETICALAPPROACHESTO DISPLACEMENT In the sectionsthat follow, the theory of the mechanismof displacementis developed from three different points of view: 1. Displacementassumingthe existenceof a sharp interface between the displacingfluid (e.g.,water) and the oil. As the water advances,the oil is displaced,and it is assumedthat there is no minglingof the oil and water.This is known as Muskatb model. Its main use here is to developconceptson the stability of advanCingtGplacementfronts (interfaces). 2. The Buckley-Leveretttheory. In this theory, allowanceis made for the possibility that there can be an interminglingof oil and displacingfluid, which changesthe front of the Muskat model to an advancinginterfacial regionwith The TheoreticalApproachesto Displacement
181
a thicknessthat increasesas the processproceeds.This interminglingcan alsobe accompaniedby larger-scale fingering. 3. A heavyoil displacementconceptthat combinessomeof the characteristicsof both (1) and (2).In this concept,it is assumedthat the flow of the displacing fluid occurs as numerousfingers. [t is assumedthat at any sectionin the reservoir, the flowing fluid in someporesconsistsentirelyof oil and that in others it is entirely water or steam.This assumptionis sometimesknown asstratified theory of C.W. Nutt. flow.It is also relatedto the capillarydisplacement Finally, the one-dimensional displacement of oil by steamis considered.This is a coupledprocess.Within the steamchamberthereis an isothermaldisplacement of oil by steam.Beyondthe steamchamber,the oil and water that have left the steamchamberflow through the reservoir.In this region,there is also somedisplacementof oil by the flowing water.Betweenthesetwo regionslies the advancing condensation interface,the positionof which is determinedlargelyby heatbalance considerations.
Perte
i . e . ,i f
FLOOD INTERFACESTABILITY_MUSKAT'S MODEL In this sectionthe problemof the stabilityof the front betweenthe displacingand displacedfluid is analyzedusing the assumptionsknown as the Muskat model (Muskat 1937).It is assumedthat one fluid (usuallyoil) is displacedby the other, and the residualfluids are ignored.On one side of the moving interface,only the displacedfluid is assumedto move and on the other, only the displacingfluid.
Usuallvcq ity within p is occurriq sumedthat If this
Darcy's Law and Interfacial Stability Considerthe inclined reservoirshownin Figure 5.2. Phase1 is displacingphase2. The flow is assumedto be one-dimensional and inclined at an angle0 to the horizontal. It is assumedthat only phase 1 flows behind the front and only phase 2 flows beyondit. Darcy'slaw may be written for eachphaseas1
(#), (#), =-
VtP"t
-Pr$slnd
k
(s.1)
Vzpz = P29sna k,
If a smallpenetrationsuchas that shownformsby somerandomperturbation,then it cangrow forward if the absolutepressuregradientwithin phase1 is lessthan that within phase2. with this condition true, the pressureat the end of the protuberance can overwhelmthe pressurein phase2. This condition may be written as equation5.2.
Converselv are unfar'ff
In betq'een in stabilitl ing terms. The tr zontalor if stabilitfis c p2 sin 0-i-r
tln
equations5.1 the velocity 4 is equal to the volumetric fluid flow divided by the crosssectionalarea for flow, i.e., qlA. lt Is equal to the averagevelocity within the poresof the matrix multipliedby the porosity,d.
The Displacement of HeavyOil
Chap.5
Flood Interfa
his interminglingcan i the characteristics of f [o*' of the displacing rr sectionin the reser'oil and that in others es known asstratified orr of C.W. Nutt. rm is considered. This xhermaldisplacement ter that have left the hereis also somedisons liesthe advancing rrgelyby heatbalance
Figure5.2 One-Dimensional Flooding with an Incipient Finger
Penetrationcan occur if
-(#),--(#),
i . e . ,i f Vtut
Vu,
p ) ss i n 0 < 0
t-t*br:en the displacingand ns the Muskat model isplacedby the other, nE interface,only the Ledisplacing fluid.
Usuallyconservationwill requirethat the velocityin phase1 be equalto the velocity within phase2. This will not be the caseif a phasechangesuchascondensation is occurring at the interface.We considerthis caselater. For the presentit is assumedthaLV: lrin equation5.2. If this is the case,then it is apparentthat the flow will be stableif
t, is displacing phase2. n angle0 to the horiLrntand only phase2
-rmperturbation,then rase1 is lessthan that end of the protuber)n may be written as
l,r* divided by the cross:r the pores of the matrix
r HeavyOil
Chap.5
f,
and p1sing > p2 sin0
(s.3)
Conversely,the flow is alwaysunstableif both the viscosityand the gravity terms are unfavorable,i.e., if,
t.f
(s.1)
(s.2)
a n d p 1s i n 0 < p 2 s i n I
(s.4)
In betweentheseconditionsthere are combinationsof conditionsthat can result in stabilityor instabilitydependingupon the relativemagnitudeof the counteracting terms. The term involving gravity in Equation5.2 will be zero if the flow is horizontalor if the densitiesof the two phasesare equal.In this casethe conditionfor stabilityis determinedby the mobility ratio, as given in equation5.5. If pr sin 0 : p 2 s i n ? - i . e . , i f p r : p z o r 0 : 0 , t h e nt h e f l o w i s s t a b l e if Itr t llt i___: > :___:
kt
M o b i l ri tayt i = o U =ffi. Flood InterfaceStability-Muskat's Model
(s.5)
kz
t 183
If M is lessthan l-as, for example,when the oil viscosityis low comparedto that of the flooding material-then the front is stable.Equation5.5 is quotedvery commonly in the literature. Even if the viscosity ratio term is unfavorable,it can be overcomeby a favorable gravity term, provided that the flooding velocity is sufficiently low. The gravity term tendsto stabilizethe flow if the denseststreamis belowthe other-e.g., if light gasis displacingdenseoil downwardor water is displacinga lighter oil upward. The gravity term can stabilizethe effect of an unfavorablemobility ratio if y .(Pt
- Pz)gsin o l-tz _
l.t't
kz
k'
(5.6)
Similarly,a favorablemobility ratio can stabilizea flood havinga destabilizinggravity term if the flooding velocity is high enoughto overcomethe gravity effect, i . e . ,i f P)gsin0
V >V--hr-
I
(s.7)
t T
Itt _ ltz kt kz
\
As will be shown later, the Buckley-Leverett effects tend to improve the stability; it is shown on page 209 thal the condition for stability for a horizontal system then becomes k,of
Figurt 5 w a sE i t t
k,.f
-
This can be visualizedby sayingthat the M, is lessthan L for stabledisplacement. flooding fluid is not reallyjust waterbut a mixture of water and oil, which behaves asif it hasa muchhigherviscosity.This advantageis reallylargelyillusionary,however, because,as will be seen,the Buckley-Leverettmechanismcan leave vast quantitiesof oil behind the front when the oil is very viscous.
The effec modelsby Chu (1958).Models spacedglasspl dimensionsof t permeabilityol tween the plat Figure5instability.
Effect of Interfacial Tension
A Simple Tha
There are other stabilizing effects that tend to reduce viscous fingering. One of theseis the effect of interfacialtension;this tends to stabilizebecauseit acts to shortenthe interface. This stabilizingeffect is the largestfor smallfingersbecausethe pressuregradient acrossan interface is inverselyproportional to the radius of curvature. As a result,very smallperturbationstend to shrink; with the right conditions,largerones can grow. Fingeringcan be initiated by fluctuationscausedby nonuniformitiesin the reservoirmatrix; then those fingers that are larger than the critical dimension can grow.
Figure5.5 rep tion,whichis a is a similar ne than other*-is tendsto oppc If the increrna
M,=t*<1 Kfu
Po
184
of HeavyOil The Displacement
Chap.5
2It
can be r
2olR by balancrn ing it togetherak
Flood Interface
l\
compared to that quoted very com-
vercome by a favor:ntlv low. The grav* the other-e.g., if a Iighter oil upward. e mobility ratio if
(s.6) a destabilizing gravthe gravity effect,
(s.7) I0 lmprove the staa horizontal system
I br, sayingthat the I oil. whichbehaves rlv illusionary,howism can leave vast
Figure 5.3 Hele-ShawModel Apparatus.The Cell Could be Adjustedso That it was Either Vertical or Horizontal (from Saffmanand Tavlor 1958)
The effect of interfacial tensionhas been studied in Hele-Shawlaboratory modelsby Chuoke,van Meurs,and van der Poel(1959)and by Saffmanand Taylor (1958).Models such as that shown in Figure 5.3 consistof two parallel, closely spacedglassplates.The equationsof motion for a singlefluid flowing in the two dimensionsof sucha model are the sameas in a homogeneous poroussolid with a permeabilityof b2ll2 in two dimensions,whereb is the distanceof separationbetween the plates.The permeabilityis zero in the third dimension. Figure5.4 showsthe interfacein sucha modelin an experimentthat exhibits instability. A Simple Theory for Stabilization by Interfacial Tension
i fingering.One of : becauseit acts to >ethe pressuregraof curvature.As a rditions,Iargerones uniformitiesin the critical dimension
teavyOil
Chap.5
Figure5.5 represents an interfacewithin a poroussolid at a point wherea penetration, which is assumedto be hemisphericaland of radiusR, hasformed.Also shown is a similar negativepenetration.The pressurewithin the protuberanceis higher than otherwisebecauseof the tensionwithin the interface.This excesspressure tendsto opposethe growth of both positiveand negativeinterfacialprotuberances. If the incrementalpressuredue to interfacial tension is of the order2of 2o/R, then 2It can be shown that the excesspressurewithin a bubbleor droplet of radiusR is equal to 2olR by balancingthe pressureforce on a midplaneof the bubbleA,P(trR'?) to the tensilestressholding it togetheralongthe perimeterof the midplane o(2r.R).
Flood InterfaceStability-Muskat's Model
185
and Figure 5.4 Photographof ProgressiveFingering in Hele-ShawModel. Air is Displacing Glycerine Downwardsat a Velocity Greater Than the Critical One (from Saffman and Taylor 1958)
the incrementalpressuregradientnecessaryto make it grow is approximately2olR2 (equation5.8). dP dLt
-dP )dLt
2o R'
(5.8)
Obtainingthe pressuregradientterms from 5.1 and substitutingin 5.8 gives,with somerearrangement, the minimum radiusR of the protuberance which will be able to grow (equation5.9). The critical wavelength,\" (looking on the two adjacent hemispheresas a wave) is about 4R. The condition that the protuberancesshould grow is thus r\. =
4R>41
2o
,E-t).
11t2
-l
I
='l E-t),- )l
( P , - p 1 ) gs i n d l
2o
-l
J
II U2
(s.e)
I
V,
A more accurateand sophisticatedanalysisof this problem was publishedby Chuoke,van Meurs,and van der Poel(1959)with the resultgivenby equation5.10. This is the sameas5.9 exceptfor the constant2z', which replaces4V2. Essentially the sameequationwas publishedby Saffmanand Taylor (1958).
In addition u wavelengthol pitch of repee lent waveleng An irryt the dimensiq a critical pertr they might u flooding resd Chuokc porous soli&surface tensit propertiesau lows the rep terfacialarea This ide ger tends to I rounding rese water by imtf the absolute1 into it. If o'isl then equatic
U2
I,=2*l -n:l ,J E-fi)rv L 186
The Displacementof Heavy Oil
(s.10)
Chuokeassus tension and u Chap.5
Floodlnterfae
HemisphericolPerturbotion ExcessPressure: 20 /R Excesspressuregrodient required= 20 /R2
Figure 5.5
and Lrdel.Air is Displacing Ine rfrom Saffmanand
is approximately 2olR2
(s.8) uting in 5.8 gives,with ancewhich will be able rg on the two adjacent e protuberances should
-t 1','.', inal
(s.e) rlem was publishedby eivenby equation5.10. places4f2. Essentially 958).
(s.10)
)r- = trr{i In addition to the critical wavelengthfor finger growth, Chuoke calculatedthe wavelengthof "maximum instability,"A-. This is the perturbationwavelength(the pitch of repeatedfingers),which will grow at the fastestrate;it shouldbe the prevalent wavelength.It is shownwith equation5.10. An importantconceptin this theoryis that for fingeringof this type to occur, the dimensionsof the reservoirmustbe substantiallylargerthan the wavelengthof a critical perturbation.For example,while largefingerscan grow in field reservoirs, equipment.As a result, laboratory they might not be possiblein laboratory-scale predictions. flooding resultsmay lead to optimistic Chuokeet al. extendedthe ideajust describedto representinterfaceswithin poroussolids.To do this, they substituteda*, which they defined as the effective surfacetension,for o. The effective surfacetensiono* dependson the capillary propertiesand wetting of the matrix aswell ason the interfacialtension.Its useallows the representationof the idea that when a protuberanceforms, much new interfacialareais created,particularlyif the matrix is wettedby the displacingfluid. This ideais relatedto the conceptof imbibition.When a protrudingwaterfinger tends to form, the water within it is drawn away by imbibition into the surroundingreservoirif this is waterwet and at the irreduciblesaturation.Removalof water by imbibition tends to reduce the rate of growth of the finger by increasing the absolutepressuredifferential required to transfer the increasedflow of water into it. If o* is assumedproportionalto o and kr and kz are assumedto be equalto k, then equation5.10becomes
^.=rl
o*k
0r, - pr)(V -
,r]
\
(s.11)
Chuokeassumedthat the effectivesurfacetensionis proportionalto the interfacial tension and used equation5.11to predict the most probableperturbationwaveof HeavyOil
Chap.5
Flood lnterfaceStability-Muskat's Model
length. In this equation C is a constant (Chuoke'sconstant)for a particular reservoir material that includessomeof the precedingnumerical constantsas well as a proportionality constantfor the relationship between the effective interfacial tension and the actual surface tension. This ideawas studiedfurther by Petersand Flock at the University of Alberta (1981).Valuesof C taken from the literature are given in Table 5.1. They show the large effect that the wettability of the matrix has upon stability. The displacement of oil by water is stabilizedconsiderablyby the imbibition effect if the reservoir is water-wet. TABLE 5.1 Valuesof C, Chuoke'sConstant
Petersand Flock (1981) Chuoke
Oil-wet
Water-wet
25.4 30
190.5 200
Effect of Condensationupon Interfacial Stability
\dLl,
<
lap\ \dLl,
or
(s.r2)
Consider a one-dimensionalflood in which steamis introduced into a cold-watersaturatedreservoir.This is shown in Figure 5.6. It is assumedthat there are no transverseheat lossesand that the water saturationin the steam-sweptzone is constant and equal to S,i. Although the diagramshowsthe reservoir as being horizontal, this is not necessarilyso. Steampassesthrough the steamzone and condensesat the interface. The latent and sensibleheat raise more of the reservoirto the steam-saturationtemperature, and the condensatejoins the water alreadypresentand is pushedforward by the steam.We will considerthe stability of the interface.As was discussedin Chapter3, the temperaturefalls quickly from 75to Ta at the condensationfront if it is assumedthat there are no lateral heat losses,that the flow velocity is uniform acrossthe section, that the temperatureof the solid is equal to the fluid temperature at eachpoint, and if thermal conductionis ignored. From what has gonebefore one might suspectthat the interfacewould tend to be unstablebecausethe steamis much lessviscousthan the water. However there is another very important factor: the velocity within the steamzone is much higher The Displacementof Heavy Oil
HEATBI|..
PtV
Vn 6p,0-,
-l-l
T-T-b,-p)ssino
than that in O tion. This td dient within tl The ratb combininga r
Equation5.1'lr to that of thc r
Equation5.12is the conditionfor stabilitythat was developedearlier.
lap\
I
MATnlI
When an automobileis driven in the rain, there is a very noticeabletendencyfor water to stream down the windshield if it is dirty (non-water-wetted),whereasthe waterwill run in continuouscurtainsif the windshieldis cleanand water-wet.This effect is approximatelyanalogousto that just described.
-l-l
s
Chap.5
In the precedi the total areaa factor of U) For prd residualwater for the steam.I
Steam press Steam teryc Steamentbd Steam deasil Hot-wat€rcl Hot-watete Reservoirta Cold-waterC Rock heat cr Rock densiq Porosity Irreduciblc r
Flood Interface
icrra particular reserconstants aswell as a ectir,einterfacialtenUniversityof Alberta le 5.1.They showthe iti. The displacement rectif the reservoiris
Figure 5.6 Front
Advancing Condensation
than that in the waterzonebecauseof the shrinkagethat occursduring condensation. This tendsto stabilizethe processby requiringa higherabsolutepressuregradient within the steamzone. The ratio of the velocityof the water to that of the steammay be obtainedby combininga materialbalance(5.13)with a heat balance(5.14).
Water-wet MATERIALBALANCE
190.5 200
p z V z= p r q * 6 V $ - S , ) ( p z - p )
(s.13)
HEATBALANCE ABOVE T, = p'h(Ht hz) Vl( - 6)p,C,(T'- Tr) + dp,S,r(hr - hz) + 6pr( - S,i)(H' - hr)l
,ticeabletendencyfor -*'etted),whereasthe t and water-wet.This
(s.14) Equation5.14maybe rearrangedto providethe ratio of the velocityof the interface to that of the steam,namely,
I earlier.
V n
(s.12) ed into a cold-watered that there are no .m-sweptzoneis con;oir as beinghorizonrhe interface.The lar-saturationtemperais pushedforward by As was discussedin rndensationfront if it * r'elocityis uniform to the fluid temperaterfacewouldtendto Iter.Howeverthereis zone is much higher HeavyOil
Chap.5
Pr(Hr - hz)
6 p t $ - S , r ) ( H-r h t + 6 p . 5 . , ( h -t h r ) + ( r - 6 ) p , C , ( T t - T )
(5.14a)
In the preceding,the fluid velocitiesare definedasthe volumetricflows dividedby the total area.The actualaveragefluid velocitieswithin the poreswill be largerby a factor of 1,/6. For practicalcases,the terms involving the heat capacitiesof the rock and residualwater in the denominatorof equation5.14awill be much largerthan that for the steam.For example,considerthe followingassumedtypical numericaldata:
Steampressure Steamtemperature Steamenthalpy Steamdensity Hot-waterenthalpy Hot-waterdensity Reservoirtemperature Cold-waterenthalpy Rock heat capacity Rock density Porosity Irreduciblewater saturation
r1
Hr Pr hr p" T^ h2
C, p,
0 S,;
Flood InterfaceStability-Muskat's Model
515psia 470"F 1205Btu/lb 1.11lbft3 453 Btu/lb 50 lbft3 50'F 18 Btu/lb 0.23 Btu/lb "F '1.65 lblft3 0.3 0.25
(3.ssMPa) (243'C\ (2803kVke) (17.8kglm3) (10sakVkg) (801kg/m3) (10"c) $2 kl/ke) (0.e6kVke'C) (2643kglm3)
189
Then, by substitution, 1318 = 0.1007 296+1631,+11157
V
n
The ratio of the interfacevelocityto the actualsteamvelocitywithin the poresis, for this example,given by
4 , - Su)= 0.1007 tu6{t x 0.3x 0.75= 0'0227 The ratio Vz/Vt canbe calculatedby rearrangingequation5.13to give Vz
- 5.,)(p, -
pt,V6$
VrPzn
pt)
(s.1s)
f-
k(pt - p)g sin 0 Vtp.,
ffi"*
(s.16)
The gravityterm on the right-handsideof equation5.16can eitherhelp stabilize or destabilizethe front dependingon whetherthe steamis flowing from above or from below. The left-hand side of equation5.16has been computedfor the conditions given in the previous examplefor a number of assumedsteamtemperatureswith the resultsshownin Table5.2. TABLE 5.2 Valuesof Stability Factorfor AdiabaticDisplacementof Water by Steam
n ('F) PrlPz Vzrtzlhl-tt
100 328 I t.J
0.12
400 445 7.0 0.23
700 503 5.7 0.30
1000 545 5.0 0.36
1300 578 4.5 0.42
1600 605 3.9 0.45
The Displacementof Heavy Oil
Another mecha (1977)that tenG showsa steamo There is a t the heat transfe elsewherealong with the resultt flow to P will tc "push" available As in the d ent from Figure more than it *il mentswill stro* the field. Also. b stability.An exu
Region1 Steam
The valuesof the factor are lessthan unity, althoughthey tend to increase with temperature.This meansthat unlessthe gravity term in 5.16is quite unfavorflood shouldbe stable.The shrinkagethat occurs able,the heating/displacement during the condensationof steamis thus ableto stabilizethe steam-waterinterface. In evaluatingthe left-hand side of equation5.16,the viscosityof water at steam temperaturerather than the much higher value at reservoir temperaturehas been usedfor p.2.The logic behind this is that right at the front, the water is in equilibrium with the steamand is at the sametemperature.For a protuberanceto grow as depictedin Figure 5.2, it is necessaryfor the pressuregradientin the steamto overcomethat in the water right at the interface. If sucha protuberancedoesstart, there is an additionalstabilizinginfluencebecauseof the higher steamvelocityre190
Miller's Terrprr
Pz
This ratio can be substitutedinto equation5.2 to give the conditionfor stability.If it is assumedthat kt : kz : /c,then equation5.2 canbe rearrangedto give the following condition for stability.
Steampressure(psia)
quired to supply rate in the $eaD sult in additiooe In a nurobt tory by Baker t l! condensation iil In steamfL or downwards. i. from the steam I it. The condens
Chap.5
Directionof frm FloodlnterfaceS
i within the pores is,
27 3 to give
(s.1s) dition for stability.If angedto give the fol-
(s.16) can eitherhelp stabis flowing from above :d for the conditions ,m temperatures with
r by Steam
1300 578 4.5 0.42
1600 605 3.9 0.45
they tend to increase 5.16is quite unfavor;hrinkagethat occurs ;team-water interface. ity of water at steam temperaturehas been the water is in equiprotuberanceto grow rdientin the steamto otuberance doesstart, thersteamvelocity ref HeavyOil
Chap.5
quired to supplythe heat lossfrom the growingprotuberance. This additionalflow rate in the steamsidewill requirean additionalpressuregradient,and this will result in additionalstabilization,as is discussedin the next section. In a number of simple steamwaterfloods that were carried out in the laboratory by Baker (1973)in a three-dimensional reservoirmodel,it was found that the condensationinterface was indeed stable. In steamfloods,the condensation front is usuallystableif the flow is sideways or downwards,i.e., if gravity tendsto stabilizethe front. However,the condensate from the steamruns through the oil which is beingdisplacedand is producedwith it. The condensation interfaceis.stable,but the water-oilinterfaceis usuallynot. Miller's TemperatureGradient Stabilization Another mechanismhas been describedby Miller (1975)and Armento and Miller (1977)that tendsto stabilizesteamfronts.This is depictedin Figure5.7.The figure showsa steamcondensationfront in which a perturbation has formed at P. There is a sharptemperaturegradientat the front and,becauseP is indented, the heat transfer from it to the neighboringreservoirwill be at a greaterrate than elsewherealongthe front. This resultsin increasedflow at P abovethe interface, with the result that the finger will tend to fill up with water.Also, the increased flow to P will tend to increasethe local pressuredrop and reduce the amount of "push" availableat P. As in the discussionof the stabilizingeffectof interfacialtension,it is apparent from Figure 5.7 that the heat-transporteffect will tend to stabilizesmall fingers more than it will largeones.Again, there is the possibilitythat laboratoryexperimentswill show stabledisplacements,which may not be found on a larger scalein the field. Also, heterogeneitiesin the field tend to promotefingering and frontal instability.An extremecaseof this is the flow of steamalongeither a naturalor arti-
Region1 Steam
Region2 Water / /."
s
WavyFront
Directionof front motion ---------+ FloodInterfaceStability-Muskat's Model
Figure 5.7 IncreasedHeat Loss from Frontal Indentation(Armento and Miller 1977)
191
\leasur ering a *'i& Figure5.9The p* cludesdatati excludes thc ing),the rch The nd reservoirrn| its saturatio ure 5.10. The cu They do nu r eral shapeto dated sands algebraiceqr The rel tion .S*,and t rock is water forces.Whil pocketsare r The re* water but fall system,the r saturation.a was flooded For the dependentre mericalexan
interfacecan advance,eventhough ficial fracture.In this situationthecondensation through the walls of the fracture. vastquantitiesof heat are transferred
DARCY'SLAW FORTWO.PHASE FLOW If two or more separatephasesflow simultaneouslythrough a poroussolid, then the flow of eachphaseis lessthan that which would be producedby the samepressuregradientif it were the only phasepresent.The individual fluids competewith eachother as they flow throughthe mediumand impedeeachother'sprogress.Allowanceis madefor this by introducingnew variables,relativepermeabilities,into Darcy'sequation.Theseempiricalcorrectionfactorsare obtainedfor anyparticular porousmediumby experiment. For two-phaseflow, Darcy'slaw is modifiedby the introductionof the relative permeabilitycoefficientsk,oand k,,. Equations5.17and 5.18are the Darcy equaflow in a bed tions for the flow rate of oil, qo,and water,e., for one-dimensional of cross-sectionalareaA that is inclined at an angle 0 to the horizontal (seeFigure 5.8).If sin 0 and the flow are both positive,then the flow is uphill. In general, the pressurein the oil phase,P,, is not the sameas the pressurein the waterphase, P,, becauseof the effectof capillarypressureP".The effectivepermeabilityfor each phaseis equalto the absolutepermeabilityk multipliedby the relativepermeability k,o or k,..
Qo= -*#(*
e*= -.#(*.
+ a,ssine)
n,s'ine)
(s.r7)
(s.18)
Relative PermeabilityCurves The advantageof the relativepermeabilityconceptas a meansfor allowingfor the effect of the competitive flow of immiscible fluids in porous solids is that in many practicalsituations,it is found that the relativepermeabilityvaluesare, to a first approximationat least,functionsof the fluid saturations(i.e., the volumefractions of the individualfluids presentin the pore space)alone.In mostsituations,relative permeabilitiesare largelyindependentof flow velocityand of the fluid viscosities.
THE FRACTIONALI
For what foll ties(5.17and Kro 1,0 0.8
'*24 Figure 5.8 Darcy'sLaw for Two Phase Flow
192
The Displacement of Heavy Oil
Chap. 5
0.6 I
Fradt
The Fractiond
Measurementsof the relative permeabilitiesfor binary oil-water systemscovering a wide range of oil viscosity for a particular reservoir rock are shown in Figure 5.9. The pioneeringpaper by Leverett, from which this figure is copied, also includesdata that showthat over a wide rangeof interfacial tension(but a rangethat excludesthe extremelylow interfacial tensionsobtainableduring surfactantflooding), the relative permeabilitiesare essentiallyindependentof interfacial tension. The relative permeabilitiesare monotonic functions of the saturationof the reservoirmaterial; i.e., the relative permeabilityof either phase increaseswith its saturation.Often the curves are qualitatively of the generalshapeshown in Figure 5.10. The curves in this figure are used in the illustrative examplesthat follow. They do not representany particular reservoirsituation, but they are similar in general shapeto curvesfor the flow of conventionaloils through water-wet,unconsolidated sands. The particular curves shown correspond to the simple, arbitrary, algebraicequationsin the figure. The relative permeabilitycurve for water starts at an irreduciblewater saturation Su and risesto L at S, = 1..[t is tangentto the x axis.This is commonwhenthe rock is water-wet.At S,i the irreduciblewater is held in place by interfacial tension forces. While the water phase is still continuous,the connectionsbetween water pocketsare vanishinglythin in places. The relative permeabilitycurve for oil is generallysimilar in shapeto that for water but falls rather more sharply to the residualoil saturationSo. In a water-wet system,the residual oil saturation is not as well defined as the irreducible water saturation,and its value may be more dependentupon the history of how the core was flooded. For the purposesof this analysisit is assumedthat definite,simple,saturationdependentrelative permeability curves exist and that, for the purpose of the numerical examplesdevelopedlater, they may be representedas in Figure 5.10.
advance,even though re fracture.
I a poroussolid, then ced by the samepresrl fluids competewith h other'sprogress.Alre permeabilities,into ned for any particular ductionof the relative I are the Darcy equansionalflow in a bed e horizontal (seeFigu is uphill. In general, re in the waterphase, permeabilityfor each r relativepermeability
(s.17)
(s.18)
rs for allowing for the solids is that in many r valuesare, to a first , the volume fractions ost situations,relative f the fluid viscosities.
THE FRACTIONALFLOW EOUATION For what follows, it is useful to use the equationsdefining the relative permeabilities (5.17and 5.18)to derivean equationthat relatesthe compositionof the flowing krw 1.0
kro
atler Leveretl 1939
0.8 0.6 o.4 o.2 J..-.-J-J...IS-J
Darcy'sLaw for Two Phase
f Heavy Oil
Chap. 5
0.2 0.4 0.6 0.8 1.0
0t
0
0.4 0.6 0.8 1,0
FractionalWater SaturationS* The FractionalFlow Equation
Figure 5.9 Effect of Water Saturation on the RelativePermeabilityto Oil (left) and to Water (right) for a Particular Core with a Wide Rangeof Oil to Water Viscosity Ratios
193
kro
lt IE
c)
b
oo
, *,o =(t-t*)t-'93,
t -*=ft9"{*,.
=
E
This equatim tional f lo,r:
S w i= 0 . 2 ;S o r = 0 . 1
o.s
g
q)
E
1' -q, -or
S*i
I
t
I
'l '
0.5 WaterSaturation
Figure5.10 HypotheticalRelative PermeabilityCurves
streamto the saturationin the matrix. We will derivean equationto determinethe fractionof water/, in the flowing streamasa functionof the water saturationS, in the matrix.3The choiceof waterfractionand saturationratherthan oil fractionand saturationis arbitrary; the correspondingoil fraction and saturationcan be obtained readilyfrom the water fraction and saturation. We write the oil flow as the differencebetweenthe total flow and the water flow as in equation5.19and substitutein 5.17to give 5.20.
(s.1e)
Qo=Qt-Q*
-Q,*-!'= -n(e ' -\ + p,gsine) ++ kk,o kk,o ar I
(s.20)
l. The rari 2. The dcp 3. The effo '*'ith nd gravitvb desiraH 4. The effo br' * ritil equatim term aP mono{oo Figure 5 core hav Iarr-terd be drart
For the presc 0, horizontal. that the cafll vicinity of thc the saturatim With th equation,5.26
Rearrangeequation5.18to give 5.27,subtractequation5.20 from equation5.21, and, making use of the definition of the capillarypressure5.22, rearrangeto give equation5.23.
Tf::
-"(*
+ p,gsino)
(s.2r)
Ap=p.-po
ans sin o) n,(#,.ffi) =#* n(u-e-
(s.22) (s.23)
'.T#(#- o*"^') t*x
k,o
(s.24)
trro
The Displacementof Heavy Oil
5
=o o 0
0
oEquatim andP,=P.=P
rThis derivationfollows that of Dake (1978).
194
a y,.
G
Equation5.23 maybe rearrangedto give the generalfractionalflow equation5.24. +^ -q: *-
o
:
P,=Po-P.;
-l wa ,-
6
which can be mr
Chap.5
The Fractiorg
This equationcontainswithin it the effects of four different factors upon the fractional flow:
uheticalRelative /es n to determine the :er saturation S, in an oil fraction and ration can be oblow and the water
(s.1e) (s.20)
1. The ratio of the viscositiesof the two fluids. 2. The dependenceof the relative permeabilitiesupon saturation. 3. The effect of gravity. For upward displacement(asin Figure 5.1)of a light oil with water, Ap is positive; since sin 0 is also positive, the term containing gravity has the effect of decreasingthe water fractional flow. This is usually a desirableeffect. 4. The effect of the capillary pressureterm. The effect of this term can be seen by writing it asin Equation5.25.Both of the factorson the right-handsideof equation5.25 arc negativefor water displacingoil in a water-wetsystem.The term dP"/dS, is negativebecause,for water-wetsystems,capillary pressureis monotonicwith P" decreasing with increasingS,; a typical curve is shownin Figure 5.11.The term dS,/d, is negativewhen water is displacingoil from a core having a high initial oil saturation.It follows that the effect of the capillary term, in this case,will be to increasethe water flow-i.e., water tendsto be drawn aheadinto the oil-rich zone by capillary attraction.
oP, 0x
oP, dS, AS- 0x'
#
and
*
areboth -ve
(s.2s)
For the presentwe will assumethat the gravity term is zero (either the systemis horizontal,0 : 0, or the two phaseshave the samedensity,Ap : 0) and assume that the capillarypressureterm can be neglected.Except right in the immediate vicinity of the front, this is often a reasonableassumption,since the magnitude of the saturationgradient is small. With these assumptionsathe fractional flow equation 5.24 reduces to equation5.26:
om equation5.2L, rearrangeto glve
(s.2r) (s.22) (s.23) }ow equation5.24. 50
WaterSaturation%
(s.24))
too
Figure 5.11 Typical Capillary Pressure Curve
aEquation
5.26 can be derived very simply if these assumptions are made initially. If sin 0 = 0 q" k*Po 'aP = 40Po= q"p" -a n d p o = p * : p , t h e n e q u a t i o n s 5 . 1 7 a n d 5 . 1 8 b e c o m' e - K A 't"nt" 1"" ft* ,r"= *t""'
which can be manipulatedto give equation5.26.
lavy Oil
Chap.5
The Fractional Flow Equation
195
[-
Jw
-
,.t 3
!
This showsthat the fraction of water in the flowing streamis a function of the ratio of the relative permeabilitiesfor the flow of the two phasesand that it is also equally dependentupon the ratio of the viscositiesof the two phases.By inspection, we can seethat for a particularsaturation(whichfixes the relativepermeabilities),an increasein oil viscosityincreasesthe flow of water. Figure 5.12showscurves of/, that are calculatedfrom the relative permeability curvesof Figure 5.10for variousconstantratiosof waterviscosityto oil viscosity. The curves demonstratethe increasingtendencyfor water to flow through the reservoir(even at relatively low water saturationsor high oil saturations)when the oil is very viscous. Effect of the Gravity Term on FractionalFlow The dimensionless gravity term in equation5.24 is written in equation5.27.Itis more significant when the difference in densitiesis higher, when the reservoir is steeplyinclined, when the total flow is low, and when the ratio k/p," ishigh. ^ kk,,AApg sin d P=-
(s.27)
QtPo
The term B is proportionalto the ratio of the gravity potentialgradientA pg sin 0 to the viscouspotentialgradiente,p"f(kk,,A). High velocities(i.e.,high viscosityforces)tend to overcomethe effectof gravity. Gravity tendsto stabilizethe flood if the heavierfluid is below. For a water flood wherethe water is more densethan the oil, upwarddisplacement reducesthe fractionalwaterflow. With gasasthe displacingfluid, the flow of gasis reducedby downwardflow. For waterfloodsof heavyoils wherethe densitiesof the two fluids are very similar and when po is very large,gravity has little effect. Figure 5.13showsthe calculatedeffect of the gravity term on the fractional flow curvesfor a matrix with the samerelativepermeabilitycurvesas in the previous exampleand with a water-to-oilviscosityratio of 0.1. As the gravity term is
1
196
Figure 5.12 Effect of Viscosity Ratio on Fractional Water Flow
The Displacement of Heavy Oil
1.5F
(s.26)
Chap. 5
ft Et
f 1 L-----
{ ooh
EFn l E -t €
t
-o.u F 0
increasedin creasesmarl where the rt /, is greaterI the positive is falling cc Effect of Sr and Fractic
The relatira are both a r lated to thes and 5.18.Thi fluids, any i that-rock. Onah could havea boring volun stance,the statisticalau modynami atomicnatur It is p< water and d rate streans Such rivulet scale.For q areasmeasu size.It can r One er above the lit voir may co quently rnov
The Fractkr
(s.26) lunctionof the ratio and that it is also phases.By inspecrelative permeabilir relativepermeabilicosityto oil viscosto flow through the ,turations)when the
equation5.27. It is hen the reservoir is rt/p" is high.
(s.27) gradient A pg sin 0 c the effect of gravbelow. For a water Eementreducesthe of gasis reducedby iesof the two fluids bct. m on the fractional rves as in the previthe gravity term is
ifect of Viscosity Ratio FaterFlow
{eavy Oil
Chap.5
0.5 Water Saturatlon
Figure 5.13 Effect of Gravity Term on Fractional Water Flow
increasedin value, the fraction ofwater in the flow for a given rock saturationdecreasesmarkedly. The curve for B : -5 in the diagram correspondsto a case where the water flow is downward; there is countercurrentflow in the rangewhere /" is greaterthan 1-i.e., the oil is rising through the falling wate;,"Similarly,with the positivevaluesof B, there is a rangewhere/, is negative.In this region,water is falling countercurrentlythrough a rising oil stream. Effect of Segregated Flow on Apparent Relative Permeability and Fractional Flow The relative permeabilityconceptassumesthat at eachpoint in the reservoir,there are both a water and an oil saturationand that the flows of the two phasesare related to these saturationsby relative permeability curves and flow equations5.17 and 5.18.This conceptcannotbe true on a microscopicscale,since,with immiscible fluids, any infinitesimal volume must be filled with either water, oil, or-failing that-rock. On a larger scale,it is possibleto imaginethat a volume (of, for example,1 cc) could have an averagecompositionessentiallythe sameas that of a similar neighboring volume and that the flow within it might also be similar. In this circumstance,the saturationsand flowing stream compositionmust be looked on as This conceptis similar to our acceptanceof the intensivetherstatisticalaverages. modynamicfluid variablessuchas temperatureand density,which, becauseof the atomic nature of matter, have meaningonly as statistical averages. lt is possible-and usuallyvery likely-that somevolumescarry essentially water and otherscarry oil, i.e., that the flow throughthe reservoirconsistsof separate streamsor rivulets of water and oil moving beside each other but separately. Such rivulets or fingers may be on a small scaleor they may be on a much larger scale. For example,we might imagine individual streamshaving cross-sectional areasmeasuredin squarefeet or very small streams,each of only a few pores in size. [t can also happenthat the rivulets meanderand changewith time. One exampleof large individual streamsoccurring is when steamsegregates above the liquid streamsin a steamflood.Here the upper part of the entire reservoir may consist of steam moving separatelyabove oil and water, which are frequently moving in the samegeneraldirection below but at different velocities. The FractionalFlow Equation
197
An interestingand limiting model can be developedby assumingthat within of a reservoirin which a one-dimensional waterfloodis occurring, the cross-section the porescontaineither oil at the residualoil saturationwith water flowing pastor waterat the irreduciblewater saturationwith oil flowing past.We may alsoimagine pores that have water flowing in at one end and displacedoil leaving at the other (seethe discussionof C.W Nutt'scapillarybundle theory that is describedlater). In any one pore in such a system,the saturationsare either S"=S,;
cal endpant where the re
=
.ct o o
and So=1-S,;
E
or S, = 1 - So, and So = So,
(5.28)
The correspondingrelative permeabilitiesof water and oil for the two types of pores are k,o:
klo and k,n = 0
kro=0
and k,-=ki,
1-So.-S,r
(s.30)
whereSi is the volume averagewater saturation. The flows of water and oil are givenby equations5.31and 5.32if the effectof gravity is neglected.Comparisonof theseequationswith 5.17and 5.18leadsto the expressions 5.33and 5.34for the apparentrelativepermeabilityof the reservoirin segregatedflow.
-kk'*"A(+\ \dxl
(s.31)
Q*=
o.s
.F (E
E tr
(s.2e)
wherekl, is definedasthe relativepermeabilityto oil at S.; and k- is definedasthe relative permeability to water at ^S,: 1 - S.,. ki, and ki, are often referred to as the endpointrelativepermeabilities. The areafraction,a, of the porescarryingwater at any particular crosssection (1 - c is carrying oil) is given by
SJ _ S,,
b
o. o
The ra equation5.1 fl segregated by the exam
At first sigh much lessef from the fig As a resultc watersatun differenceis
-kkL$- ^^(#) (s.32)
Qo= Fo
kk = ki.a =
o;(, I
'
-9 + w
wl
s
ki. = kL| - a) = oi.lt
:
(s.33)
a
s0 a
s" - s;\
U-s--s-/
(s.34)
e
Equations5.33 and 5.34 show that the apparentrelativepermeabilitiesare linear functionsof saturation.They are the equationsof straightlines that join the practiof HeavyOil The Displacement
Chap.5
The Buckler
lssumingthat within erflood is occurring, rater flowing pastor \l'e may also imagine leavingat the other : is describedlater). her
cal endpointsof the conventionalrelative permeabilitycurves with the points where the relative permeabilitiesbecomezero.This is shownin Figure 5.14.
= .ct G
(s.28) or the two types of
() E b o.
0.5
o
'E
so E
(s.2e)
I
0.5 WaterSaturation
lk* is definedasthe often referred to as particular crosssec-
(s.30) d 5.32if the effectof and 5.18leadsto the tv of the reservoirin
(s.31)
1
Figu..5.14 Effect of Segregated Flow on RelativePermeabilities
The ratio of the two relative permeabilitiesfor stratified flow is given by equation5.35,which is derivedby dividing 5.34by 5.33.Fractionalflow curvesfor segregatedflow are different in shapefrom those for diffuse flow, as may be seen by the examplein Figure 5.15.
ktr kLlt - s,.- sj\ k:" k'*\ sJ - s,i I
(s.3s)
At first sightit would seemfrom Figure5.15that the displacement of oil by wateris muchlesseffectivein the systemwith segregated flow. However,it is not apparent from the figure that the two fractionalflow curvescrossat high water saturation. As a resultof this, the displacement of oil actuallybecomesmore efficient at high water saturationsfor the segregated flow casethan for the diffuse flow one. This differenceis demonstrated in later examples. Segregated
(s.32) (s.33)
{, g 0.s
(s.34)
.9 o o r
neabilitiesare linear s thatjoin the practiHeavyOil
K1
t -9 r
Chap.5
DiffuseFlow
Itwllto = 0.01 0
0.s WaterSaturatlon
The Buckley-Leverett Displacement Theory
Figure 5.15 Comparisonof Fractional Flow Curves for Segregated and Diffuse Flow
199
I
THEORY THE BUCKLEY.LEVERETT DISPLACEMENT Buckley and Leverett (1942)developeda theory that provides a quantitative description of the displacementof one fluid from a porous matrix by an immiscible flood. This theory introducedthe idea that water intermingleswith the oil as it is being displaced,so that the interfacial surfaceof the Muskat model becomesa zone with a varyingwater saturation.This conceptappliesto the casewherethe relative permeabilitiesare nonlinearfunctionsof saturation,as, for example,in the curves of Figure 5.14,and also to the casewhere the effectivepermeabilitiesare linear functions. The theorymakesuseof the fractionalflow concept.It is assumedthat a fractional flow curve is availableand that this curve represents the flow processthat is taking placein the reservoir.This curve may or may not be similar to that which occursin laboratoryflood testsusingsmall-diametercores.For example,flow segregationcan produce fractional flow curvesvery different from those for the flow found in laboratorycore floods. Dake (1978)discusses a numberof factorsthat can affect the fractionalflow curves. The Velocity of the Shock Front When oil is displacedfrom a porous medium by a waterflood, a front advances throughthe reservoir,and acrossthis front thereis an abruptchangein the saturation profile (i.e., there is a discontinuityin aS,ldx).There may also be a discontinuity in the saturation,S,, but this is not necessary. Aheadof the front, oil is flowing withoutwaterthrougha reservoirwith a saturation corresponding to the initial irreduciblewater saturationS,i. Immediatelybehind the front, the flow of wateris just sufficientto keep up with the movingfront. Figure 5.16depictsthe situation in the immediatevicinity of the front. In time dt the front advancesby a distance dx1. During this period the water that flows past the planewith an initial abcissaequalto x/ is just sufficientto provide the extrawaterthat remainsbehindthe front in the elementaldistancedxr Amaterial balancefor this is given by equation5.36. WATERBALANCE5
e,f,rdt = A66q-
S,)dx1
(s.36)
This ma1'ben tional \*ater fk FROT{T\IE
The term in h known if the fr ing the point o off" venus 5.There is tangent,as sho tion 5.37r'iel* tb€ ( represents this conditisrt For segrq and the water r meratorand tb However. thsrt In this casetlx usingL'Hosfiti
The Saturatir
Behind the frq tion down to I Figure5.17. Consider in Figure5.18 to changewith the sameas tht tionship is rep
x|at t Water and 3
Oil Flowing
tr l.- x1+or1 al t+clt
Figure 5.16 Conditionsat the Shock Front
tlater on, it is shownthat the transition zonebehind the front may be terminatedby a "trailing" front, which is accompaniedby a seconddiscontinuity,in dS"/ax.The velocity at which this trailing front movescan be found in an analogousmanner to that developedhere. At the trailing front, the upstreamfractional water flow is equal to that of the injected flooding fluid-usually unity.
200
of HeavyOil The Displacement
Chap.5
e05 6
-o lr
o
0
The Buckley-L
s a quantitativedeix by an immiscible with the oil as it is >delbecomesa zone e wherethe relative rmple,in the curves eabilitiesare linear assumedthat a fracflow processthat is milar to that which : example,flow segr thosefor the flow r of factorsthat can
d. a front advances hangein the satura; alsobe a discontieservoirwith a satuS-, Immediatelybe:h the movingfront. ity of the front. In riod the water that ufficient to provide istancedxr. Amate-
(s.36)
This may be rearrangedto give the front velocity dxyfdt as a function of the fractional water flow behind the front and the saturationbehind the front. FRONTVELOCITY
k, \ 4!t = !t( dt A6\5.r - S.,l
(s.37)
The term in brackets on the right-hand side of 5.37 is a function of S,y and is known if the fractionalflow curve is known. It is the slopeof the straightline joining the point correspondingto the front conditions to the point (S",, 0) on a graph of/, versusS,. There is a maximum value to this slope,which may be found by drawing a tangent,as shownin Figure5.17.The slopeof this line when substitutedinto equation 5.37yields the maximum velocity at which a shockfront can move, and this representsthe conditionsfor the shockfront that forms in practice.A shockfront at this condition will overrun any front having a different saturation. For segregatedflow, the maximum slopeoccurswhen/" : 0 (seeFigure 5.15) and the water saturationat the shock front is S,i. For this condition, both the numeratorand the denominatorof the term in bracketsin equation5.37becomezero. However, there is still a discontinuity in the water-saturationgradient at the front. In this casethe front velocity can be found from the limiting form of equation5.37 usingL'Hospital'stheorem.
dxr = q, (df,\ dt A6\dS*ls*=s.,
(s.38)
The Saturation Behind the Front Behind the front, the water saturationfalls from 1 - So,right at the point of injection down to the saturation at the shock front, as found by the construction in Figure 5.17. Considerthe changein saturationin the differential reservoirelementshown in Figure 5.18.The saturationwithin this stationaryelementwill, in general,tend to changewith time becausethe concentrationof the streamflowing from it is not the sameas that of the streamthat is entering;it is beingdepletedof oil. This relationship is represented by the continuity equation5.39. Slope -1,,,
= 3 o
rditionsat the Shock e terminatedby a "traile velocityat which this rd here.At the trailing f loodingf luid-usually
leavy Oil
Chap. 5
s;h,
I
atfront conditions
tr
for highest velocity
o
(s*, f"r)
s 0.5 5
6 o o o
(S*,,o)
L
0
0.5 Water Saturatlon
The Buckley-LeverettDisplacementTheory
Figure 5.17 ShockFront Conditions
201
1I I
to,u.Eli?n,\u _ Totol flow q1
,
Froctionol
Figure5.18 Conditionsbehindthe Front. S" VariesContinuously
(*).=#(*),
q! wheref* =
(s.3e)
Behind the front, the water saturationS, is a continuousfunction of x and t. and a generaldifferential (equation5.40)may be written.
ds,-(*),r,.(+1,*
(s.40)
From this, the partial differential@xlil)s, is obtainedasequation5.41.This may be combinedwith 5.39,as shownin the secondpart of 5.41.
(*). e, (*), -m= = d1(qerJ \t/'" /a'\
(s.41)
The term @f,/ax),1@S*f ax),is simplifiedto df,ldS,. This is written as an ordinary differential,sincef, is assumedto be a function of S, alore. Thlq-sqb-stitution results in equation(5.42),which is known as the.,tsuckley-Leverett eqqqtl_odIt shows that the velocityat which a planeof a fixed saturationadvanceiisproportionalto the averagefluid velocitymultiplied by a function of saturation.
=/u"\ -Q,.df, /l\ r \ /,. \ar/r, 0A ds*
(s.42)
or ' 6 A x fQi ,,t lllf\
(Note ff
1
is written as/i/
whereN is the numberof pore volumesof injectedwater (basedon the volume of poresuB to ihe pointx) that are requiredto bring the watersaturationat positionx up to the level correspondingto fI. S. must be greaterthan S"y.If it is not, the assumptionthat S, is a differentiablefunction of .r and /, which is implied by the use of equation5.40,is not correct. The differentialcoefficientin the right-handsideof equation5.42is the slope of the fractionalflow curve. This has been plotted for a typical examplein Figure 5.19.Also shown is the tangentthat determinesthe conditionsfor the shock front. The conditionsbehindthe shockfront correspondto that portion of the fracThe Displacementof Heavy Oil
Chap.5
fl
Onfy:til to t'e an C, blt dash€d
I
ET
io"l EI EI 'i t l.'
.,
0r0
tional flow cu ration cun'e" , stratified fbr 1 - So,becau The Uppcr I
In Figure5.19 hand limit-i. flow curve he resultis that tl the water enta The resi performance1 form of the fn It is of ir troducedat th importancein downstreamq sateand oil ar If the flo is fixed, and movesalonga that is introdn tion is 1.0. In Figun streamcompo tion,f, : 0.9 sistsdownstre to the slope< Leverettzon€ of 0.'74.
The Buckley-
Onlyth6 partsof the cuNes to th€ rlghtof the vertical dashedlinearesignificant.
!tw,s*r) 4
3 o
Conditions behind the rresContinuously
(s.3e)
tr
-^-oF
o
$ o.u .9
rtion5.41.This maybe
(s.41) written as an ordinary :. This substitutionrerett equatig4 It shows ncesis proportional to tion.
(s.42)
rasedon the volumeof saturationat positionx S"r.If it is not, the as:h is impliedby the use luation5.42is the slope 1-picalexamplein Figrnditionsfor the shock hat oortion of the fracof HeavyOil
Chap,5
2g
Trailing front 1 velocity
(g
(s.40)
o
Front velocity
(E
o
us function of .r and /,
o
lJ-
0.5 Water Saturation
1
o -
o o
Figure 5.19 Slope of Fractional-Flow Curve
tional flow curve for which S, > S,t i.e., to the upper right-handpart of the saturation curve. At the shock front, the saturation drops rapidly from S,y to S,i. For stratified flow, the whole range of effective water saturationsoccurs from S,r to 1 - So,becauseof the shapeof the fractionalflow curve. The Upper Shock Front In Figure5.19,the curve for the slopedoesnot fall completelyto zero at the righthand limit-i.e., at S, : (1 - So,): 0.9. This is becausethe assumedfractional flow curve has a small slopeat its upper end. This is a commonoccurrence.The resultis that the saturationcurvesin Figure5.22havea smallhorizontalpart where the water entersthe reservoir. The residualoil saturationextendsa finite distanceinto the reservoir.The performancepredictedby the Buckley-Leverett theoryis extremelysensitiveto ihe form of the fractionalwater flow curve at high water saturations. It is of interestto considerthe situationwherethe flood stream,which is introducedat the start of the reservoir.containsoil. While this circumstanceis not of importancein normal waterflooding,it is significantin consideringthe conditions downstreamof the condensation front in a steamflood.In this case,steamcondensateand oil are forced continuouslythrough the condensationfront. If the flood streamcontainsoil, then the fractionalwaterflow at the entrance is fixed, and this flowing-streamcondition persistsup to a shock front, which movesalong at a velocity correspondingto the velocity for the fractional water flow that is introduced.In the caseshown in Figure 5.19,this fractionalflow composition is 1.0. In Figures5.20 and 5.21,the diagramof Figure 5.19is redrawnfor flooding streamcompositionsof 0.95 and 0.5. In Figure 5.20 the flooding streamcomposition,/, : 0.95,corresponds to a water saturationof S, : 0.78.This saturationpersistsdownstreamup to a shockfront, which is moving with a velocity corresponding to the slope of f* at S.: 0.78. Beyond this front is the intermingled,BuckleyLeverett zone in which the water saturationfalls to the main shockfront saturation of 0.74. The Buckley-LeverettDisplacementTheory
203
4
,t
{
II
3 o
a constantsh the slopeof t (compare,5.{
4o
I
II
3
o
Conditions.l
ao "=
G
3 o.s G
tr .9 (,
l1gaklhlerrgh when-r; : 1. I
2o o
tity of watertl a rearrangedI
CL
-9
G L
1@
lr
00
00.5
1 WaterSaturation
Figure 5.20 Diagram for Flooding withf : 0.95
In the situationshownin Figure 5.21,the saturationof the upper shockfront falls below that of the lower front. In this circumstance,there is only one shock front, and the flowing-streamcompositionswitchesabruptly from l, : 0.5 to f" : 0 at the front. Note that in this case,the front velocity is higher than that which would correspondto the normal front velocifvdeterminedby the tangency condition. Figure 5.22 showsthe saturationdistributionfor the exampleof Figure 5.19. The uppercurvedparts of the lines aredxfdt (from equation5.24)multipliedby the appropriatetime from the start of the flood. At the point where the water saturation falls to the shockfront saturation5,6 the saturationcurve switchesto the verticalline with the water saturationfalling abruptlyto the connatewater saturation S,;. It shouldbe noted that identicalcurvescould have been obtainedby using equation5.42 over the whole saturationrangeand using the combinedfractional flow curve of Figure5.19,which is drawn by usingthe experimentalfractionalflow curve to the saturationfront conditionsand then the tansentline. This tansenthas
Recovery at I
At some tinre and the a!'em! equation 5..1{-
Subsrir gives
Substituting I results in equ tion 5.47.Thb
I -9 l!
o t!
3 o.s (!
.9
@
o
G tI.
= 0.5 WaterSaturation 204
Figure 5.21 Diagram for Flooding with, = 0.5
of HeavyOil The Displacement
Chap.5
The Buckley-La
a constantslopeover the rangeof saturationsthat exist acrossthe shockfront, and the slopeof this tangentgivesthe shockfront velocitywhen it is insertedin 5.42 (compare5.42 and 5.37).
4o
Conditions at Breakthrough
^c) "; 2o
Breakthroughoccurswhen the shockfront reachesthe limit of the reservoir-i.e., when.ry: L.up until this time only oil is displacedfrom the reservoir.The quantity of waterthat hasbeeninjectedcan be found asqrt from equation5.43,which is a rearrangedform of 5.42.
o
16
c''t , t = -
6AL (df,/ds*)f
(s.43) ,l
the uppershockfront :re is only one shock tlv from ,f, : 0.5 to 1 is higher than that ined by the tangency
No. of PV to breakthroush ._D.-=
Ii
a
+ @f./dS*)r
I
I
Recoveryat and after Breakthrough At sometime after breakthrough,the saturationprofile will be as in Figure 5.23, and the averagewatersaturationover the lengthof the reservoirL will be givenby equation5.44.This can be integratedby parts as shown.
t,=!rs.dx:i{rr;; fi, ,ds.}
ampleof Figure 5.19. i.2,1)multipliedby the rhere the water satu:urve switchesto the connatewater satura-
(s.44)
Substitutingx dS, : (q,tldA)df. from equation5.42 in 5.44 and integrating glves
s-,:s,r+ ffiO f;
en obtainedby using : combinedfractional nental fractionalflow line.This tangenthas
(5.4s)
SubstitutingL for x in equation5.42 and combiningthe resultwith equation5.45 results in equation 5.46, which, when rearranged,gives the remarkableequation 5.47. This was first publishedby Welge(1952).
@
o 6
= Diagram for Flooding Distancetrom Inlector
rf HeavyOil
Chap.5
The Buckley-LeverettDisplacementTheory
Figuri 5.22 Distribution of Water Saturation
205
*
S. : S,t -.
t!
--
l-
Figure 5.23 AverageWater Saturation after Breakthroush
r+- r; f, ft
S, _ S,I,
(s.46)
6.n)
In the more generalcasewhere the flooding fluid alreadycontainsoil, the lower to the limit of the integralin equation5.44 shouldbe the saturationcorresponding floodstreamwater fraction,f. Equation5.41then becomes
r: = Jr-lL -
JL
S"
S,r
The geometricsignificanceof this equationmay be seenfrom the construction shownin Figure 5.24. For any point on the fractionalflow curve, which lies at or abovethe point correspondingto the shock front (5"r, f"t), a tangent drawn upward intersectsthe line /, : f; at a water saturationcorrespondingto the averagewater saturationin the reservoir.This is indeeda remarkablysimpleanswer-an almostmagicalresult. method is employedas follows: The Buckley-Leverett-Welge 1. Draw the fractionalflow curve. 2. Draw the tangentfrom the foot of the curve and determine the conditions at the shockfront (S,r,/,r) and the averagewater saturationat breakthrough.S,1, from the intersectionwith the linefi, = f,(ft is usually1). 3. Calculatethe oil recoveryat breakthroughfrom Porevolumesof oil recoveredat breakthrough = S,/ - S,i
(s.48)
Effect of Visco
Figure 5.25sho the tangentsc( examplethe *z decreases. The breat in Figure5.25. As the vb that can be inir throughboth ia saturationat th slight increar through the lat tained at break
!
lr
a = a
4. Calculate the time of breakthrough from the total injection volume qi from 5.43and the injectionrate.6 5. For various arbitrary valuesof S,7.,draw the tangentsand calculatethe correspondingrecoveriesand injection volumes.
t
E lt
uAlthoughit hasbeenassumedthroughoutthis discussionof the Buckley-Leveretttheory that the injectionrate is constant,this is not necessaryfor caseswhere/, is assumedto be independentof rate, i.e., of q,/A. For a given injectionvolume, the sameconditionswill prevail even though the injection rate varies.
n
Chap.5
The Buckley-La
206
The Displacementof Heavy Oil
eragewater saturation ush
(s.46)
Figure 5.24 RelationbetweenOutlet Conditionsand AverageWater Saturation
(s.47)
t or abovethe point pu'ard intersectsthe 3 water saturationin lmostmagicalresult. r\\'s:
ine the conditionsat at breakthrough,S,y, '.
(
-s
(s.48)
I
Figure 5.25 showsthe seriesof fractionalflow curvesthat was drawn earlierwith the tangentscorrespondingto the conditionsat breakthroughdrawn in. In tbis examplethe water saturationat breakthroughincreasesas the viscosityof the oil decreases. The breakthroughconditionslistedin Table5.3wereobtainedfr"omthe curves in Figure5.25. As the viscosityof the oil is decreased, the fractionof a pore volumeof water that can be injectedbeforebreakthroughand the fractionalflow ofwater at breakthroughboth increase.It shouldalsobe notedthat with very viscousoils, the water salurationat the front is only slightlyhigherthan the irreduciblesaturation.Only a slight increasein water saturationis required to allow much water to percolate through the largely oil-saturatedreservoir.Only very low oil recoveriesare obtained at breakthroughwhen viscousoils are displacedwith water.
rm the construction
I
I li
tion volumeqi from Parameter is ltt ltw o
I calculatethe correk le1'-Leverettheory that med to be independent of evail even though the in-
1
00.5 WaterSaturation
Figure5.25 Effectof ViscosityRatioon Breakthrough Conditions HeavyOil
Chap.5
I
t
Effect of Viscosity Ratio
ntainsoil, the lower ;orrespondingto the
tI
The Buckley-LeverettDisplacementTheory
207
TABLE 5.3 Conditionsat Breakthroughfor VariousRatiosp,*fp,"
t",lt". 0 0.0001 0.001 0.01 0.1 I
10
f"r 0.60 0.73 0.75 0.81 0.90 0.98 1.0
Recovery(t)
Swf
0.2 0.24 0.29 0.39 0.54 0.73 0.88 0.90
0 0.06 0.13 0.28 0.41 0.58 0.69 0.7
0.2 0.26 0.33 0.48 0.61 0.78 0.89 0.90
0 0.09 0.19 0.40 0.59 0.83 0.99 1.0
shown as e$r by Hagoort(l'
Pressure Gradient Ratio(2)
FOR STAI
2.64 2.28 1.70 0.97 0.33
where
(r)Fraction of movableoil recovered. (')Pressure gradientin oil bank/pressuregradientjust behind front.
Table5.4 showsthe viscosityof Cold Lake crude and water as a function of temperature.It is instructiveto comparethe viscosityratios for this systemwith thosein Table5.3 above.Obviouslydisplacement with waterwould be much more effective at higher temperatures.Similar viscosityratio data are shown in Chapter 4, Figure 4.7. PressureGradients during Displacement
Graphsc with waterfor I dimensionles positionof the
The ratio of pressuregradients before and after the shock front are shown in Table 5.3 for the seriesof oils discussedpreviously.The pressuregradientsupstream and downstreamof the shock front were calculated by Darcy's equation (equations5.49). Upstream: Downstream:
(#) (#) -
-
-Qtf*flL*
_
Akk,,1
(s.4e)
QtlLo
AkkL
105
If the absolutepressuregradientupstreamof the front is smallerthan that downstream,then the systemwill be unstable,since any small penetrationof the front will be ableto grow.The conditionfor this to be so is givenby equation5.50,which may be developedas shown to give the condition for stability of the front (which is TABLE 5.4 Viscosity Ratio for Cold Lake Crude as a Functionof Temperature TEMPERATURE 'C "F
100 200 300 400
208
38 93 r49 204
Pr
ltw
(cp)
(cp)
15,300 181 20.9 6.3
0.70 0.30 0.19 0.14
PnlPo
0.000046 0.0017 0.009 0.022
tt"/tt"
22,000 603 110 45
tr o E io4 (t L
='to3 an o o t io2 o o -9 10l .E o c
E roo E
Dlmenslor The Displacementof Heavy Oil
Chap.5
TheBuckley-L
shownaq equation5.51).This may be rewritten as equation5.52,which was given by Hagoort (1974).
Pressure Gradient Ratio(2)
FORSTABILITY
(#)'-(#)
2.64 2.28 1.70 0.97 0.33
Fok,,f
f*rP.k|"
^,1 fwf =
(s.s1)
-----------:p*krof
.
, r -1--;-
rater as a function of ' for this system with uould be much more r are shown in Chap-
lLo Krwf
k,of , k,*f
(s.s2)
#
Graphs of dimensionless pressuregradientswithin reservoirsbeing flooded with waterfor the variousratiosof oil viscosityto waterviscosityare plottedagainst dimensionless distancein Figure 5.26. The stepsin the curvescorrespondto the positionof the shockfront. In this figure the dimensionless quantitiesare
i front are shown in )ressuregradientsupI by Darcy'sequation
^o(y\ Dimensionless pressure gradient=
(s.4e)
;#
105
aller than that downnetration of the front r equation 5.50, which of the front (which is
tr .g tt IE
(5 o :t
rratu re i/,
Follt"
.l(-|r6
22,000 603 110 45
l
rf HeavyOil
Chap,5
o o o o. o o -9 c .9 o c o
Parameter ispolr
w
10,000
104
1000
103
fi2
101
1' '000 .E o
5
10
Dlmenslonless Dlstancefrom Injector The Buckley-Leverett Displacement Theory
1s
Figure 5.26 Changeof PressureGradient at Front
209
and
TABLE 5.5 CJ
Dimensionlessdistance: 4 t
5.
Q,t
0.30
For high viscosityratios, there is an abrupt increasein pressuregradientat the shockfront. This promotesinstability, and fingering of the floodwater into the oil bank may be expected.For the particular systemshown,the front becomesstable whenthe oil viscosityis ten times that of the water.For lower oil-to-waterviscosity ratios,there is a drop in pressuregradientat the shockfront.
0.3-<
0.{} 0..15 0.50 0.55 0.60 0.6-< 0.70 0.75 0.80 0.85
NumericalProblemon Buckley-LeverettTheory The relative permeabilitiesof oil and water in a particular core are given by the following equations:
- s,\' . /o.ss o-: \ oss / -
. ls" 0.3\' *"=\ oss /
from the inte lareed scale i
where 1-So.=0'85
5-cp orl ri 150-cpvcr
S'i = 0'3 Plot the fractionalflow of water againstthe water saturationfor two oil viscosities: 5 cp and 150cp. Assumethat the viscosityof the water is 1.0 cp, that the core is horizontal,and that capillarypressurecan be neglected. For eachcase,usingBuckley-Leveretttheory, calculatethe averagewater saturation of the core during a waterflood when water first breaksthrough. What is the composition of the produced fluid immediately after breakthrough? How many pore volumes of water have been injected and how many pore volumesof oil have been producedat the breakthroughpoints? Each of the floods is carried on to the point wherethe oil-waterratio in the effluent is 0.025.At this point, for eachcasecalculatethe fraction of the original oil in place(OOIP) that hasbeenrecovered. How many pore volumesof water have been injected in eachof the cases? Solution Calculate fractional water flows for each oil viscosity using equation5.26(seeTable5.5):
t0.9 ' 0.8 -: h tr a
ts \
0.7 0.6 -
L
{
0.5 -
$ a
0.4 -
E
e }{^
0.3 0.2 -
f*
0.t -
r * ?.k* K*
Fo
Plot fractional flows againstwater saturation.See Figure 5.27. Many more pointswere usedto define the curve than are given in Table5.5. Draw tangeng_frgmthe origin and ottain the water s-atuntionand fractional flows at the tangencypoints. Obtain the averagewater saturationat breakthrough 210
The Displacementof Heavy Oil
Chap.5
6( o-3
The Bucktey-L
: I t
TABLE 5.5 CalculatedFractionalWater Flows
a
Fractional Flow
s,
t-
0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85
:essuregradientat the loodwaterinto the oil front becomesstable ' oil-to-waterviscosity
'e are given by the fol-
1.000 0.751 0.548 0.385 0.258 0.162 0.094 0.048 0.020 0.006 0.001 0.000
150cp
'{ "a nv
0.000 0.001 0.006 0.020 0.048 0.094 0.162 0.258 0.385 0.548 0.757 1.000
0.0000 0.0050 0.0520 0.2087 0.4827 0.7432 0.8963 0.9640 0.9896 0.9978 0.9998 1.0000
0.0000 0.1304 0.6221, 0.8878 0.9655 0.9886 0.9962 0.9988 0.9996 0.9999 1.0000
ru
r.0000
'l
from the interceptswithl, : 1. The resultsare shownin Figure5.27 andon an enlargedscalein Figure 5.28.
s.
s,r 0.575 0.415
5-cpoil viscosity 150-cpviscosity
for two oil viscosities: ..0 cp, that the core is
0.833 0.'t37
0.630 0.456
( -( 0.33 0.156
NO GRAVITY EFFECT
the averagewatersatuks through. d immediately after
EI tr
a h q o I
i and how many pore rts? e oil-waterratio in the iractionof the original
{ \ ri
n eachof the cases? h oil viscosity using
eure 5.27.Many more l e5 . 5 . ltuation and fractional rrationat breakthrough of HeavyOil
Chap.5
s ?
I I
L b
{. ta
0.3
0,7
0.5 -
VATER SATURATION |SOCP sCP
Figure 5.27
Effect of Oil Viscosity
The Buckley-LeverettDisplacementTheory
211
Compariscr r Flows (0.5r5,0.976)
(0.667,0.976)
The numeric to the case*{ The effc systemconsid
F $ a N (0.575,0.833)
E o F a
\ { s e
(0.4r5,0.737)
It is assu of either-i ? tially. As befo Buckley ure 5.29.
h
b
\
s\
Conditions d 0.5
0.3
_
{ff^
In the segreg volumeof the the composit through.In tb through,and t 5- and 150-cp
0.7
tnru-trolouo ",
Figure 5.2E Effect of Oil Viscosity(enlargedscale)
At breakthrough,volumesof oil produced: ,3, - S,; The volumesof water injectedup to breakthroughare equal to the volumesof the oil displaced. : 0.976. Draw tangentsat intersectionswith f. : 1.000/1.025 : I.0 to obtain averagewater saturations Read interceptsof tangentswith f" and measureslopesof tangents.
. 0.tr1
= 0.9 -
q h s ts
0.8 0.7
i
\
o L o
At f" : 0.976
r/f:,
s" 5-cp oil viscosity 150-cpviscosity
0.708 0.560
0.584 0.545
Total pore volumesof water injected = Uf ,
t.7l 1.84
0.6
{
0.5
{ s e
0.1
l\
(,) .( F la h
at f* : 0.976
0.1
: : {llgll lgl - 91lltl - 0'3)= 58'3voror5-cpoil vo oorprecovered oil [too(0.s60 0.3)/(1 0.3) 37.lVo for 150-cp
0.3
usinglesswaterfor the lessviscousoil' Moreoil wasrecovered 212
The Displacementof Heavy Oil
Chap.5
The Buckley-Le
Comparisonof Displacementwith Diffuse and Segregated Flows The numericalexampleof the Buckley-Leveretttheory is extendedin this section to the casewherethe flow is consideredto be completelysegregated. The effectiverelativepermeabilitiescorresponding to segregated flow for the systemconsideredare:
,,.'o =
0.95_ s, 0j5
_ 0.3
s, ano k." = -lB-
It is assumedthat the porousmediumis saturatedwith oils havinga viscosity of either 5 cp or 150cp and that the water saturationis at the irreduciblelevel initially. As before,the viscosityof the water is taken as 1,cp. Buckley-Leverettdiagramsfor the segregated flow casesare shown in Fignre 5.29.
I
Conditions at Breakthrough
I
In the segregated case,only 0.11pore volumeof the 5-cpoil and a mere0.004pore volumeof the 150-cpoil are recoveredat the breakthroughpoint, but in eachcase the compositionof the effluent streamis still nearlyall oil immediatelyafter breakthrough. In the diffuse case,0.33 and 0.156volumesof oil are recoveredat breakthrough,and the compositionsof the effluentsjump to 83Voand74Vowaterfor the 5- and 150-cpoils, respectively.
el
. - ,s,i ual to the volumesof
(0.416,0.976)
(0.789,0.976)
).976. agewater saturations \l I i
\ t
r/f:" r.7r 1.84
s& { { e h
Q
a
\:\ f . : 0.976 rc
'(
for 5-cp oil for 150-cpoil
f HeavyOil
0.5
0.7
VATER SATUR/ITION Figure 5.29 Effect of Oil Viscosity-SegregatedFlow
ril. Chap.5
lt it
The Buckley-LeverettDisplacementTheory
213
l
Conditionsat Breakthrouqh
S"r 5-cp oil Diffuse Segregated 150-cpoil Diffuse Segregated
f"r
S"r
;-
s.;
0.575 0.3
0.833 0
0.630 0.410
0.330 0 . 11 0
0.415 0.3
0.'737 0
0.456 0.304
0.156 0.004
5-cpoil Diffuse Segregated 150-cpoil Diffuse Segregated
0.6 -
h
o.u-l
b Rt
o . o- l
{ a e
0 . ,- l
t
0.2 -,
a q
I
orl
I
0t
0.667
0.976 0.976
0.708 0.845
0.408 0.545
0.515
0.976 0.976
0.560 0.509
0.260 0.209
Comparisonof Oil Recoveries
0
Figurt ! l5{-rcp
The dista to the slope o jt,ll,)(I - S0.9 _
0.8 I
a
Water Saturation Profiles
I I
0.7 -
!
& tr ! vj
The fractional recoveriesof mobile oil for the four casesare comparedin Figure 5.30as functionsof the pore volumesof water injected.
t' I
\ x
tl
;_S,;
flow has surpassedthat for At this point, the performancefor the segregated the diffuse flow for the 5-cp oil; 0.545PV of oil hasbeen recoveredcomparedto 0.408for the diffuse flow. The reasonfor this differenceis that the relativepermeflow ability for oil is significantlyhigherat high watersaturationsfor the segregated than it is for the diffuse flow. For the 150-cpoil, the recoveryis muchbetterthan might havebeenexpected from the poor resultsat breakthrough;0.209PV of oil hasbeenrecovered,as compared to 0.260for the diffuse flow case.As may be seenby the data in the next caseeventuallyresultsin better performanceif the process section,the segregated is continuedlong enough.
0,6 -
ET a E
o . s)
I
:
Watersaturationis plottedas a function of distancefor the two casesinvolving5-cp oil in Figure 5.31.A similar diagramcould be drawn for the moreviscousoil. The abcissain Figure 5.31is $Axfq,t, or/,1,.Severalfeaturesshouldbe noticed: 1. The abrupt changein saturationat the front for the diffuse flow. 2. The much greaterdistancethat the segregatedfront has reached. case. 3. The positionof the trailing shockfront of mobile oil in the segregated 214
0.E -
o
Conditiona st O/W = 0.025
s4
E
0.7 -
The conditionswhenthe oil-waterratio falls to 0.025are shownby the upperpoints of tangencyin Figure 5.29.The resultsare summarizednext.
f,r
0.9 -
s
Conditions when Oil-Water Ratio Fallsto 0.025
S"r
s
of HeavyOil The Displacement
Chap.5
i 0.4 -, I i
I
o.s10
Fq
The Buckley-Leu
(.- (
H
rrl
0.330 0 . 11 0 0.156 0.004
$
a
x \
5 FI b El
by the upperpoints
q
{a
T a F
t* b
_ s,i
rl \ra
il t*
0.408 0.545
o
havebeenexpected I recovered,as com:he data in the next nanceif the process
4
I
I
10
t2
t4
t6
t8
20
PORE VOLUtrTES INJECTED Figure 5.30 Fractional Recovery of Oil-Segregated 150 cp
0.260 0.209
s surpassed that for overedcomparedto : the relativepermethe segregated flow
2
and Diffuse Flow; 5 and
The distancethat the trailing edgeof mobileoil hasadvancedis proportional to the slope of the fractional flow curve at f" : L This is a positive value, - So.- S,i), for the segregated flow casebut is zero for the diffuse flow 0-,,,1t-r.)(l o.9
o.8 i
0.7
a E a (4
e comparedin Fig-
E I! a
0.6 Diffuse Flov
0.5
f
casesinvolving5-cp roreviscousoil. The I be noticed:
0,4
o.3
useflow. reached. case. the segregated HeavyOil
Chap.5
02468 DI TTE N SI ON LE,SS'.TSTllvCg Figure 5.31 Water Saturation*Segregated and Diffuse Flow; 5 cp
The Buckley-LeverettDisplacementTheory
215
becauseof the tangencyof the oil relativepermeabilitycurve to the water saturation axis for this particular problem. It is clear from this hypothetical examplethat the effectivenessof a waterflooding operationis critically dependentupon the shapeof the fractional flow curve-particularly the shapeat high water saturations.
ol a o
=o o
= a
o a
II
rV
0
FI
C.W NUTT'S CAPILLARYBUNDLEMODEL The approachto the displacementof oil from a porousmedium discussedin the last sectiondependsupon the conceptof both oil and waterflowing in the sameregion, with the relativefluxes determinedby the saturationsof the phases.This concept allowedthe developmentof relativepermeabilityand fractionalflow curves.The mathematicalextensionof the idea that was developedby Buckley and Leverett and addedto by Welgeresultsin a realisticmodel of the flooding process. A paperby C.W Nutt (1982)explainsthe observedphenomenafrom a different viewpoint. He showsthat most of the phenomenaof waterflooding,including the effect of viscosityratio, can be explainedby consideringthat the poroussolid behavesas a simplebundle of capillariesof varying radii. He introduceshis idea by consideringa situationin which the porous solid is represented by meansof two capillariesconnectedin parallel,as shown in Figwe 5.32. It is assumedthat the flow resistancein the feed and dischargelines can be equaneglectedand that the flow in eachcapillarycan be calculatedby Poiseuille's tion. Also, the effectsof capillaryforcescausedby the oil-waterinterfaceare neglected at first. Considerthe casewherethe capillariesare first full of an oil that is moreviscousthan water.Wateris injectedat a constantrate. The expectedperformanceis shownin Figure 5.33,where it will be seenthat the interfacemovesto the outlet
Figurt 5J! ing Disp{:
(L
;
o q)
o c) o) E
o 0 Ftt
Figure 5.3-i Cr in left half of F
Figr
Figure 5.32 Displacementfor Two Capillariesof Different Diameters (after Nutt 1982)
216
The Displacementof Heavy Oil
Chap' 5
end more rag drop, the ave proceeds. the
C.W Nutt's Ca
lo the water satura-
o1 o' &
>1
o
tivenessof a waterthe fractional flow
;o
;o o o 0 o E
I
=o o 4
o 1
-o12
FluidIniectedin PoteVolumes
discussed in the last I in the sameregion, :hases.This concept ral flow curves.The uckleyand Leverett line process. -rmenafrom a differ:rilooding,including hat the poroussolid ich the poroussolid lel. as shown in Figschargelinescan be br Poiseuille's equaIter interfaceare ne-
Figure 5.33 Positionof Interfacesduring Displacement(after Nutt 1982)
FluidIniected in PoreVolumes Figure 5,34 Cumulative Oil Production (after Nutt 1982) 10
1
c!
Ps
IL
89
x o .9 60
;
o o o C) o
x o ^ .!p ob 'o.
6
(r o 0
?o a
4<)
o
d
Ez
2 Pc
f
f
z
012
0
FluidInjectedin PoreVolumes
0
0 0.2 0.4 0.6 0.8 1.0 1. 2
z
Radiusin mm
Figure 5.35 Comparison with Experimental Data from Sandpack Waterf loods. Parameter in left half of Figure is p.lp* (after Nutt 1982)
r oil that is morevis:cted performanceis movesto the outlet Parameter is interfacial tensionin N m-1
o. ;o o o o () E,
o
Floodrate=0.05mh-1
0
Fluidlnjectedin porevolumes Figure 5.36
)rsplacement for Two DifferentDiameters ,lt Heavy Oil
Chap. 5
Effect of Interfacial Tension on Recovery for an Oil-Vy'etSystem
end more rapidly in the largercapillary.This occursbecause,for a given pressure drop, the averageflow velocity is greaterin a larger capillary. As the displacement proceeds,the ratio ofvelocitiesincreases becausethe largercapillarycontainsrelaC,W Nutt'sCapillaryBundleModel
217
t{ L,
T t I
i
l
I
o, E
o. .=
E O a
E o o o o o)
o (, o
E
tr
o
o
0.1Nm-1
I
2
Figure 5.37 Effect of Flood Rate for Oil-Wet System
t-iSr hert Srrdil Usrq
tively morewater; this is lessviscous,and, as a result,the pressuredifferencebetween the inlet and outlet of both tubesdecreases. { When the water reachesthe end of the largecapillary,breakthroughoccurs; after that, relativelylittle oil is producedbecauseof the low pressuregradient.Most of the injectedwaterflows throughthe largecapillary.Figure5.34showsthe qualitative effect on oil recoverythat would be expected. Nutt expandsthis idea by consideringa wholerangeof capillariesof varying diametersin paralleland adjustingthe distributionof sizesto match observedresults.One of the more interestingcomparisonsis shownin Figure 5.35. reIn the left part of this figure, the points showexperimentaldisplacement sultsreportedby Blackwellfor a seriesof flooding experimentsusinga singlesandpack and various oil-water viscosity ratios. The curves in the diagram were calculatedfor the experimentalconditionsusingthe pore-sizedistributionshownin
the right haff cosityratioc predictspmn cc;-us oits.
i
o_ .E (I) q)
o) E
FluiJ IL .c 0) q)
o-
;o
q) E.
Intertacialtension = - 0.02 N m
o o (,
-1
o
= o
-1 lnterfacialtension = -0.0 N m
FluidInjectedin porevolumes Figure 5.38 Effect of Flood Rate for a Water-WetSystem
218
The Displacementof Heavy Oil
Chap,5
Analysis of Sta
o. ; o o o o o tr
o 012 FluidInjectedin PoreVolumes
:r oi Flood Rate for
Figure 5.39 An Effect of Temperature.Recoveryof a Mixture of n-decane,nhexadecane, and Squalanefrom a Core. Pointsare ExperimentalData from Sudibjoet al. (1978);The Curve is a CalculatedOne for all Three Temperatures Using a SelectedCapillary SizeDistribution
,uredifferencebe-
|| il
'1 tt
the right half. Nutt's simpletheory givesa good predictionof the effect of the viscosityratioonthedisplacementefficiency. predictspoorerdisplaceqentefficienciesand gritlelSleakJ[fqugh for the moreviscousolls.
akthroughoccurs; ure gradient.Most i4 showsthe qualipillariesof varying natchobservedrere 5.35. rell displacement rsinga singlesandthe diagram were ,tributionshownin
o_ ;
O
E
o -
0'1 Fluidlnjectedin PoreVolumes
.42
Figure 5.40 Another Effect of Temperature(after Nutt 1982)
o
.-r'1982
;o o o (, o
tr o 2
I
FluidIniectedin PoreVolumes eavy Oil
Chap.5
Figure 5.41 Effect of Temperature Combinedwith Changein Wetttbility (after Nutt 1982)
Analysis of SteamfloodUsing the Buckley-LeverettTheory
219
I
I
The effectof interfacialtensionis alsoincludedby Nutt in his theory.The interfacialtensionslowsdown the displacement of the oil if the solid is oil-wet and viceversa;in either case,the smallerthe radiusof the capillary,the greaterthe effect. Thus the interfacial tension effect tends to make the displacementfor capillaries of different radii more uniform in water-wet systemsand less uniform in oil-wetones. Nutt showshow a high oil-water interfacial tension may be expectedto have little effect on the recoveryat breakthroughfor oil-wet systemsbut that it will have a significant effect on the ultimate recovery-high interfacial tension gives lower recovery.This is shownby Figure 5.36;the breakthroughpoints occur where the recoverycurvesdeviatefrom the initial straightline. Nutt alsopredictsthat in an oil-wet systemwith a finite interfacialtension,a higherrecoverywill be obtainedwith a higherflood velocity.Predictedresultsare shownin Figure5.37. For water-wet systemsNutt's theory predicts that lower flooding velocities should give better recoveriesbecausethe capillary force tends to improve the displacementin the smallercapillaries.The effect is shownin Figure 5.38. Another effect that Nutt considersis that of temperature.He showsthat for someporoussolids(i.e., for somepore-sizedistributions),the effectof temperature shouldbe negligible-as it hasbeenshownto be by Sudibjoet al. for one core.See Figure 5.39. Conversely, Nutt predictsthat for other pore-sizedistributions,there should be a temperatureeffect(Figure5.40).By alsoassumingthat the wettabilitychanges with temperature,an effect very similar to the experimentaldata can be predicted (Figure5.41). Although Nutt's capillary model theory is ableto explain many of the observed phenomena,it is not a completeexplanation.The classicalBuckley-Leverett theory is alsoableto explainthe samephenomena.What is clear,however,is that the processesoccurringin the displacement of oils-and particularlyheavyoils-by water from porous solids are complexand are affected by a multitude of variables. It is also apparentthat attemptsto extrapolateexperimental data widely by theoreticalconceptsmay lead to inCorrectpredictionsbeiause of the incorrect representationor even omission of important phenomena.It appearsthat the recent tendencyto replaceexperimentalstudieswith complicatedmathematicalmodels based on simplistic conceptsis still very premature. Simple predictions based on realisticexperimentalinformation are muchto be desired.We needto keepour laboratoriesfor a while vet!
densesabrq heat of tb c initial teqr steam displ that therc r section,thl and that ttc In thc the oil fru can be dcrr Boberg 197 flooding. l* is at constal saturatimil or if therc a liquid watcr sumedthat I even if wala mobility wi! steam-swep The pn heat liberar sate from tt Figure 5.42i tion of the o the steam-s At thc tion increc gion beyond steamregio front into tL In thc r in the floodi region.Becr densationfm in connectic
ANALYSISOF STEAMFLOODUSING THE BUCKLEY.LEVERETT THEORY In this section,the behavior of a one-dimensional. adiabaticsteamfloodis analyzed.The processthat is consideredis shownin Figure 5.42. This diagram showsthe flooding processat an intermediate stage.Steam is introduced at the left and grveepsthrough the steam-sweptregion, in which the temperatureis constant at Zs. The small drop in temperaturedue to the pressure drop in the steamzone is ignored. At the condensationfront, all the steam con'/
220
The Displacementof Heavy Oil
Chap.5
sIEf
Movin
Analysis of Sl
his theory.The insolid is oil-wet and , the greaterthe efrlacementfor capilnd less uniform in e expectedto have bur rhat it will have tensiongiveslower rtsoccur where the rterfacialtension,a 'redictedresultsare flooding velocities to improvethe disure 5.38. . He showsthat for ifect of temperature rl. for one core.See rtions,there should wettability changes ta can be predicted anyof the observed lley-Leveretttheory :ver,is that the proreavyoils-by water : of variables. rntaldata widely by rf the incorrectreplars that the recent 'athematicalmodels redictionsbasedon :edto keepour labo-
densesabruptly and the liberated heat of condensationtogetherwith the sensible heat of the condensateis absorbedin raising the reservoirand its contentsfrom the initial temperatureTn to Ts.The sameassumptionsare made as for the caseof the steam displacementof a water-saturatedreservoir (see Figure 5.6). It is assumed that there are no lateral heat losses.that the fluid velocitiesare uniform acrossthesection,that the temperatureof the solid is equalto that of the fluids at eachpoint, and that thermal conductioncan be ignored. ln the steam-sweptregion, steamflows at a relatively high velocity and moves the oil forward at the saturationtemperature.The displacementof oil in this region can be described quantitatively using the Buckley-Leverett theory (Shutler and Boberg 1972;Boberg 1987)in the same manner as has been describedfor waterflooding. No condensationof steamoccurs within the steam-sweptregion, since it is at constanttemperatureand it is assumedthat there are no heat losses.The water saturationin the regioncorrespondsto the irreduciblevalue,56. If the steamis wet, or if there are heat losses,a higher water saturationis requiredin order to move the liquid water to the interface; this is discussedlater. For the presentcase,it is assumedthat the steamis introduced dry and saturatedand that there are no losses; even if water is flowing, the increasein water saturationrequired to provide water mobility will usually be small. The oil saturationincreasesfrom left to right in the steam-swept regionin Figure 5.42. The position of the condensationfront is determinedby a heat balance.The heat liberatedby the condensationof the steamand by the cooling of the condensate from the start of the processto the time correspondingto the situation in Figure 5.42is conservedas sensibleheatwithin the steam-swept region.The position of the condensationfront can be found from this heat balance.The volume of the steam-sweptregion increasesproportionally to the quantity of injected steam. At the condensationfront, steamsaturation drops to zero, the water saturation increasessomewhatbecausethere is need for water to flow in the oil-bank region beyond, and the oil saturationrises abruptly. The oil which is swept from the steamregion, togetherwith the condensate,flows forwards from the condensation front into the waterflood region. In the waterflood region, someoil is displacedby the flowing water. The oil in the flooding streamfrom the steamchamberalso flows through the waterflood region.Becauseof the high proportion of oil in the flooding streamleavingthe condensationfront, the conditionsare similar to thosewhich were discussedpreviously in connectionwith Figure 5.21.Immediatelybeyondthe condensationfront, the satuCondensotionFront Steom condenses S t e p c h o n g e so f s o t u r o t i o n s
'HEORY
^^d
steamflood is anaSTEAM-_>
liate stage. Steam is egion, in which the due to the pressure . all the steam conHeavy Oil
Chap.5
+am^a.^+'
r.a
Woterflood Front Step chonges of oil ond woter soturotions
SteomfloodReoion WoterfloodRegion Originol ...-_--_-.> Oil Sot
T e m p e r o t u r e=
MovingFluids:
Steom*Oil
Oil+Woter
i Oil only
Figure 5.42 Diagram of Adiabatic, One-DimensionalSteamflood Analysis of Steamflood Using the Buckley-Leverett Theory
221
ration conditions correspondto the fractional flow of oil and water that is leaving the front. If the fractionalwater-flowcurve is concaveto the left, as in Figure5.21, then theseconditionsremain constantin the reservoirup to the waterfloodfront, where the saturationchangesabruptlyto correspondto those in the initial reservoir. The waterflood front advancesmuch more rapidly than doesthe condensation front, and water breaksthrough long before the arrival of the condensationfront.
areamartl the areasI -t;; l"
The rolum
Buckley-LeverettTheory Applied to the Steam Chamber The generaldistribution of saturationsthat occur within the steamchamberare shown in Figure 5.43.The abscissain this diagramis the dimensionless distance, which is equalto df"/d9".The regionwith constantoil saturation,So.occursonly if the curve of f, is not tangentto the saturationaxis at its upper terminal point. The water saturationis constantat S,; throughoutbecausethere is no water flow within the steamfloodregion.As has been mentionedpreviously,if the injectedsteamis wet, then the water saturationwould be somewhathigherthan Su. The curve of steamsaturationversusdistancein Figure 5.43 is obtaineddirectly from relativepermeabilitydata for the flow of steamand oil in the reservoir matrix with an irreduciblesaturationof water.In Figure 5.43,the steamsaturation is plotted downward.
The quant in the losr
The correq ume bv thc
The fractkt vided b1'th
Calculationof Volume of Steam Within the Reservoir Considerthe positionwithin the steamfloodregionthat corresponds to the vertical dottedline shownin Figure 5.43;this represents somepoint behind the condensation front. The numberof pore volumesof steam(measuredasvapor and basedon the total pore volumeof the reservoirbetweenthe point of injectionand the point corresponding to the vertical dottedline) that hasbeeninjectedis equalto 1/fl (see equation5.42). Another way of looking at the horizontalscalein Figure5.43is to regardit as the distancealongthe reservoirexpressed in porevolumesof reservoirper volume of injected steam.At any particular time, some of the injected steam remains within the steamfloodregionto the left as steam,and the remainderhaspassedbeyond.The volumeof remainingsteamper volumeof injectedsteamis given by the WATER
-l
TI
E,"* o
E o
I
STEAM
222
(S
This I equation -i.5
S ol
f s , f ' s , a n dS
s
otL
H,:
!o,
I ' i f t
At anv part ance.At th tional cold r within the r denses:the lowing eqru
P*l
\.)
ot
Heat Balrr
's Dimensionless Distance
Figure 5.43 Saturationsin the Steam Chamber
of HeavyOil The Displacement
Chap.5
tl -
The h In. H. is the Analysisof !
ater that is leaving l. as in Figure 5.2L, e r.raterf lood front, in the initial reser:s the condensation 'ondensationfront.
area marked STEAM in the figure; it is convenientto expressthis as the sum of the areasmarked L and2. This sum is given by V
fi,=ur"u
I +arear=
f1_so,_swi
The volumeof water is given by the areamarkedWATER,which is equalto
v,_ V"i steamchamberare distance, :nsionless n. 5o,occursonly if terminalpoint. € there is no water :er.iously, if the inrat higherthan S,;. 5.-13is obtaineddioil in the reservoir he steamsaturation
(5.53)
fldS,+,fiS,=1-i+flS,
Jr,
S.if i
(5.54)
The quantityof oil remainingis calculatedby subtractingarea1 from the rectangle in the lowerleft corner.i.e..
#,="s'-1+i
(5.ss)
The corresponding volumeof rock matrix is givenby multiplyingthe total porevolume by the ratio (1 - il16. -w =-I
Vni
r-6", 6
(s.s6)
The fractionalrecoveryof oil is equal to the pore volume occupiedby steamdividedby the porevolumeinitially filled with oil, i.e., by
_ Recovery-ruds to the vertical :hindthe condensavapor and basedon :ction and the point is equalto 1//,1(see .{3 is to regardit as eservoirper volume :ted steam remains inderhaspassed beeam is given by the
r - [ + /;s, /;(l - s*,)
(s.s7)
Heat Balance At any particulartime, the limit of the steamchamberis determinedby a heatbalance.At the condensation front, the injectedsteamis condensingand heatingadditional cold reservoirmaterial.The balanceis determinedby equatingthe total heat within the contentsof the chamberto the heat suppliedby the steamwhen it condenses;the condensate coolsto the reservoirtemperature.This is shownby the following equation: (Steamdolumesupplied)' H, : (steamvolumein chamber). H, + (watervolumein chamber). H. * (oil volumein chamber). H, * (rock volumein chamber). H, This balance,based on a unit volume of injected steam,is expressedin equation5.58. **ftt, H , = ( 1 - i + l ; s " ) H " * s , , / J H , + ( / J S , - 1 + . [ ) H , 'o
rturations in the Steam
HeavyOil
Chap.5
(5.58)
The heat contentterms H; are all measuredabovethe rdservoirtemperature &. H, is the heatin a volumeof steamvapormeasuredaboveliquid water at 7n.In Analysis of SteamfloodUsingthe Buckley-LeverettTheory
223
t ,1
inr
il
I
any particular numerical example,all the terms on the right-hand side of this equation will be either constantsor known functionsoffl. It is thus possibleto plotlhe right-hand side against/J and thus determine the value of /j which balanies the equation. NumericalExample The following numerical example illustrates the use of the Buckley-Leverett methodto analyzea steamflood. Problem A one-dimensional, adiabaticsteamfloodis carried out using dry saturatedsteamat 3.5 MPa (243"C). The steamis injectedinto the core at a rateof 10kg m-2 h-1.The corehasthe following properties:
b. Plot a di along thr
c. Calculag sured as
Heat Balanca
The problemr gram. The fd flow of steam the computed Linear Stearnflot
Initial temperature Length Porosity Initial oil saturation Irreduciblewater saturation
25"C 50 cm 0.35 0.83 0.17
oil Saturation
both initially and for steamfloodedcore 0.06 after exhaustivesteamflood basedon oil at Tn 0.9 p,m2 1.0 p,,m2
Residualoil saturation Permeabilityto steamat S,i and .!o, Permeabilityto oil at S"i and S" : 0
The materialsinvolvedhave the followingproperties: PhysicalProperties
oil Density at 25'C kg/cu m Viscosityat25'Ccp Viscosityat Zs cp Mean heat capacitykykg "C Enthalpy at G above7n k/kg k/cu m H,, H,, H", H"
966 2,000 4 2.1, 458 442,235
Rock
Water
2,600
1,000 0.9
Steam 17.54 0.018
0.84 183 476,112
4.2 945 944,700
2,697 47,293
Assumethat the flow in the steamchamberis segregated-i.e.,that the relative permeabilitiesare linear functionsof So. a. calculate the time required for steamto breakthrough, the number of pore volumesof steam (measuredas liquid water) that have been injected at this time, and the correspondingpercent recoveryof the original oil in place. 224
The Displacementof Heavy Oil
Chap.5
0.060 0.060 0.095 0.130 0 . 16 5 0.200 0.235 0.270 0.305 0.340 0.375 0.410 0.445 0.480 0.515 0.518 0.550 0.585 (r)In kiloloulespcr
Figure5.. of the reservci ( i . e . , / ' ) .I t * i l l the steam for a steamchambe Alternati required to hea be convertedto of the densitie Analysisof Sts
I sideof this equapssible to plot the rhich balancesthe
Buckley-Leverett ried out using dry '. The corehasthe
b. Plot a diagramof saturation(water, steam,and oil) versusfractional distance along the core at steambreakthrough. Calculate the recovery as a function of pore volumesof steaminjected measured as liquid and plot a curve.
Heat Balance,Saturations, and Recovery The problemwas solvedby meansof a tabular calculationusing a spreadsheet program. The following table showsthe calculated relative permeabilities,fractional flow of steam, andf ' as a function of the oil saturation.The sixth column shows the computedheat content of the chamber. rl r,
LinearSteamfloodNumericalExample
;- and for rd core ;tive steamflood al Tn
Water
1,000 0.9
Steam
r7.54 0.018
A1
945 r-r.700
2,697 4'7,293
-i.e., that the relahe number of pore rn injected at this ral oil in place. eavy Oil
Chap.5
Permeabilitypm2
oil Saturation
Steam
0.060 0.060 0.095 0.130 0.165 0.200 0.235 0.270 0.305 0.340 0.375 0.410 0.445 0.480 0.515 0.518 0.550 0.585
0.900 0.900 0.860 0.820 0.780 0.740 0.700 0.650 0.610 0.570 0.530 0.490 0.450 0.410 0.370 0.360 0.330 0.290
Oil
0.000 0.000 0.050 0.090 0.140 0.180 0.230 0.270 0.320 0.360 0.410 0.450 0.500 0.550 0.590 0.590 0.640 0.680
f
f'
Steam
Steam
1.0000 1.0000 0.9998 0.9995 0.9992 0.9989 0.9985 0.9981 0.9977 0.9972 0.9966 0.9959 0.9950 0.9940 0.9928 0.9927 0.9913 0.9894
0.0000 0.0065 0.0071 0.0078 0.0087 0.0097 0.0108 0.0122 0.0139 0.0159 0.0185 0.0216 0.0257 0.0311 0.0382 0.0389 0.0483 0.0628
Chamber Heat(r)
Recovery Vo OOIP
0 7,193
92.77 92.77 92.58 92.01 91.05 89.72 88.00 85.91 83.43 80.57 77.32 73.70 69.69 65.31 60.54 60-20_ 55.39 49.86
? Rq5 I 715
9,678 10,818 12,181, 1,3,824 1,5,827 18,300 21,394 25,330 30,433 ?7 to?
46,408 47,271, 5q 171
78,385
(t)In kilo.loulesper cubic meter of injectedsteam.
Figure 5.44 showsthe heat required to heat the steamchamberas a function of the reservoir pore volumesthat have been heatedper volume of injected steam (i.e.,f ').It will be seenthat the heatrequirementsare equalto the availableheatin the steam for a reservoir pore volume of 0.0389.This is the pore volume in the steamchamberper volume of injected steam,measuredas vapor. Alternatively, we can saythat I/0.0389 : 25.7volumesof steam,asvapor, are required to heat and sweepone pore volume of reservoir.The steamvolumescan be convertedto the more conventionalwater equivalentby multiplying by the ratio of the densities,i.e., by I7.54/1000. Analysis of SteamfloodUsing the Buckley-LeverettTheory
225
, i
I
Required o
t
6oooo
b c.
40000
? x
Available
o-
o
b60
(0.0389, 47293)
t
o o40 o
6
fi zoooo ,; o o I0
*eo 0
0.02
0.o4
0,06
Figure 5.44 Heat Balancefor Steam Chamber
ReservolrPoreVolumeeper VolumeInlectedf'
Porevolumeof core : 50 x 0.35cm3/cm2 : 0.175^'l^' Displacemrrl
Steamrequiredfor breakthrough= 0.175x 25.7 x I7.54
The fluid mir water. Its cc chamber:this
: 78.9ksl^' Time requiredfor steambreakthrough: Z# = 7.89h 1o The saturationsare plotted as a function of /'in Figure 5.45,and the position of the condensate front is alsoshown.The water and oil saturationsbeyondthe front are discussedlater. The oil recoveryhasbeencalculatedin the seventhcolumn of the preceding table using equation5.57.The percentoil recoveryis plotted as a function of the steaminjectedin Figure 5.46.The pointsfor beyondthe steambreakthroughcome from the previoustable; up to breakthrough,the percentrecoveryvarieslinearly with the steaminjection.tIt shouldbe noted,however,that in general,the recovery is not volumetricallyequalto the steaminjection.
MaterialBalarrce
Steam Ch. Connatc Remaro Steam Total po
Injected sr Effluent r: Displaced
0.8
l" in effl*
z I 0.6
E P o.+
Condensationlronl
in Figure 5.46 should really be two straight lines, as in Figure 5.49. The changein slope occurs when water condensatebreaksthrough. However,with the linear relative permeabilityrelationsassumedhere,the oil displacedaheadof the condensationfront is very small and can be neslected.
The materialt for the left-ha (measured asli About 2% of r placedoil. Thc paniedby l.lO the steamchar sationfront aQ lar to that sbo curve is muchI
226
Analysisof Sre
o
0
0.01 0.02 0.03 0.04 0.0s 0.06 o.o7 o.o8 (l/PvInlected Distance measured asvapor)
Figure 5.45 Saturationsduring Steamflood
TThestraight line
The Displacement of HeavyOil
Chap.5
SteamIniected(PVas Vapor) 50 100
6 o E60 o40
SteambreaKhrough
o c)
seo Heat Balancefor Steam 0.5
1
1.5
2
Steam Iniected (PVas Liquid)
m.',/cm2
2.s
Figure 5.46 Oil Recovery as a Function of the Quantity of Steam Injected
:
I
The fluid mixture flowing from the steamchamberconsistsof viscouscold oil and water. Its compositionmay be obtained from a material balancefor the steam chamber;this is shownin the followine table.
rh i-5.and the position of ,tionsbeyondthe front 'lumn of the preceding 'd as a function of the rm breakthroughcome ecoveryvarieslinearly n general,the recovery
MaterialBalancefor Steam at Breakthrough Basis:One volumeof iniectedsteam Steam measured as vapor Steam Chamber Contents: Connate water Remaining oil Steam Total pore volume of chamber Injected steam Effluent water Displaced oil /" in effluent
S a t u r a t i o n sd u r i n g
n.\. as in Figure 5.49. The .:r.uith the linear relative : c : r s a t i o nf r o n t i s v e r y s m a l l
of HeavyOil
'{
Displacementof Oil ahead of the CondensationFront
- x 17.54
Chap.5
0.0066 0.0129 0.0194 0.0389 1 (vapor) 0.0172 0.0194 0.41
Steammeasured as liquid
0.377 0,73s 0.019 2.218 1 (asliquid) 0.981 1.108 0.47
The materialbalanceis basedon one volumeof injectedsteammeasuredasvapor for the left-hand column and liquid for the right. One volume of injectedsteam (measuredas liquid)producesa steamchamberhavinga total porevolumeof 2.218. About 2% of the injectedsteamremainsbehind to replacethe volume of the displacedoil. The steamcondensate or effluent watermeasures 0.981volumes,accompaniedby 1.108volumesof displacedoil. The fractionof waterin the effluent from the steamchamberis 0.47.The reservoirsaturationdownstreamfrom the condensationfront adjustsitself to correspondto this fractionalflow; the situationis similar to that shown in Figure 5.21,althoughin this casethe water fractional flow curve is muchsteeper.With the relativepermeabilitycurvesassumedhere and the Analysisof SteamfloodUsingthe Buckley-Leverett Theory
227
I
muchlowerviscosityof watercomparedto that of oil, only a slightincreasein water saturationis requiredto accommodatethe water flow. It is calculatedthat the water saturationwill rise from the irreduciblevalue of 0.17to about0.171-a very small change.A waterflood shock front racesaheadof the condensationfront, and it is characterizedby this very slight increasein water saturation. In this example,the waterflood effect downstreamof the condensationfront is very small. The main effect is that of the displacedoil moving through the reservoiras it leavesthe conwater condensate is ableto flow with very little densationfront; the accompanying changein water saturation.The calculatedsaturationsare shownby the solid lines as functionsof the distancealonsthe core of Fieure 5.47.
,r= o G
o
V
0L
Distancr I
EFFECTOF SHAPEOF RELATIVEPERMEABILITY CURVES In the proceedingnumericalcalculation,it wasassumedthat the relativepermeabilities were linear functionsof saturation.The calculationhas been repeatedin this sectionassumingthat the relativepermeabilitiesvary with the cube of the mobile saturation.The resultsare tabulatedin the followingtable.The calculatedsaturations are shown as dotted lines in Fisure 5.47. Assumedto Vary with the Cubeof the Mobile Flood NumericalExamplewith RelativePermeabilities Saturation Permeabilitiespm2
oil Saturation
Steam
0.060 0.095 0.130 0.165 0.200 0.235 0.2'70 0.305 0.340 0.375 0.40'r 0.410 0.445 0.480 0.515 0.550 0.585
0.90 0.78 0.68 0.58 0.49 0.42 0.35 0.29 0.23 0.19 0.15 0.15 0.11 0.08 0.06 0.04 0.03
f'
f
oil
Steam
Steam
0.00 0.00 0.00 0.00 0.01 0.01 0.02 0.03 0.05 0.0'7 0.09 0.09 0.13 0.16 0.21, 0.26 0.32
1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9997 0.9995 0.9991 0.9983 0.99'72 0.99'71 0.9950 0.9914 0.9852 0.9739 0.9531
0.0000 0.0000 0.0002 0.0006 0.0013 0.0025 0.0047 0.0082 0.0141 0.0240 0.0389 0.0407 0.0694 O,IZOL 0.2t21 0.3851 0.7224
Chamber Heat(r)
Recovery Vo OOIP
0 49 239 666 1,482 2,938 5,443 9,682 t6,823 28,901, 47,3tl 49,556 85,508 149,593 26'7,253 490,864 931,479
92.77 90.05 87.18 84.t7 81.02 77.72 74.29 70.71 66.99 63.t4 59.49 59.15 55.02 50.76 46.38 41.90 37.34
point and lessn ferencein the r a considerabl casethe \.\'ateri tial recoverr.is I ditions at the E The calcu Figure5.49. The follor
1. In the inir relativepe becauseol tion front2. At steam two exan{ 3. After stea lationship low oil sat
PRESSUREDROPFOR
The pressuredn particularlywitl reservoiris freg
(t)In kilojoulesper cubic meter of injectedsteam.
It is interestingto note that the quantityof oil remainingin the steamchamber is almostthe samefor the cubic relativepermeabilitycurvesas for the linear ones.However,it is distributeddifferently. More oil remainsnear the injection 228
The Displacementof Heavy Oil
Chap.5
Pressure Dropfor
ight increasein water ;ulatedthat the water t 0.171-a very small ntion front, and it is In this example,the ery small. The main r as it leavesthe conr flow with very little rwn by the solid lines
STEAM
.E 0.6
orL
(!
fr 0.4
""'f'v-J'o'"'' "''
Q
Linear Rel.Perm. Curves 0
0.02
0.04
0.05
0.08
Distance(1/PVinjected,measuredas vapor)
rerelativepermeabilibeenrepeatedin this re cube of the mobile 'he calculatedsatura-
rh rhe cube of the Mobile
lhamber Heat(t) 0 49 239 666 t,482 2,938 5,443 9,682 I 6,823 28,901 4 7 , 3 I1 19,556 85,508 149,593 ?67,253 490.864 93t,479
Recovery Vo OOIP
92.77 90.05 87.18 84.r7 81.02 77.72 74.29 70.71, 66.99 63.1,4 59.49 59.15 55.02 50.76 46.38 41.90 37.34
point and lessnear the front for the cubic curves.There is also a considerabledifferencein the waterflooding zone aheadof the steamfront. With the cubic curves, a considerablyhigher water saturation is required to provide oil mobility. In this casethe water is ableto sweepadditionaloil aheadof the steamfront, and the initial recoveryis better.The Buckley-Leverett diagramin Figure5.48showsthe conditions at the water front. The calculatedoil recoveryis plotted againstthe volume of steaminjected in Figure5.49. The following featuresshould be noted. 1. In the initial stages,additionaloil is recoveredin the examplewith the cubic relativepermeabilitycurvesas comparedto that with the linear ones.This is becauseof the additional oil displacedby water downstreamof the condensation front. 2. At steambreakthrough,the recoveriesare almost exactlythe samefor the two examples. 3. After steambreakthrough,the systemwith the linear relativepermeabilityrelationshipsshowsincreasinglybetter recoveries.The reasonfor this is that at low oil saturations,the oil is more mobilein this system. PRESSUREDROPFOR STEAMFLOODING The pressuredrop required to force steaminto the reservoiris of great importance, particularlywith viscousoils. The rate at which steamcan be introducedinto the reservoir is frequently controlled by the pressuredrop.
' o
0.8
tr b o.o 6
WaterFront Sw= 0 223 f*= o'+23
= G
v.e
.9
rg in the steamchamlrves as for the linear ins near the injection f HeavyOil
Chap.5
Figure 5.47 Saturationsduring Steamflood. Effect of RelativePermeability Curves
E 0., L
0
0,2
0.4 0.6 Water Saturallon
PressureDrop for Steamflooding
Figure 5.48 CalculatedConditionsat Water Front for Steamfloodwith AssumedCubic RelativePermeability Curves
229
f!
,t
H
100
q
Linearrelative
80
CubicrelativoDermeabilitv
E60
*
SteamBreakthrough
i40 o
e
&. zo 0
WaterBreakthrough
a
0123 SteamInlectedIn PoreVolumesas Water
Figure 5.49 CalculatedOil Recovery as a Function of SteamIniection
steamfloodusedin the numerical Consider,for example,the laboratory-scale exampledescribedpreviously.Resultsof the calculationpertainingto the pressure drop are given in the following table. PressureGradientsin SteamfloodNumericalExample Steam Zone At front
Inlet
Compositionof flowing stream Oil Va Water Steam
0 0 100
0.'73 0 99.27
Zone Ahead of Condensation Front
53 47 0
VolumetricFlow Rates oil m3/m'zh Water Steam
0 0 0.5701
0.0042 0 0.5660
0.0111 0.0098 0
Permeability Oil pm2 Water Steam
0 0 0.900
0.590 0 0.360
0.9996 0.0004 0
PressureGradient kPa/m psift
3.17 0.14
7.86 0.35
6160 272
This table showsthe conditionsat the inlet to the core,just beforethe condensationfront and just beyondthe condensationfront. The flowing streamconsists almost entirely of steam even immediatelybefore the condensationfront (99.27volVosteam).The very high ratio of steamto oil is the reasonfor the high of the steamin driving the oil forward.Immediatelybeyondthe front, effectiveness where the steamhas shrunk in volume becauseof its condensationto water, the ratio of oil volumeto watervolumein the flowing streamis much smaller;also,in this region,the temperaturehas fallen to the reservoirtemperatureand the oil is 230
The Displacementof Heavy Oil
Chap.5
much more viso zonesare shorl that in the ccld flow of the stcr and the temper cal examplesh 6 MPa/m. For ti 3 MPa, or over Steamhe but as it forces creasesenornxl Steamcan flog r dense,it mug c posedonly if th to becomeexpc out the other. Imaginea Steamis beingir by the continrn temperatureand The steam process.If the ra densationfront, voir beyond.thc pressuregoesup A problem very high value. fracture occurs. voirs when ecom steamfloodingm injectedfluids fl pressuredrop im Under thes rection of the fna duced. The pres in parting the re maybe verticalo within the reserv changeas the rer tions; it has bee originally were \ (Denbina, Bobeq It is interes the condensate n region-either w doesnot increase
Pressure Dropfor
alculated Oil Recovery rf Steam Injection
tsed in the numerical rining to the pressure
Zone Ahead of Condensation Front
53 47 0
0.0111 0.0098 0
0.9996 0.0004 0
6160 2',72
:, just beforethe con: flowing streamcone condensationfront re reasonfor the high rtelybeyondthe front, :nsationto water, the muchsmaller;also,in reratureand the oil is il HeavyOil
Chap.5
much more viscous.At the bottom of the table,the pressuregradientsin the two zonesare shown.The pressuregradientwithin the steamzoneis only about0.1%of that in the cold zone beyondthe condensationfront. There is little restrictionto flow of the steamand oil within the steamzone, but as soon as steamcondenses and the temperaturefalls, there is a very greatresistance. In the particularnumerical example shown, the pressuregradient within the cold flow zone is over 6 MPa/m. For the 500-cmcore of the numericalexample,the pressuredrop is about 3 MPa, or over 400 psi. Steamhas little problem in sweepingthe oil from the steam-saturatedzone, but as it forcesthe oil through the condensationfront, the resistanceto flow increasesenormously.The flows within the steamzone and beyond are coupled. Steamcan flow only if it can condenseat the perimeterof the steamzone.To condense,it must contact fresh cold reservoir. Fresh cold reservoir can become exposedonly if there is sufficient pressureto force the oil through it and thus allow it to becomeexposedto the hot steam.one phaseof the processcannotoccur without the other. Imagine a steamfloodingprocessin which the mechanismsare balanced. Steamis being introducedcontinuouslyand is condensedby the coolingprovided by the continuously uncoveredreservoir. The swept reservoir is heated to steam temperatureand the oil within it is forceddownstream. The steamchamberpressurereachesan equilibriumvalue that balancesthe process.If the rate of injectionof steamis increased, moreoil is suppliedto the condensationfront, more pressureis required to force this oil through the cold reservoir beyond, the required pressuredifferential increases,and the steam chamber pressuregoesup accordingly. A problemarisesif the oil is very viscousand the injectionpressurerisesto a very high value. In this situation the pressurecan reach a level at which reservoir fracture occurs.This is the situationin many, indeedmost,virgin bitumen reservoirs when economicsteam-injectionratesare achieved.Under theseconditionsthe steamfloodingmechanism,which hasbeendescribedpreviously,fails. Instead,the injectedfluids flow into the openingfracture beyond,and becausethere is little pressuredrop involved in their transport, the fracture extends. Under theseconditions,the heatingoccursas a finger extendingalongthe directionof the fracture.The amountof oil displacedby the processis drasticallyreduced. The pressureis dissipatednot in advancinga broad condensationfront but in parting the reservoirmatrix. The situationis shownin Figure5.50.The fracture may be verticalor horizontaldependingupon the initial in situ compressive stresses within the reservoir.This is discussed further in Chapter6. The in situ stresses may changeas the result of stressesintroduced by neighboringthermal recoveryoperations; it has been found at least in one project that reservoirsin which fractures originally were vertical change so that subsequentfractures become horizontal (Denbina,Boberg,and Rotter 1987). It is interesting to note that although the fracture may advancerapidly and the condensatemay be carried away alongits length, the areal extent of the heated region-either vertical or horizontal, dependingupon the fracture orientation)doesnot increasemuchfasterthan it would if a broad condensationfront were beins PressureDrop for Steamflooding
231
,l
;N
C O L DR E G I O N I M M O B I LOEI L
Figure 5.50 SteamFlow and Condensationwithin Fracture
carried forward by the samesteaminjectionrate in a reservoircontainingoil of a lower viscosity.The readershould refer to the resultsof the comparisonof the heatingof a reservoirfrom a fracturewith thoseof the Marx-Langenheimfrontal advancethat were given in Figure 3.I2. In that example,for instance,the heated area for the fracture was about double that for the frontal advancein a reservoir 100ft thick. When steam advancesinto the fracture, heat is still transferredto the oil sand,and the oil becomesfluid. The volume of oil heatedby a given amount of steamis approximatelythe same.However,the pressureavailableis largelyspentin disruptingthe reservoirmatrixorather than in moving the oil. In Figure 5.50,the oil is movedforward somewhatby the pressuregradientalongthe fracture,but this is generallyinadequateto achievemuchmovement.The hot oil remainsbesidethe reaches fracture,and the steamand waterrun throughit. Eventuallythe condensate the pressuresink, and steambreaksthrough without having displacednearly as much oil as is possiblein a nonfracturingsystem. STEAM OVERRIDE In a lateralsteamfloodin which steamis injectedat a pressurebelowthat required for fracturing,with the purposeof pushingoil horizontallytowardone or moreproduction wells, there is a tendencyfor the condensationfront to become tilted so that steamruns over the top of the colderoil below.This is shownin Figure 5.51. As the steamfront advances,the volumeof the steamchamberincreasesand oil is displaced.This oil tends to flow downward and sidewaystowards the production well, and it is accompaniedby condensate from the steam. The effectivenessof this displacementis generallysimilar to that described previously.However,becausethe steamis advancingrapidly under the colder over'The energyis expended in carrying out work againstthe stressesin the reservoirmatrix. This work, evenfor a vertical fracture,resultsin a lift of the surfaceof the ground abovethe reservoir. In cyclic steamprojects,someof this energybecomesavailable,during the productioncycle,to provide compactiondrive to move the reservoirfluids (Denbina,Boberg,and Rotter 1987).
232
The Displacementof Heavy Oil
Chap.5
burden.the b areathat mus ward and sidr horizontaldis for an easiert Another is that the cc increasingll's step-liketenp ual. In Chapt advancinefm vance(seeeq to estimateth Eventua the drive is m ity. Meansfr describedb1 ! ationsVogelp the productiu steambypass which is ecorx As the p well, the mecb oil is driven ar in a direction; parallelto the with the drag tivelysmallun well is hindere well with the r As is me horizontal pro( and by makir4 proach is to dr injectionand p SteamOverrb
_ Eo t L I II
I
i,,A
I
}
WATER
FlowPaths Oil + Condensate Figure 5.51 SteamOverride during Steamfloodingof Mobile Oil
rir containingoil of a re comparisonof the x-Langenheimfrontal ' instance,the heated dvancein a reservoir transferredto the oil br a given amount of ableis largelyspentin il. In Figure5.50,the r the fracture,but this oil remainsbesidethe reaches he condensate rg displacednearly as
re belowthat required ward one or more proIt to becometilted so shownin Figure5.51. rcr increases and oil is ruards the production rilar to that described underthe colderover:s in the reservoirmatrix. re ground abovethe reserng the productioncycle,to . and Rotter 1987).
rf HeavyOil
Chap.5
burden,the heat lossesare greaterthan for a linear flood becauseof the greater area that must be heated.The advancingsteamchambertends to produce a downward and sidewaysdrive over a larger area than would be achievedwith a simple horizontaldisplacement flow. The enlargedcondensation front areatendsto allow for an easierdisplacement of the oil. Another factor which becomesimportant with highly overridingsteamfronts is that the conductivetransferof heat beyondthe condensation interfacebecomes increasinglysignificantas the surfaceof the condensation front grows.The sharp step-liketemperaturegradientwhich occursinitially at the interfacebecomesgradual. In Chapter2 it wasshownthat the quantityof heatwhich is movedaheadof an advancingfront is, in the steadystate,inverselyproportional to the velocity of advance(seeequation2.45 et seq.).The methodsdescribedin Chapter2 can be used to estimatethe heatwhich is aheadof the advancingfront. Eventuallythe steamchamberreachesthe productionwell, and at this time the drive is mostlydownward,so the movementof oil is assistedsomewhatby gravity. Meansfor calculatingthe thermalefficiencyof processes suchasthis havebeen describedby Vogel(1984)and were describedin Chapters3 and 4. In thesesituationsVogelpointsout that the injectionof excesssteamresultslargelyin bypassto the productionwell. The rate of injectionshouldbe controlledso as to minimize steambypass;however,in suchsituationsthe rate of productionmay be belowthat which is economic. As the point is approachedwhere steamcan break through to the production well, the mechanismby which oil is moved gradually changesfrom one where the oil is driven awayfrom the advancinginterface through the colder oil beyond (i.e., in a direction awayfrom the interface) to one where the movementis more or less parallel to the interfacewith the driving force being provided by gravity combined with the drag of the steamflowing within the steamzone.This last effect is relasteambypassis permitted.The flow to the production tively smallunlessexcessive nature of the radial flow to it and the limited contactof the is hindered by the well well with the reservoir. As is mentionedin Chapter7, the processcan be improvedby using extended horizontal productionwells, which increasethe collection capacityfor draining oil, gravity drainageprinciple. A related apand by making use of the steam-assisted proach is to drill in-fill wells to recover someof the remaining oil left betweenthe injection and production wells; this is discussedin Chapter 4. Steam Override
233
i
H I
I
The useof hot water or low steamquality is also describedin Chapter-4as a meansfor recoveringfurther oil from mature steamfloods where steamhas broken throughto the producers.The densityof the waterallowsit to fall to the bottom of the steamchamberand thus invadethe regionoccupiedby the remainingoil. Another approachis to employlow quality steamthroughoutthe drive; this approach is discussed in Chapter4 in conjunctionwith the correlationsdevelopedby Gomaa.
In thE- | have been cm assumedthal t ing form:
EFFECTOF STEAM OUALITY In the analysisof the adiabatic,one-dimensional steamfloodshownin Figure5.42, it was assumedthat the steamwas dry and saturated.In practicalprocesses, wet steamis employed.Qualitatively,the effect of water in the steamis to increasethe watersaturationin the steamfloodregion,sinceliquid wateraswell as steamhasto flow. The heat in the liquid water that reachesthe condensation front is alsotransferred and this contributesto the advanceof the front. On a weightbasis,the total heat of wet steamis lessthan that of dry steam;however,on a volumebasis,with the volumemeasuredas that of the wet steammixture, the heat contentis larger. Water at its boiling point has a higher heat content per unit volume than does steam.For a given quantityof injectedheat,the condensation front movesforward a slightlysmallerdistancethan it doesfor dry steaminjection.The reasonfor this is that the flooded steamchambercontainsslightlymoreheatbecausethe watersaturation and oil saturationare both slightly higher.However,the differenceis relatively small,as will be seen. The conditionswithin the steamfloodedregioncan be approximatedby assuming that the flowing ratio of steamvapor to liquid water remains constant within the steamfloodregion. This assumptionis reasonableexcept in extreme casesbecausethe amountof water left behind to provide the increasedwater saturation is only a small fraction of the total steamand water flow. The fractionalsteamquality,f,, is definedby the following equation. t
QtPt
-
J'-
q*pJ
q'p'
(s.60)
Q" P"L I' J The flows of the individual componentsare given by the Darcy equations: Qo
=
-
Qn
=
dX
k*A AP 0x Pw
234
where
Thesum
Eliminat
This ma1 tion as a furrti
The rr.ate
(s.61)
Equation for any given o before;the com
k,A aP Qt=
This ma1'bere termsof the s&
K"A AP &o
--
Equating leadsto
(s.se)
This may be rearrangedas follows to give the ratio of water flow to steam flow (on a volumetricbasis):
q!=e:ft;nl =o
wheren.C-C From thc the ratio R can
lt,
6x
The Displacementof Heavy Oil
Chap.5
Effectof Stean t
d in Chapter 4 as a :e steam has broken all to the bottom of remaining oil. Anirive; this approach r elopedby Gomaa.
In thesethree equations,the relativepermeabilitiesand absolutepermeability have been combinedas singleterms. For the purposeof this analysis,it will be by equationsof the followassumedthat the three permeabilitiescan be expressed ing form: ko = Co(So -
k, = C,(S* -
t,,)'l
r"'rl
(s.62)
ft, = C,(S,)' oun in Figure5.42, tical processes, wet m is to increasethe *ell assteamhasto r front is alsotrans:iqhtbasis,the total , rolumebasis,with at contentis larger. volume than does ront movesforward 'he reasonfor this is ausethe watersatue differenceis relarpproximatedby as'r remainsconstant except in extreme rcreasedwater sature equation.
wheren, Co,C*, and C, are constants. From the expressions fot q, and 4" in equation5.61,a secondexpressionfor the ratio R can be obtained.
Q *= ! ' P ' = R Qt
(s.63)
KtF*
rt
Equating the right-hand sides of equations5.60 and 5.63 and rearranging leadsto
?=ff^=?(+)'
(s.64)
I
This may be rearrangedto give the followingexpressionfor the water saturationin termsof the steamsaturation: S,=S,r*FS, where
B_
(?r^)"
(s.6s)
The sum of the saturationsof the three individual phasesmustbe unity.
(s.se) later flow to steam
(s.60)
S,+S,*So=l
(s.66)
Eliminating S, from 5.65and 5.66leadsto
s,,+(L+p)s,*s,=l
(s.67)
This may be rearrangedto give the followingexpressionfor the steamsaturation as a function of the oil saturation:
Darcy equations:
-S,-S,;)
s,=( 1 ( 1+ p )
(s.68)
The water saturationis obtainedbv difference.
(s.61)
S,=L-S,-So
(5.69)
Equations5.68and 5.69allow the steamandwatersaturationsto be calculated for any given oil saturation.The Buckley-Leverettmethod may now be applied as before;the combinedwater plus steamstreamis treatedas a singlecomponent. teavy Oil
Chap,5
Effect of Steam Ouality
;! I
235
We define the fractional flow of water plus steamas " rwr
Q,*Qs qo + q, + q,
(1 +R)4, q, + (I + R)q,
'* n*J;=)
(s.70) .9 0.6
The ratio of oil flow to steam(vapor)is given by
L f
Qo
KoF,
p,C"ls"-so,\n
Q,
K,Fo
lroC,\
S,
t
a
I
0.4
(s.71)
Combiningequations5.70and 5.71leadsto the following expressionfor f^.
0.02
I
Pore Volun
Jws
The calc the distance6 per Gigai:ule r heat, the frff qualities.The , of the steamfi steam saturat 'l alsobe seen. through the cl remainingbet injected stearn interface. The cakr Figure5.53.R of the oil at ba would be abh
(s.72) - 'So'\' / S' ,*r[T/
where
n-tL:C'l
t
\
tlo C" \1 + R/
This may be differentiatedto give an expressionfor f!",. c-cl df,, df*,_---"r/s,-.\'-trI _ , , _= -K= = * /; r"f,",\= +sJ d(s, s-l ilt ffil
rs.z:l
The equationsdescribedhere can be usedto predict the saturationsand recovery from a steamfloodby meansof a tabular calculationsimilar to that describedpreviously.The positionof the condensate front is determinedby the same type of heat balance;it is necessaryto treat the wet steamas a singlecomponent and to use the volume of the combinedvapor and liquid in the calculation.The heat available in a cubic meter of the wet steam (measuredas mixture) will be higherthan that in a cubic meterof vapor. The resultsof a seriesof calculationsof this type are shown in Figures5.52 and 5.53.Thesenumericalexampleswere calculatedusingthe data from the previous numerical example.The only difference in the input data is the steamquality. Figure 5.52 showsthe oil, steam,and, by difference,water saturationin the steamchamberfor caseswherethe steamqualityis l00Vo,50Vo, and25Vo.As before, the horizontal axis representsthe distancefrom the injector measuredin pore volumesper pore volume of injectedsteam,the steambeing measuredas the volume of the mixture of vapor and water. Decreasingthe quality of the steamhas the effect of increasingthe heat supply per pore volume and the distanceto which the condensationfront advances. The Displacementof Heavy Oil
Chap.5
0.8 E
o
^^
L f
o (n
nr v.a
v
u.a Cubic Mr
Effect of Stean
1\ +Rl
(s.70) .9 0.6 L
J -^
nA
(n
Heot in Steom
(s.71)
100% 50% 25%
I expressionforfi". o
rs.z:t
: saturationsand rer similar to that de:rmined by the same ; a single component the calculation.The as mixture) will be rown in Figures5.52 data from the previis the steamquality. rter saturationin the and25Vo. As before, neasuredin pore volrred asthe volumeof steamhasthe effect ce to which the con-
l-leavyOil
Chap.5
0.o4 0.06 0.08 0.02 PoreVolumesper lnjectedPoreVolume
Figure 5.52 Effect of SteamQuality on Saturations.Linear RelativePermeability Functions
The calculatedsaturationsare also shownin Figure 5.53.Here the scalefor the distancefrom the injector has been expressedas cubic meters of pore volume per Gigajoule(GJ) of injected heat. These curves show that for a given quantity of heat, the frontal advanceis nearly the samefor each of the three injected steam qualities.The effect of lowering the steamquality is to reduce,slightly, the advance of the steamfront becauseof the higher heat capacityof the chamber.The smaller steam saturations and the larger oil and water saturationsof the chamber can also be seen.The water saturationis higher becauseof the need for water to flow through the chamber(i.e., saturationsaboveS,; are required).The oil saturations remainingbehind the front are also'higherbecauseof the lower volume of the injected steam. Less steam flow is available to drag the oil to the condensation interface. The calculated percent recoveriesof the OOIP are tabulated in the box in Figure 5.53.For a given injection of heat, the dry steamis predictedto remove60Vo of the oil at breakthrough,whereas,for the sameheat injection, 25Voquality steam would be able to remove about5l% from a slightly smaller steamedvolume.
(s.72)
!o-Jo'l ,(t + B )l
47293 62758 92142
t
, 1 O O %Q u o l i t v ,/ 50% ---./
/'
25%
:" :' 1'1':t':' ; :.:.S-:-- :'
0.8 't
,/
u.o
;'m T a a
t
l
-S
I
I
6a
0.2
,"t
t/ i
tl / O
o:n
-,i
lsoz lccq-
0.6 0.8 0.4 0.2 Cubic Metres of Pore Volume per GJ
Effect of Steam Ouality
1
Figure 5.53 Effect of Heat Input on Linear RelativePermeSaturations. abilityFunctions
237
l;
H
{
EFFECTOF VERTICAL HEAT LOSSES In the analysisjust described,it is assumedthat there are no vertical heat losses from the expandingsteamchamber.Considerthe situationshown in Figure 5.42, in which heatis lost by verticalconduction,both upwardsand downwardsfrom the steamfloodregion.Suchlosseshave the effect of reducingthe heat availableto advancethe front and also of reducingthe quality of the steamthat is flowing. The effectwill vary with time. Initially in the flood, therewill be little areafor heat to be conductedaway,and the effect on the processwill be small.As the flood progresses, the rate of heatlossincreases, and a smallerand smallerfractionof the injected heat is availableto advancethe front. Heat balancesfor this effect were discussedin Chapter 3 for severalsituations.These may also be applied to the presentsituationusing the averagesteamchamberheat capacity,as predictedbefore. It is suggested that for practicalpurposes,the magnitudeof the effect upon the recoveryof oil can be estimatedby includingthe lossesin the calculationof the heat availableto extendthe front and by using an averagequality of the steamin order to estimateits effect upon recovery. More elaborateproceduresfor carrying out suchcalculations,which invorve the approximationof the steamchamberas a number of discretevolumes,have beenproposed(Shutlerand Boberg 1972;Boberg1987).Thesemethodsare rather involved and complicated;in many cases,the accuracyof the input data would probablynot justify the complexity.The methodsdescribedhere are relativelysimple and can be readily carried out using tabular calculationswith a spreadsheettype microcomputerprogram. EFFECTOF INCREASINGSTEAM VISCOSITY If the steamhad a higherviscosityit would be more effectivein displacingthe oil from the steamchamber.As an exampleof this effect, the numerical example which was describedstartingon page224 wasrepeatedassumingthat the viscosity of the steamwas 0.05cp insteadof the true value of 0.018cp. This changehad the resultof decreasing, substantially,the oil saturationswhich remainedin the steam chamberand improving the recoveries.The oil recoveriesare plotted againstthe volume of steaminjectedin Figure 5.54.There was also a slight reductionin the quantityof steamrequiredto reachbreakthrough.This differenceresultedfrom the lower heat capacityof the steamchamber. This calculationindicatesthat additivessuch as foam producingmaterials should,becauseof their effectin increasingthe apparentviscosityof the steam,result in a lower residualoil saturationin the steam-swept regionsaswell as increase the steam-drageffect.
o E60 o o40
*eo
2. In the 1l6rth greater prodr.rc 3. Becaus steamb floods t strongtl 4. InaEa fingen I a succe sateas i fer. tbc (steamf shownb tempere vancein Until al the sen With ho more fin 5. With ve practica ture as flo*'s al to the fr the prod
GENERALCONCLUSIONSON DISPLACEMENT The following qualitativeconclusionson the nature of displacementprocesses for heavyoils can be drawn: 1. when heavyoils are displacedby water,the watertendsto breakthroughvery quickly.This would be so evenif therewere no frontal instability. 238
The Displacement of HeavyOil
Chap.5
Ann,teNro.\t. I Media."SPE Bibliography
ro vertical heat losses hown in Figure5.42, downwardsfrom the : heatavailableto adl that is flowing. The little areafor heat to all. As the flood proller fractionof the in; for this effect were so be applied to the rcitv,as predictedbede of the effect upon the calculationof the rality of the steamin ations,which involve scretevolumes,have e methodsare rather :he input data would 3reare relativelysims with a spreadsheet-
: in displacingthe oil e numericalexample ringthat the viscosity This changehad the lmainedin the steam 'e plotted againstthe ight reductionin the nce resultedfrom the producingmaterials rsity of the steam,rens aswell as increase
80
6 o E60 ([t
B qo o
szo
0.5
Steam Iniected (PVa8 Liquid)
HeavyOil
Chap.5
Figure 5.54 Effect of Higher Steam Viscosity upon Calculated Oil Recoveries. Steam Injected (PZ as Vapor)
2. In the production of heavy oil by waterflooding,the water tends to run of this processis throughthe oil and dragsomeoil with it. The effectiveness greater the lower the oil viscosity. Higher temperaturesgive better oil-water productionratiosbecauseof the betterviscosityratio. 3. Becauseof the stabilization resulting from the shrinkage on condensation, steamhas a much lower tendencyto finger than doeswater. In many steamfloods the steamcondensationfront is more or lessstable,although there is a strongtendencyfor the steamto overridethe liquids. tendsto drain throughthe oil either as 4. In a steamflood,the watercondensate fingers or in diffuse flow. This is often not undesirable,since in order to have to removethe condena successful heatingprocessusingsteamit is necessary in the section on convectiveheat transit is formed. As was discussed sateas fer, the heat in the condensatecan be effectively transferred to the front (steamfront) as long as uncondensedsteamremains at the front. As has been shown by Miller, there is also a tendencyfor the front to be stabilizedby the temperaturegradient. Steamfloodingfronts can be relatively stable and advancein a regularmanner through the reservoirwith the steamoverriding. Until all the latent heat of the steamis lost supplyingvertical losses,most of the sensibleheat of the condensateis given up at the steaminterface as well. With hot waterflooding, the front is much more unstableand there is much more fingering of heat into the reservoir. 5. With very viscousoils, reservoir!_4cturingcan occur if steamis injectedat a practical rate. This resultsin the heating of the reservoiradjacentto the fracture as the steam flows into the fracture and condenses.The condensate flows alongthe fracture. Although largevolumesof oil can be heatedadjacent to the fracture, there is little driving force availableto move the heatedoil to the production well, and oil production is small.
rcementprocesses for to breakthroughvery instability.
11.522.5
BIBLIOGRAPHY Anl,rENro,M.E., and MrLLrR, C.A., "stability of Moving CombustionFronts in Porous Media," SPEJ,423-430,December1977.@ 1977SPE, Bibliography
239
f f!
,t
I
BAKEn,P. E., "Effect of Pressureand Rate on SteamZone Developmentin Steamflooding," SPEJ,274-284, October 1973. BoneRG,R. C., "Thermal Methods of Oil Recovery,"J. Wiley, New york, 1987. BucrLey, S.E., and Lnvnnrrr, M. c., "Mechanismof Fluid Displacement in Sands,"Trans. AIME, 146,t07-n6, (L942). cuuore, R. L., vaNMEuns,P., and vANDERPonr-,c., "The Instabilityof Slow,Immiscible, viscousLiquid-Liquid Displacements in PermeableMedia," pet. Trans.AIME, 216,1gg194,(t959). @ 1959SPE. Dere, L. P., "Fundamentalsof ReservoirEngineeringChapter L0," Elsevier Scientific PublishingCo., New York, 1978. DeunrNA,E.S., Bonrr.c, T.c., and Rorrrn, M.B., "Evaluation of Key ReservoirDrive Mechanismsin the Early Cyclesof SteamStimulationat Cold Lake," SPE 16737,Dallas, 1987. Haooonr, J., "DisplacementStability of Water Drives in Water-WetConnate-Water-Bearing Reservoirs,"SPEJ,63-74, February1974. LrvenErr, M.c., "Flow of oil-water Mixtures Through UnconsolidatedSands,"Trans. AIME, L32,I49-t7t, (1939). O 1939SpE. MILLln, C.A., "Stabilityof Moving Surfacesin Fluid Systemswith Heat and MassTransport, III. Stabilityof Displacement Frontsin PorousMedia," ArchE Journal,21,474-479, (May 1975). MusKer,M., "Flow of Homogeneous Fluids," McGraw Hill, New york, 1937. Nurr, C.W., "The PhysicalBasis of the Displacementof Oil from PorousMedia by other Fluids: a CapillaryBundle Model," Proc. Roy. Soc.Lond., A3BZ,I55-I78, (1982). PErnns,8.J., and FLocK, D.L., "The onset of InstabilityDuring Two-phaseImmiscible Displacementin PorousMedia," SPEJ,249-258,April 1981. SannveN,P.G., and reyLoR, G.I., "The Penetrationof a Fluid into a porousMedium or Hele-Shawcell containing a More ViscousLiquid," Proc. Roy. Soc., 4245, 3rz-329,
(1es8).
sHurr-en,N. D., and BoneRG, T. c., 'A one-Dimensional,Analytic Techniquefor predicting Oil Recoveryby Hot Water or Steamflooding,"SpEJ, 489-498,Dec. 1972. Suunro, R., and BanooN,C., rn EuropeanSymposiumon Enhancedoil Recovery(ed. J. Brown), Edinburgh: Institute of Offshore Engineering,Heriot-Watt University, 303-334, (1e78). vaNMnuns, P., and vANDERPou, C., 'A TheoreticalDescriptionof Water-DriveProcesses InvolvingViscousFingering,"Pet. Trans.,AIME, 2I3,103-112,(1958). voceL, J. H., "SimplifiedHeat calculationsfor steamfloods,"Jpr, rrzT-t136,July 19g4. wELGe,H. J., "Simplified Method For computing oil Recovery By Gas or water Drive," Trans. AIME, 195,91,-98,(1952).
240
The Displacement of HeavyOil
Chap,5
Cycli
INTRODUCTION
The useof crr proven to be ar ditions,and th A signiF tratednearto I ents are highe do the mostgs tional steamfb heated as it flo mustpassthru At one eo ing oil thatis x hereis to "meh requirementsft quiredto raiser The othe preciablemotilr circumstancetl tance;this canI ment is relatedt be much lower In the fin make it mobile by reducingthe injection decrea the injectionc.u generalreservc
ent in Steamflooding," turk, 1987. ment in Sands,"Trans. t1-of Slow, Immiscible, rans.AIME, 216,I88:lsevierScientificPub'Key ReservoirDrive ;e." SPE 16737,Dallas,
CyclicSfedm Stimulqtion
lon nate-Water-Bearing
f
lidated Sands,"Trans. Heat and Mass Transi Journal,21,474-478, rk, 1937. lorous Media by other 155-178,(1982). Two-PhaseImmiscible o a PorousMedium or Soc., 4245, 312-329, :chniquefor Predicting :c. 1972. i Oil Recovery(ed. J. rt University,303-334, Water-DriveProcesses b8). ,r?'t-1136,July 1984. Gas Or Water Drive,"
HeavyOil
Chap.5
f INTRODUCTION The use of cyclic injection of steamto increasethe flow of oil from reservoirshas proven to be an effective technique.It is useful over a wide rangeof reservoirconditions, and the mechanismby which it worksvaries. A significant feature of steamstimulation is that the injected heat is concentrated near to the well bore wherethe streamlinesconvergeand the pressuregradients are highest.Steamstimulationtends,inherently,to put the heat whereit will do the most good. A major differencebetweencyclic steamstimulation and conventional steamfloodingis that in stimulation,the displacedoil becomesand remains heated as it flows to the production well whereasin conventionalflooding the oil must passthrough cooler reservoir until the flood becomesmature. At one end of the scaleis the cyclic injection of steaminto reservoirscontaining oil that is soviscousthat it may be consideredas almostsolid.The role of steam here is to "melt the solid" and thus allow it to flow through the reservoir.The steam requirementsfor this mode of operation are related to the quantity of steam required to raise the reservoirto steamtemperatureafter an allowanceof heat losses. The other extremecaseis where the oil within the reservoiralreadyhas appreciablemobility and conventionalproduction is possiblebut at a low rate. In this circumstancethe role of steam injection is to decreasethe near-well bore resistalaei thii can be looked on as a true stimulationof production.The steamrequirement is relatedto the heat requiredfor the near-well bore region; normally this will be much lower than that required for generalreservoir heating. In the first case,the role of steamis to heat oil throughout the reservoir to make it mobile. In the second,the role of steamis to increasethe production rate by reducingthe near-well bore flow resistance.In both cases,the effect of steam injection decreasesas the heated region cools, and it becomesnecessaryto repeat the injection cycle.Also, in both cases,subsequentcyclesbecomelesseffective. In generalreservoir heating it is necessaryfor successivecyclesto heat the reservoir
{
which is more and more remote from the production well. For the near-well bore cyclesdeteriorates stimulationmechanism,the effectof subsequent as the reservoir pressure(or other driving mechanism)becomesdissipated. At any point in the spectrumof applicationsof the cyclic steamstimulation process,theremustbe an effectivemeansto force the oil to the productionwell. If the oil alreadyhassubstantialmobility and can be producedby conventionalmeans without steamstimulationat appreciablerates,then the samedriving force, the reservoirpressure,can transportthe oil to the well. The flow is fasterthan in conventionalproductionbecauseof the reductionin the near-wellbore resistance; this is discussedlater. Reservoirpressureis inadequateto move the oil at a practical rate to the productionwell when the cold oil is initially immobileor nearlyso. In this case,other driving forcesare required. In some reservoirs,compactiondrive resultsfrom the consolidationof the reservoirsand,with an accompanying in averageporosityasthe pore presdecrease provide pressure transport the oil. The oil is squeezed surefalls; this can drive to from the porousrock as it compactswhen the pore pressureis lowered.This mechanismhasbeenimportant in the productionof oil from the Bolivar Coastof Lake Maracaiboin Venezuela. Another form of compactionrecognizedasbeingimportantto the production of oil in the earlycyclesof steamstimulationin the bitumenreservoirof Cold Lake is the compactionthat followsreservoirexpansionas the resultof steaminjectionat fracturing pressure.In this reservoir,injection at fracturing pressureis the only meansby which steamcan be injectedat practicalrates.Steaminjectioncausesan increasein the pore volumeof the reservoir,which is reflectedby an increasein the elevationof the ground surfaceabove.Someof the energyusedto injectsteaminto the reservoiris storedaspotentialenergyby lifting the ground.When the well pressureis lowered,fluids can be squeezed towardsthe well by the settlingof the lifted ground.The effect is not reversible,sincemovementof the sandgrainsin the vicinity of the fracturewill preventthem from shifting backto their initial position: there is hysteresis. A very important sourceof drive to moveoil to the well in steamstimulation projects,particularlythoseproducingbitumen,is gravity.This can only have a significant effect if there is a low-densityphaseto replacethe oil as it drains downwards. Steamcan fill this role. As oil is drained from the reservoir,an existing steamchambercan expandto replaceit. The cyclic steamstimulation processis also known as huff and puff, as steam soaking,and as steamstimulation;theseare all acceptabledescriptions. COLD FLOW THE STIMULATIONOF WELLS WITH APPRECIABLE
CyclicSteamStimulation
Well Bore Sti
Theremar.bc not character may occur as I forations.chea migratineresc to flow is repr
Even if the sL tance,-\P./9.< reducesthe vir in the skin ef! the factorS. T] other deposits sistance bl'tcz lies in the welt neededto hea Near-Well 8q
The steadl.sg around the s'd
;tt :3
Rei
Steaminjected into reservoirs,which are saturatedwith relatively mobile oil, flows into the formation by displacingreservoir fluids away from the well. At the same of steamoccurs. time, heatis transferredto the reservoirmatrix and condensation The condensatefrom the steam is cooled as it flows into the reservoir and more heat is transferred.Heat is also lost to the overburdenand underburden. 242
The effc by consideri throughthrec
Chap.6
t The Stimuhtbn
the near-well bore atesas the reservoir ic steamstimulation l productionwell. If conventionalmeans e driving force, the s fasterthan in conthis bore resistance; tical rateto the pror. In this case,other :onsolidationof the ;ity asthe pore presThe oil is squeezed lowered.This mechrlivar Coastof Lake nt to the production rrvoir of Cold Lake of steaminjection at pressureis the only n injection causesan by an increasein the I to inject steaminto When the well pressettlingof the lifted and grainsin the vitheir initial position:
The effect of steamstimulation can be visualizedin an approximatemanner by consideringthe flow to the well as being controlled by the steady-stateflow through three concentriccylindricalregions,as shownin Figure 6.1. Well Bore Skin There may be specialrestrictionsto flow in the immediatewell bore regionthat are not characteristicof flow through the reservoiras a whole. Resistancein the region may occur as the result of damagedue to mud invasion,inadequateor blocked perforations,chemicaldamagesuchas that causedby clay swelling,and damagedue to migratingreservoirfines blockingthe pore structureof the matrix. The resistance to flow is representedby the effect of a skin factor, g in the formula AP" _ pS q Zrrkh
(6.1)
Even if the skin factor remains unchangedduring stimulation, the well bore resistance, A,P,fq,decreaseswith steam stimulation becausethe increasedtemperature reducesthe viscosity,p.rn additionto this, steammay effect further improvement in the skin effect by cleaningthe poresin the well bore region;i.e., it may reduce the factor S. This is particularly important where the skin effect is causedby wax or other depositswhich can be removedby steam.The reductionof well bore skin resistanceby heating can have a very dramatic effect if much of the flow resistance lies in the well bore skin. This effect is largelyindependentof the quantityof heat neededto heat the bulk of the reservoir. Near-Well Bore Region The steady-stateresistanceto flow in the cylinder of radius Rr, that is heated aroundthe well bore is given by
in steamstimulation can only have a sigil as it drains downeservoir, an existing
DrainageRadius Re
ff and puff, as steam scriptions. Y
Resistances in series:
rely mobileoil, flows he well. At the same tion of steamoccurs. : reservoir and more derburden. itimulation
Chap.6
Skin
HotZone
trhs znkh
IrhLn(Rh/R$)
Cold Zone IrcLn(Re/Rh)
Figure 6.1 Steady-State Radial Flow to a Steam-Stimulated Well The Stimulation of Wells with Appreciable Cold Flow
243
LPn_ p" ln(Rn/R*) q 2rrkh
(6.2)
This resistanceto flow is reduced if the region is heatedbecauseof the effect of temperaturein changingthe viscosity,pr,. Far-Well Bore Region Beyondthe heat front of radiusRa, the resistanceto flow is given by LP, p.ln(R"lRn) = q Zrrkh
(6.3)
If the sum of the resistances to flow for the cold situationis divided by the similar sum for the hot, the resultis
M
p.S. * p.,ln(R"/R,) pnSn* p.nln(RnfR*) * p"ln(R"/R)
(6.4)
lroon],-
Alltrr methodssr The re equationd6
If the total pressuredrop, )AP, is the samefor both cases,this becomes Qn_
e,
p"S. * p,, ln(R"/R,) * FnSn p.lln(R6lR*) * t",ln(R"/R)
(6.s)
Two extremecasesof this are of interest. l. If p.ais negligiblecomparedto pr..,then q n_ 5 , * l n ( R " f R , ) ln(R,/R1) Q,
(6'6)
2. If Rh = R"-i.e., the wholereservoiris heated-and S, = S",then
q!=y: Q,
(6.7)
ltn
This assumesthat the skin factor remainsconstant.If Sr,is lessthan S., then this too will tend to improve the flow and the ratio could, in favorablecircumstances, be largerthan that given by equation6.7. BOBERGAND LANTZ'S MODEL A quantitativeanalysisof the processoutlinedin the previoussectionis described in a classicalpaperby Boberg andLantz (1966);their methodpredictsthe performancefor isolatedsteam-stimulatedwells in reservoirscontaining relatively low viscosity oil. The basicidea involvedis shownin Figure 6.2. It is assumedthat steamflow is radial and that the heatedzone is a cylinder centeredon the well.''The reservoirmay, if it is appropriate,be representedas shownby a numberof thin sandsdivided by horizontal, impermeableshalebarriers. 2M
Cyclic Steam Stimulation
Chap.6
After injecri< tically and r estimatedas dition, allorl ducedfluids. The cal ing equationt
In this equar oil producrim verticalhearI wise integrat
rln rherr p as shown in Figr memberand lr is lationof ro. lf rhr reservolras a sil Boberg and La
(6.2) ruse of the effect of olt SAND SHA!E
ven by
OIT SAND
(6.3) 5l{AtE
vided by
ott 'AND
thesimilar
-?'t-
Allowanceis madefor the heat lossfrom the well bore during injectionusing methodssuchas that describedin Chapter2. The radiusof the steamheatedzoneis calculatedusingthe Maix-Langenheim equationdescribedpreviously.l
(6.4)
-?-
ris becomes
I
(6.s)
= S., then (6.7) :ssthan S", then this rrablecircumstances,
{
Stimulation Chap.6
(6.8) -1
After injectionstops,the temperatureof the heatedzonefalls as it losesheat vertically and also horizontally to the colder surroundings.These heat lossesare estimatedas a function of time from solutionsto the conductivityequation.In addition, allowanceis madefor the heat removedfrom the heatediegionby the producedfluids. The calculationis carried out in a stepwisemannerin time usingthe following equationto estimatethe averagetemperatureof the heatedcylinder at eachstep: = Tn + (fs - TR)lrRrzg - 6) - 6l Tuue (6.e)
(6.6)
ed zone is a cylinder e. be representedas neableshalebarriers.
+ 2
In this equation,6 is a term that accountsfor the energyremovedby the water and oil production, and la and v7 are dimensionless factorsthat allow for the radial and verticalheatlossesfrom the heatedcylindricalvolume.6 is obtainedfrom the stepwise integrationof the heat balanceequation, ^
I {
I
A-
H'dt [' | J,,mih(pC),(fs - f*)
(6.10)
'In their paper, Boberg and Lanz considera numberof equal-sized,separatesandmembers, as shown in Figure 6.2,with thick shalemembersbetween.In this case,11,is the heat injection per memberand y'lis the thicknessof eachindividual member,both in equation6.4 and alsoin the calculation of rn. If the shalemembersarethin, then their effect shouldbi allowedfor by consideringthe reservoiras a singleentity.
Bobergand Lantz'sModel
IF st
p
if
{
4K2p2C2t 4qzt =h'(p,C,)'- h2
.
rH
:
hH"f (tD) 4IGr(Ts - TR)
f(td = e'o erfc({t)
s sectionis described I predictsthe perforing relativelylow vis-
Figure 6,2 Boberg and Lantz,s Steam_ stimulation Model (from Boberg and Lantz 1966)
245
where1{ is the rate at which heat is withdrawn with the products.At eachstep,it is changedusingthe quantitiesof the products,their heat capacities,and the production temperature.There is a decline in the production rate and temperature with time. The factors 7aand i2 are obtainedfrom Figure 6.3. Thesewere obtainedfrom approximatetheoreticalsolutionsto the conductionequation(lp can be obtained from equation2.85). The productionrate at eachtime is calculatedusing the idea that the flow is through two concentricreservoircylindersand the skin, with allowancebeing madefor the changingresistanceof the skin and heatedcylinderas the hot-oil viscosityfalls. At the end of the production cycle, Boberg and Lantz add the heat remaining in the reservoirto the heat injectedwith the steamin the next injectionperiod in order to calculatethe total heat injected.This is usedto estimatethe new heated radius.This approximationis conservative,sinceit neglectsthe heat storedin the overburdenand underburdenat the end of the cycle.The methodhasbeenshown to producegoodpredictionfor reservoirshavingoil with an in situ viscosityof a few hundredcentipoises. For the assumedmechanismto be effective,it is necessarythat there be an effectivereservoirpressurethat is ableto move the oil to the well bore in the cold condition. The increasedproductionof the stimulatedwell comesfrom the increasedflow that this natural drive can producewhen the effectiveradiusof the well bore is increasedby heatingthe reservoiraroundit. Effect of ProcessVariables Bobergand Lantz describea studyof the theoreticaleffect of variousprocessvariablesand draw a numberof interestinsconclusions: 1. The methodis intendedfor reservoirswith substantialdrive and cold mobility; their method is not suitablefor tar sands. 2. Wells having a high skin factor respondmost favorablyto stimulation even if no cleanup(i.e. reductionof S) is achieved.Figure 6.4 showsthe calculated effect of steamstimulation on the oroduction for a well assumingseveralskin
fl
Figure 6.3 Chart for Estimating7p andzyin Equation 6.6. (from Boberg and Lantz 1966) Cyclic Steam Stimulation
Chap. 6
ol@ c
o
?ro I.,
!co
z o
U.o o
92q
c
6l FE:r Bobq
factorsneck- c
n
tive. re ties srr (negati 1967l. effect d Chapre the skil 3. The fa o Higb r thar i o Lon, proxi greatl fecr d ofal shour ratesI from I
o Lorl p rated r beas. o High c
increa Bobergard La
lcts. At eachstep,it aiities, and the proIte and temperature
o G
o ao I tll
were obtainedfrom (vncan be obtained
e
z I
: idea that the flow ith allowancebeing ler as the hot-oil vis-
L'
D
o
o
e a J
J the heatremaining ;t injectionperiod in natethe new heated re heat storedin the hod hasbeen shown ;itu viscosityof a few
o
ve and cold mobility; o stimulationevenif showsthe calculated ssumingseveralskin
I
Chap.6
IF F
B
factors.Steamstimulationallowsoil to flow more easilythrough the ,,bottleneck" createdby a high skin factor.
varlousprocessvan-
Stimulation
t{
Figure 6.4 Effect of Skin Damage on steam stimulation Response(from Boberg and Lantz 7966)
ary that there be an well bore in the cold comesfrom the infective radiusof the
hart for Estimating 7p ation 6.6. (from Boberg 6l
40 60 80 t00 120 140 160 rso IIMT SINCESIARIOF SIEAMINJECIION . DAYS
The skin factor is a variablethat representsthe additional(or, if negative, reduced)pressuredrop around the well bore causedby local irregularities such as plugging (positive) or cleaning treatments such as acidizing (negative,it is hoped).It is definedby equation6.1(seeMatthewsand Russell 1967).The effect of the skin in radial fluid flow to a well is analogousto the effect of insulationon the flow of heatthat wasdiscussed in the latter part of Chapter2. In somecasesan additional effect of steamstimulationis to reduce the skin factor S by cleaningout depositsaroundthe well bore. 3. The factorswhich tend to give higher incrementaloil to steamratios are: o High oil saturationand high oil sandto shaleratios.Thesereducethe heat that is requiredper unit volumeof reservoiroil. o Low producedwater-oilratio (woR). water has a heat capacitythat is approximatelytwice that of oil and thus water productiontendsto accelerate greatlythe drainageof heatfrom the stimulatedreservoir.The predictedeffect of producedwoR ratio can be seenin Figure 6.5 which showsresults of a processvariable study made by Boberg and Lantz. Figure 6.5 also shows the beneficial effect which is predictedfor using higher injection ratesand also larger steaminjectionquantities.Theseimprovementsstem from the lower fraction of the heat which is lost. o Low producedgasto oil ratio. This is beneficialsinceproducedgasis saturatedwith watervapor and the heatin this, particularlythe latentheat,can be a seriousdrain on the heat pool. o High oil viscosity.The viscosityof very viscousoils dropsmorerapidlywith increasingtemperaturethan doesthat of lessviscousonesand, as a result. Bobergand Lantz's Model
247
{
J 2.4 (o o 4 2.0 E
E t.2 H t/t :.8
zut
E.4
ttl 4
\,
o ro
I
o ol
o rO
I
I
= STEAM RATE(LB/HR)/NETFT = 0.5(5T8/Ol/FT cotD Ol[ RATE
mr/h,
lot
I
m./hn = $g
/
rI 7 5 7
r6
I
mr/hn = 151
I WOR=O 2,/\
rt
Pt
a,
mrlhn = l5QO;
(n
t.a
E t.2 trl
ffit
J
t.o
o
o.t z
lt
E 0.6
lt
e (,,
-o loo
150
300 250 200 m,t;/h - M LB STEAM/FIOF GROSSINTERVAL
50
Figure 6.5 Theoretical Prediction of Incremental Oil-Steam Ratio versus SteamInjected(from Bobergand Lantz 1966)
the effect of steam stimulation can be larger with very viscous oils. Figure 6.6 showsthe predictedeffect for a particular set of conditions. o Large sandthickness.This improvesthe OSR becauseof the reducedfraction of the injectedheatwhich is lost. 4. Back-pressuring the well during the earlypart of the productioncyclecan be beneficialby reducingheatedzonecoolingcausedby the flashingof water. Bobergand Lantz'smethodhasbeenextendedand coupledwith calculations for gasJifting wells using the Orkiszewskicorrelationsfor calculatingthe twophasepressuredrop in a vertical pipe (Boberg,Penberthy,and Hagedorn 1973).
SCALINGOF THERMALMODELS Physicallaboratorymodelsare usuallyscaledto the field situationby employingdimensionalanalysis.The most commonschemeemployedfor doing this is to make the physicalmodelgeometricallysimilar to the field situationand to usethe same fluids in the model,i.e., oil, waterand steam.Scalingis usuallycarriedout by makine the Fourier number
z 0.4 I Figrrt andLr
equal for the I gree of heat pc the time scah will be smaller
or if a.oa.i = o
whereR is the Thus. fm t h in the mod The othe the sameratio I i.e.,
,o=# 248
CyclicSteamStimulation
Chap.6
Scalingof Tfrern
o
t.8
!o !o
ro
t.6
I
o
1 .4
4,
E 1.2 ul
(n
t.o
6 0.8
5 f,l
z rlj
HI
il
€ w oc
0.6
z
0.4 L 40
fif
Fl
5
t",
250 300 TERVAI.
t00
I
t000
I
- cP ortvtscostTY
Ratio versus
h very viscous oils. set of conditions. r of the reducedfracduction cycle can be e flashingof water. rledwith calculations calculatingthe twod Hagedorn1973).
Figure 6.6 Effect of Viscosity on Incrementaloil-Steam Ratio (from Bobers a n dL a n t z I 9 6 6 )
equalfor the model and the field at corresponding times.This meansthat the degreeof heatpenetrationby conductionwill be the samefor each.It alsomeansthat the time scalewill be shortenedbecausethe correspondinglengthsin the model will be smaller. lmodet a.oo.r _ /Lroa.r\2 =
t*"
"r"r
\t*"
/
of if a-o6"1 = @fierd,
+*=(L,"*,)'_n, Iri.ro \ lri"ro / tion by employingdidoing this is to make and to usethe same y'carriedout by mak-
whereR is the geometricscalingfactor. Thus, for example,if 1 cm in the modelequals1 m in the field, R : 0.01and t h in the modelwill be equalto 104h : 1.14y in the field. The other criterionusedis to makethe pressuregradientsdue to oil flow bear the sameratio to the potentialgradientdue to gravity in the modeland in the field; i.e.,
=(#fr),,,,, (m)^.,,,
itimulation
Chap.6
Scalingof ThermalModels
249
The velocityV in eachcaseis proportionalto Llt.If the samefluids are usedin the model as in the field, then Ap and lr.owill be the samein each,so
=(f),,",, (f)..,",
and k m o c e_t kr,",o
t Rl,,",o lmodel R
I
Becauseof the need to shortenthe time scaleby the factor R2 in the model,it is necessaryto increasethe permeabilityof the modelby a factor of llR in order to maintain the viscousdrag forcesproportionalto the gravity forces.This scaling procedurewas describedby Pujol and Boberg(1972). More elaboratescalingprocedureswhich allow modelsto be operatedat pressuresmuch lower than thosein the reservoirare discussedby Stegemeier, Laumbach, and Volek (1980).The approachof operatingscaledphysicalmodelsunder low pressureconditionsusing oils different from those in the reservoirand with steamof a differentquality hasbeenusedby Shelland othersfor the physicalmodel simulationof oil recoveryprocesses usingsteam. NIKO AND TROOST'SCYCLICSTEAM STIMULATIONMODELEXPERIMENTS Niko and Troost (197I) carried out an interestingseriesof low-pressure, scaledmodel studiesof the steamstimulationprocess.Their physicalmodel represented the near-wellregionof a reservoirin which therewas adequatecold-oilmobility to providedrive. In sucha model,it is necessary to representthe ability of the reservoir beyondthe model to supplyand to receivecold oil during the productionand stimulationcycles. Niko and Troostovercamethis problemby usinga seriesof resistanceand capacitortubesconnectedto the end of the sandpack.This arrangementis shownin Figure 6.7. The seriesof tubesand capillariesprovideda volumeinto which liquid from the sandpackcould be squeezed. The conditionswere arrangedso that the heat remainedwithin the sandpack. A numberof processvariablestudieswere carriedout. The followingconclusionsare expressed in termsof the full-scalefield that wasmodeled.The field data which were represented were for a typical VenezuelanBolivar coastfield.
Figrrt r Troog I
Soak time
Soaktiru that hot-oil sro future lifting c
r977). Differential p
The prod the resen'oirp Oil viscosity
The prod stimulationto I larger proporti Reservoirthil
Thickerk did not penetr reservoir,the s and per unit ol
Effect of ProcessVariables Injection rate
TABLE 6.1 Effed
A steam-injectionrate in the rangeof 19 to 60 t/d into a 9-m layer of reservoir had little effect on subsequent performancefor a given total quantity of injected steam.
250
CyclicSteamStimulation
Chap,6
Viscositl r
Productrrr
Niko and Troost'
fluids are usedin the ;h. so
ELEVATION
R: in the model,it is tor of L/R in order to i' forces.This scaling o be operatedat presb1'Stegemeier, Laumrh1'sical modelsunder he reservoirand with for the physicalmodel
lXPERIMENTS low-pressure, scaled:al model represented te cold-oilmobility to re ability of the reserrg the productionand
-l
F
Figure 6,7 Niko and Troost's Steam Stimulation Apparatus (after Niko and Troost 1971)
$(
H bl
Soak time
F
Soaktime wasnot a significantvariablein the rangeof 1 to 160d. This means that hot-oil storagewithin the reservoircan be looked upon as a cushionto meet future lifting demands.This has also been found in field experience(Borregales
r977). Differential pressure The production rate was found to be proportional to the difference between the reservoirpressureand the well pressure. Oil viscosity
s of resistance and ca'angementis shownin ume into which liquid arrangedso that the
The productivityindex improvement(the ratio of the productivityindex after stimulationto that before)was greaterfor more viscousoils becauseheatinghad a largerproportionaleffect on their viscosity(Table6.1).
The followingconcluodeled.The field data rr coastfield.
Thicker layersdid not respondaswell asmight be expectedbecausethe steam did not penetrateto the bottom.For a fixed injectionof steamper unit thicknessof reservoir,the steamwas found to penetratefarther horizontallyfor thicker layers and per unit of original oil in place.For a 980-cpoil, a 1133-tsteamslug injected
Reservoirthickness
TABLE 6.1 Effect of InitialOil Viscosity on ProductivityRatio
r 9-m layerof reservoir al quantity of injected
Stimulation
Chap.6
Viscosityin centipoise Productivity ratio
980 6
4000 IJ
Niko and Troost's CyclicSteam StimulationModel Experiments
8000 20
25',l
I {
into a 9-m layergavean increasedproductivityratio of 4.5; three times this quantity of steaminjectedinto a27-m layer gavea ratio of 3.8.
4
Steam slug size
-9 @
:3
The effect of steamslug size was found to be rather complex.A given quantity of steaminjected as a number of small treatmentsrather than as fewer larger treatments(see Figures 6.8 and 6.9) gave a higher initial oil-to-steamratio (Figure6.10)and higher cumulativeproductioninitially (Figure6.11).
E
a o o
z2 o
30
6
=1
E f
Steam-soak experiment
!,
e)
o
Steam-slug size: 3400tons Cyclelength:1230days
E
20 at
0
o E tr o
F€r
Ero :
g a),u
tt
o o-
E
c o o
0
1000 Figure 6.8
2000 Time in days
f !,
3000
o CL
- 10,(n o
Large Steam-Slug Size (after Niko and Troost 1971)
o
30
G f
E
Steam-soak experiment
!t G)
f
o
Steam-slug size:1133tons Cyclelength:625days
E
20 ot tg G
o r!
tr o
E 10 I
After a 1-e passedthat frou steamratios apg
!t
o o. 0
Cycle length
1000
2000 Time in days
3000
The effect of c1c eachcycle.It *'as earlierin eachcr ducedthe cumu
Figure 6.9 SmallerSteam-Slugs (after Niko and Troost 1971)
252
CyclicSteamStimulation
Chap.6
SteamStimulatio
three times this quan-
4 "9 (6 -o
rmplex.A given quanrr than as fewer larger :ial oil-to-steamratio ure 6.11).
E
(E
o o
E2
o .: g =1
---------,I
E 5
)eriment I I
l*3',t,=l I
6800 tons/cycle
o 0
1000
2000 Time in days
3000
Figure 6.10 Cumulative Oil-SteamRatio (after Niko and Troost 1971)
oa 20.000 E i o
l
--l
1133 tons/cycle 3400 tons/cycle
(t :t tt
ir.r*ronrt';%;19,'n
o CL
- 10,000 o o .:
rost1971)
_,
)€riment
|
1
tl 1133tons | @5 days |
\d
(E
E E 5
|
o
| |
1000
Il
2(X)o Time in days
3000
Figure 6.11 CumulativeProduction(after Niko and Troost 1971)
After a year or so the cumulative production from the large treatment surpassedthat from the smallertreatments(Figure 6.11)and the cumulativeoil-tosteamratios approachedthe samelevel (Figure 6.10). Cycle length The effect of cyclelength was also studiedfor a fixed injection quantity of steamto eachcycle.It was found that decreasingthe cyclelength (i.e., cutting off production earlier in each cycle)increasedthe cumulative oil production (Figure 6.12)but reduced the cumulative oil to steamratio (Figure 6.13).
ost 1971) Stimulation
0
Chap,6 ,
Steam StimulationProductionMechanism
STEAM STIMULATIONPRODUCTIONMECHANISM
6
In the Boberg-Lantzanalysisof the steamstimulationprocessand also in the experimentsof Niko and Troost discussedin the previoussection,the production mechanismfor the steam-stimulated well was assumedto be basicallythe sameas that for cold production.A reservoirpressurepushedthe oil to the well; the effect of the steamwas to make the oil flow more easilyby heatingthe reservoiradjacent to the well bore. The pressurethat moved the oil was the reservoirpressureexistingbefore the operationstarted.In the exampleof the Quirequirefield usedby Bobergand Lantz as a field example,this view of the mechanismis a reasonable one. In this casethe cold-flow rate was already135B/d, and this was increasedto 350 B/d by steaming. Factorsignored in the Boberg-Lantzmethod include the following: 1. The movementof the oil from around the well by displacement with steam during the injectioncycleand the refilling of the steam-saturated regionduring the productionare ignored.The Boberg-Lantztheory assumesthat the steam heats the near-well bore region but does not move oil away from the well bore.This is inconsistent with the ideasdescribedin the previouschapter. During the productioncycle,the oil mustfirst build an oil bank as it flows to the productionwell. Also as the pressurearoundthe well bore is decreased during the onsetof production,there will be vaporizationof water and the generationof steam.Eventually,however,the steamwill be displacedfrom the systemand liquids will flow
20,000 c,
E E
o o J
t,
o 010,000 o o
"z (E E
c =
Sizeof steamslug: 1133tons/cycle
o
0
1000
2000 Time in days
Cyclic Steam Stimulation
6
E
t4 6
o o
Ez : E 5
o 0
o
Figrn I and Tm
2. The rheq falling.ra cool fluid in the cfli conducti< partialh.I coolingwr considere den. This tially'ar rl heatedsq losses.cal the adjre heat loss h 3. As Boberg of oil rl ithi ration.Th in this ma men)is so evenif tha even ttK}q becauseit is produca
This las pt fornia fields.thc thanthatwhich well bore radius
3000
Figure 6.12 Effect of Cycle Length on Cumulative Oil Production(after Niko and Troost 1971)
254
-9
Chap.6
SteamStimulatb
6 , and also in the ex:ion, the production rasicallythe sameas r the well; the effect he reservoiradjacent ;sureexistingbefore usedby Bobergand sonableone. In this reasedto 350 B/d by
lacementwith steam :aturatedregiondur)rv assumesthat the ;e oil away from the the previouschapter. ril bank as it flows to e is decreased during nd the generationof r the systemand liq-
..-4
..-Go-) 'l, t t
I
I rnmary | rduction I
II
tons/cycle
I I
I
//
E
E4
,r'\
-.
| l, l. Ir-/l-
-1
..t -rt
I t l.
Cyclelength InOayS 1l7o,------?'-
o o o
E2 J
E J
o
Sizeof steam-slug: 1133tonspercycle
0
1000
2000 Time in days
3000
i{
ti ll|
lt
Figure 6,13 Effectof CycleLength onCumulative Oil-Steam Ratio(afterNiko andTroost1971)
|i fl
2. The theory assumes that the near-wellbore regionremainsat a uniform, but falling, temperature.In practice,muchof the coolingcomesfrom the flow of cool fluids into the perimeter,and a temperaturegradientwill be established in the cylindricalregion.The heatedcylinderis assumedto cool by thermal conduction.In the radial direction, this conductionwill be offset, at least partially, by the flowing fluids carrying heat back by convection.The radial coolingwill be lessthan estimated.The other mechanismof cooling that is consideredis the verticalconductionof heatto the overburdenand underburden. This estimationassumesthat the overburdenand underburdenare initially at the reservoirtemperature.In practicethey will have alreadybeen heatedsomewhatduring the spreadingof the heat chamber,and the heat losses,calculatedfrom the Marx-Langenheimformula,are alreadypresentin the adjacentreservoirboundaries.This, too, will tend to make the estimated heat losshigh. 3. As BobergandLantz point out, the methoddoesnot allow for any depletion of oil within the heatedzone-i.e., replacement of oil saturationby steamsaturation. They recognizethat in many casesthe major part of the oil is produced in this manner.Thesecasesare thosein which the cold oil (or usuallybitumen)is soviscousthat it cannotflow at a practicalrate to the heatedboundry evenif that boundaryis very largein radius.Thesecasesare alsothosewhere, eventhough the reservoiris thick, there is a relativelylow oil-to-steamratio becauseit is necessary to heat the entire reservoirvolumefrom which the oil is produced. This lastpoint hasbeendiscussed by Burns(1969)who pointsout that in California fields, the increasein oil rate found in steamstimulation is often much larger than that which would be expectedfrom the conceptof an increasein the effective well bore radius.
3000 ;tion (afterNiko
Stimulation
/
0
following:
@ -tazc
o o
Chap. 6
Steam StimulationProductionMechanism
255
i(
rl
I
I
Assumingsteady-state conditionsand neglectingany contributionof skin factor, the ratio of the productionrate for a well surroundedby a heatedregionof radiusRl, to that for an unheatedwell shouldbe given by equation6.11(compare with equation6.5): R"
F,, Qn Q"
*'" RR n , F,, R. rn + R. *t" R,
(6.11)
If the ratio of viscositiesis very large,then this equationmay be reducedto equation 6.12;i.e., the effectivewell bore radiusis increasedby heatingfrom R, to Rr (comparewith equation6.6): qo_ i
!
l
Q'
tn&
R*
(6.72)
t., -- &
Rr,
As Burns points out, for reasonable valuesof R7,,the productionratio from equation 6.12 is limited to relatively low values.For example,if R, : 0.25 ft ind R" : 1000ft, the followingvaluesfor the productionratio may be calculated: Heatedzone radius,feet: 50 Productionratio: 2.8
100 ' 3.6
200 5.2
However,asmaybe seenfrom Table6.2 (takenfrom Burns'paper),the ratiosfound in the field are usuallymuchlarger;the averagevalueof qnfq.in this tableis r2.g or 9.0 if the extremelyhigh value for the third row of data is left out. Although large skin factorsand/orreductionsin the value of the skin factor could causetheoreticalincreasesin the productionratio that are as largeas those shown in Table 6.2, this is not consistentwith the valuesfound for the oil-steam ratio. When the improvementin productionrate ariseslargelyfrom its effect upon the skin factor,then it would be expectedthat a relativelysmall amountof steam would be sufficient,i.e., that there would be a relativelyhigh oil-steamratio. In Table4.7 it was shownthat for generalreservoirheatingto be achieved,steam-tooil ratios of at least0.5 to 2 would be required.Thesevaluesare for production without heatloss.If allowanceis madefor lossesand for incompletedisplacement, then considerablymore-probably severaltimes more-steam would be required. Assumingthat at leasttwice asmuchsteamwould be requiredthen the SORwould be expectedto be at least1 to 4 (i.e. oSR would be no more than 0.25 to 1) for generalreservoirheating.[n Table6.2, only the first three or possiblyfour of the projects shown display oil-to-steamratios sufficiently high for skin and nearwellborestimulationto be the main causeof the improvedproductionrate. In the other cases,the quantityof steamthat wasrequiredwould be expectedto be sufficient for there to havebeenextensiveheatineof the reservoirwell bevondthe well bore zone.
256
Cyclic Steam Stimulation
Chap.6
:ributionof skin fac, a heatedregionof ration6.11(compare
i-N:UF
O.OOi66F O@hNSf
F YFAE .:P-P
r;6i
= UR - ., 'Ee
v ? 9 9Nn$ \. ancno n€ on€no
q
0.o9
(6.11)
^i -idddddd
\ociN*oooooo
a
I a
=;(=.=;===x:
--6;l'i<;.b5il;
-
be reduced to equarating from R, to Rr
O'O-O\***6€N
I Xr >f.x
na€nnh€t+$\o
E
"A
(6.r2) o
.oF
ion ratio from equaif R" : 0.25 ft and v be calculated:
lm 5 .2
N$O
r
nO+OhOOTOFss+€€o.Nr$€
(h
235
>er),the ratiosfound n this tableis 12.8or I out. ue of the skin factor are as large as those rnd for the oil-steam from its effect upon rall amountof steam h oil-steamratio. In : achieved,steam-tos are for production mpletedisplacement, r would be required. then the SORwould e than 0.25 to 1) for possiblyfour of the for skin and nearoductionrate. In the expectedto be suffi*ell beyondthe well
;timulation
>d
Chap.6
e.
o'l o(!
ooc'tooroono SNNnNO$nr€ NNN*NN
NOi
NN*::6i
:$F-
\oo i+r-sai
:i o
€\OS-€nnn€N
QU)
co='= <.= 5 E F - ; u iov ; c 4 5 D b q t
E
c
r
!
P
=ssFgriE'gE t
::q r - -5 r .
-:ooo
==i=-
!_q5o5-""S8 qPP 5
>=
6b >, >F
€t r d :s:ESieo ci€-E66=-n i,5E=gE=5;f
E3 .
7A >=
#8 257
INJECT STEAM STEAI\4 ZONE
COLDZONE
2nd CYCLE
1st CYCLE
r
olL
T- .. repro
Nth CYCLE
Figure 6,14 Gravity DrainageEffect (after Doscher1966)
The Boberg-Lantzexplanationdoesnot allow for the displacement of oil from the steam-heated regionby the effectof an expanding,overridingsteamzonecombined with gravity drainageto the well bore.2This mechanismwas describedby Doscherin 1966(seeFigure 6.14). This mechanismis basicallydifferentfrom that involvedin the cold flow process.[t can, particularlywith thick reservoirscontainingvery viscousoils, become the dominantproductionmechanism,particularlyin the latercycles.In this mechanism, the heatedregion around the well bore is not just a conduit for the transportation of the heated oil but, as it becomesdepleted,is the source of the producedoil. For this mechanismto be dominant,it is necessary for the cold, in situ viscosity of the oil to be high enoughto contain the injectedsteamin the vicinity of the well and thus to allow the steamchamberto be an expandablesourceof vapor to replacethe oil and condensate asthey drain. The compression and expansionof the steamwithin this chamberprovidesthe cushionto accommodatethe changesin liquid volumethat are requiredduring the steamingand productioncycles.In the BobergandLantz modeland in Niko and Troost'sexperimentswith mobileoil, it is the movementof the fluid in the cold reservoirthat providesthis flexibility. Gravity drainagecan occur only if there are two fluids of differentdensities: in this caseheavyoil and water (which havealmostthe samedensities)and lighter steam. 2Evenif the condensatefront is assumedto remain vertical, the volume occupiedby the insteam is not accountedfor in the Boberg-Lantztheory. During injection,steamis expectedto iected sweepoil away from the well bore, as describedin the previouschapter.This steam-drivenoil is pushedthrough the condensationfront and into the oil bank beyond.During the productioncycle, this heatedoil must flow backward toward the well. The steamwill either flow to the production well and be producedor rise abovethe oil, forming an overridingchamber.As the oil flows through the hot rock matrix, it becomesheatedand highly mobile.
258
CyclicSteamStimulation
Chap.'6
The srca watertendlo ductedinto tt Produti ing steamchr becomesnerc in the depleic by evaporair denseat the b continuesto g steamratioFor thc 1 alsothat it h SanArdo f-rl (25 B/d cold tr it containslO after steamir Lennqt portant in Ecz nia, includin differencein I tional envirm the reservoir voir layersin (g themselves
SIMPLIFIEDANALYS RESERVOIRCOOL
Insightinto th lowing simpli usedto obtain Supposc the productic will assumeth production ral then the ratec tiplied by the r to allow for tt moved from tl will includea
SimplifiedArd
rrti DrainageEffect '66)
rcementof oil from rgsteamzonecomr *'as describedby the cold flow proscousoils, become :les.In this mechaduit for the transthe source of the :old,in situviscosthe vicinityof the sourceof vapor to d expansionof the ate the changesin :Iion cycles.In the 'ith mobileoil, it is risflexibility. differentdensities: nsities)and lighter
ne occupiedby the in1. steamls expectedto :is steam-driven oil is r the productioncycle, lo*'to the production s the oil flows through
nulation
Chap.'b
The steamtendsto rise and move awayfrom the well, and the heavieroil and water tend to fall to the well. As the liquid drains away,heat continuesto be conducted into the cooler reservoiradjacentto and below the growing steamchamber. Productionis accompaniedby a falling pressureand temperaturein the growing steamchamber,and, as the whole systemcools,anothersteaminjectioncycle becomesnecessary. During the period of falling pressure,sensibleheatin the rocks in the depletedsteam-chamber is transferredto the residualwater and is removed by evaporationof the water to steam.At the sametime, steamcontinuesto condenseat the boundariesof the chamber.With successive cycles,the steamchamber continuesto grow, and the vertical heatlossesgrow larger.This reducesthe oil-tosteamratio. For the processto be effective,it is desirablethat the reservoirbe thick and also that it be continuous.For examplemuch better resultswere obtainedin the SanArdo field in California,which contains220 ft of moreor lesscontinuoussand (25 Bld cold to 360Bld after steaming)than in the Coalingafield, which, although it contains107ft of pay,is split into layerslessthan 30 ft thick (3 Bld cold to 528/d after steaming);seeTable6.2. Lennon (1976)has reviewedthe geologicalfactorswhich havebeenfound important in steam-soak projectsin the west sideof the SanJoaquinBasinin California, includingthe Coalingaand Midway-Sunset fields.He showsthat much of the differencein the performanceof projectsin this areacan be relatedto the depositional environment(particularlythe presenceof marineshaleswhich tend to divide the reservoir),to the reservoirstructureand type of trap (e.g.the dip of the reservoir layersin the Midway-Sunsetfield), and to the nature of the reservoirrocks themselves(porosityand permeability).
SIMPLIFIEDANALYSIS OF PRODUCTIONRATE DECLINEDURING RESERVOIRCOOLING Insightinto the natureof the cyclicsteamingprocesscan be obtainedfrom the following simplifiedanalysisof the productionrate decline.The methodcan alsobe usedto obtain descriptiveparametersfor the comparisonof projects. Supposethat a quantityof heat,Q;, is injectedrapidlyinto a reservoir.During the productioncycle,heatis removedcontinuallyfrom this stored"heatbank." We will assumethat the rate of withdrawalof heatfrom the bank is proportionalto the productionrate of the oil. tf the heat in the producedoil were the only heat loss, then the rate of losswould be given by the heat capacityof the product streammultiplied by the differencebetweenits temperatureand that of the reservoir.In order to allow for the other sourcesof loss,particularlythe heat in the water that is removed from the reservoir and also the heat loss to the reservoir surroundings,we will includea facror,11,and write. d Q = -nqpC(T T,) dt
SimplifiedAnalysis of ProductionRate DeclineDuring ReservoirCooling
(6.13)
259
r, ti
il 11 rl fa
ll
d rt
,a
wherep r n pC T TR
is the heat storedin the bank is the time is a dimensionlessfactor is the volumetricheat capacityof the oil is the temperatureof the heatbank is the reservoir temperature
This mal bc
As heatis withdrawnfrom the initial bank, the temperatureof the bank declines.If it is assumedthat the massand compositionof the material that constitutesthe heat bank remainsconstantor approximatelyconstantand that it has a constant heat capacity,then Q_T-T^_r* Q, Ts-T* whereTx is the dimensionless temperatureof the bank. This equationmay be differentiatedto give
whereC is r Elimin
(6.14)
dQ _ o '' d T * dt dt
(6.15)
Combiningequations6.13and 6.15leadsto
-,1qpC(Ts-T^)T*
O,T=
(6.16)
As the temperatureof the heatbank falls, the productionrate 4 will decrease with time becauseof an increasein the viscosityof the producedoil. For simplicity,we will assumethat the rate q is proportionalto T*', wheres is constant.If, for example, we assumedthat q was proportionalto the reciprocalof the oil viscosity,then s would be equalto the parameterm for a viscosityequationof the form 11
-
:-
lL
(6.r7)
:T+m
lt'
This type of equationis used in Chapter7 in the material on gravity drainage, where it is shown that the parameterm hasvaluesof about 3 for typical heavy oils in thermal recoverysituations.If, as happensfor steam-assisted gravity drainageto horizontal wells, the rate is proportional to the squareroot of the reciprocal viscosity,then s might be expectedto havea valueof aboutml2. ln general,it would be reasonable to expectthat s shouldbe of the order of m/2 to m.The production rate is given as a function of the reducedtemperatureby the equation I
Q _ 7 * ,,"
r
(6.19)
Qi
In this equation,qi is the oil productionrate extrapolatedto zerotime.3Eliminating q from 6.18and 6.16leadsto 3Inpractical situations,the productionrate normallygrowswith time during the initial stages of the productioncycle.The reasonfor this is the needto purge steamfrom the steamchamberand also,frequently,the throttling of the productionwell to control excessivesteamvelocities.The initial rate usedin equation6.18is the initial rate found by extrapolatingthe productioncurve after the initial period back to the start.
260
Cyclic Steam Stimulation
This a days/barrel ) the straiehtI ory indicate to be greate factor 4. It r vided bv thc quantitieso{ the oil liesd clinewouldI 4 would be r The fractiqr have a stror that the pro< larly in the e A facto not uniform the heatban radial flor ir willxot fall r Althoq contain corq publishedca draw reasor deviationsfn of Chapter7 Burns( of steaminjc fornia.The c tDeclinc
( 1 9 6 9 )m e n t r o n t
s t e a ms t i m u l a t i ical curves \er_
SimplifiedAn Chap.6
dr* dt
- _lQiPC(Ts
- Tn).*,*,
(6.1e)
Q't
This may be integratedby separatingthe variablesto give -L-nq'PC(T:-Tilst Z*' Q, rebank declines.If rat constitutesthe t it has a constant
q
(6.14)
(6.1s)
(6.16) *'ill decrease with For simplicity,we ;tant. If, for examoil viscosity,then the form
(6.r7) r gravity drainage, ' typical heavyoils
.
(6.18)
rime.3Eliminating uring the initial stages he steamchamberand am velocities.The iniluction curve after the
nulation
Chap.6
(6.20)
1
(6.2r)
whereC is an integrationconstant. Eliminating Z* from 6.18and 6.20 leadsto
1
gravitydrainageto the reciprocalvisn general,it would z. The production uation
*r,
t'
\PC(Ts - 7^)s -t+ Q,
Qi
This equationindicatesthat a plot of reciprocaloil productionrate (e.g.,in days/barrel)shouldgive a straightline whenit is plottedagainsttime.4The slopeof the straightline is a measureof the rate at which the productiondeclines.The theory indicatesthat this declineis expectedto be lessfor largeheatinjectionS, p;, and to be greaterfor higher steamtemperaturesand particularly for higher valuesof the factor 4. It will be recalledthat this factor is equal to the total heatloss rate divided by the rate of sensibleheat removalin the oil. Thus, for example,if large quantitiesof water were producedwith the oil-as, for example,might happenif the oil lies abovea water leg-then 4 would be higherand the productionrate decline would be greater.Similarly,in thin reservoirswith higherverticalheatlosses, 4 would be expectedto be greater,and the rate of declinewould also be greater. The fractionof the condensate from the injectedsteamthat returnswith the oil can have a strongimpact (see,for example,Martin 1967).rn many projects,it is found that the producedwater is muchlessin quantity than the injectedsteam-particularly in the early cyclesand in mobile oil reservoirs. A factor not consideredhere is that the temperaturewithin the heat bank is not uniform. There is a tendencyfor the near-well bore regionto remain hotter as the heat bank cssls. Sincethe flow restrictionis greater,becauseof the nature of radial flcwr in the near-well bore regionand also in the skin, the productionrate willxot fall quite as fast as expected;i.e., it is possiblefor 4 to be lessthan 1. Although the precedinganalysisis crude and seemsto, perhapsfortunately, contain compensatingerrors, it does representthe type of decline rate found in publishedcases,and it is also possibleto comparevaluesof the factor, 4, and to draw reasonableconclusions.In the following, it is assumedthat s : m, and any deviationsfrom this are includedin the factor q; m is obtainedusingthe methods of Chapter7. Burns (1969)givesdata for the declinein the oil-productionrate for two cycles of steaminjectionin the PotterSandin the Midway Sunsetfield in southernCalifornia. The data are shownis Figure 6.15. aDecline curvesof this type are often referred to as harmonicdecline curves.Sebaand Perry (1969)mentionthe useof suchcurvesfor the successfulcorrelationof productionrate data for cyclic steamstimulationin the YorbaLinda field. They alsoindicatethat harmoniccurvesfit their theoretical curvesvery closely-maximum deviation5Voand mostly within 17o.
SimplifiedAnalysisof ProductionRateDeclineDuringReservoirCooling
261
r{ ii q rt l{
fa
tF
rl ,i
d/B
WellMccuflochM&M No.7completed4-921 l.P.25Bld 205 ft of 410 ft zone open to production E
t o o
0.03
6
E
6
E tr o
E 5
@
@
o
50
'
r 30
E 6
@
It
o
o. 6
o loTi 1965
J
J
A
S
O
N
1966 --------------l
Dl
Figure 6.15 Typical Responseto Cyclic SteamInjection in the Midway Sunset Field (after Burns 1969)
Thesedata are replottedas the reciprocalof the oil-productionrate against time in Figure 6.16;the data are represented well by straightlines. The slopesof thesestraightlinescan be usedto calculatevaluesof the apparent lossfactor 4 (Table6.3).
Crcle Sur
Steam pressun
Steam temp
TABLE 6.3 DataforWellM & M No.7
Steam injectrc pC BtulB 'F
CycleNumber Steampressure,psig Steamtemperature,"F Parameterm : s Steaminjection,B Heat per barrel of steamassuming 70% quality pC Btu/B "F Slopeof graph,B 1 Factor 4
TABLE6..r O
320 428 2.5 6,156 314,000
350 436 2.5 10,040 315,000
1"15 0.00023 3.1
Slope of graph. Factor 4 (Boberg and L
r75 0.000059 1.27
(Burns1969).
The factorsindicatethat there was considerably lesslossin the secondcycle than in the first one. Possiblymuch of the heatinjectedin the first cyclewas conserved,and this reducedthe lossin the second. Figure 6.17showsdata for the Quiriquire field studied by Boberg and Lantz plotted in the sameformat. Apart from the first points for each cycle that reflect the throttling of the well during the startup,thesedata also fall on straightlines. However,in this case,the secondcycle (T = 2.53) showeda more rapid, rather than a slower,declinein the productionwith time. Possiblythis reflectsthe declining reservoirpressure.Data are shownin Table6.4.
262
CyclicSteamStimulation
Chap.6
Iitrrt Quin
Simplified An
-l
dtB
II
0.(x}
1stCycle 2nd Cycle
I
0.02
I
0.01
--l
D a t a f o r W eM ll &MNo.7 MidwaySunsetField from Burns1969
J-,1 ) n Dl
100 idway Sunset
hrction rate against iles. valuesof the appar-
350 436 2.5 10,040 315,000 r75 0.000059 t.27
Figure 6.16 Reciprocal Production Rate for Cyclic Steam Stimulated Well in Midway SunsetField
200 Time in Days
TABLE 6.4 Data for CyclicStimulationin the OuiriquireFieldin Venezuela Cycle Number
770 516 2.4 5r,714 r75 0.0000187 1.8
Steampressure,psig Steamtemperature,"F Parameterrn = s Steaminjection,B pC Btu/B'F Slopeof graph,B-1 Factor 4
800 520 2.4 54,857 r75 0.000025 2.5
(Bobergand Lantz 1966)
d/B 2nd Cycle
0.01
1st Cycle o
in the secondcycle first cycle was cony Boberg andLantz ch cycle that reflect rll on straight lines. i more rapid, rather Dreflects the declin-
linrlation
Chap. 6
0.005 Datafor Quiriouire fromBoberg& LanE1966
400 200 300 500 Time In Days Figure 6.17 Reciprocal Production Rate for Cyclic Stimulation in QuiriquireFieldin Venezuela 0
100
SimplifiedAnalysis of ProductionRate DeclineDuring ReservoirCooling
the
263
dlB 0.02
o.01 Datalor Midway-Sunset AveragePotterSand fiom Burns1969
20
40 Timein Days
60
80
Figure 6.18 Reciprocal Production Rate for Cyclic Stimulation of Average Potter Sand
Data for other wells are shownin Figures6.18,6.19 and 6.20. The datain Figure6.20 arefor a well that had a poor cementjob and in which it wasthoughtthat steamwaslost to nonproductivehorizons.The lines are steeper than thosein Figure 6.15,which is for the samereservoir-presumablythe effective heat injectionQ; was lessin well M & M 5,A,becauseof the steamloss. Severalpapersdescribetheoreticalmethodsfor the analysisand predictionof steamstimulatedproductionin which the Bobergand Lantz approachis extended to includegravity drainage(Towsonand Boberg1967;Sebaand perry 1969;Kuo, Shain,and Phocas1970;and Jones1977). Each of thesestudiesassumesthe initial formation of a heatedzone that is analyzedusingthe Marx Langenheimapproach.Variousapproximationsare made concerningthe state of the region around the heatedzone (e.g., it is cold; it is heatedby conductionfrom the hot zonebut is at a uniform temperature;it is heated by radial conductionand the temperaturedistributionvariesaccordingly).
The raf and Lefkor-it of gravitl' dn The rtx zone rise-fro Doscher.As I terfacecalcu Figure6.21.1
2n
150 E
.9 -9100
dtB
J.
p =
0.06
II
50 0.04
0 0
San Ardo
20
264
40
60 80 Timein Days
100
120
140
Figure 6.19 Reciprocal Production Rate for Cyclic Steam Stimulation of Coalinsa and San Ardo Sands
CyclicSteamStimulation
Chap.6
Figlrt Phoca sThis rheo perature gradicn gradient in viscc d i s c u s s e di n C h e
SimplifiedArd
dlB
0.04
0.02
;iprocal Production itimulation of Average
t.20. :nt job and in which 'he lines are steeper esumablythe effece steamloss. ,isand predictionof )proachis extended td Perry 1969;Kuo, heatedzone that is rimationsare made :.g., it is cold; it is )erature;it is heated cordingly).
50 Timein Days
100
Figure 6.20 ReciprocalProduction Rate for Cyclic SteamStimulationof a Midway SunsetWell with Poor Cementing
The rate of drainageof the oil is calculatedusing the methodsof Matthews and Lefkovits (1956),who developedan analyticalmethodfor predictingthe effect of gravity drainagefor conventionalisothermalreservoirs.s The theories predict that the interface between the liquids and the steam zone risg-from a level at the bottom of the well in the manner envisagedby Doscher.As the liquid is drainedaway,the interfacefalls. The positionsof the interface calculatedfor a specific exampleby Kuo, Shain, and Phocasare shown in Figure 6.21.This also showsthe calculatedtemperaturedistributions. 200
200 I I I I I
a a a I I I a I
0'i
Wellspacing= 2112acres
50
100 Radius, ft
30 Parameter is timein y
150
:rprocal Production iteam Stimulation of n Ardo Sands
Well (after Kuo, Shain, and Figure 6.21 ConditionsAround Steam-Stimulated Phocas1970) tThis theory assumes that the viscosityof the oil is uniform. In practice,there is a sharp temperaturegradientin the oil layer adjacentto a growing steamchamber,and there is a corresponding gradientin viscosity.It is largelythe oil adjacentto the chamberthat is flowing. This mechanismis discussedin Chapter7.
mulation
SimplifiedAnalysisof ProductionRate DeclineDuringReservoirCooling
Chap.6
265
THE PROBLEMOF THE FIRSTCYCLEIN THE CYCLICSTEAM STIMULATION OF TAR SANDS During one of the later cyclesin the productionof very viscousoils by steamstimulation, the steamflows into the low-pressuresteamchamberleft from the preceding cycle;as steaminjectioncontinues,the temperatureand pressureincrease.Steam condenses both within the chamberand at its perimeter.More oil is heated,and this drainsto the lower part of the chambertogetherwith the steamcondensate. In the first cycle the problem is different becausethere is no preformed lowpressuresteamchamberthat is ableto acceptthe steam.If the in situ oil is reasonably mobile, a chambercan be formed by pushingoil away from the well. Most of the outwardlydisplacedoil, togetherwith someof the condensate, will be returned laterby the natural reservoirpressure.A similar resultcan be achievedif there is a high water-saturation layerin which thereis fluid mobility.Another similar circumstancemight occur with a layer of high gassaturation. If the in situ oil is practicallyimmobileand if the water saturationis too low for water to be mobile,as is often the casewith tar sands,then it is necessary, in the first cycle,for the injection pressureto be high enoughto disrupt the reservoir. The sandmustbe physicallymovedin order to make room for the steam.Someof the volume can come from the compressionof the reservoirmaterials,but most comesby lifting the surfaceof the ground and creatingnew void space.Sincethe volume of the injectedsteam(measuredas liquid) -s larger than that of the oil it produces,it is apparentthat the increasein liquid volume accommodated by the disruptionof the reservoirmustbe very substantial. For example,considerthe injectionof 50,000B of steaminto a reservoirwith a sandthicknessof 100ft. Injectionsof this order are commonlycarriedout in the cyclic steamstimulationof the Cold Lake reservoir.If this injectionresultedin a singlefracture having the height of the reservoirand a total length of 800 ft (400ft either sideof the well), then, if it wereof uniform width and containedthe condensatefrom the steam,it would needto be 3.5 ft wide. In practice,of course,it is very unlikely that the increasein reservoirwould be of the simpleshapesuchas this. Nevertheless it is apparentthat injectionsof this magnitudewill causesignificant changesto the reservoirmatrix. Whether this increaseoccurs through the creationof "cracks"or by a distributed increasein the pore volumeover considerable volumesis still obscure,althoughthe latter seemsmoreprobablein unconsolidated sandswhen one considers the largepore volumethat must be generated. In their original state,tar sandsare often-and perhapsalways-very closely packed (Dusseault1977).They are often describedas locked. By this it is meant that protuberances on individual sandgrainstend to fit into hollowsin their neighbors. This makes the sand much strongerthan would be expectedfor a noncementedmaterial.It is the locking of grainsthat is thoughtto explainthe strength of the near-verticaloil sand cliffs found where the tar sandsform outcrops along the bank of the AthabascaRiver. This is in distinctcontrastto the low ansleof reposefound for typical loosesands.
266
CyclicSteam Stimulation
Chap.6
When il r the separatod seemslikely d pore voluur- | within the rc! ing volurnc' As thct ume is creatcd is also neceie the heatedrcr mulationof q through opco I into the undi than simplyL tributed regir In the fl the sandis bo the actiond r steamis cmw into the tar sr In the rq conductioniil tumenwithin I sure beyond I steam-saturat loosensthe sar The whole m vancessteadil Thermalexparsil dlslodgingsanda fluidsto penetr*
sr +
Il 1'
Figurt 632 voir with Stc
The Problem d
'h/IULATION
s oils by steamstimuit from the preceding sure increase.Steam re oil is heated,and : steamcondensate. is no preformed low: in situ oil is reasonom the well. Most of nte, will be returned achievedif there is a othersimilar circumsaturationis too low en it is necessary, in disruptthe reservoir. r the steam.Someof ' materials,but most roid space.Sincethe lan that of the oil it :commodatedby the into a reservoirwith tly carriedout in the rjectionresultedin a ngth of 800ft (400ft rntainedthe condenr, of course,it is very : shapesuchas this. rill causesignificant tracks" or by a dis:s is still obscure,als whenone considers always-very closely . By this it is meant rllows in their neighexpectedfor a nonI explainthe strength form outcrops along r the low angleof re-
itimulation
Chap.6
When the tar sandsin Athabascaare mined and separated,it is found that the separatedsandoccupiesa volumethat is about25Vogreaterthan the original.It seemslikely that fracturing oil sandsin situ also createsan irreversibleincreasein pore volume. In any case,in the first cycle, it is the creation of additional volume within the reservoirby disruption from the entry of steamthat providesthe working volume. -As the steamentersthe reservoir, fracturing occurs and additional pore volume is created;this allows the accommodationof the condensatefrom the steam.It is also necessaryto accommodatethe volume of the steamthat is flowing through the heatedreservoiron its way to the regionwhere condensationoccurs.The accumulation of condensatemay be quite remote from the well. The condensateflows through open fracturesto fill the volume behind the fracture front as it encroaches into the undisturbed reservoir. This fracture front is probably distributed rather than simply being the edgeof an advancingcrack. One conceptof how such a distributed regionmight advanceinto the reservoiris shown inFigure 6.22. In the steam-saturatedregion, the pressureis abovethe fracture pressureand the sandis loose and free to move. Steamflows through the disturbed regionunder the action of a small pressuregradient.At a surface,the condensationsurface,the steamis convertedto water, and this liquid water flows through multiple fractures into the tar sandbeyond.As it flows, it coolsrapidly. ln the regionbeyond and closeto the condensationsurface,heat is carried by conductioninto the disturbedsandbetweenthe fractures.This heat causesthe bitumenwithin the poresto try to expand(seeButler 1986).The increasedpore pressure beyond the condensationsurface causesa backflow of fluid toward the steam-saturatedregion. This increaseof pressurebeyond the condensationsurface loosensthe sandparticles,and theyjoin the loosesandwithin the disturbedregion. The whole mechanismproceedsin a coupledfashion, and the disturbed region advancessteadily.There is a dilation of the sandmatrix; the porosityincreases, and Thermalexpansionof bitumenis dislodgingsandand allowing
AdvancingCondensation Surface
fluidsto oenetrate
+
Steam-saturated DisturbedRegion- loosesandheld againstfaceas in a filtercake
.
..,
\_ \
Condensate'filtrate"
\
flowingwithinfractures Limitof Bulk MatrixDisturbance advancingin front of condensation surtace Figtre 6.22 PossibleMechanismfor the Disruption and Fracturingof a Tar SandReservoir with Steam
The Problem of the First Cycle in the Cyclic Steam Stimulation of Tar Sands
267
overall the increasein pore volume is achievedby raising the surfaceof the ground way beyond the disturbed region. As the disturbance and fracturing continues, an increasinglylarge bank of disturbed, higher-porositysand is created.Later on, when the pore pressureis releasedduring the production cycle, this "fluffed-up" sand becomesCompressed by the weightof the overburdensinking upon it and the porositybecomesreduced,although not to its original level. During the reduction of porosity, there is a squeezing of the fluids back to the productionwell. As the fracture closes,the fluid pressureacts to move oil as well as the condensateto the well. However, much of the steam condensateis relatively remote from the well and is trapped. This trapping of the condensatebeyond the oil explains why water production is lessthan might be expectedduring the first production cycles. Although this mechanismis similar to that describedpreviouslyfor the steam stimulation of mobile heavy oils, there are important differences.With the mobile oils, the volume of the condensatefrom the steamwas accommodatedby the movement of oil awayfrom the well bore and by the invasionof the condensateinto the oil, probablyeither as fingersor stratified fingerlets.With essentiallyimmobile bitumen containedin tar sands,the accommodation is by the dilation of the tar sands as the fracturingstressis exceeded.In the first case,the flow of fluids toward the well bore during the productioncycleis driven by thr reservoirpressurearoundthe perimeterof the heatedregion.In the secondcase,muchof the driven force comes from the compactionof the matrix squeezingfluids toward the production well. In later cycles,as hasbeendescribedpreviously,the steamand its condensate are accommodatedby the compression of steamwithin the existingchamber,and gravity providesmuch of the drive. The similarity of the mechanismsis also seenby comparingthe production curvesfor cold Lake bitumen shown in Figure 6.23 to those found by Niko and Troost for mobile heavy oil in Figure 6.8. Figure 6.24 showsthe corresponding cumulativeoil and water productionfor the samecold Lake project.The water-to-oilratio in the producedsteamis only slightly larger than 1 after the first cycle; after four cyclesit is about 2. Denbina,Boberg,and Rotter (1987)have studiedthe productionof oil in the early cyclesof steamstimulationat Cold Lake using numericalsimulation.They find that the field data can be closely simulatedby incorporating a model for the responseof the reservoir sand to shear failure during steam injection.6This provides increasedpore volume during injection and allows a compactiondrive Ouiing production. The pore volume decreasesas the sand consolidatesduring the relaxation of the pore pressure.They also incorporate a relative permeability hysteresis into their model;this allowsthe penetratonof condensate into the dilatedreservoir but restrictsits back flow during the compactiondrive. In their paper,Denbina, uThereis no shearstresswithin a static fluid in which the compressivestressis equal in all directions.In a solid however,it is possibleand usualfor the compressivestressesto be different in different directions.If this is the case,there must also be accompanyingshearstress(see,for example,Holtz and Kovacs 1981).In many casesthis can lead to the failure ofthe solid in shear.
268
Cyclic Steam Stimulation
Chap.6
!
-1
.s €
C
C
I
rt =
o
rtr PrqE
Boberg, ard I voir drive fu tant. In the ct doesnot flot The nco performarrc t lem. It has br simulaton ca assumedto h proximatelyI Dietrich for o
Ir I
!ar' = o
o o a t
E t
(,
Iigut, ulatb
The ftoblern d
surfaceof the ground :asinglylarge bank of le pore pressureis re:comescompressedby , becomesreduced,alsity, there is a squeez-
300 It
o
s o 200 (E
E c
.9 oil as well as the con:e is relatively remote rte beyondthe oil exrring the first produceviouslyfor the steam rces.With the mobile nodatedby the movee condensate into the ntially immobilebituation of the tar sands ' of fluids toward the r pressurearoundthe re driven force comes re productionwell. In its condensate are acchamber,and gravity raring the production e found by Niko and water production for oducedsteamis only is about2. oductionof oil in the ical simulation.They rting a model for the injection.6This prorpactiondrive during rtesduring the relaxermeabilityhysteresis r the dilatedreservoir heir paper,Denbina, r s r v e s t r e s si s e q u a l i n a l l stressesto be different in shear stress (see. for exof the solid in shear.
itimulation
Chap,6
C'
E 100 I o o-
o 0
0
200
400 600 Timein days
8oo
q
Figure 6.23 oil-Production Rates from Esso'scold Lake Steam-stimulation Project.Data for "averagewell,, (after Denbina,Boberg,and Rotter l9g7)
{ n
Boberg, and Rotter conclude that formation compactionprovides the main reservoir drive during early cycles.In later cycles,gravity becomesincreasinglyimportant. In the early cycles,muchof the steamcondensate flows into the reseivoiibut doesnot flow backbecauseof the permeabilityhysteresis. The needto useunusualrelativepermeabilityrelationsto matchthe observed performanceof cyclic steamingprojectsby numericalsimulationis a commonproblem' It has been discussedby Dietrich (1981)who finds that conventionalthermal simulatorscan match the field performanceif the relative permeability for water is assumedto be extremelysmall.The value of k,nfor water saturatedsandwith approximately50Vomobilewater and 50Vomobileoil from the curve recommendedby Dietrich for cyclicsteamingis comparedto the corresponding value recommended 140 Datafor averagewell
I rzo L
f; 100 = -80 o
-
Field Model
5eo o
.2 40 (6
Ero f
oo o
200
400 600 Timein days
8oo
Figure 6.24 cumulative oil and water productionfrom Essot cold Lake Stimulation Project(after Denbina,Boberg,and Rotter l9g7)
The Problem of the First cycle in the cyclic Steam stimulation of rar sands
269
Fl q
il
r
LI fl t
I I
I
by Gomaa (seeFigure 4.32) for steamflooding,and to the range found in the conventionalwaterfloodingof sandcoresin the followine table: Cyclic stream,Dietrich (1981) Steamflooding,Gomma (1980) Conventionalwaterfloodins
0.001 0.004 0.02-0.1
CYCLIC STEAIITG This reserxir perature is l(l ture is abql bitumenin A cousthan Ad
The difficulty is that if conventionalcurves are used for the relative permeability of water, then the water production predicted by the model is far greater than that found in practice.Water doesnot flow back to the productionwell as fast in the field aswould be predictedby the simulator.Dietrich, like Denbina,Boberg, and Rotter,discusses the possibilityof therebeinga hysteresis in which watercould flow very easily into the formation but in which the relative permeabilityfor backward flow would be far less. A factor which could contribute to such hysteresisbut, which seemsto have beenignored,is that of the instabilityof the water-oilinterfaceduring injection.As hasbeen describedin Chapter5, the flowing streambeyondthe condensationinterface is largelywater but, becausethe viscosityof water is much lower than that of the oil, the water-oil interface is highly unstable and the water flows as fingers which can be describedasrivuletsthroughthe oil. For the segregated flow, the saturation required for movementof the water is only very slightly larger than the irreduciblewater saturationand the water becomesrapidly disperseddeep into the oil. It seemspossiblethat when the well pressureis lowered for the production cycle, the rivulets of water becomeunstableas the flow direction is reversedand they become broken by the oil into pockets.Then, as the oil proceedsto displacethese pockets of water back toward the well, the relative permeabilitiescorrespondto those for diffuse flow. It is suggestedthat the flow away from the well is characterized,becauseof the abundantsupplyof water and the instability of broad oil-water interfaces,by the segregated flow of smallswift waterrivulets;this disperses the intrudingwaterover considerabledistances.The flow back to the well is with more normal flow because it is now the oil which is displacingthe water. This processwould be expectedto be modified by the override of the steam chamber. In this circumstance,heated oil tends to be bypassedbelow the steam, and watercondensate will flow with the heatedoil with both tendingto be dragged forward by the pressuregradient.In this drag-layer,the temperatureis considerably above that of the reservoir and the ratio of oil viscosity to water viscosity will be lessthan it would be at reservoirtemperature(seeFigure 4.7). As a result the water saturationwithin this mobile layer will be substantiallyhigher and more water will be availableto flow backwardswhen the flow is reversed.Thus. someof the steam condensatecan be distributed far aheadof the advancingfront, while somewill remain with bypassedoil and will be much closerto the well. For cyclic steamingof bitumen with fracturing, the fractureswhich were able to carry the water away from the condensationinterface during steam injection, close,or at leastpartially close,during the production cycle.This effect may be expected to contribute substantiallyto the hysteresiseffects.
It is interestiq of reciprocalp The datr the oil-steamr showthe ham reasonable. Bott etsO it possibleto c
270
CyclicSteacil
Cyclic Steam Stimulation
Chap.6
A pnir
scribesthe rct 450ft thick,I wasset into o linear was scl As mayl duction l:rt6r tion pressurc and 4. It secc that in c1'ch describedpet tent with rlF i oil not being r this heat is co TABLE5.5 CF Cycle Steaminjectioo pressure B Production oil, B Water,B Oil B/SD avenlr OSR (from Bott 1967
te found in the con.001 .004 t-0.1 the relativepermemodel is far greater oductionwell as fast re Denbina,Boberg, n whichwatercould :rmeabilityfor backihich seemsto have duringinjection.As : condensation interh lower than that of ter flows as fingers eatedflow, the satulargerthan the irreed deepinto the oil. le production cycle, :versedand they beds to displacethese lities correspondto cterized,becauseof ter interfaces,by the intrudingwaterover rormalflow because i'errideof the steam :d below the steam, ndingto be dragged atureis considerably rterviscositywill be \s a resultthe water and morewaterwill r. someof the steam . while somewill rerreswhich were able ing steaminjection, ris effectmay be ex-
:imulation
Chap.6
CYCLICSTEAMINGOF VACCA TAR, OXNARD,CALIFORNIA This reservoircontainsa 5" API crudeoil at a depth of 1870ft. The reservoirtemperatureis 100"F.The extrapolatedviscosityof the crude oil at reservoirtemperature is about 1 million centipoise;this is approximatelythe sameas that of the bitumen in Athabasca.Although the Vaccatar is heavierand basicallymore viscousthan Athabascabitumen,the temperatureis higherin the Vaccareservoir. A projectto recoverthis tar hasbeendescribedby Bott (1967).His paperdescribesthe resultsof four cyclesof stimulationin well 702.The reservoirwasabout 450 ft thick, but the well was drilled into only the upper 2I7 ft of the pay. Casing wassetinto the upper 107ft of this hole,leaving110ft of pay openbelow.A slotted linear was set in the open hole and packedwith gravel. As may be seenfrom Table6.5, the projectwasvery promising,and high productionrateswereachievedwith excellentoil-to-steamratios.Very high steaminjection pressureswere requiredin the first two cyclescomparedto thosein cycles3 and 4. It seemslikely that fracturingof the reservoiroccurredin cyclesL and 2, but that in cycles 3 and 4, injection occurred into an existing steam chamber,as describedpreviously.The lower oil-steamratiosfound in cyclesI and2 are consistent with the idea of steambeinginjectedinto a fracturewith much of the heated oil not being availableduring the subsequent productioncycle.However,much of this heat is conservedand reducesthe requirementsin the subsequent cycles.
q
{
*l rd
B( i{
H
r
hf il{ tl
TABLE 6.5 Cvclic Stimulationof VaccaTar (Well 702) 5'API; /t = 217ft.; k = 5.5 D; Ip = 166'P Cycle Steaminjection pressure B Production oil, B Water, B Oil B/SD average OSR
r23
Total
1,600 22,839
1,750 14,756
1,200 7,500
1,050 r0,671
55,766
5,153 r,904 115
13,192 4,358
11,497
t3,125 9,181 "t5
42,967 21,018 99
0.23
t3r 0.89
5 575
107 1.53
1.23
0.77
(from Bott 1967).
It is interestingthat the productiondatafrom the Vaccaprojectplot asstraightlines of reciprocalproductionrate againsttime. This is shownin Figure 6.25. The datafall, in general,on straightlinesfor eachcycle,and the slopesreflect the oil-steamratio. It is interestingthat thesedata,for an initially immobileoil, still showthe harmonicdeclinediscussedearlier.Also, the calculatedvaluesof 4 seem reasonable. Bott also reports the water-to-oil ratio found for each cycle, and this makes it possibleto calculatethe averageheat capacityof the products.This is compared CyclicSteamingof VaccaTar, Oxnard,California
271
dtB
Bbl Steam 22,389 2 14,7ffi 3 7,500 4 10,671 Total 55,766 't
0.02
OSR 0.23 0.89 1.53 't.23 O.77
Eta 8.3 3.0 1.1 1.7
The rc drawn frm load is trad ment (partil in overall p squeezedfr|o This g is of grealcl matricesYI when the rcr to the sacl tion. An er! ing grouod r partly un& denceof tb was done to If rhsl would be lir as the pqe I duced.In ad from water b also tendstn dencedby d this, sincet (1977),plcs r mulativepm denceof 50 r of about23 r
4th Cycle
0.01 Datalrom Bott(1964 tor VaccaTransamerica Well702
0
50
100 Timein Days
150
Figure 6.25 Cyclic Stimulationof VaccaTar, Oxnard, California. 5'API, Reservoir Temperature 100'F.
to the slopesof the declinecurvesin Table6.5. The comparisonindicatesthat in cycles1 and2, more heat was lost from the heat bank than could be accountedfor by the heat carried awaywith the products.This is shownby the ratio in the last line of the tablebeinggreaterthan 1. In cycles3 and 4, the reversewas true. This indicatesthat heat lost in the first two cyclesaugmentedthe heat bank in the latter two. Thesecomparisons were madeassumingthat the parameters was equalto la; however,it is possiblethat with the mechanismof flow, s would be lessthan m and this, in turn, would make the calculatedloss factors in the last row of Table 6.6 smaller than they should be. TABLE 6'6 Comparisonof Slopeof DeclineCurvesfor VaccaProjectwith ReportedWater-Oil Ratiosin Product. Cycle Slopeof line in Figure 6.4 B-1 x L000 CalculatedqpC, Btu/B "F Water-oilratio in product pC for product, Btu/B61"F qpCfpCp,.a
1
0.326 1459 0.369 304 4.8
0.157 519 0.344 295 1.8
0.r17 200 0.485 345 0.58
0.120 297 0.700 420 0.71
COMPACTIONDRIVE IN CONVENTTONALHEAVY OIL RESERVOTRS There has been extensiveproduction of heavy oils both by conventional,nonthermal meansand by cyclic steamstimulationin the Bolivar regionof the eastcoastof Lake Maracaiboin Venezuela.The reservoirsin this area arevery large, and enormous quantities of oil have been produced.The cold production from these reservoirs (the main ones are Tia Juana,Lagunillas and Bachquero)is very substantial, and the recovery, without thermal stimulation, is much higher than would be expected. 272
CyclicSteam Stimulation
Chap.6
L o 6
o80 o o c
I Maintv l+ I Solution
l-
o
ecoriw
I
I
8 6 0 t= I E I o40 (, c o
!t o,
I II
8 2 0 r-
o
l/
o
l-/
E o 5
a-4-tz---
E 3
o
020, Cumulativc t
CompactionD
The reasonfor this higher production is compactiondrive. As fluids are withdrawn from the reservoir,the pore pressuredecreasesand additional compressive load is transferredto the rock matrix. This matrix is sensitiveto load, and rearrangement (particularly of plasticallydeformableclay constituents)occurswith a decrease in overall pore volume and a subsidenceof the ground surface. The fluids are squeezedfrom the reservoirrather like water from a sponge. This type of behaviorprobablyoccurs to someextent in most reservoirsbut it is of greatestpractical significance in reservoirs(both petroleum and water) with matriceswhich are sensitiveto increasedstress.It is thought that this is the case when the reservoirmatrix has not been previously stressedin its geologicalhistory to the sameextent asoccurswhen the pore pressureis relievedduring fluid production. An extreme,well-documentedcaseof compactiondrive and the accompanying ground subsidenceis that of oil productionfrom the Wilmington field which lies partly under the city of Long Beach,california. In this case,the maximumsubsidenceof the ground surfacewas greaterthan 8 metersand very substantialdamage was done to surfacefacilities such as buildings and bridges(Mayuga 1970). If there were no compaction drive in the Bolivar reservoirs,the recovery would be limited to about 5vo of the original oil in place(Figure 1.12).However, as the pore pressureis decreased,the reservoircompactsand additional oil is produced.In addition to compactionof the sandreservoir,there is also a contribution from water being squeezedfrom the pores of interbeddedshale streaks;this water alsotendsto displaceoil. The compactionin this areais well documentedand evidencedby the settlingof the ground surface.Measurements have been made of this, since the 1930sin somecases.Figure 6.26,which is taken from Borregales (1977),plots the cumulativesubsidenceof the surfaceof the ground againstthe cumulative production for a project in the Tia Juana field. In this diagram, a subsidenceof 50 million barrels correspondsto a changein the elevationof the surface of about2.3 m.
;lic Stimulationof 'rd. California. 5"API, :rature 100'F.
on indicatesthat in ld be accountedfor the ratio in the last /ersewas true. This at bank in the latter er J wasequalto m; I be lessthan rn and st row of Table 6.6
ReportedWater-Oil
0 . 11 7
n 0.485 r5 0.58
0.t20 297 0.700 420 0.7r
I o
Productiondue to: Compac-
Compaction
6
o80
Solution GasDrive:
o ao c
Chap.6
i
^2; ^B
,t
)/
o40 (,
tr o p o
o
820
a o E
o o
A ActualProduction B PrimaryRecovery C MaximumRecovery (26.2%STOilP)
@
Eo f
E f
o imulation
:
t/
.s
rventional,nontherr of the eastcoastof ery large, and enorln from these reserI is very substantial, her than would be
reactts vaea
;C
sof'n , ,' :gsdriv€i / + oll;lerVl
8eo E
RS
Compaction
rion : witfr,
i ,
o
20 40 60 80 100 120 Cumulative Withdrawal in Millionsof Barrels
Figure 6.26 Drive Mechanismsin the D-2/E-2 Projectin the Tia JuanaField (after Borregales1977)
CompactionDrive in ConventionalHeavy Oil Reservoirs
273
During the initial production,when the drive was largely due to the effect of solution gas,there was relatively little subsidence.Over the bulk of the production period shown, the surface subsidencetracks the cumulative production along a 45' line; the drive is essentiallydue to compactionalone.This would continueto the limit B if no steamwere introduced. Cyclic steamstimulation not only acceleratesproduction, it also increasesthe recoveryachievable.One reasonfor this is the additionalgasdrive that is initiated by the effect of the steam;oil is displacedby steamvapor remaining in the reservoir. [n addition, the more rapid production rate makes more extensivedepletion economic.The limit shownby the point C for cyclicsteamstimulationcorresponds to a recoveryof 28% of the original oil in place.The projectedrecoveryfor other projectsin the Bolivar Coastis shownin Table6.7.It canbe seenthat the increase in oil recoveryby steamsoakingis between5 and 15 Eo of.the original oil. The very high oil-to-steamratiosindicatea stimulationmechanismrather than one depending on generalreservoirheating.Figure 6.27showsthe averageproductionbehavior of all of the steam-soaked wells on the Bolivar Coast. TABLE 6.7 CyclicSteam Results-BolivarCoast Recoveryas % STOIIP
Proiect Name
STOIIP Bx106
Primary
D2/82 J-7 H-7 D-6 T-6
454 713 98 604 305
19.8 10.6 8.2 4.4 7.5
Total
8.2 12.2
28.0 22.8
tJ.z
11
13.1 5.6
17.5 13.1
i
Compaction VoSTOIIP 18.9 t4.6 16.I 14.l zt.+
2.94 4.94 5.03 7.37 4.83
(Data from Borregales1977)
Borregalesconsidersthat, after the recoveryof 20 to 30Voof the oil in place,these projectsshouldbe convertedto steamdrives;presumablythis would allow recoveries of the order of 50%. He points out that it is desirableto continuethe cyclic steamprocessto the point wherecompactiondrive is no longeroperative.At this point, the reservoiris hot and the reservoirpressureis low. This allowsthe easier introductionof steamin the steamdrive, which, at a lower pressure,is thermally more efficient.A particularly important considerationis that if compactiondrive were still availablewhen flooding steamis introduced,then the valuablecompactiondrive might be dissipated,movingcompressible steamratherthan the hardto-push oil. The result would be a lower overall recovery and/or a higher overall steamrequirement. FRACTURING AND RESERVOIR EXPANSIONDURINGSTEAM INJECTION
I
I
I
I
a
Iitil livar (
When fl are usuallyth zontal or verti tion. Even wi which the fre Settari, fractures aru fracturesweil It is ro situ stresses t Howard and I onal, principe vertical and tl Fracture to the minirm happensto h minimum prir be vertical ao Stress Oue t
Both fluids a stressesmust I whicb stresses tain a shape. As a siu hypotheticals mannerexpG the readerto i
In orderto obtain practicalratesof steaminjectionin oil sandreservoirs,it is usual to use steampressureshigh enoughto fracture the reservoir and thereby allow injection. With lower pressuresin a virgin reservoir, the injection rates are usually negligible.
Limited.
274
Fracturing and
CyclicSteamStimulation
Chap.6
tThis
exrr
r due to the effect of rlk of the production production along a is would continueto
g
f; ooo E Euoo ogc 0=o
= E4oo
, it alsoincreases the Jrivethat is initiated naining in the reser: extensivedepletion nulationcorresponds rd recoveryfor other eenthat the increase :riginal oil. The very er than one dependproductionbehavior
Compaction -r STOIIP 18.9 t4.6 16.1 1A I
23.4
OSR
2.94 4.94 5.03 7.37 4.83
he oil in place,these *ould allow recovercontinuethe cyclic er operative.At this his allowsthe easier ressure,is thermally if compactiondrive r the valuablecom'atherthan the hardI or a hisher overall
JECTION reservoirs,it is usual nd therebyallow inion ratesare usually
Fc
E *soo iEg z o o E 55 g€100 66
E
E0
o
20
40
80
100
Time in Months
I
Figure 6.27 AverageProductionBehaviorof Steam-Stimulated Wellsin the Bolivar CoastFields (after Borregales1977)
I
,l
When fluids are injected into porous cementedrocks, the fracturesthat form are usuallythin cracks,and thesetend to be approximatelyplanar and either horizontalor vertical. With vertical fracturesit is found that there is a preferredorientation. Even with horizontalfractures,there tendsto be an azimuthaldirection in which the fracture spreadspreferentially (Aughenbaughand Pullen 1966). Settari, Kry, and Yee (1988)have reported the formation of asymmetrical fractures around steam-injectedwells at Cold Lake in a region where horizontal fractureswere expectedfrom measurement of the initial reservoirin situ stresses. It is acceptedthat the orientationof the fracturewill be controlledby the in situ stressesthat exist within the rock at the time of fracturing (see,for example, Howard and Fast1970).In generalthesestresses may be resolvedinto three orthogonal, principal compressive stresses, and it is usuallyassumedthat one of theseis vertical and that the other two are horizontal. Fracture theory predicts that the plane of a hydraulic fracture will lie normal to the minimum principalcompressive stress.Thus,if the minimum principalstress happensto be vertical, then the fracturewill be horizontaland vice versa.If the minimum principalstressis horizontalin a specificdirectionthen the fracturewill be vertical and will be at right anglesto the directionof the minimum stress. Stress Due to Gravity in a Semi-infinite Strain-FreeSolid Both fluids and solidscan supportcompressivestresses. However,in a fluid, the stresses must be equalin all directions(the pressure),whereasa solid can support stresses which differ with direction.It is this propertythat allowsa solid to maintain a shape. As a simpleexampleof the stressesT within a solid, considera semi-infinite hypotheticalsolid that is stress-and strain-freeand that is then in someimaginary manner exposedto a gravitational field normal to its surface.It might be useful for the readerto imagine a block of an elasticsolid such as an eraser. TThis
exampleresultedfrom a discussionwith Dr. S. Bharatha of Esso ResourcesCanada
Limited.
timulation
Chap.6
Fracturingand ReservoirExpansionDuring Steam Injection
275
r{ rd dl
H q
hl rl s,
,
I I
I
The gravitywill compressthe solid downward,and this will alsotend to make it extend horizontally. We will assumethat the horizontal growth of a large horizontallayer of the solid is constrainedby somedistant immovablebarrier and that, as a result,the horizontaldimensionsremain consranr. A small elementin the solid is shown in Figure 6.28.rt is beingcompressed downwardby the vertical principal stressand horizontallyby the two equil horizontal principal stresses. The condition that the strain (i.e. the contraction per unit length) in directionL be zerois given by equation6.22.This statesthat the sumof the contributionsto the straincausedby the threeprincipalstresses shouldbe zero.From this is derivedan expressionfor the horizontalstressas a function of the verticalstress. Op Ct=--:---=U
.EEE
ltCn
UOV
or
v oH = ;-L-v
ov
(6.22)
where E is Young'smodulus op is horizontalstress ay is vertical stress z is Poisson'sratio But z < 0.5; therefora,o171 6y. Poisson's ratio must alwaysbe lessthan 0.5, since,if it were not, therewould be an expansionin volumewhen a body is compressed.s For a fluid, poisson,s ratio is 0.5.If Poisson's ratio is lessthan 0.5,then equation6.22 indicatesthat the horizontal stresswill be lessthan the vertical.In sucha situationonly verticalfracturescan form if the materialis fracturedby the injectionof a fluid within its poresand if its tensilestrengthis either negligibleor the samein eachdirection. This conclusionappliesonly to the imaginaryunstrainedsemi-infinitesolid for the conditionsjust considered.A similar analysisappliedto a large spherical body to which a gravity was suddenlyapplied (the gravity coming from lts own mass)would lead to a resultin which therewas a residualhoop compressive stress at the surface,and, near the surface,horizontalfractureswould be possible. In Situ ReservoirStresses
like. In senera fracturestend I shallowdepths The directiono form can be in boresusinga fo ter is that of th Usingthb of the maximu a map for .{lba In the reg tion with the m are thus erpect Agar (198,iirep sandreservoir5 than 250 m. an( tical fractur* a Lower Grand R this changedto Part of rhe Lake, commun entialdirection in thevicinitl th Daneshr. in a gaswell:thc tion. Drilling mr mediatelyafter t the pressuredal the positionof t In situ stn Gronseth,and I Fracturing hel
ln actualpractice,the stresses within the earth'scrust are mostcomplexand are relatedto eventssuchasthe movementof tectonicplates,mountainbuilding,and the
Figure 6.28 Principal StressesActing on Solid Element
The minimump cipal stress.It il stresscorrespqx by the densitva 22.6 kPalm. lf t duringa fracturi half of it (Hona Ground Heave
that in equation6.22, opwonld be equalto cvand henceto the stressin any direction if v : 0.5. In this circumstance, the materialwould act like a fluid.
There hasbeena fracturein uncq cracksformingas
276
Fracturing andRe
'Notice
CyclicSteamStimulation
Chap.6
will alsotend to make ,rowth of a large horivablebarrier and that, It is beingcompressed rv the two equal horiper unit length) in the sumof the contriruldbe zero.From this r of the verticalstress. UV
(6.22)
,*'erenot, there would a fluid, Poisson's ratio catesthat the horizon; r.erticalfracturescan :hin its poresand if its tion. red semi-infinitesolid d to a large spherical coming from its own xlp compressivestress ruldbe possible.
like. In general,it is found that in the real world, horizontalrather than vertical fractures tend to form from the hydraulic fracturing of porous rocks at relatively shallowdepths(downto about 1200ft.); belowthis, verticalfracturesusuallyform. The directionof the horizontalprincipal stresses in regionswhereverticalfractures form can be inferred from measurements made of the out-of-roundness of well boresusinga four-armcaliper.The directioncorresponding to the smallestdiameter is that of the largerhorizontalprincipal stressand vice versa. Using this techniqueit hasbeenpossibleto plot mapsshowingthe directions of the maximumand minimum horizontalstressdirections.Figure 6.29showssuch a map for Alberta. In the regionshown,the maximumstresslies generallyin the NE/SW direction with the minimum stressnormal to it. Fracturesat depthsbelowabout IZ00ft are thus expectedto be vertical and to occur in the NE/SW direction.Chhina and Agar (1985)report the resultsof fracture testsat 12 locationsin the Alberta tar sandreservoirs.They find that horizontalfracturesnormally occur at depthsless than 250 m, and verticalonesoccur at depthsgreaterthan 400m. In between,vertical fracturesare likely, althoughhorizontalones may occur. In one test in the Lower Grand Rapidsformation at342m, a horizontalfracturestartedgrowing,but this changedto a vertical orientationas it grew. Part of the datausedin drawingFigure6.29wasthe observationthat at Cold Lake, communicationsbetweensteam-fractured wells tend to occur in this preferential direction.Goughand Bell alsomentioncalipermeasurements madeon a well in the vicinity that indicateda directionof 41' eastof north for the maximumstress. Daneshyet al. (1986)describemeasurements of in situ stresses at variouslevels in a gaswell; thesewereobtainedfrom microfracturetestsduringthe drilling operation. Drilling mud was usedas fracturefluid and orientedcoreswere obtainedimmediatelyafter the microfracturetests.The minimum stresses were obtainedfrom the pressuredata and the directionsof the vertical fractureswere obtainedfrom the position of the fractureswithin the retrievedcores. In situ stressmeasurements in the cold Lake field are describedby Kry, Gronseth,and Morgenstern(1989). Fracturing Pressure
st complexand are rertainbuilding,and the
?rincipalStresses Acting ent
The minimum pressurerequiredto form a fractureis equalto the minimum principal stress.It is usual to take the vertical principal stressas being equal to the stresscorrespondingto the weight of the overburden,i.e., to the depth multiplied by the densityand gravity. This givesvaluesof about 1 psi per foot of deptl, or 22.6 kPalm. If vertical fracturestend to form, the fracturing pressuremeasured during a fracturingoperationwill be lessthan this valueand can be assmallasonehalf of it (Howard and Fast1970). Ground Heave
, thestress in anydirection
There hasbeen a lot of discussionwithout much data in regardto the nature of the fracturein unconsolidated tar sand.From this it seemslikely that, ratherthan thin cracksforming asin the fracturing of consolidatedrocks, relativelylargevolumesof
S t i m u l a t i o n C h a p .6
Fracturing and Reservoir Expansion DuringSteamInjection
277
LEGEND P R O D U C T I OW NE L L I N J E C T I OW N ELL B E N C HM A R K
a
c a
The ertr calculatedr.r It seemsposs stimulation.
EFFECTOF FRACTT EIPLAIIATIOII I.rlh!fr horltont.l tlraar orlanlallon Inlarrrd lrgn b.talgctr Ilnlnun horl.onlal rlraar orlanlrllon Infaaaad Iton braalo!tr
0 + 0
IOO tO
mln loMil.r
If gravitr dra crudesbv stea zonethat is al might specu madeof the r might be mtr There sr However it n Shepherd197 operating*itl in spiteof thc reportedin tl steaming.hor Kr1'. Gr Lake, the ma mostimmedia
Figure6.29 PrincipalHorizontalStress Directions in Alberta(fromGoughand Bell 1981) tar sand become disrupted when high-pressuresteam is injected. Evidence for this is contained in measurementsof the surface disruption observed in a McMurray steam injection pilot, where it was found that substantial permanent ground heave resulted as a result of the steam injection (Agnew 1976).Figure 6.30 shows contours for constant elevation increase for one of the patterns at this pilot.
--l(r\ - uro time curue follo, neous shut-in pn shut-in pressurc
278
Effect of Fract
CyclicSteam Stimulation
Chap.6
a-.
LEGEND PRODUCTION WELL INJECTIONWELL B E N C HM A R K
-^s4
Figure 6.30 Changesin Ground Elevation at Texaco'sIn Situ SteamFlooding Pilot Near McMurray Alberta. Contoursare for constantincreases in ground elevationmeasuredin hundredthsof a foot. Data for May 12Nov. 24, 1976(from Agnew 1976)
The extentto which steamcan penetratea fracturebeforeit condenses can be calculatedusingHearn'sequation,which was describedpreviously(equation3.57). It seemspossiblethat this relationwill find more applicationin the theoryof steam stimulation. EFFECTOF FRACTUREORIENTATION ON PRODUCTIVITYFROMSTIMULATION Itororro'l )(
K1
l-
XN -t-
'rOett,X
ifrom Gough and
If gravity drainageplaysan important role in the productionof extremelyviscous crudesby steamstimulation,then the orientationof the fracture-disrupted reservoir zonethat is allowingsteaminjectionwould seemto be important.In particular,one might speculatethat vertically oriented fractures,becausethey allow use to be madeof the vertical thicknessof the reservoirto provide headfor drainageof oil, might be muchbetter than horizontalfractures. There seemsto be little data,eitherpositiveor negative,to supportthis view. However it might be noted that the Esso pilot at cold Lake (Buckles1979and Shepherd7979)and the subsequent commercialextensionsare successfulprojects, operatingwith economicoil-to-steamratios and with economicwell productivities in spiteof the very high in situ oil viscosity.Predominantlyvertical fractureswere reportedin the early operations,althoughit has been found that with extensive steaming,horizontalfracturesmay be formed (Denbina,Boberg,and Rotter 1987). Kry, Gronseth,and Morgenstern(1989)have shown that, in a test at Cold Lake, the maximum in situ stress,e measuredby mini-fracturetests,increasedalmostimmediatelyfrom 9.3 to 10.5MPa as a resultof steaminjectioninto neighbor-
cted. Evidence for this served in a McMurray rmanent ground heave rre 6.30 shows contours s pilot.
Gronseth,and Morgensterndefine the pressureat the point ofinflection in the pressure time curve following the well shut-in after the mini-injection as being the in-situ stressor instantaneousshut-inpressure."Judgementis requiredto infer the value of the in-situ stressfrom measured shut-inpressures."
r Stimulation
Effect of FractureOrientationon Productivitvfrom Stimulation
Chap.6
eKry,
279
In thc I sivelyas thc r steamis firs NE/SW car an areaof thr erally horin tion is probd treatment.tI cal stressthe upward expt abovetherm
Figure 6.31 Stress Redistribution Could Result in Interwell Communication (from Dusseault1977) Stage1: Initiation of multi-well simultaneoushydraulicfracture. Fracturepropagationis normal to minor stress. Stage2: Increasein minor principal stresscausesrelocationand changein fractureorientation (casewhere 01 remainsvertical)
ing wells. This was interpreted as an increasein the horizontal stresswhich had to be overcometo initiate a vertical fracture from the well bore. [n succeedingminishut-inpressure(ISIP)fell in less fracturetests,it wasfound that the instantaneous than two hours to a stabilizedvalue of 9.8 MPa. This is significantlyhigher than the initial ISIP of 9.3 MPa and approximatelyequalto the calculatedverticalstress. This behavior was interpreted by Kry, Gronseth, and Morgensternas indicating that the vertical fractures initiating from the well bore had turned to becomepredominantly horizontal. Another factor is that vertical fractures may assist recovery of the oil by providing an improved means of passageof the oil past horizontal tight streaks. Horizontal movementof the fluids in the unfractured reservoir is usually less restricted than vertical movement.Vertical fracturesshould improve this situation. POSSIBLEPRODUCTIONOF ORTHOGONALVERTICAL FRACTURES FROM THE FRACTURINGOF A LINE OF WELLS An interestingpossibility that was describedby Dusseault(1977),basedon an earlier suggestionby Schuckand Advani, is that the fracturing of a row of wells may so modify the stressfields in the reservoirthat fracturesnormal to the usual direction may alsobe formed.This possibilityis shownin Figure 6.31. 280
CyclicSteam Stimulation
Chap,6
AcNrw, H.. U" AucHeseel€l Symp.on Sd Bosenc,T.C. t Well,".fPT, t Bosenc,T. C-, PerformaG 1973). Bonnecer-rsC sium, Edrm CIM Specid Borr, R. C.. I Bucrles, R. I,
(1e7e).
BunNs,J.. A X o 1969SPE Burr-En, R. M(September-
CHHrNe,H. S. r men from CI Tar Sands,L D,quessv,A. /l surementsD nn HeeN, H. J. Project in tL DeNsrNa,E. S' Mechanism (1e87).O rgt DrnrnrcH, J. K Reservoirs, Doscnen,T. M try Confereu Calif., 76-81 Bibliography
In the Essoproductionareaat Cold Lake, reservoirfracturingoccursextensivelyas the resultof steaminjection.Vertical fracturesare normally found when steamis first injectedinto a new reservoir,and thesegenerallyhave the expected NE/SW orientation(Mainlandand Lo 1983).Howeverit hasbeenfound that after an areaof the field has undergoneintensive steaminjection, new fracturesare generallyhorizontal(Denbina,Boberg,and Rotter 1987).This changein fracturedirection is probablythe result of changesin the tectonic stressescausedby thermal treatment.Heatingincreasesthe horizontalcompressive stresses, leavingthe vertical stressthe minimum principal stress.The vertical stresscan be relievedby the upwardexpansionof the ground.This is evidencedby the surfaceheaveobserved abovethermal in situ operations. BIBLIOGRAPHY
munication(from
rgein fractureori-
stress which had to
n succeeding minire (ISIP)fell in less icantly higher than latedverticalstress. rsternas indicating red to becomeprex'ery of the oil by ontal tight streaks. r is usuallylessreove this situation. ES r), basedon an earrow of wells may so the usualdirection imulation Chap,6
(1976). AcNew, H., U.S. Patent4,143,714 AucnnNnaucH,N. B. and PuLLeN,M.W., "DirectionalHydrofracturing:Factor Fiction," 3d Symp.on Salt Proc.2,393-403 (1966). Bonenc,T. C. and LeNrz, R. B., "Calculationof the Productionof a ThermallvStimulated (December1966).O 1966SPE. Well.".IPZ 1613-1623 Bonenc,T. C., PeNnenrHy,JR.,W. L., and HecnoonN,A. R., "Calculatingthe Steam-Lifted Performanceof Gas-Lifted and Flowine Heavv-Oil Wells." JPT. t207-1215(October
re73). BonneGeles,C. J., "SteamSoakon the Bolivar Coast,"Canada-Venezuela Oil SandsSymposium, Edmonton, May 30-June 4, 1977pub. as The Oil Sandsof Canada-Venezuela 1977 CIM SpecialVolume17,(1977). Borr, R. C., "Cyclic SteamProject in a Virgin Tar Reservoir,"JPT, 585-591,(May 1967). Bucrres, R. S., "SteamStimulationHeavyOil Recoveryat Cold Lake, Alberta," SPE 7994,
(re7e).
BuRNs,J., 'A Reviewof SteamSoakOperationsin California,"JPT, 25-34 (January1969). @ 1969SPE. Burrrn, R. M., "The Expansionof Tar SandsDuring Thermal Recovery,"JCPT, 5L-56 (September-October 1986). CnuINe,H. S. and AceR, J. G., "PotentialUse of FractureTechnologyfor Recoveryof Bitumen from Oil Sands,"3d UNITAR/UNDP InternationalConferenceon Heavy Oil and Tar Sands,Long Beach,Calif.,77l-789, (July 1985)publishedby AOSTRA 1988. DeNesuv,A.A., Slussen,G.L., CHrsHoLu, P.T.,and MecEe,D.A., "In-SituStressMeasurementsDuring Drilling," JPT 891-898,August 1986. oe HaeN, H. J. and vANLooKEREN, J., "Early Resultsof the First Large-ScaleSteamSoak Project in the Tia Juana Field, WesternVenezuela,"JPT, l0l-ll0 (January1969). DeNuNe, E.S., BoneRc,T.C., and RottEn, M.B., "Evaluationof Key ReservoirDrive Mechanismsin the Early Cyclesof SteamStimulationat Cold Lake," SPE 16737,Dallas (1987).O 1987SPE. DrErnrcu, J. K., "Relative Permeability During Cyclic Steam Stimulation of Heavy-Oil Reservoirs,"IPT, 1987-1989(October 1981). DoscHen,T. M., "FactorsInfluencingSuccess in SteamSoakOperations,"PetroleumIndustry Conferenceon Thermal Oil Recovery,Sponsoredby Rockwell Mfg. Co., Los Angeles, Calif.,76-80, June6, 1966.(referencefrom Burns 1969). Bibliography
281
Dusseaur-r,M. B., "StressStateand HydraulicFracturingin the AthabascaOil Sands,',Oil Sandsof Canadaand Venezuela,2T-35, CIM SpecialVolume 17,(1977). Dussnaulr,M. B. and MoRGeNstpRr.r, N., "samplingand Testingof AthabascaOil Sandsfor stability studies,"oil sandsof canadaand venezuela,260-269,cIM Specialvolume 17. (t977). GoucH, D. I. and Bnr-r-,J. S., "StressOrientationsfrom Oil-WellFracturesin Alberta and Texas,"Can.J. Earth Scl., 18:638-645(1981). Hourz, R. D. and Kovecs,w.D.,An Introductionto Geotechnical Engineering"Englewood Cliffs, N.J.: PrenticeHall (1981), HoLzueusrN,G. R., et al., "Resultsof DeformationMonitoringDuring SteamStimulation," Conf. on Appl. OilsandsGeoscience, Edmonton,Alberta (June11-13,19g0). HowenD,G. C. and Fasr, C. R., "Hydraulic Fracturing",SpE Monograph1970. JoNns,J., "Cyclic Steam ReservoirModel for Viscous Oil, PressureDepleted,Gravity Drainage Reservoirs,"SPE 6544(1977). Knv, P.R., GRousnrH,J.M., and MonceNsrrnrv,N.R., "Geotechnicalproperties," In: AosrRA TechnicalHandbookon oil sands,Bitumensand Heavy oils, Heprer,L. G. and Hsi' C. (Editors),Alberta Oil SandsTechnologyand ResearchAuthority, Edmonton, Alberta. Kuo, c.H., SHATN, S.A. and PHoces,D.M., "GravityDrainageModelfor the Steam-Soak Process,"SPEJ,119-126(June 1970).O 1970SPE. Lerrovlrs, H. C. and MArrHrws, C. S., 'Applicationof DeclineCurvesto Gravity-Drainage Reservoirsin the StripperStage,"Pet. Trans.AIME, 213:2i5-280 (1958). LeNNoN,R. B., "GeologicalFactorsin Steam-SoakProjectson the West Side of the San JoaquinBasin,"lPT, 741,-748,J:uly1976. MatNLeNo,G. G. and Lo, H.Y., "TechnologicalBasisfor CommercialIn-Situ Recoveryof Cold Lake Crude," 11thWorld Pet. Cong..London,SessionRDT3(1)(1983). ManlIN, J. C., 'A TheoreticalAnalysisof SteamStimulation,"JPT, 411-418(March 1967). ManrHEws,c. S. and Lerrovrrs, H. c., "Gravity DrainagePerformanceof Depletion:Type Reservoirsin the StripperStage,"lPT, 207 265-274(December1956). MettuEws, C.S. and Russrlr-, D.G., "PressureBuildup and Flow Testsin Wells," SpE Monograph l, (1967). Mavuce, M. N., "Geologyand developmentof California'sgiant-Wilmington Oilfield," In: Halbouty,M.T, (Editor), "Geologyof giant petroleumfieldsl' Mem. Am. Ass. pet. Geol., 14, 158-186,(1970).
SsrpHelD ence.Ed and Tar ! SrrcevgrE with \-r S u s .R . J - ." ing Surfr (\oserfr
Tousor, D130-135 |
Ntro, H. and Tnoosr, P. J. P. M., "ExperimentalInvestigationof the Steam-Soak Processin a Depletion-typeReservoir,"JPT 251:1006-1014 (AugustI97t). @ 1971SpE. OweNS,W. D. and Suren, V. E., "SteamStimulation-NewestForm of SecondaryPetroleum Recovery,"Oil GasJ., 82-90 (April 26, 1965). Purol, L. and BoneRc,T. C., "ScalingAccuracyof LaboratorySteamFlooding Models,,, sPE 4t9t (1972\. SEnn,R. D. and PERRy,G. E., 'A MathematicalModel of RepeatedSteamSoaksof Thick Gravity DrainageReservoirs,"JPT, 87-94 (January1969). Serraru, A., KRy, P.R., and Yen, C.T., "Coupling of Fluid Flow and Soil Behaviourto Model Injection into UnconsolidatedOil Sands," 39th Annual Technical Meeting of the Pet. Soc.of CIM (June 12-16,1988),Preprintspaper88-39-72. SueruEr.o,D.W., "Predicting Bitumen Recoveryfrom SteamStimulation," WorldOil, 68-72 (September 1979). 282
Cyclic Steam Stimulation
Chap.6
Bibliogr4lt
b'asca Oil Sands,"Oil 9 r 7) . habascaOil Sandsfor l{ SpecialVolume17, :turesin Alberta and tneering,"Englewood r SteamStimulation," li. 1980). aph 1970. re Depleted,Gravity
SurrHenn,D.W., "SteamStimulationRecoveryof Cold Lake Bitumen," 1stUnitar Conference,Edmonton,Canada(Jtne 4-I2, L979),reportedin The Future of HeavyCrude Oils and Tar Sands,New York: McGraw-Hill, 349-360(1981). D. D. and, VoLnr, C.W., "RepresentingSteamProcesses Srncuraunn,G. L., LeurvrnecH, June 1980. with VacuumModels,"SPEI, 1.51.-t74, SuN,R. J., "TheoreticalSizeof HydraulicallyInducedHorizontalFracturesand Corresponding SurfaceUplift in an IdealizedMedium," J. GeophysicalRes.,74, no. 25: 5995-6011 (November15, 1969). TowsoN,D. E. and Bonnnc, T. C., "Gravity Drainagein Thermally Stimulatedtilells," JCPT, 130-135(October-December 1967).
rical Properties,"In; tils,Hepler,L. G. and \uthority, Edmonton, :l for the Steam-Soak s to Gravity-Drainage I 958). ['est Side of the San I In-Situ Recoveryof I r t 1983). l-,118(March1967). tce of Depletion:Type 56l. Testsin Wells," SPE ningtonOilfield,"In: Am. Ass.Pet.Geol., team-SoakProcessin 1971SPE. SecondaryPetroleum n Flooding Models," 'teamSoaksof Thick nd Soil Behaviourto rnical Meetingof the n." WorldOil,68-72 mulation
Chap.6
Bibliography
283
Sfec
Drcl
INTRODUCTIil
The recoq come knor In this prr forces, aod interfacetl steamchat A rh. velopedby been desc Stephensl! with reced CONCEPT
The intenti vise a mea ner in ord steamflood Gravi chief drivir geringth4r It wa well that w
Steom- Assisfed Gravity Drsinqge
INTRODUCTION The recovery of heavy crudes using a specialform of steamfloodingthat has begravity drainage(SAGD) is discussedin this chapter. come known assteam-assisted In this processthe movement of oil to the production well is causedby gravity forces, and the geometry is such that the oil moves approximatelyparallel to the interfacethat formsthe boundaryof a growing,steam-saturated zoneknown asthe steamchamber. A theory that predictsthe rate at which this processwill occur has been developedby the Heavy Oil ResearchDivision at Esso Resourcesin Calgary and has been described in a series of papers (Butler, McNab, and Lo 1981;Butler and Stephens1981;Butler,Stephensand Weiss,1980;Butler 1985).This theory,together with recent developmentsis summarized. CONCEPT The intention in developingthe steam-assisted gravity drainageprocesswas to devise a meanswherebyheavyoil or bitumen could be removedin a systematicmanner in order to give a more complete recovery than is possible in conventional steamfloodingprocesses, wherethe oil is movedby pushingit with injectedfluids. Gravity is already present throughout the reservoir, and by using it as the chief driving force to effect oil movement,it ilpgssible to avoid the differential fin- zort
gs4lss.t*hat-oe.e-ur!,whe!..yp.qg'i&
Up*qgbugty{L!-!9!s-vidu',..fld{ -*Pd/,
It was reasonedthatlf steamwere injected above but close to a production well that was completedat the baseof the reservoir,the steamwould tend to rise 7
,
"-
Ctt (ttq
we,..,
|
u, " i;
\
r.r1lJ
.')t,.",t, t ' {
and the condensates, togetherwith warmed oil, would fall. The oil and condensate would be removed continuously from the production well. It-w-as*tb$ght that if theqeliqu16. were not removedtoo quickly, then the tendencyof the steamto flow directly to the productionwell-and thus to bypassthe reservoir-could be re_!g9,dg-pos9!b_!y g_ve_aghtnllatg4This is analogousto the ability of i steim mp to allow the flow of condensatefrom the bottom of a steam-heatedradiatorwithout allowingsignificantbypassingof the steam. An attraction of this conceptis that, although the injection well and the productionwell can be very close,the mechanismwill causethe steamchamberto expand gradually and eventually allow drainagefrom a very large area. The injector and producerdo not have to spanthe drainagearea.Another advantageis that the heatBd --:--;---:-oil remains Lrpt-a-cit ilows towards-the pro?uciion wetffi;;diFfif tasl'waili;cus.ied"in Chaptei 5, ilre-oii itrat is displacedfrom the
rotheproduction weir. i[ffiT:fiil3i ff.I3ll'ilT;:ilL ropush rnsAcnTne oil remainsheatedas it flows around the steamchamber.r Although the conceptis attractive,it wasnot clearinitially whetherthe mechanism could produceoil at practical rates.The first efforts were to analyzethe process theoreticallyto determine the production rates that might be anticipated. Followingthis, a numberof scaledrecovery-model experimentswere carriedout in the laboratoryto studythe process,and the resultswere comparedwith theory.
RELATIONSHIP TO CONVENTIONALSTEAMFLOODING In previouschaptersit hasbeenshown that steamfloodingtendsto producea stable displacement without steamfingering.Condensate that leasesthe steamzoneflows through the oil zone either as fingersor, in exceptionalcases,by diffuse BuckleyLeveretttype flow. A major problemwith conventionallateralsteamfloodingis the tendencyfor steamto overridethe oil zoneand breakthroughat the productionwell. This effect can be reducedby completingthe producernear to the baseof the reservoirand by removingproductat a controlledrate in order to allow gravity to keep the steam zonesegregated. A considerable improvementcan be achievedif the reservoirdips and if the steamis injectedso that it flows downdip. Operationin this fashionhas much in commonwith the steam-assisted gravity drainagediscussedin the following sections.However,with conventionalwells the pressuregradientsassociated with radial flow to the productionwell make the maximumrate that is achievablewithout steamconingrelativelylow. In the steamassistedgravity drainageprocess,horizontalwells are employed,and production ratesof the order of 0.3 B/d per foot of horizontal well are indicated to be practicable without steamconing; with long horizontalwells this providesan economic drainagerate. A majorpotentialfor the steam-assisted gravity drainageprocesslies iq overthe shortcomings of conventional steamflooding that are createdbi-iTe_coming
eqiqt-oJ
thq steamto dri_rg:_:
tThere
is a similarity betweenthe SAGD processand reversein-situ combustionwhich is describedin Chapter9. From one point ofview SAGD can be looked upon as reversesteamflooding.
286
Steam-AssistedGravity Drainage
Chap.7
GRAVITYDRAN'I
In the dets meanswbct moved as i shownin Fi Stean heaviercc for introdr cold oil a I lower locli filled with r A hni the well,ar horizontalr someapplh well (for h In reservcin reservoir.n The g cess.The d within the c into the col it to drain b is removed the steamd steamcond In sc bathtub.In t
Mechanism: o Stearn o Oilart o Florl i o Chafll -3
//a /
\k^ \\ \\
J \
steam ' Continuous injectionintocharrb
GravityDrd
ril and condensate as thought that if the steamto flow oir-could be retr of a steam"t?a-p d radiatorwithout n'ell and the prorm chamberto exarea.The injector
;qnlase is-tt'e1Jbg l. In conventional isplaced from the rell. In SAGD-th-* lhether the mecho analyzethe prott be anticipated. ;ere carried out in ed with theory.
o producea stable steamzoneflows i diffuse Buckleys the tendencyfor ,nu'ell.This effect e reservoirand by to keep the steam the reservoirdips eam-assisted gravconventionalwells ion well make the low. In the steamC. and production ted to be practicaides an economic
{ f
1
GRAVITYDRAINAGETHEORY In the developmentof the conceptjust described,the objective was to develop a meanswhereby steam could be introduced continuously and the condensateremoved as it formed, togetherwith the oil that has been heated.The conceptis shownin Figure7.1. Steamis introducednear the bottom of the reservoirand tendsto rise; the heaviercondensateand heatedoil tend to fall to the bottom. Meansare provided for introducing steam quite near to the bottom if there is difficulty in displacing cold oil or higher up if the oil is mobile, and for removingliquids as they drain to a lower location.As the liquids are removed,the spacethat is left in the poresis filled with steam. A horizontalwell is placedat the bottom. A steamchamberis formed above the well, and steamis injectedcontinuouslyinto this chamberby meansof another horizontalwell placedcloseto and usuallysomewhatabovethe productionwell. [n someapplicationsthe injectionwell may be a verticalwell rather than a horizontal well (for long horizontalproductionwells,a numberof verticalwells may be used). In reservoirscontainingmobileoil, a horizontalinjectionwell placedhigher in the reservoir,rather than low down, can be usedwith advantage. The steampressureis usuallymaintainedconstantduring much of the process.The chamberis surroundedby colderoil sand.Steamflows through the sand The liberatedheatis conducted within the chamberto the interfaceand condenses. surfaceand allows into the colderoil sand.This heatsthe oil near the condensation alsodrains.As the oil it to drain by gravityto the productionwell. The condensate is removq4 the -steamchambergrory-supwards and sideways.The pressrlFwi-iliin the steam-ihdmbeiifitils a;ieitiafiv constant.Flow is causedby gravity.Oil and drain downwardsand steamrises. steamcondensate In somerespectsthe processis analogousto that of water draining from a gravitydrainage,steamdoesnot bathtub.In the majormechanismof steam-assisted Mechanism: o Steamcondenses at interface o Oilandcondensate drainto wellat bottom o Flowis causedby gravity o Chambergrowsupwardsandsideways
Heatedoil flows to well
'ocesslies in over.,;-'+
re created Dy the
mbustionwhich is de:\ ersesteamflooding. rainage
Chap. 7
steam Continuous injectionintochamber GravityDrainageTheory
Oil and condensate Figure 7.1 Steam-Assisted Gravity draincontinuously Drainaee 287
I
]N I
(
q tl rl d
{
q
t
tl
rl
push the oil out anymorethan the air pusheswater from the tub when it empties. Yet' eventually,the steamfills the volumeoriginallyoccupiedby oil just asair eventually fills the tub. It has long been realized that the gravity drainageof conventionalcrude oil from below a gas cap can produce unusuallyhigh oil recoveries.Dykstra (197g) summarizes work in this area.Terwilligeret al (1951)showedthat the recoverydecreasesand the drainagerate increaseswhen pressuregradientsare imposedupon the gravity drainageprocess.Increasingthe rate by lowering the production well pressuretendsto leaveadditionalliquid behind in the gas-saturated region. While the dynamichold-upof oil in the gas-saturated steamchamberis significant, it is relativelysmall,sincethe viscosityof the oil within the chamberis-very low comparedwith the averageviscosityof ihe oil drainingbelow and around it. The averageoil saturationremainingin the steamchimber can be estimated usingthe integratedform of an equationdevelopedby cardwell and parsons $9a\; this is shownin equation7.1. b-l)lu3$/\rrtt-tt a Jor = ----l-l ,, I D \DKgt I
(7.1)
where S-o, is the average residual oil saturation after time I
Z is the drainageheight k is the permeability b is thb exponentin cardwell and parson'sequationfor relative permeability,k, : Sb ls is the kinematicviscosityof the oil at the temperatureof the steam If b is set equalto a typical valueof 3.5 and Z is setequalto the maximumpossible valueh, then the resultis equation7.2.
s.,= o+z(z&!)'^
(7.2)
residualorl I order a-sthd In rhc grou'th of th up*'ard erot becomescrit seriesof pan The ho w e l l so n e i t h m a t i c a l l l ' a tt reservoirand g-lESteam Ia1 w e l l s .T h i s u initial anallr This theon i Darcy's Lar
-.-1 Figure sh heated br ge wards the prr The se c o n d e n s i n g: sho'*n. is inc 15. Heat is tt face. into th from the inte the oil is r'. C into the papt
Typical field valuesfor a steamchambertemperatureof 216"Cand for Cold Lake crude are as follows. vs = 0.452m2/d (5.2 cs) k = 0.987x 10-12m2(1 darcy)
6 :0.3;
ft=30.5m
g = 7.32 x 1010m/d2
The averageresidualoil saturationhas been calculatedin Table 7.1 for various times /. TABLE 7.1 So.as a Functionof Time t (days)
s,,
100 0.34
200 u.zo
1,000 0.14
2,000 0.10
Note that thc ps, and pip., within the el U and it is as ture aheadol is the same a
10,000 0.06
For a practicalcasewith a projectlife of 6 to 15 years,the averagetime that the chamberwould drain might be of the orderof 2000days,and the corresponding 288
Steam-AssistedGravity Drainage
Chap.7
GravitvDrana
:ubwhen it empties. v oil just asair evennventionalcrude oil ries. Dykstra (1978) hat the recoveryde.s are imposedupon the productionwell Lratedregion. n chamberis signifithe chamberis very low and aroundit. €r can be estimated and Parsons(1949);
(7.r) et
rtionfor relative eratureof the steam r maximumpossible
(7.2)
residual oil saturationwould be 0.1. values calculatedfrom (7.2) are of the same order as thosegiven in Figure 4.9 in Chapter4. In the initial analysisof this concept,it appearedthat the upward rate of growth of the steamchamberwould be larger than that sideways.Eventually the upward growth is limited by the top of the reservoir,and the sidewardgrowth then becomescritical. Figure 7.2 showshow steamchambersare expectedto grow for a seriesof parallel horizontal production wells in a reservoir. The horizontalwell shown in the centerof Figure 7.2 is flanked by similar wellson either side.The positionsof the condensation surfaceare showndiagrammaticallyat successive periodsof time. The__steam chambglsgrow to the top of the reservoirand then s?tqadljdp:WgyC.4_tt-er a periodlhey intermingle and form a sing-lE-steamlayeiabove the oil. Heating continues and oil drains to the horizontal wells.This method allowsalmostcompletecoverageof the reservoirvolume.The initial analysisfocusedon the rate at which steamchamberscan grow sideways. This theory is discussedin the next sections. '----?-----'
Darcy's Law Figure 7.3 showsa small part of the drainageinterface.It is a vertical section.Oil heatedby steamflows approximatelyparallel to the condensationsurfacedown towardsthe productionwell somewherebelow the left of the depictedregion. The steamis at a temperature25,and the reservoiris initially at Zn.Steamis condensingat the condensationsurface,or the interface,which, in the region shown,is inclined at an angle d to the horizontal.The interfaceis at temperature Heat is transferred into the Zs. ien -Beyond the inter--^-.# face, into the reservoir,successivelayersof material are cooler.At a distance€ from the interface,wherethe viscosityof the oil is pr.and the kinematicviscosityof the oil is z, Darcy'slaw may be written, for a sectionwith unity thicknessmeasured into the paper,as: -! x 1)(p, - pr)gsin 0 ,^ = _ k(dt uq t7.51 a\
and for Cold Lake
=kgtino dt
= 30.5m " ^/d' tble 7.1 for various
Note that the€gllgntialgradientis (vpo- gc)g sin g. p, is neglectedin comparisonto ps, and p/pois set equal to z. The equation-f,v€3-tlierate of drainageof oil, dq, within the elementd{.If the interfacevelocitymeasurednormal to the interfaceis
er-rcbyconduc-tf .o-gpply,thenthetempera.93lLtl1eSjg$"d-tl$.f lgU9g*-rats-f ture aheadof the interfacefor a steady-state advanceis givenby equation7.4; this is the sameas equation2.44.
) ).10
10,000 0.06
Figure 7.2 Growth of SteamChambers Above ParallelAdjacentHorizontal Wells
e averagetime that 1 the corresponding Drainage Chap.7
Gravity DrainageTheory
289
function of di temperaturetc The vari the particular correspondsre terestis giveo
POSTTtOiloF
"r"
T=Ts lX STEAT CHATBER
,. T=Tr ll{ ORIGII'AL BESERYOIR
NOBTAL VELOCITY
u
\
xerr
CONDUCTIOT
Figure 7.3 Small Vertical Sectiono{ Interface
T-To
-ultd =
Ts-T^
(7.4)
P
High valuesof u result in the temperaturefalling rapidly with distance,and low valuesgive a slowlyfalling temperature. If the reservoir were unheated,then the correspondingdifferential flow would be given by equation7.5:
d q ,= W d t
(7.s)
Up
It is useful to subtractthis flow from that given by equation7.3 to give the increasedflow due to heatins.
dq - dq, = kg sino(-l-- 1)rE \ z
val
*)r*
(7.7)
This manipulationis done becauseotherwisethe total flow that would be determined by integrating7.3 would be infinite, since 24,althoughit is likely to be very large,mustbe finitq By making this change,the difficulty is overcome.2 Integrationof equation7.7 resultsin 7.8.
q= kssin aJ(+- +)"
lntegrated Flo
Eliminatingtb equation7.ll I volvesthe unk
(7.6)
We now redefinedq as (dq - dq,), as given in 7.7.
dq= k8,," u(+_
This functim r of the integra In order t temperature.I the paramete The inrq equation7.10
(7.8)
To evaluatethe integralit is necessaryto know the viscosityof the oil as a function of distancefrom the interface.SinceequationT.4givesthe temperatureas a
There is r zero, then q ca zero, then tlx provide an int would be need Material Bab
A secondrelat fined by consi regiondepicte If the int fasterrate thar advanceof the verticaleleme
2An alternative meansfor circumventingthe problemof the infinite cold flow is to neglectvp in equation7.8 and make the upper limit of the integralsomehypotheticalfinite value 4.,*. In principle, f."* is chosento be suchthat I has fallen to a value at which the drainageis negligibte.
290
Steam-Assisted GravityDrainage
Chap.7
Gravity Drainag
function of distance,it is necessaryto know the viscosityonly as a function of temperatureto evaluate4. The variation of viscosity with temperaturedependsupon the properties of the particular oil in the reservoir.One arbitrary form of temperaturefunction that correspondsreasonablywell to the performanceof actual oils over the rangeof interestis given by equation7.9.
:=(#)^ rall Vertical Section of
(7.4)
(7.e)
This function also has the attractionof being of a form that makesthe evaluation of the integralof 7.8 particularlysimple.Also, zn is infinite, i.e., 1,fvp= g. In orderto useequation7.9it is necessary to specifythe viscosityat the steam temperature,Zs,and a value for the parameterm. For heavycrudes,it is found that the parameterlz should have a value of about 3 to 4. The integral of equation 7.8 may be evaluatedwith the result shown in equation7.10.
ith distance, and low
f - 1 1 , 1l d\ .€ = ; a - 1 I f - - -val U l7lu5
.ro \z
ing differentialflow
(7.10)
Integrated Flow
(7.s) n 7.3 to give the in-
Eliminating the integralfrom equations7.8 and 7.10givesthe expressionshownin equation7.11.for the flow 4. By itself this equationis not too useful, since it involvesthe unknown variablesU and sin 0. kga sin 0 q= ^rru
(7.6)
(7.7) that would be deterit is likely to be very overcome.t
(7.8) of the oil asa functhe temperature as a
There is a trivial solutionto 7.11.that shouldbe noted.If both U and sin 0 are zero,then q canbe any arbitraryvalue.The significanceof this resultis that if U is zero, then the steady-statetemperaturedistribution that was assumedwould provide an infinite amount of heated reservoirand only an infinitesimal slope would be neededto move any amountof oil. This is, of course,unrealistic. Material Balance A secondrelationshipbetween the flow of oil q and the front velocity can be defined by consideringthe materialbalanceat the interface.Consideragainthe small regiondepictedin Figure 7.3. If the interface is advancing,then oil must be flowing out of the region at a fasterrate than it is flowing in; it is the differencein the ratesthat determinesthe advanceof the interfaceratherthan the rate itself.A materialbalanceabouta thin vertical elementresultsin equation7.12.
cold flow is to neglect zp frnite value {,"*. In prinainage is negligible.
7 Drainage
Chap.7
(7.11)
(#),=do''(q). Gravity DrainageTheory
(7.r2)
291
Velocity of the Interface
Position of tb
The velocityof the interfaceu is relatedto the term (ay/at)in equation7.12 and to the angle0 by equation7.I3.
u : -cos ,(x).
(7.13)
In this expressionthe term @yl$ can be expected to be negative.U from equation7.13 is substitutedinto equation7.11,and this is simplified by setting sin 0/cos0 : tan 0 : @y/Al. When this is done,the resultis 7.1.4. q- =
kga sin 0 tnus cos 0(0y/0t)
- -------------
*(x) ^"'(x)
(7.14)
_ _klad LS. - lay\ ^r, \M), Equation7.r4 maybe rearranged andintegrated by separating the variables, asin 7.1,5.
tTlUS
l2gAS,kga(h - y) ^r4
one side3
Note that the hc dent of time. If above the prodr of time t and be
(7.1,s)
Equation7.20 m sionlessvariable
or, at the bottom of the steamchamberwherey = 0. q=
Multiplying eqr and substitutir equation7.18.
Equation 7.19 r equation7.20.
ln , [ o - , 6 \ S "-k "s q dv I q d q = Jg| r0 t=V
The horizonta
(7.16)
This is a remarkableresult,sinceit indicatesthat the rate of drainageis a function of the drainageheightbut is not dependenton the shapeof the interfaceor on its horizontalextension.Extending the interface horizoniallyincreasesthe area for heat transfer,but this effect is just counterbalanced by theeffect of the longerand more slopingpath in restrictingthe flow. It is interestingto realizethat all the variablesin equationT.16and similar oneshaveequalweight.For examplg,changingany of them by a factorof 2 changes the predictedrate by a factor of rt. 3Equation
7.16 is marked one side. It gives the rate at which oil drains from one side of the steam chamber' For the usual field situation where oil is draining from both sides of the steam chamber, the rate must be doubled.
292
Steam-AssistedGravity Drainage
Chap.7
Valuesof Y calcr A characte face moves hori.
Gravity Drainage1
Position of the lnterface I in equation7.12andto
The horizontal velocity of the interface is given by equation7.17.
/a,\ t_t =
(7.13) r be negative. U from is simplified by setting It is 7.14.
\atl,
-(#). Q.17)
/q\
\ri,
Multiplying equation7.r7 by equation7.14 (as shown on the secondline of 7.14) and substitutingthe value for 4 from equation7.15results,after rearrangement,in equation7.18.
ks" /a'\ _ T\ti,= Vrow"r;,(h-y, (7.r4)
(7'18)
Note that the horizontal velocity is a function of the vertical height but is independent of time. If it is assumedthat the steamchamberis initially a vertical plane abovethe production well, then the horizontal displacementis given as a function of time r and heighty by 7.I9.
x=rti t
ting the variables,as in
rr"
(7.1e)
,rry*rg1,-g
Equation7.19 may be rearrangedto give y as a function of x and /, as in equation7.20. ksa
.
|rY
(7'20)
Y=h-rots"^"'\;)
(7.rs)
Equation7.20 may also be written in the dimensionless form of 7.21.The dimensionlessvariablesX, Y, and /' are defined by 7.22.
n,Y=r-+(+)'
(7.16) f drainageis a function i the interface or on its increasesthe area for :ffect of the longer and
dty Drainage
Chap.7
t lroa
\-
I 14.4
(7.2r)
/v\
t=\i)
x=(il
uation7.16and similar by a factor of 2 changes drains from one side of the oth sides of the steam cham-
J' I
t
(7.22)
k* - ' _- _i\l 6AS,*r ,h .
f
Valuesof Y calculatedfrom equation7.21 are plotted againstX in Figure 7.4. A characteristicfeature of this set of curvesis that the lower part of the interface moves horizontally away from the production well. If the well were at the
Gravity DrainageTheory
293
Equaair gral which b temperaturci above unncc tion 7.9. ttrca In this r function can I porated(&d
1 U.'J q)
c o o
0.6
i5 0 . 4 E FL
o.2
Changeof S
Q)
Figure 7.4 Calculated Interface Curves
origin of Figure7.4, then it is apparentthat the oil would haveto movefarther and farther horizontally along the base of the diagram as the bottom of the interface moved away. of equation7.11it waspointedout that, basedon the assumpIn the discussion tions made,oil could indeedmove horizontallybelowa stationaryhorizontalinterface.This was indicatedto be possiblebecausethere is assumedto be an infinite thickness of oil, all at steamtemperaturebelow a stationary interface. With such conditionsonly an infinitesimalslopewould be neededto causeoil flow. Although this is not realistic,the conceptof two interfacialcurveswith oil slidingdown one that is advancingand then moving alonganotheralmoststationaryone with a much somepracticalsituations.a lower slopeis conceivableand resembles Another way of looking at this resultis to imaginethat a pool of heatedoil is maintained around and above the horizontal well with the rate of removal being controlledin order to maintain the level of the liquid constantwithin this sump. becauseof the receding As the processproceeds,the width of the sumpincreases interface. Becauseof the problem of the recessionof the interface from the production well, the ratescalculatedby equation7.16 arerecognizedasbeingtoo high. This is discussedfurther in the discussionon TANDRAIN, which is given later.
The dependa tion 7.4. Usiq 7.8 from distr obtainedby d nating the eq
Substitutim r equation7.8.
The integralo which contain relation. Equr pendenceofv only of the ef also of the ef, In ordcr nient to redef resultsin exp
THE EXPONENTm-AN EXTENDEDDEFINITION with the empiricalequation7.9 to allow for the efThe properlXm wasirluo-duced viscosity. In the development*ofthe-ili66iyl"ltrisTorm"ot _;eet--irti'aup-}4!@t" -equation iJpariii[iurty"iiiracfive, since it allows the evaluation of the reciprocal integral(equation7.8)and providesa simpleand useful result. viscosity-distance aOneexampleof suchbehavior is given by the processshown in Figure 7.63.In this experiment oil from a steamchamberdrained downwardsto a horizontal shalebarrier which was heated from below.The oil was able to f low alongthe surfaceof the barrier with an interfacethat was inclined only very slightly.
294
Steam-AssistedGravity Drainage
Chap' 7
This definesa the steamt€n matterto writr
5It is also 1 gral of 7.25 and parameter.Tbir readily;misadi tions it is adequ
The Exponentr
Equation7.9providesa particularlysimpleresultbecauseit resultsin an integral which is evaluatedreadily; it also makesthe viscosityof the oil at reservoir temperatureinfinite and makesthe manipulationto eliminatethe cold flow used above unnecessary.If the temperatureviscosity relationshipis limited to equation7.9, then it is not possibleto allow for the effect of reservoirtemperature. In this sectionit will be shownhow any realisticform of viscosity-temperature functioncan be employedand how the effectof reservoirtemperaturecan be incorporated(Butler 1985). Changeof Variable of Integration
rveto movefarther and )ottom of the interface .t.basedon the assumpionary horizontalinter,umedto be an infinite ry interface.With such auseoil flow. Although th oil slidingdown one ionaryonewith a much ,rations.a rt a pool of heatedoil is l rate of removal being stantwithin this sump. )ecauseof the recedins Lcefrom the production , beingtoo high.This is is siven later.
The dependence of temperatureon distancefrom the interface{ is given by equation 7.4. Usingthis relationshipit is possibleto changethe variableof integrationin 7.8 from distanceto temperature.The expressionfor d{ given by equation7.23 is obtainedby differentiatingequationT.4andcombiningthe resultwith7.4 by eliminating the exponentialterm.
dt=
ddT -Ta-k)
(7,23)
Substitutionof df from 7.23 givesthe following expression for the integral of equation7.8.
f (+-i)'r= ! [ " / 1
UJa\,
_1\
dr
,^lT-Tn
(7.24)
The integralon the left-handsideof 7.24waspreviouslyevaluatedby equation7.L0, which containswithin it the exponentlz from the empiricalviscosity-temperature relation.Equation7.24 allowsthe evaluationof the integralfor any specifieddependenceof viscosityz on temperature7l furthermore,it allowsthe inclusionnot only of the effect of the steamtemperatureG (equation7.10also allowsthis) but also of the effect of the reservoir temperatureTn. In order to continueto use the expressiondevelopedpreviously,it is convenient to redefineln usingequation7.25. Combining7.10and7.24 and solvingfor rn resultsin expression 7.25.
*=1.,r:e-+)f^l'
( 7.2s)
r 7.9to allow for the efhe theoiv. this form of ,rationof the reciprocal rple and useful result. r Figure 7.63.ln this experirle barrier which was heated ith an interface that was in-
vity Drainage
Chap.7
This definesm as a function of the viscosity-temperature gf the oil, characteristics the steam temperature,and the reservoirtemperature.tIt is a relatively simple matterto write a computerprogramthat will calculatethe integralof equation7.24 5It is alsopossible to considerthe term mvsas a propertyof the oil that is definedby the integral of 7.25 and is a function of Za and 7s. In the developmenthere,m is consideredas a separate parameter.This has someadvantage,since /s is a strongfunction of temperatureand is visualized readily;m is a dimensionless numberthat doesnot vary rapidlywith either Tnor ?r. In many applicat i o n s i t i s a d e q u a t e t o c o n s i d e r r ? ?a s a c o n s t a n t .
The Exponentm-An ExtendedDefinition
295
or the correspondingvalue of m for specificcrudesand input parameters.Specific valuesof the parameterm are calculatedin a later sectionusingequation 7.25 and viscosity-temperature curvesfor specificoils.
DIMENSIONALSN
As discussed i beine heatedI
ORIGINALSCALEDVISUAL MODEL The earliestexperimentscarried out in Esso Canada'slaboratoryinvolvedthe use of glass-sided reservoirmodelsoperatedat atmosphericpressure.The resultsof an experimentof this type are shownin Figure 7.5 as a seriesof positionsof the observedinterface. -49es-lgde! +Odel ?9 cy l-ong,11cm h1gLltd25_cm thick was filled with glassbeadsand saturatedwith cold Lake crude.A 1vi1emeshalongthe left-hand vertical side of the model representeda fracture. Stea;t?fr6spheJc pressurewas introducedinto the top of the model,and liquids were allowedto driin from the bottom as shown. The permeabilityof the glassbeadswas chosento make the model dimensionallysimilar to the field. If the theory describedpreviouslywere completeand accurate,the dimensional similarity betweenthe model and the field could be achievedby making the dimensionless time as determinedby equation7.22the samefor the model as for the field. For a givenvalueof /', equation7.2! predictsa specificcurve of yversusX. Examinationof equation7.22indicatesthat with this restrictionalone,it would be possibleto compensatefor a low permeabilityt by employinga matrix with a high thermaldiffusivity a. The low mobility of the oil would be compensated for in this caseby allowing a deeperpenetrationof the heat below the interface.Sucha compensation is realisticonly if there is, in fact, a sufficientdepth for heat flow to occur; i.e., the assumptionthat the reservoirextendsto infinity that is implicit in the integrationof equation7.8 may not be realistic. An analysisof this problemhas shownthat a conditionfor dimensionalsimilarity that overcomesthis problemis that not only must/' (asgivenby equation7.22) be the samefor the model and the field, but also,a dimensionless number,B3given by equation7.26 mustbe madethe same. (7.26) Glass-sided reservoir model -...--_
F, is sometic sionlesstinr, t that is beingb larity betwecr
IfF, andt'el quotient,
will alsobe eq If therc r velocity at rti the field shou spondingp
This equatio voir matrix. R be proportitn the samefq t sin 0 will alsoI then, that thc time t" should
-
1
I E E
If equation7l similarity.
o
j 296
Figure 7.5 Glass-SidedReservior Model (after Butler, McNab and Lo 1981)
Steam-AssistedGravity Drainage
Chap.7
Dimensiord Si
parameters. Specific ng equation7.25 and
DIMENSIONALSIMILARITY As discussedin Chapter2, the extentof the rise of the temperaturein a solid body beingheatedby conductionis determinedby the dimensionless number F,=*
rory involvedthe use rre. The resultsof an f positionsof the obthick wasfilled with h alongthe left-hand Jsphericpressurewas ed to drain from the chosento make the accurate,the dimenachievedby making rme for the model as recificcurve of Yver"ictionalone,it would f ing a matrix with a e compensatedfor in the interface.Sucha epth for heat flow to ity that is implicit in br dimensionalsimii'enby equation7.22) lessnumber83 given
(7.26)
n'
(7.2t)
F, is sometimesknown as the Fourier number.It may be looked upon as the dimensionlesstime, which comparesthe depthof the penetrationof isothermsinto a body that is beingheatedby conductionto its physicaldimensions.For dimensionalsimilarity betweena model and the field, both I'" and /' shouldbe the same.
.tT"kp
't ' : - a l h Y 6AS.mvth
(7.28\
If F, and t' are eachequalin the field and in the model,then it followsthat their quotient,
B' F. o_ L =
ad L,S"mvs
(7.2e)
will alsobe equal.This is the conditionthat wasmentionedin the previoussection. If there is dimensionalsimilarity betweenthe model and the field, then the velocityat which the fluid is running down the interfaceat any particularpoint in the field shouldbe equal,in scaledterms,to the velocityin the modelat the correspondingpoint. The velocityat the interfaceis given by
g - kS,sin velocityat interface: -+(g\ 6AS"\dtl+s vQA,So
(7.30)
This equationrecognizesthat the flow is confinedto a fraction @AS, of the reservoir matrix. For thereto be similarity at the point, the velocityof the interfacemust be proportional to hft, and it follows, therefore, that kgt sin 9lhvs$ AS, should be the samefor both the model and the field. If theseare dimensionallysimilar, then sin 0 will alsobe the same,and it can be droppedfrom the expression. A condition, then, that the fluids shouldbe draining at similar ratesis that the dimensionless time /" shouldbe the samein both.
kst
,,
-t ' = :
6 A,S"vsh
(7.31)
If equation7.31is divided by 7.28,there resultsanotherconditionfor dimensional similarity.
ksh* VB, = T
a s s - S i d e dR e s e r v i o r utler, McNab and Lo
r Drainage
Chap.7
V
DimensionalSimilarity
(7.32)
"dAS',,t
297
It will be notedthat fnrit equalto mB3.6Theparametermwillbe the samefor the field and the model if they operatewith the sameoil, steamtemperature,and reservoirtemperature.Even if theseconditionsare not true, the valuesof z will not differ very much; as a result,althoughit will be impossibleto satisfyboth 7.31 and 1.32simultaneously, the error is probablynot very great. If it is assumedthat m hasthe samevalue in both the field and the reservoir. then the conditions7.29or 7.32 canboth be replacedby
Ur:r/ffi
(7.33)
It is suggested that the conditioninvolving83, equation7.29,shouldbe used,since this is the one that comesout of the improvedtheoryasa dimensionless parameter; this is discussedlater. The dimensionless time definedby equation7.31is quite similar to the drainage modulus x time referredto in the paper on gravity drainageby H. Dykstra (1e78). For the modelexperimentshownin Figurei.5,the corresponding model and field conditionsare given in Table7.2. Modeland FieldParameters MODEL mlr) Kg m'/d' hm om'fd ,, mtfd dAS, Bz atlh2
3.9 107gtr) 0.105 0.0557 1 2 . 2 5( 9 8 " C ) 0.4 10.3
5.0s1:'
FIELD
3.9 0.072s) 30.5 0.0557 0.4s2(21s.C) 0.21 10.3 6.00x 10-5r('z)
The 5 b e n o t e dt f l i n e st o c u l of the mcd the model ' also tend tr by the the< It als of the rcse desirableir loss- parti As rr; to about l. conditions The I resultsare The t The agreei due to iacr fective her heat is use willbe rhs t u t i n g 1 . 5t modified it it is in bett
"'l he data in the table come from the original paper on this subject. It was not realized then that 721 could be expressed as a function of 7p and 15, and it *ur as.umed that since the oil was the same, rn would have the samevalue for both the model and the field.
(')t in days. \'/Corresponds to 15000D. (o)Corresponds to 1.0 D.
ln order to obtain dimensionalsimilarity, it is necessaryto employa much more permeablemedium in the modelthan is presentin the field. The time scaleis very compressed_ in this example; 1 min for the model is equivalent to (5.05/ (6.00x 10-5))min, or 0.16y, in the field. 682has been defined in this way in order to make it consistentwith the usagein the cited papers.
298
Steam-Assisted GravityDrainage
Chap.7
Dimensiona
r will be the samefor 3amtemperature,and . the valuesof rn will 'le to satisfyboth 7.31 Leldand the reservoir,
(7.33) shouldbe used,since ensionless parameter; : similar to the drainrinageby H. Dykstra espondingmodel and
FIELD
i.9 0.07zto) i0.,s 0.0557 0.1s2(215.C) t1.21 10.3 6.00x l0-5t(2)
The positionof the interfaceat 10-minintervalsis shownin Figure7.5. It will be notedthat the oil drainedin a systematicmanner.The tendencyof the interface lines to curve upwardat the top is believedto be due to heatlossesthroughthe top of the model.Thesecausepressuregradientsin the steamchambernear the top of the model that are not recognizedin the precedingtheory.Suchpressuregradients alsotend to causethe actualproductionto be somewhatlower than that estimated by the theory. gaswill tend to accumulateat the top It alsoseemslikely that noncondensable of the reservoirand reducethe rate of heatingalongthe top. Suchan effectmay be desirablein somecases,sinceit will limit the overrideof the steamand reduceheat loss-particularly in isolatedwell systems(Butler and Yee I986a,1986b). As was shownpreviously,10 min in this particular experimentis equivalent to about 1.6 y productionin a full-scalefield experimentcorrespondingto these conditions. The recoveryof oil from the modelis plottedagainsttime in Fig.7.6, and the resultsare comparedwith the recoverypredictedby equation7.16. The observedrate was of the sameorder as that predictedbut slightlylower. The deviationof the observedrate is thoughtto be The agreementis encouraging. due to factors not recognizedin the derivation of the equation.With time, the effective heightbecomeslower than /ebecauseof depletionand becausesomeof the heat is usedto causethe lateraltransferof the drainingfluid to the fixed well (as for approximately by substiwill be shownlater,this lasteffectcan be compensated tuting 1.5 for the constant2 within the squareroot sign in equation7.16.The line modified in this manneris also shownin Figure 7.6 whereit is markedTanDrain; it is in better agreement.
1.0
Eouotion7. 16
A
i not realized then that m e the oil was the same, m
TANDRAIN
L
c) o (J
AA
-q 0.5 V
AA
l,^^^
E rmploy a much more fhe time scaleis very equivalent to (5.05/
c o U
o L
L
/tL
^^ I Experiment
40 Time in Minutes
th the usagein the cited
80
Figure 7.6 Recovery of Oil from Model
1 Drainage
Chap.7
Dimensional Similarity
299
ORIGINALSCALED,PRESSURIZED MODELS EssoCanadahas carried out gravity drainageexperimentsusinga scaled,pressurized reservoirmodelin additionto atmospheric-pressure, visual-models. Filure 7.7 showsa photographof a horizontal section through one of these modelsalter the oil had been partially producedby gravity drainageusing steamat about 3 Mpa. The centralcircular steamchambercan be seenclearlyin contrastto the black oilsaturatedregionthat surroundsit. The well arrangementthat was usedfor this experimentis shownin Figure 7.g. In this particular experimentthe flow was radial. Steamwas injectedfrom a vertical well locatedalmostimmediatelyabovethe productionwell. The shapeof tlS-tg.lttambgr for_med.is depictedby rhe .uru.i in Figure 7.s; ttrieF#m=rrom-!-h.elmocouples that were buried in the reiervoir sand. - catedgt obs€rvations ProduCtioniaGdTiom these experimentswere about the same ii would be predictedby the gravity drainagetheory with an allowancefor radial flow.
r I
| ,-.t I Uat* " lffi
lsr|('r ls.;:ol
l*" I
CALCULATEDDRAINAGERATESFORFIELDCONDITIONS Figure 7.9 showsthe expectedrate of drainageto a horizontalwell under a practical field condition' The curvespredict the raiesof drainageof Lloydminster, Cold Lake, and Athabascacrudesfor the particularset of reservoirconditionsshown as a function of the steamtemperatureemployed.
The p temperatur zontalwell i 500 m long This is cakr the valuess and averag Thesc the wholerr t a l w e l l .I n ' researcher
s!
o
I'
E r')
E
o o E o o o .g o
o Figure 7.7 Photographof High PressureGravity DrainageModel (from Butler, McNab and Lo 1981)
300
Steam-AssistedGravity Drainage
F4r for t Chap.7
CalculatedD
{ a scaled,pressurmodels.Figure 7.7 'e modelsafter the n at about 3 MPa. ist to the blackoil1susedfor this ex'as injectedfrom a *ell. The shapeof j.g: tne]e-u,==-er|=lohe reservoiisand. sameas would be radialflow.
Height: 38.7 cm Diameter: 55.9 cm
Permeability: 180D Sandporosity:0.,144 56; : 0.86 Sleamoressure:3 MPa
tt
Production Production
from iliJ,liJ;1"#'#:::1.:'"#:::face
I
fl
d
'ell under practia .loydminster, Cold rnditionsshownas
The predicted rates increasewith steamtemperaturebecauseof the effect of temperatureupon oil viscosity.Ratesfrom about 0.05to 0.8 m3/d per meter of horizontalwell are predicted(0.1to 1..6Bldft). For example,at200'C a horizontalwell 500 m long would be expectedto produce about 150 m3of Cold Lake oil per day. This is calculatedfrom equation7.16.In practice,maximumratesof about807oof the valuesshownmight be expected.Also, of course,depletionwill lower the rate, and averageratesthat are only a fraction of the maximumwill be found. Thesecalculationsassumethat the steamchamberstartsout extendingover the wholevertical height of the reservoirand alongthe whole length of the horizontal well. [n practiceit may take time for the chamberto grow to theselimits. Esso researchers(Griffin and Trofimenkoff 1986)have suggestedthat the rate at which a so = 0.825;Sor = 0"175;9- 0.325:K"ff = 1 pn?tPc = z'tzskJ/m3oc kf, = t.Z W/moC;h - 20 m; T = 12o C
B/Doy ft
!
E
1.5
r.)
-
q) +
1.0
0.5
o E. q) ql
AE
c t-
o rom Butler,
'ainage
n
100
-rn 200 Steom Temperoture o C
3oo
Figure7.9 PredictedDrainageRatefor VariousCrudes(basedon Equation7.16 for typical conditions;2 sides)
Chap. 7
Calculated Drainage Rates for Field Conditions
301
il il f il
I ( {
I
{ I
I I
I
I
A I
steamchamberspreadsalongthe horizontal well if the chamberstartsfrom a vertical injector can be calculatedfrom equationT.lg by settingl:0; they present laboratory results to support this. Rates abott 50Vofaster than this were found when the horizontal well was heated. TANDRAIN.AN EXTENSIONTO THE ORIGINALSAGD THEORY The theory described in the previous sectionshas been modified and extended (Butler and Stephens1981)in two ways: 1. The calculatedinterfacecurvesof Figure J.4 weremodified so that they remain joined to the productionwell. 2. The theory was modified to allow for the confining effect of adjacentwells. Whereasin the previous treatment the interface spreadhorizontally to infinity, in this paper it spreadsonly to a vertical no-flow boundary located halfway to the next adjacentwell. A point of concernwith the solutionderivedpreviouslywasthat the oil draining down the interfacecurveswould have to drain horizontallyto the well after it reachedthe bottom. Someof the availableheadmustbe usedto causethis lateral flow. As a simpleapproximation,it is assumedthat the lower parts of the interface curvesof Figure 7.4 canbe replacedby tangentsdrawn from the well to the curves. This is shownby the curvesin Figure 7.10. The name TANDRAIN was used at one time for a computerprogramwhich drew thesecurves. Figure 7.11showsthe effect for a typical interface.The TANDRAIN assumption reducesthe rate of drainageof oil to the value given by Equation 7.34.
< 0.8 Q)
o.o P o
The rate is &l the recovery, proportion.t Anotbcr headcausing of the head b Effect of l|o
The theory in interface cun The din ently from th expressionfu tance betwec The rw on the drainA found that it r
4
,a
o
o
The relatiood is shownin F
0.4
C)
E g 0 .2 00.5
7A variari
1 1.5 HorizontolDistoncex/h
the interface rtr size this straigl intermediate p
2
Figure 7.10 CalculatedInterface Positionsfor an Infinite ReservoirUsins the TandrainAssumption
302
Steam-AssistedGravity Drainage
Chap.7
Tandrain-An I
:r startsfrom a verti-l = 0; they present han this were found
-c
1
q,
o c o o
0.8
a o o)
0.4
.9
o.2
i5
dified and extended
a
q)
ified so that they re:ct of adjacentwells. :orizontallyto infinw boundary located asthat the oil drain!' to the well after it to causethis lateral rarts of the interface rewell to the curves. )uter programwhich ANDRAIN assump:quation7.34.
0.6
05 .E o
Decreosein Recovery ot t'=0.4 (13%) 0.5 1 1.5 Dimensionless Distonce x/h
2
Figure 7.11 Effect of Tandrain Assumptionon PredictedRecovery
q=
1..5kga$!,5"h
(7.34)
The rate is 87% of that calculatedby 7.16,and-as may be seenfrom Figure 7.11the recovery,for the samevalue of the dimensionlesstime, is reducedin the same proportion.T Another way of comparingequations7.19and 7.34 is to saythat the effective headcausingvertical drainagehasbeenreducedfrom ft to 75% of ft. The remainder of the head is used to causehorizontal movementof the draining oil. Effeet of No Flow Boundary The theory in the TANDRAIN paper (Butler and Stephens1981)leadsto the set of interface curves shown in Figure 7.12 for a confined reservoir. The dimensionlesstime and the abscissausedin this figure are defined differently from those of equation 7.25; w rather than h is used as the dimensionin the expressionfor the dimensionlesstime; w is defined as half of the horizontal distance betweenwells. The revised theory provides a relation that allows for the effect of depletion on the drainagerate. A numerical solution was developedin the paper, and it was found that it could be representedby the simple equation7.35a.
Q.=1/,-f'\n
(7.35a)
The relationshipbetweenthis and the previousexpressionsfor the rate of drainage is shownin Figure 7.13. 7A variation of the abovederivationis termedLINDRAIN. In this variation it is assumedthat the interface remains straight right up to the top of the reservoir. As the steam chamber grows in size this straightinterface becomesmore inclined and longer. It is also assumedthat, at a limiting intermediatepoint on the interface,the heat aheadof the interfaceis just equal to the steadystate value.Above and belowthis critical point there is lessheat aheadofthe interfacethan would correspondto the steadystate.The location of the critical point is chosenso that the drainagerate is a maximum; this leadsto a position of y/h = 1/V3. With theseassumptionsit is found that adrainage rate equationsimilar to 7.34 is obtained exceptthat the constant1.5 is replacedby 0.75V3 = 1.3.
voir Usingthe
Drainage
Chap.7
Tandrain-An Extensionto the OriginalSAGD Theory
303
o a u,l J
z o 0.s (D
z
ut
= o
D I M E N S I O N L E S SX .
A
'. * =; L ^ l k g a vTTSmi, Figure Z.l2 Confined Horizontal Well Interfaces
Further Expt
The cumulative recovery of mobile oil may be obtained by integrating equation7.35awith respectto dimensionless time; ihe resultis
Esso Resour model experu box havinetri
Recovery=
t,
Q*dt*= {t.
-:tr'
(7.35b)
of Th" lu]y9 /* requiredto obtain a particularrecovery,/ may be obtainedby solving (7.35b)for 11 The root of intereit is siven bv t;
q) +J d
t^
-'t-/)\
t o t -) t* = 2r/*.or{11-: v2 3 \ For instance,if f : 0.5, then t* = 0.4253. The correspondingcurvesfor cumulativerecoveryare shownin Fieure 7.14. 1.5
o
EO
!-+-el---Th-e-e-ry-..4.1-=lT-r*
s-r!-l.g-tr.--7-:1-1.g-l:.-1-j..._
d
.'.1 -
a a (,]0J O.l
Eqn 7.35
de :v 0 d 0)
II
0.5
*
a'' Numerical
d
0
0.4
DimensionlessTime 304
Soluti
0.8 .*__ f
t w
Figure 7.13 Comparisonof Drainage Ratesfrom Different SAGD Eouations
Steam-AssistedGravity Drainage
Chap.7
*2l cqt!::L
ratedwith Co meabilitl of rl The ptx steamchamh into the chan centerof the The elapsedt front windon In thisr ter of the bott centric tubes flowed out. T wastypicalll' configuratim Figure prediction mr steam*as inj horizontalprt The rnq reservoirand theorydoesrr that the steau the theon'pr and it reprme
Tandrain-An I
|1
Original Equation (7.16) \ TANDRAIN Infinite
o
0.5
Depleting Reservoir
Reservoir
Equation
7.35
h h
OJ
oo'
0.5
Dimensi.onless Tirne
--
w
Further ExperimentalData
tained by integrating :is (7.35b)
ru'be obtainedby solv-
shownin Fisure7.14.
Comparisonof Drainage ifferent SAGD Equations :y Drainage
*t
Figure 7.14 Cumulative Recoveryfor a Horizontal Well
)ffi*. a':
l
Chap. 7
Esso ResourcesCanada has carried out a considerablenumber of gg!g[1gga| -model experiments.One such experiment(Butler and Stephens1981)involved a bcix having transparentfront and rearwalls thatwas 36 cm wide,26 cm high, and 2.5 cm thick. The modelwaspackedwith a coarse-grained sandthat wasfully satu;Ca;ii[eoid Lake crude. The grain size of the sandwas chosenso that the permeabilityof the packingwould make 82 the samefor the model and for the field. The photographsin Figures 7.15 show the stagesin the developmentof a steamchamberdue to the gravity drainageof oil during continuousflow of steam into the chamber.The steamchamberis the lighter-colored,growingregionin the centerof the photographs. The major part of the oil has drainedfrom this region. The elapsedtime is indicatedat the bottom of eachpicture;the grid drawn on the front window of the model has a line spacingof 20 mm. In this modelthe steaminlet and productoutlet wereboth placedin the center of the bottom of the model,with the inlet 2 cm abovethe outlet; they were concentric tubes.Steamflowed in to replacethe hot oil and the condensateas they flowed out. The residualoil saturationin the drainedspaceof the steamchamber wastypically5%. Modelsof this type with a varietyof differentpermeabilities, well configurations,and overall geometrywere used. Figure 7.L6comparesthe production rate from one of these modelswith the prediction made by the TANDRAIN theory. In this particular experimentthe steamwas injected into a central well, which was located slightly above a lower, horizontal production well. The measuredrate rises as the steamchambergrows toward the top of the reservoir and then decreasesas the reservoirbecomesdepleted.The TANDRAIN theory doesnot predict the rising-rateperiod, becausein its derivation it is assumed that the steamchamberextendsfor the whole vertical height at the start. However, the theory predictsa maximum production rate that is closeto the measuredvalue, and it representsthe decline during depletionreasonablywell. Tandrain-AnExtension to the OriginalSAGDTheory
305
i
/,'*
:.it .t,'
a a 3
T T T c
it t
t
I
E FEr
Extrapolatkn
Usingthe the t( extrapolated
THE RISINGSTEAM
In this sectio considered. an at which oil is The deri Weiss(1980). a lar to thosein It is assu the steamcha shapeis, at lea suchas thoses In the pn that would be not all the hea tally to the we is within the sr headis availab Duringtt assumed that I any particular the equation.u tion 7.16.This
Figure 7.15 Developmentof the SteamChamberDuring Gravity Drainagein Laboratory Model
306
Steam-AssistedGravity Drainage
Chap.7
The RisingStea
o 1.5 Experiment
6 G
c o
g 1.0 It
o
r
o o o nq E -'-
\
\\ TANDRAIN\.
.9
.D E
o
.E o0 0
0.5 1.0 DimensionlessTime
1.5
Figure 7.16 Oil-ProductionRate from Low-PressureLaboratoryModel
Extrapolation of the Model Experimentsto the Field Using the theory and the scalingmethodsdescribed,the model experimentswere extrapolatedto the field scaleas shownby the data in Table7.3.
THE RISINGSTEAM CHAMBER In this sectionthe vertical growth of a steamchamberabovea horizontalwell is considered,and equationsare derivedfor the rate at which it risesand for the rate at which oil is produced. The derivation that follows differs from that given by Butler, Stephens,and Weiss(1980),althoughthe final results(i.e., equations7.43and7.44)are very similar to thosein the reference,and the sameexperimentaldata are used. It is assumedthat the problemis a two-dimensional one and that the shipe of the steam chamberremains geometricallysimilar as it rises. This similarity of shapeis, at leastto a first approximation,found in experimentswith visualmodels such as those shown by the earlier seriesof photographs. In the previoussectionson TANDRAIN, it wasshownthat the drainagerate that would be predicted from equation 7.16overestimatesthe production because not all the headh is available;someof the headis required to move the oil horizontally to the well. For TANDRAIN, this is allowed for by changingthe factor 2 that is within the squareroot signto 1.5.This is equivalentto assumingthatT5Voof the head is available. During the rising-chamber period,similar considerations apply,and it may be assumedthat the availablehead is lessthan the total height of the chamber,h, at any particular time. We will allow for this by including an unspecifiedfactor B in the equation,with the expectationthat it will turn out to be lessthan the 2 in equation 7.16.This is shownin equation7.36.
rn Laboratory
Drainage
Chap.7
The RisingSteam Chamber
307
The fa is drainingto from onlv c
:El 5 U cl
,:nll
*nl* = rl ;\ -t
6 o >
F-riFr<.i nO\olF-d **N
X HI E o1l
Sinceit r grows,the cu areamultiplio wherethe cq chamberis I
tr
LH
)
o
ooo\\oo$ cO\OO\hOi
Differentiatiq tion rate. egu
o
L)
rrl
Settingthe ri equation7.39 heiehtof the r
: O*h*Oi ON$nh ii -xoidr-iodo
V)rO\*6 \OO$*r d.j.jGi6i
n NNOV)
rN€
d
E l!
a,
@
o
E
..1 o trt : ot Y ' - l
x lu o)
ol
E
^ ^
3ltq r!l Y!
oc)h EFOTNNF
iN00oo\ r)o\c.lOh *Na]
ooo
€"do+oos-e Z oo
6v
o'-n
\
>l E l(5
tl -----ll
.= o
(t? Llr 6
:> OFtt\Ohd \o 6 N $
E N
O-
? ;
^e. E
E,-a-
),t
il:l
gt
il d-l
cr tl !t
I
trl > vil a"
sl$ll sl$9 l { t ->l--> FI\
a o
x u.l
'1.-:-
Value of ho;
E
E
y
H
.;.
|-t,
s t-s
st\
tl
ooSN-*\Fis{'
:I E
:_r .r I
H I :
c,
Equation7.{l first brackets secondbracke The init perimentsimi heightof the c ples implante measuredtenq eachthermoc steamtemper
TheRisingSta
The factor 2 outside the squareroot sign in equation7.36 recognizesthat oil is draining to the well from both sides,whereas7.16 gavethe quantity draining from only one side. (7.36)
Q:2
Sinceit is assumedthat the steamchamberremainsgeometricallysimilar asit grows, the cumulative oil productionwill be proportional to the mobile oil per unit areamultipliedby the squareof the chamberheight.This is shownby equation7.37, wherethe constant7 is determinedby the shapeof the chamber;the area of the chamberis 7h2.
e c u= f o n o , = y d a s " h 2
(7.37)
DifferentiatingT.3Twith respectto time givesanotherexpressionfor the production rate, equation7.38.
q = zvSA^S,hff
(7.38)
setting the right-handside of 7.36 equal to the right-handside of 7.38 resultsin equation7.39,which may be integratedas in 7.40 to give an expressionfor the heightof the chamber,h, as a function of time. This is equation7.41.
=z 2tSAS,hff
kga$ L,S"h
(7.3e)
*rt
[orr,r*r=irlffifr*
(7.40)
^=(+i)"(m)"
=(i#)"0#n1'''u'
(7.41)
r
Value of Proportionality Constant in Height Equation ci F:
tl > il vil ao
9 ll .€S
ii
st\
€lE =l !
:
EI
Y
Equation 7.41 showsthat the chamberheight ft should be equal to a constant(the first brackets),multiplied by a factor involving the reservoir and oil properties(the secondbracketedterm), and multipliedby the time raisedto the J power. The initial constantterm in 7.4Ihas beenevaluatedfrom a scaled-model experimentsimilar to that shownin the earlierphotographs.In this experimentthe height of the chamberwas determinedfrom the behaviorof a seriesof thermocou: ples implantedinto the model in a vertical line above the productionwell. The measuredtemperatures are shownin Figure 7.17.As the steamchamberapproached eachthermocouple,the temperatureincreasedabruptly from the initial level to the steamtemperature. The RisingSteam Chamber
309
100
o
o_ o J
i: 50 e, CL
E
o
F
Timein Minutes Figure 7.17 MeasuredTemperaturesaboveproduction Well
From these measurements it was possibleto plot the height of the steam chamberagainsttime, as in Figure 7.18.Also shownin Figure 7.1gis a theoretical line basedon equation7.41with the constantset equal to 2; i.e., this theoretical curve is basedon equation7.42.The slopeof the experimentalcurve is closeto the theoreticalvalue of ?.
,=,(ffi)',f''
(7.42)
Equation7is verr':atis
Shape of S
If it is assu circle.then of gamma! ment*ith t
The Oil-productionRate When the valueof ft from equation7.42 is substitutedinto equation7.37, the result is equation7.43.This haswithin it theshapefactor, y. By cuive fitting the oil-rateproductiondata from the experiment,7 hasbeenfound to be about *9. Qcum
=
^r(ffi)" roLSo)1/3 f/z
(7.43)
From curve fitting, = 2.25 or y
= zzs(tv)"($ Q"u^
q 10
AS.)rt3t4t3
310
dt
= t(Bg\'''(,fAS,;r/3rrl3 \mvsl
Steam-AssistedGravity Drainage
; o o o o 810
o (7.44)
Using this value leadsto equation1.44 for the cumulativeoil production,and differentiatingthis with respectto time resultsin equation7.45 for the instantaneous productionrate.
q- =+
s
0
(7.4s)
Chap.7
The RisirgS
-t
tr
I
200
I eisht of
150 q)
c
I
Theory Experiment
100
rermocouple I lvewell,mml
q)
a 0)
II
50
I
rrl
...*..
?n q)
trn
71020 fime in Minutes
-
60
Figure 7.18 SteamChamberRise
on Well
: height of the steam re 7.18is a theoretical ll i.e., this theoretical al curve is closeto the
(7.42)
luation7.37,the result rve fitting the oil-ratee about*9. (7.43)
Equation7.44is comparedto the experimentaldata in Figure 7.19.The agreement is very satisfactory. Shape of Steam Chamber. If it is assumedthat the shapeof the steamchamberis approximatelya sectorof a circle,then the anglesubtendedby the sidesof the sectorthat gives*aas the value of gammais 64"; this is shownin Figure 7.20.This shapeis in approximateagreement with the observedshapesof rising steamchambers.
20
Equation7.u14
I f o o C) o 810
o (7.44)
O Experiment I production,and diffor the instantaneous
(7.4s)
ty Drainage
Chap.7
20 40 Time in Minutes
60
Figure7.19 Oil Recovery DuringChamber-Rise Period
The RisingSteamChamber
311
o G
E o ct) G^ o 't6r E ^= qt
-@ gr?
H
Eg,
E .9 th
Figure 7.20 ApproximateShapeof Rising ChamberSectorwith y : 9116
'(
o
E i5
AvailableHead It is also possibleto calculatethe value of the head availabilityfactor B. This is donein equation7.46; the result-!, or 1.125-indicatesthat nearly half the availableheadis requiredto move the oil laterally.
Figrr
4v2
B=8r-i-
9 8
(7.46)
This value is lessthan the value of 1.5 found for the TANDRAIN equation.The photographs in Figure 7.15indicatethat duringthe chamber-rise period,the top of the steamchamberis ill-defined becauseof the instabilityof the rising front (but the sidewaysspreadingfront hasa stableinterface).Becauseof the raggednatureof the front, it is not surprisingthat lessof the headis availableto effect drainageto the productionwell. The photographsshowclearlythe effect of gravity in stabilizing and destabilizingsteamfronts. Equation 7.39 (with F = 1.125)predictsa lower drainagerate at the point where the chamberreachesthe top of the reservoirthan does the TANDRAIN equationfor the samevalue of h. It is practicalto continueto use equations7.44 and 7.45 after the chamberreachesthe top until the rate reachesthat predictedby the TANDRAIN equation.After this point the TANDRAIN equationshouldbe employedto follow the further depletionof the reservoir.This approachis shown in the numericalexamplewhich is developedstartingon page316. The ratepredictedby equation7.45 for the rising chamberperiod and that by equation7.35for the depletionperiod can be plottedon a singlechart, as shownin Figure 7.21.
ture. It alsopr eachother an gerswhich int Tl pical 1 of the fineen
Visctrsi:J;'
Velocits oi rt.c I Steam temp.er Steam tenr;'crr Steam temprcr
Finger dimcns:tx Steam tr-mP'e Steam tenp=::: S t e a m t em ; r : a tThe
top oi trc f
EFFECT OFSTEAM ON I PROPERTIES FINGERRISETHEORY
Steam and R Another approachto the predictionof the rate of rise of a steamchamberhasbeen describedby Butler (1987).This paperdescribesa theoreticalapproachin which the frictional drag for the falling oil around a rising finger is balancedwith the frictional dragwithin the finger and the driving force providedby gravity. The theory predictsa rate of rise for the fingerswhich is proportionalto the permeabilityand inverselyproportionalto the viscosityof the oil at steamtempera-
The equation effect of rere Figurc tion 7.1-ias a of 129.1mm:
312
Effect of Steat
Steam-AssistedGravity Drainage
Chap.7
3
o G
E o ct) Q^
'EF0 ,p =o _o 9C
vao
E o o tr o
pproximateShapeof :r Sectorwith y = 9/16
.E o lity factor B. This is nearlyhalf the avail-
1
$ a
*
,'--_..-,/ Parameteris w/h w is (wellspacing)/2
'.. \
Drainage from
0.5
tl
TANDRAIN- startingwith l- - - verticalhot plane
\
risingunconfinedchamber
\
\
\
o'25 o'zs d = 1.a5(w/h) 1R""ouery1
a 0
\
\ I
00.s1
t r
Fractionof UltimateRecovery Figure 7.21 CalculatedDrainageRatesfor Rising and DepletingChambers
(7.46) IAIN equation.The iseperiod,the top of the rising front (but the raggednatureof to effect drainageto of gravity in stabilizLgerate at the point es the TANDRAIN o use equations7.44 res that predictedby i equationshouldbe rs approachis shown 316. :r period and that by le chart, as shownin
tl
r{
ture. It alsopredictsthe curvatureof the top of the risingfinger.Fingersrisebeside eachother and the oil flowing downwardsbetweenthem falls as meanderingfingerswhich interferewith eachother and with the rising steam. Typical predictedvaluesof the rate of rise and of a characteristicdimension of the fingersare given in the followingtable:
i
fI i{
q
ilrl
Viscosity of reservoiroil at 100'C Velocity of rise mfd Steamtemperature f00'C Steamtemperature200"C Steamtemperature 300"C Finger dimension/o m (seeequationbelowl) Steamtemperature 100"C Steamtemperature 200"C Steamtemperature300"C tThe
0.0163 0.0822 0.190
0.0082 0.0571 0.149
0.0043 0.0415 0.r21
8.97 4.47 2.56
4.57 3.29 2.22
2.65 2.53 L.94
top of the finger is parabolic according to the equation
lYlfot = $lft')
AND OIL TEMPERATURE, RESERVOIR EFFECTOF STEAM TEMPERATURE, ON DRAINAGERATES PROPERTIES Steam and ReservoirTemperatures m chamber has been pproach in which the anced with the fricv gravity. s proportional to the :lil at steam tempera-
The equationusedfor the generaldefinitionof m (7.25)allowsthe predictionof the effect of reservoirtemperatureon production rate (Butler 1981). Figure 7.22 showsa plot of the integrandin the right-hand side of equation 7.25 as a function of temperaturefor a typical heavycrude havinga viscosity --t/s (or cs) at 100"Cand 6.8 mm'/s at200"C. of 129.1,
' Drainage
Effect of Steam Temperature,ReservoirTemperature,and Oil Properties
Chap,7
{
313
!
{
1.6
. ^
PARAMETERIS RESERVOIRTEMPERATUREOC
E
1.4
'i t.,
OF ?r r.o
3
o
6 ?oa l!\
(J
!; ou i 0.4 = o.z o.o
j
!
a I
o 2 50
150 200 250 STEAM TEMPERATUREOC Figure 7.22 Effect of remperatureon value of Integrandin Equation 7.25
3
o
curves are showncorresponding to reservoirtemperatures of 0, 20, and 40.c. Increasingthe reservoirtemperaturehas the effect of increasingthe value of the integrand and, thereby, the correspondingvalue of the integral and the oilproductionrate. The curvesin Figure 7.22 wereintegratednumericallyand the corresponding valuesof mwere calculated, with the resultsshownin Figure7.23.rtis found thai z changessomewhatwith steamtemperatureand decreases with increasingreservoir temperature.A lower value of m for a given set of conditionshasthe effect of increasingthe drainagerate. In general,it is found that the rateof drainagevariesinverselywith the square root of mv*This factor is plotted againststeamtemperaturefor the samecrudeoil in Figure7.24.This figure showsthe significanteffectof the reservoirtemperature and how it may be allowedfor by the extendedtheory. Oil Properties
very vlscous ( more fluid m termed a con Lor'r'ert more slo'* lr drainagerate temperatureI The cal ure 7.26. Tlx but the overa
The three curvesin Figure 7.25 givecalculatedvalues of m as a function of steam temperaturefor three differenthypotheticaloils. The uppercurve corresponds to a a/,J
a a
R E S E R V O ITRE M P E R A T U R E
o uJ
Ij
2 o
J
z o ah
c 2
fie
I
I
o E
= I
E
t
o
lr
O3 u.l
I
f
80
120 200 150 240 'C STEAMTEMPERATURE Figure 7.23 Effect of Reservoirand SteamTemperatureson rn
314
Steam-Assisted Gravity Drainage
Chap.7
Effect of Stea
n'""_l
R E S E R V O ITRE M P E R A T U R E
)
.rs/1
I\ IF
/,Y1 'l '///
0.2 ct o
|
F
o rr 0,1 u,l
I
o.oo fr o
I 0
= 0.04
250
E,
o
u.oo=129.1SQ MM/SEC
r Equation7.25
rresof 0, 20, and 40'C. asingthe value of the integral and the oiland the corresponding e 7.23.It is found that *'ith increasingreseritionshasthe effect of rerselywith the square for the samecrude oil reservoirtemperature
80
160 200 120 'C STEAMTEMPEBATURE
240
'l
rl
Figure 7.24 Effect of Tn and Ts on Rate Factor
veryviscousoil similar to Athabascabitumen.The middle curve is for a somewhat morefluid crudesimilar to Cold Lake crude.The lowestcurve is for what might be termeda conventionalheavyoil similar to the oils found in the Lloydminsterarea. Lower valuesof m are calculatedfor the lessviscousoils becausez changes more slowly with temperature;this has the effect of tending to give predicted drainagerateshigherthan would be expectedfrom the viscosityof the oil at steam temperaturealone. The calculateddrainage-ratefactorsfor these three oils are plotted in Figure7.26. The calculatedeffect of the oil propertieson drainagerate is significant, but the overall effect is not overwhelmins.
as a function of steam lurve corresponds to a
R E S E R V O ITRE M P E R A T U R=E1 3 ' C t! J
z 9
4.5
o
z 4.0 UT
=
3.5 lr
o UJ f J
3.0 2.5
ty Drainage
PARAMETER IS CRUDE vtscoslTY AT 100'c/200'c SQ MM/SEC
,.0--;;, OC STEAMTEMPERATURE Figure 7.25 Valuesof rn for Different Crude Oils
tes on /n
Chap.7
5 t.
i
1
t
ilrl
I q
{ I
1 {
I o o
:
1 q
Effect of Steam Temperature, Reservoir Temperature, and Oil Properties
315
bitumenand r the sand used representI )(a) Obtain wt obtainingan :
PARAMETERIS CRUDE vtscostTYAT 100"C IN SQ MM/SEC
t\
s t
o o lt lrl F E |rJ
(, =
R E S E R V O ITRE M P E R A T U R=E1 3 " C
t
o
80
120
160 200 240 OC STEAMTEMPERATURE Figure 7.26 Drainage-RateFactorsfor Three Heavy Crudes
Estimating lrt
There are,of course,othervariablesin equationssuch as7.16that are equally effectivein modifying the drainagerate;these(e.g.,thicknessand permeability),ai well as the oil properties,can vary significantlybetweenreservoirs.
(b) Tabulatcp
NumericalProblemon Steam-Assisted Gravity Drainage A tar sandreservoirhas the following properties: Reservoirtemperature Oil viscosityat f Bitumendensity Bitumenviscosityat 100"C Reservoirthickness Thermal diffusivity Porosity Initial oil saturation Residualoil saturation Effective permeability for oil flow
15"C 100,000cs 7.00glcc 80 cs 20 m 0.0j m2lD 0.33 0.75 0.13 0.4 d8
(c) Calcularc
The field is to be drainedby a seriesof parallelhorizontalwells with a spacingof 75 m betweenwells.The wellswill be located2.5 m abovethe baseof the ieservoir. Steamwill be injectedfrom separatehorizontalinjectionwells placed above the producers.Assumethat initial thermalcommunicationis achievedand that the system will be operatedwith a steampressureof 1.2MPa. Estimatethe percentrecovery of the original oil in placeas a function of time for a period of 7 y. It is plannedto carry out a model experimentrepresentingthe field in the laboratory.The modelwill have a heightof 35 cm and will operateusingthe same
(d) Equation
sAssumed to correspondto an absolutepermeabilityof 1.0 D.
316
Steam-AssistedGravity Drainage
Chap.7
Effect of Stean
bitumen and at the samepressureas the field. What shouldbe the permeabilityof the sand used in the model? How many minutes in the model will be required to represent1 y in the field? (a) Obtain value of parameterm: Determine m using either equation 7.25 or by obtaining an approximatevalue by interpolation from Figwe 7.25.
-
I
Zs = 188'C
I
Zn = 15"C vs = 7.8 cs (by interpolation on Figure A.5.2)
=13ccI
=ll'l.rt*,,"'"^''"'
-_l x)
Estimating m from Figure 7.25 leadsto
mdcs
m=3.4
7.16that are equally nd permeability),as xin.
(b) Tabulateparametersfor problem:
6 = 033 AS,=0.75-0.13=0.62 k = 0.4 x 10-12mz I = 9.81ry/s2 q. = 0.07/(24x 3600)m'fs = 8.10x l0-7 m2fs h=20-2.5=17.5m m=3.4 vs = 7.8 x 10-6m2/s w = 75/2 = 37.5m (c) Calculatefactor to convertq to q*:
lls with a spacingof nse of the reservoir. ls placed above the vedand that the syste the percent recovodofTy. ting the field in the ef,ateusing the same
F a c t o=r - l - *
'-1<.1
!ffi=
= 17'67 dlm2 l'527x 106 s/m2
(d) Equation for t*:
t* =
t
,f ---t*-
w Y f\S,mvrh
(seeFigure7.12)
= 4.2L5 x L0-a/6un Drainage
Chap.7
Effect of Steam Temperature, Reservoir Temperature,and Oil Properties
?17
(e) Calculate rates and recovery for depletion assuming chamber starts as vertical plane:
0. a o
g
o GI
TIME IN YEARS
I
(2)
(1)
0 1 2 3
0 0.154 0.308 0.462 0.615 0.769 0.923 1.077
A
5 o
1.225 1.205 1.147 1.050 0.916 0.'742 0.529 0.278
7 (r)From equation7.35a. (t)Fractional recoveryof mobile oil.
q = 2q*/17,67
J o.at
q'
0.139m3/md 0.136 0.130 0 . 11 9 0.104 0.084 0.060 0.031
0 0 . 18 8 0.369 0.539 0.690 0.818 0.916 0.979
€0 E
(t-
E o 6
tr o. c o () : t, o o.
(f) Rates and recovery during rising-chamber phase: l,-^-\21
= 2.zsl:n'| 16As,;"'ro" Qcu^
sary,then. to s from the deph
\musl
= 32.11.t0' (with r in years) Fractionalrecovery: q"" f(17.5 x 75 x 0.33 x 0.62) = 0.120t413, with t in years. 4.,- (in m3/m; =
3'il(ff)
= 0.0r23t1!:y"
Years
0 0.5 1.0 1.53 2.0 3.0 4.0 5.0 6.0 7.0
Differentiating with, o,*, ;r:: ;, r:rff il;, i, l, ooru Rate and Recoveryduring Rising-Chamber Period Time Years
0 0.5 1.0 2.0
q
Fractional Recovery
0 0.093 0.117 0.148
Summary Table h
0 0.048 0.120 0.302
(l)Fractional
recorr
Theseratesare The recoveryratesare plotted againstthe percentrecoveryin Figure 7.27. The two curvesintersectat 2l7o recoveryand a rate of 0.135m3/m d. Assumethat the rising-chambercurve appliesup to the point of intersection and that the rate then followsthe depletioncurve.The changeoverpoint occursat 558d, but this point corresponds to only 401d for the depletioncurve. It is neces-
(g) Scalingo.ft) for the model a
318
Effect of Stean
Steam-AssistedGravity Drainage
Chap.7
ber starts as vertical
o o p o
0.15
ol q -- 2q*/17.67
0.139 m3/md 0 . 13 6 0.130 0 . 11 9 0.104 0.084 0.060 0.031
€ E
558 days R.C.curve .101days on dep curve
0.1
ct\
E o
(E
E o.o5 tr o o 5
rl t1
o o o.0
'l
q
ri
20 40 60 80 % Recoveryof MobileOil
0
100
q
d
Figure 7.27 Oil-ProductionRate versusRecovery.
\
ll
sary, then, to subtract157 d from the time in order to calculateconsistentrates from the depletionequation. )t'3, with / in vears.
nal Recovery
0 0.048 tl.120 t.).302
qt*q*
0 0.5 1.0 1.53 2.0 3.0 4.0 5.0 6.0 7.0
0 0.093 0.1,17 0 . 13 5 0.133 0.124 0.111 0.093 0.071 0.044
'l
il
Recovery(l)
0.169 0.242 0.395 0.549 0.703 0.857 1.011
1.202 1.17'7 1.097 0.979 0.821 0.625 0.390
( |! { \1
0 0.048 0.120 0.2r2 0.293 0.467 0.627 0.766 0.878 0.957
{l
t
(l)Fractional recoveryof the movableoil abovethe productionwell.
These rates are plotted in Figure 7.28. igure 7.27. The two pint of intersection lver point occurs at r curve. It is necesDrainage
Chap.7
(g) Scalingof theModel The dimensionlessnumbers83 and /* shouldbe the same for the model as for the field: i.e., -
Br=(
*kgh \ :( O Ls"o^rrlrr,,o
i
'l
SummaryTablefor Ratesand Recoveryas a Functionof Time Years
Ir
r- *kgh \ O AS"o*rrl-"0,,
Effect of Steam Temperature,ReservoirTemperature,and Oil Properties
319
100
u. tc
STEAM-INJECT
bi
There arc t posed to I drainage:
€ tr
o c)
nl
F}
o
>50
l. Hori, 2. \'ertic
a) o E.
0.05
L
q)
o
HorizontJ
o
o Q) t
!
o n
0O o
2
4 Time in Yeors
6
8-
Figure 7.28 production Ratesand percentRecovery
Sincethe temperaturesand pressurewill be the samein the model and the field, the only variablesthat will differ will be h andk (we will assumethat the porosity, saturation,and thermal diffusivity will be the same).Then (kh)t*,6 = (kh)^oa"r
and the permeabilityof the sandto be usedin the modelwill be hu"ra 20 , = kmodcr kri"rd= x 0.4 = 229 D effectivepermeability ,-.", f.,
i i
Using the samerelativepermeabilityof 0.4 assumedinitially, this meansthat a porous medium having an absolutepermeabilityof 22.9/0.4: 55 D shouldbe used. If the dimensionless time for two correspondingstagesin the model and the field are the same,then 'kgo\
=(:
*=(*
6 AS"-rr) ,,,,0
I
ts" I
r/:l Y $LSomvsl.o6",
In thi Ttrc e would girc the oil viscc theseare sl Birun separaticrs simisticin r radiusthat estimatedtl shownin F
Hence, /fi"ta /model
,model
Ifl11s1a:1y:
320
-
= 161 min. 525,600min, then /moder
Steam-AssistedGravity Drainage
In this am ducer. Fr et al. lS7) catedjus b are drilled I gether.abo Communb them qclIn rhi top of thc r If rhc to locateth mobilitl of chamberto length of ti condensat cation peri The I proximatet allow for tl from this q
Chap.7
Steam-inie
STEAM.INJECTION WELLS
U. JJ
There are two general arrangementsof steam-injectionwells that have been proposed to be used with horizontal production wells in steam-assisted gravity drainage:
L
0.1
rr)
tr
1. Horizontalinjectionwells,with one well positionedaboveeachproducer. 2. Vertical steam-injection wells locateddirectly,abovethe producers.
Q)
E. nnq
Horizontal Injection Wells
o o
J
f !
o_
8
rri.
model and the field, rme that the porosity,
lbe permeability tially,this meansthat ..1= 55 D shouldbe in the model and the
In this arrangementa horizontal injection well is placed directly above each producer. For example, in AOSTRA's Underground Test Facility project (Edmunds et al. 1987)horizontalwells are drilled upwardfrom the mined tunnel,which is locatedjust belowthe Athabascatar sandreservoir,and then horizontally.The wells are drilled asinjector-producer pairs.In this application,the wellsarevery closetogether,about 2 m apart, to allow interwell reservoirheatingand communication. Communicationcan be-achiqvedinitially by heating both wells 4!rd pressuring th_e-1g -qyc-lically. In this application,the steamchamber,as it forms,mustgrow upward,to the top of the reservoir,in order to achievehigh vertical conformance. If the reservoircontainsoil havingan appreciable mobility,then it is possible to locatethe injectionwell higherup in the reservoir.The limiting factoris that the mobility of the oil within the reservoirshouldbe high enoughto allow the steam chamberto advancedownwardsfrom the injector to the producer in a reasonable length of time. During this advancethere is a displacement of cold oil and steam condensateto the productionwell, and, with adequateoil mobility, this communication period can be highly productive. The length of time requiredto achievecommunicationcan be estimatedapproximatelyby calculatingthe breakthroughtime from equation4.23. In order to allow for the changingconditionsduring the displacement,the time calculated from this equationshouldbe divided by 2; this hasbeendone in eqtation7.47. LBT _
I
(7.47)
In this equation,s represents the interwell distance. The allowablevertical separationbetweenthe injector and the producer that would give a one year breakthroughtime hasbeenplottedagainstthe logarithmof the oil viscosityin Figure7.29.Typicalvalueswere assumedfor the othervariables; theseare shownin the figure. Bitumenshaveviscositiesrangingfrom 105to 106cp, and it will be seenthat separationsof 2 m or less are required.The lower curve in Figure 7.29 is pessimistic in this range,since it doesnot allow for the effect of well bore heating.The radiusthat is heatedcan be estimatedusingFigure 2.12.For typical tar sand,it is estimatedthat a radiusof 3 to 5 m is heatedappreciablyin a period of 60 d. Also shownin Figure 7.29is a curve for a well bore radiusof 3 m.
/ model
y Drainage
$ AS,p.,s"ln(s/Rr) 6k LP
Chap.7
Steam-injectionWells
321
tl
tl
F
I rl
tl
350
tr p
E+o .,
Ero 6 tr
3. zo
Rw= 3 m
OJ
0
310 rJ !
f u - 0 . 1m 3+56 Log16(Oil Viscosity in cp)
Figure 7.29 Allowable Vertical Separation for One Year Breakthroush Time
It is clear from Figure 7.29 that if the viscosityof the oil in the reservoiris belowabout10,000cp, then quitehigh verticalseparations canbe employed,particularly if the productionwell is preheated.A largeseparationis advantageous, since the pressuregradientresultingfrom the flow of steamassiststhe drainageof oil. tn somesituations,there may be an advantagein employingtwo horizontalinjection wells,with one locatedcloseto the producerto initiate steamchamberformation and a secondlocatedhigherin the reservoirto be usedasthe steamchambergrows to it (Butler 1984). The quantity of oil displacedduring the establishment of thermal communication can be estimatedusingthe ideasof inter-welldisplacement discussedin the developmentof equation4.24in Chapter4. This equationwaswritten for two fullypenetratingverticalwells.It can be rewritten as follows,with a changeof symbols to representtwo parallel horizontal wells having lengthswhich are great enoughfor the problemto be consideredas two-dimensional:
(s'zdAS,) Vu,= @13)
(7.48)
wheres representsthe distancebetweenparallelhorizontalwellswithin a reservoir of infinite extent and Vt,is the productionvolumeper unit lengthof well at breakthrough. Although this equationis also applicableto other arrangements we will considerthe casewherethe injectionwell is verticallyabovethe producer. When oil is displacedby downwardsteamfloodingthe volume that is displacedis somewhatlessthan would be calculatedby equation7.48becauseof the differencebetweenthe propertiesof the steamand the oil, becauseof the needfor the condensate from the steamto flow with the oil, and becauseof the needto heat the reservoir. The displacementof oil by downwardsteamfloodingin two dimensionshas beenstudiedtheoreticallyby Butler and Petela(1989).In their theoreticalmodelit is assumedthat the streamlinesfor the steamfloodingphaseremain the sameas they would be for singlefluid flow. As the oil is displacedfrom eachstreamtubethe condensationinterface advancesalone it as determinedby a heat balance.The ef322
Steam-AssistedGravity Drainage
Chap.7
fect of this rs thanu ithin h smallerdisplt the positiond ing to fractim the figure is tl the breakthrq smallerfor th If the ir boundarl'and placedoil at b boundedb1 h given br':
wherethe a'm 61% of that ft for steamflod Figure7.31-I breakthrougl
t ,.rf vt(w
"L
t.rL
'" ,'",
04l-
Steam-injectr
$able VerticalSepaar Breakthrough
in the reservoiris employed,particuJl'antageous, since drainageof oil. In Lorizontalinjection :hamberformation amchambergrows
fect of this is that the velocitywithin shorterstreamtubesincreasesmore rapidly than within longeronesand breakthroughoccursrelativelymorerapidly(i.e.with a smallerdisplacedvolume)than it would with single-fluidflow. Figure 7.30 shows the positionof the interfacefor a particular set of conditionsat times corresponding to fractionsof 0.25,0.5, 0.75,and 1.0of the breakthroughtime. Also shownin the figure is the brokenline which correspondsto the position of the interfaceat the breakthroughpoint for singlefluid flow. The volume of the displacedzone is smallerfor the steamfloodingcasethan for the singlefluid case. If the injection well is at the top of the reservoirjust below the upper boundaryand the productionwell is at the lower boundarythen the volumeof displacedoil at breakthroughis lessthan for the previouscalculation.For reservoirs boundedby horizontalsurfacesthe volumeof displacedoil for singlefluid flow is givenby: Yu,= (2/rr)(s2dAS,)
(7.4e)
wherethe symbolsare asbefore.This equationleadsto a displacedvolumewhich is 67% of that for the unboundedreservoir.Butler and Petelastudiedthis geometry for steamfloodingand calculatedpositionsof the condensation front are shownin Figure 7.31.The broken line in this figure showsthe position of the interfaceat breakthrough.Again, asfor the unconfinedcase,the volumeof the displacedzone
vl(U2l t = 0.25tg1
thermalcommunirt discussedin the 'itten for two fullychangeof symbols 'e great enoughfor
t = 0.50tg1 t = 0.75tg1 t = 1 . 0 0t A t
(7.48) Singlefluid
within a reservoir h of well at breakangements we will : producer. olume that is dis.-18becauseof the useof the need for of the needto heat ,ro dimensionshas heoreticalmodelit :main the sameas achstreamtubethe rt balance.The ef)rainage
Chap.7
0.8
Producer
Steam-injectionWells
1.0
Figure 7.30 Positionsof SteamFront for Times Correspondingto 0.25,0.5, 0.75and 1.0Timesthe Breakthrough Time in an Unconfined Reservoir.The Broken Line is the Positionof the Interface for SingleFluid Flow at Breakthrough (from Butler and Petela1990)
323
yl(u2) 1.0
t = 0.50tg1
xl(u2)
5
Figure 7.31 Positionsof SteamFront for Times Correspondingto 0.25, 0.5, 0.75 and 1.0 Times the Breakthrough Time for a Reservoirwith Horizontal Boundaries.The Broken Line is the Positionof the Interfacefor Single Fluid Flow (from Butler and Petela
leeo)
abovebut ri tion of the e sourceand I The re grar assisted ber the hear other experi to someerte steamis inF Inpctin which gror: pressure dnv High ratesfo rateschamb to operaterOil draining saturatedreg tachedbv a r only a part ( overburdena keep steamI doingthis he Vertical kic
at breakthroughis smallerthan for singlefluid flow. For the particular example shownthe volumeof the displacedregionis 9I% of that for singlefluid flow.e The downwardvertical steamfloodingof a Lloydminster-typeheavyoil has been studiedby Sugiantoand Butler (1989)usinga scaledphysicalmodel.In their experimentsthey found that the time for steambreakthroughcould be predicted reasonably accuratelyby the theorydescribedabovebut that the shapeof the interfacewasratherbroaderthan that shownin Figure7.3L The reasonfor this wasthat the injectedsteamspreadbeneaththe overburdenand, as a result,the steamsource wasmorelike a distributedplanethan a line (a line is a point on a two dimensional diagramsuchas Figure 7.31). Steamfloodingcalculationsmade by Butler and Petelashow excellentagreement betweenthe shapeof the experimentalinterfaceat breakthroughand that which they predictedfor steamfloodingusing the samemethod that is described
Verticalu'ell At Yan dergroundcl wells,which The H< drilled horiz Steam*as iq operatedfor ratio wasven
eln
estimatingthe volumeof displacedoil it is necessaryto includethe factor @AS,. The value of ASomay be rather lessthan for the long term projectbecausethe drainageof oil may not be complete at the time of steambreakthrough.For examplesupposethat in a vertical flood projectthe vertical distances is 20 m, f is 0.35,S, is 0.85,and S.. is 0.3 (this might be a reasonable value for a time of about 150days;seeTable 7.1),then the volume of displacedoil at steambreakthroughmight be expected to be about 0.91 of the volume calculated from the above equation li.e. V6,= 0.91(2/tr\\s'z6LS"):0.91(21rX202 x 0.35 x 0.55): 45 m3/ml.For a 500 m well this would correspondto a productionof 22500m3.or 140kB, during the establishmentof thermal communication. This productioncould have a very significanteffect on the economics.
324
Gravity Drainage Steam-Assisted
Chap.7
Steam-inject
r s i t i o n so f S t e a m F r o n t :spondingto 0.25, 0.5, nes the Breakthrough :rvoir with Horizontal e Broken Line is the Interface for Single m Butler and Petela
: particular example nglefluid flow.e r-type heavyoil has sicalmodel.In their r could be predicted Leshapeof the interson for this wasthat rlt, the steamsource n a two dimensional
abovebut with a planar steamsource.Figure 7.32showscomparisonsof the position of the experimentalinterfaceand thosepredictedby theory for both a linear sourceand a planar one. The reasonfor the spreadingof the steambelow the overburdenis the steamassistedgravity drainageeffect (seeFigure 7.33).At the edgeof the spreadingchamber the heatedoil falls away and allows the steamchamberto spreadlaterally. tn other experimentsit hasbeenfound that the degreeof spreadingcan be controlled to someextentby adjustingthe verticalpositionof the injectorand the rate at which steamis injected. Injectingthe steamat an intermediateelevationresultsin a steamchamber which grows upwardsbecauseof the SAGD effect and downwardsbecauseof the pressuredrive. The relativeextentof theseeffectsdependsupon the injectionrates. High ratesforce the chamberdown to the productionwell rapidly,whereaswith low rateschamberrise is the predominanteffect. Under theseconditionsit is possible to operatewith a steamchamberwhich is only in the upper part of the reservoir. Oil draining to the bottom of this chamberis forced through the interveningoil saturatedregionto the productionwell. This operationwith a steamchamberdetachedby a considerable distancefrom the productionwell is undesirablebecause only a part of the potential drainagehead ii employedand the heat lossesto the overburdenare excessive. It is desirablethat steambe injectedat a rate sufficientto keep steamlow down in the reservoir.There may,in somecases,be difficultiesin doingthis becauseof inadequatesteamgenerationcapacity.
Drainage
Chap. 7
I flf
(!
rl
fl \
I
r il
I
Vertical Injectors
i
vertical wells can alsobe usedfor steaminjectionabovehorizontalproducers. At Yaregain Russia,horizontalproductionwells have been drilled from underground chambersand steam injected above them from separate,near-vertical wells,which are drilled from separateundergroundworkings. The Hopco project in California involved eight horizontal production wells drilled horizontallyfrom an undergroundchamberat the foot of a mine shaft. Steamwasinjectedfrom separateverticalwellsdrilled from the surface.The project operatedfor about 1l y; althoughit was successfulin producingoil, the oil-steam ratio wasvery low. However,the operatorsconsiderthat this approachis promising,
{
how excellentagree:akthroughand that od that is described e factor @AS,.The value :e of oil may not be comcal flood projectthe verrsonablevaluefor a time r breakthroughmight be ue equation li.e. V6,= l well this would corre:hermalcommunication.
t,
:\
., \.
Theoru SurfaceS6urce -) Theory-{,'in Line Source i t 49 min ,.;' _-l /'/ Experimenta/ 64 min
Steam-injectionWells
Figure 7.32 Comparison of the Experimental and Theoretical Positions of the Steam Front at Breakthrough (from Butler and Petela 1990)
325
tl
lll Il rl tl
1 ,l
q
ll
lntrusionof SteamBeneathOverburden
Noleson Mschanlsm Oil and condensate flow is drivenby gravity. Sieamrequiremenllo heat overburdenand r€ervoir ls hlgh. Steamflow ls limitedby viscousresislance. StsamAP can not exceedgravily head.
Figure 7.33 Mechanismof Spreading of SteamChamberJust Beneaththe Overburden
and they ascribethe poor resultsobtainedto a pilot site that wasunfavorable.They suggestthat further projectsshouldbe considered(Dietrich 1988). The EssoResourcesfirst horizontalpilot at Cold Lake (Bezaireand Markiw 1979)involveda deviatedproductionwell drilled from the surfacein order to pass horizontallynearthe baseof the formation.A verticalinjectoris drilled from above. Although there have been no detailedresultspublishedfrom the Esso project, a paper at the 1983PetroleumCongressindicatedthat it had producedmore than 100,000barrelsof oil. It is believedstill to be producingoil in 1990. A secondhorizontalpilot has been drilled at Cold Lake by Esso,which has about1 km of open horizontallength.The latestplansare to usethis togetherwith a numberof vertical wells above.Thesevertical wells will producefirst by cyclic steamingand then, presumably,someor all of them will be usedfor injection. the horiIn the Sceptreoil projectin the Tangleflagsfield in Saskatchewan, zontalproduceris locatedtoward the bottom of the oil zone.Steamis injectedfrom existingverticalwells above.The projectis consideredto be successfuland, during the downwardflooding phase,very high productionrateshavebeen achieved. There are several advantagesto using vertical injection wells. They are cheaperand simplerto construct,and there is not the sameneedfor drilling accuracy that would be requiredfor horizontalwells.Also, it is possibleto changethe point of injectionof the steamverticallyasthe projectmatures.In the initial stages it is desirableto have the steaminjectioncloseto the productionwell to facilitate to communication.However, as the project continues,it becomesadvantageous raise the point of injectionso that the motion of the steamthrough the chamber producesa favorablerather than an unfavorablepressuregradient. of vertical injectionwells is that each injector covers A major disadvantage only a relativelylimited lengthof the producer.For very long producers,it is necessary to employmore than one injector.It has been shown by Griffin and Trofimenkoff (1986)that equation7.L9 can be used to estimatethe half-lengthof the activewell. In their paper they point out that with someproductionsystems,the well will remain unheatedfrom the end of the activeportion in one direction,but becausethe hot fluids are flowing within it, it will be heatedin the other direction.
326
GravityDrainage Steam-Assisted
Chap.7
In theirl* horizontalr the heatedr dictionb1'r the tempsn their exarq 50% in tlrc Inap only the rer overcomeb Other the follo*-ir
l. Expe gener 2. In nl u'ould for lhi shon t theirI 3. The a media c a l 1 1" assum to thc of oil I ratio t res€n in this
Joshiand T injecton an significant fracturesin the earlvnq A thin product of n is removedI as the renr chamber.ar be controll drainedliqr p needlesslv
"'Thrsc
Steam-injec
lechanismof Spreading tber JustBeneaththe
as unfavorable.They )88). Bezaireand Markiw face in order to pass rsdrilled from above. r the Esso project, a producedmore than
r990. r bv Esso,which has rs€this togetherwith 'oducefirst by cyclic >edfor injection. katchewan, the horiteamis injectedfrom rccessfuland, during e beenachieved. ion wells. They are gedfor drilling accurssibleto changethe ;. In the initial stages tion well to facilitate nes advantageous to hrough the chamber lient. each injector covers rroducers,it is neces,r Griffin and Trofire half-lengthof the duction systems,the in one direction,but n the other direction.
y Drainage
Chap.7
In their laboratoryexperiments,theseauthorsfound that the activeportion of the horizontalwell spreadmore rapidly than would be calculatedfrom equation7.19in the heateddirection.They suggested that this effect could be includedin the prediction by usinga value of m in the equationfor the hot end that corresponded to the temperatureof the productionfluids rather than the reservoirtemperature.In their example,it was found that this effect increasedthe spreadingrate by about 50Vain the hot direction. In a productionsysteminvolving multiple injectors,it would presumablybe only the remoteend that would be cold. Even in this case,the difficulty might be overcomeby employinga production tubing reachingto the end of the well. Other interestingobservationsin the Griffin and Trofimenkoff paper include the following: 1. Experimentsin both high-pressureand low-pressuremodelsagreewith the generaltheory presentedhere. 2. In systemswith vertical injectionwells, the productionis much greaterthan would be calculatedfrom the active length of the productionwell. The reason for this is the production from the ends of the steamchamber.The authors showthat if allowanceis madefor this, good agreementis obtainedbetween their laboratoryexperimentsand the theoreticalprediction. 3. The authorsfind, in their experiments,that the extentof steamoverrideimmediatelyunderthe overburdenis muchlessthan would be expectedtheoretically. They recommendthat the width of the heatedsurfacebe estimatedby assumingthat the interfaceis a straightline rising from the productionwell to the top of the reservoir.While this assumptionhaslittle effect on the rate of oil production,it affectsthe estimatesof thermal efficiencyand oil-steam ratio by reducingthe area for heat loss both to the overburdenand to the reservoirbelowthe interface.l0 The estimationof heatlossesis discussed later in this chapter. Joshiand Threlkeld (1985)of Phillips Petroleumcomparedhorizontaland vertical injectorsand found the horizontalinjectorto be the most effectiveand to provide significantlyfasterrecovery.Joshiand Threlkeld also studiedthe effect of vertical fracturesin the reservoir.They found that theseare desirablein that they promote the early rapid productionof oil. Multiple fracturesare better than singleones. A third areastudiedin this paperfrom Phillipsinvolvesthe effectof the rate ofproduct removalupon the efficiencyofthe process.It is found that ifthe product is removedtoo slowly,the thermalefficiencyis low, but that it risesto an optimum as the removalrate is increased.At very high rates,steamis bypassedfrom the chamber,and the efficiencyfalls again.The rate of withdrawalof productshould be controlledto preventsignificantbypassingof steam.If the rate is too low, then drained liquid product buildg up above the productionwell, and the processis prolonged.This adjustmentis found to be straightforwardin practice. nebdlessly toThis correspondsto the LINDRAIN assumptionsdescribedin the footnote to page303.
Steam-injectionWells
327
t
r ilt
n
ll \ {
I
I
I ll tl
4 { c
rl
I{ rl
ASSUMPTION AVOIDINGTHE STEADY.STATEHEAT.DISTRIBUTION
t-
In the precedingtheoreticalmaterialin this chapter,it has been assumedthat the temperaturedistribution aheadof the advancingfront is that correspondingto the steadystatefor the particularlocal advancevelocityU; this is givenby equation7.4. It is this assumptionthat gives rise to the discrepancyof the front advancingfrom the productionwell; this was discussedearlier.Also, since the heat aheadof the front will generallybe somewhatless than that correspondingto the steadystate, the earlierequationstend to overestimatethe productionrate. heat assumptionhas beendescribed An approachthat avoidsthe steady-state (Butler 1985).The interfaceis divided into small elements,and the heat storage time stepsusing an approximate aheadof eachof theseis calculatedat successive flow of oil behind the elementis caldifferentialequation.For eachtime step,the is interface obtainedfrom materialbalance culatedand then the movementof the considerations similar to thoseinvolvedin equation7.12. Figure 7.34 showsthe positionsof the interfacecalculatedusing this technique for a caseinvolvingan unconfinedwell with the parameter83 set equalto 8. In the new theory it is found that the resultsdependsomewhaton B:; this is defined by equation7.29. Although the curvesfor differentvaluesof Bt arc generallysimilar to thoseof Figure 7.10,they tend to becomemore S-shapedasB: is increased.This tendency toward an S shapewas also displayedby the experimentalcurves shown in Figure 7.5. Calculatedinterfacecurvesfor variousvaluesof Bz at a constantdimensionless time of /* = 0.5 are shownin Figure7.35. Also plotted on Figure 7.35is a dottedcurve drawn from equation7.21;this curve is basedon the assumptionthat the heat aheadof the advancinginterface correspondsto the steadystate.As B: is increased,the curvesfrom the improved theorybecomecloserto the original theory.This is consistentwith the calculations 1.0 0.8 Q) C)
0.6
o
i5 E 0.4 o
E0)
0.2
0
0.5
1n
1.5
HorizontolDistoncex/h Figure 7.34 Positionof Interfacefor an Unconfined Well
328
Gravity Drainage Steam-Assisted
Chap.7
-c 0. o
30" -o
i5 -0. o o !
>0-
for the transic Chapter l. F! smaller valu6 Figure 3. of an advancin for larger valu Thus for a gir. steadystate\a t h e s m a l l e rt h This erp ure 7.35.The t steady state ua ahead of the fi permeabilitf it steadystate hc oil drains. bur gravity. high t thin la1'enof r thick la1ers.O lished becaus The buil becausethe fn (Figure1.8t./ state is includ vance of the ir will be noted i the reserroir a
Avoidingthe S
)N Porometer is volue of 83
n assumedthat the rrresponding to the en by equation7.4. rnt advancingfrom heat aheadof the to the steadystate, hasbeendescribed rd the heat storage ing an approximate the elementis calm materialbalance ed using this techrr 83 set equalto 8. rt on 83; this is dei similar to thoseof sed. This tendency rves shown in Fig, a constantdimenequation7.21;this advancinginterface from the improved 'ith the calculations
|ell
Drainage
Chap.7
c 0.8 q,
3 o.o
t* = 0.5
o o
i5 E 0.4 o
E
I o.z 0
Dottcd line is from originol equotion 7,2'l
0.s
1.0
1.5
HorizontolDistoncex/h Figure 7.35
r
'r
Effect of Parameter 83 on Shape of Interface
rl
for the transienttemperatureprofile aheadof an advancingfront that were madein Chapter 2. Figure 2.8 showsthat the approachto the steadystate increasesfor smallervaluesof a. Smallvaluesof a alsogive largervaluesof B: in Figure 7.35. Figure2.8 showsthat the approachto the steady-state heatequilibriumahead of an advancingfront is a function of U2tla.For a giventime, /, this approachis less for largervaluesof a; theselargervaluesof a correspondto smallervaluesof .B3. Thus for a given value of /* the degreeof heat penetration(i.e. the fraction of the steadystatevaluewhich is achieved)will tend to be lessthe largerthe valueof a or the smallerthe value of B:. This explainsthe effect of B: on the position of the interfacecurvesin Figure 7.35.The smallerthe valueof B: the farther awaythe heatpenetrationfrom the steadystatevalue.As a result there is a lower drainagerate while the heat bank aheadof the front is building. Largevaluesof ,B3correspondto the casewherethe permeabilityis large comparedto the thermal diffusivity. In this circumstancea steadystateheat distribution is achievedrapidly and only a very thin layer of heated oil drains,but it drains quickly becauseof the favorablepermeability(and/orhigh gravity,high head,low viscosity,and so on). High valuesof ,B3result in relatively thin layersof rapidly-flowingmobileoil whereaslow valuesof ,B3resultin the flow of thick layers.Considerable time is requiredfor a thick flowing layerto becomeestablishedbecauseof the need to build up the heat bank beyondthe advancingfront. The buildup of the heat bank takes longerin the lower part of the reservoir becausethe frontal advancerate is slower there and for a given time U2tfais lower (Figure 2.8). As a result, for the calculationwhere the deviationfrom the steady stateis included(Figure7.34)comparedto that whereit is not (Figure7.4),the advanceof the interfaceis slowernear the baseof the reservoirthan it is at the top. It will be notedin Figure 7.34 that initially the steamchamberdoesnot advanceinto the reservoirat the bottom; it overridesat the top without steampenetratingto the
Avoidingthe Steady-stateHeat-distributionAssumption
329
ll \ {
F rl
r
il tl
xl
c{
s
rl
u
I
,I
rI
AthabascaCrude; 300cs at 1000C; 10 cs at 2OOoC q = 0.069mzlday; ReservoirTemperature 12 oC
Coid ---.
C
a=38
Parameteris kh in darcy metres
Paramelef 6 Er an darcy neinla
20
(')
(f)
dl
co
= >10
-(u 1n
c.)
=
1oo
oc steam r#fierature
3oo
Figure 7.36 Effect of SteamTemperatureand kh on 83
productionwell.l1This is reminiscentof the behaviorpredictedby van Lookeren's theorydescribedin chapter 4 (seeFigures4.29 an44.30).The phenomenonshown for earlytimesin Figure7.34, andwhich would be evenmoreevidentif the valueof 83 had beensmaller,occurseventhoughit is assumedthat initially the entirevertical plane abovethe productionwell is at steamtemperature.The flow of draining oil preventsthe advanceof the steamdownwards. Values of the Parameter83 Figures7.36,7.37,and 7.38 give valuesof -83as a function of steamtemperature and the productkh for three different crude oils using typical valuesof a and rn. Valuesof 83 for a whole rangeof situationscan be estimatedfrom thesediagrams by interpolation. ttThe theory describeddoesnot allow for steambeing introduced at a higher pressurethan the draining oil. In practicethe steamchambercould be forced to the productionwell more rapidly by either increasingthe steaminjection pressureor by lowering the pressurewithin the production well. Strategiessuchas this are desirablebecausethey make the wholedrainageheadavailablemore rapidly. Also there is a needto allow for the resistanceto radial f low in the immediatevicinity of the productionwell; this too requiresan increasein the pressuredifferencebetweenthe injectorand the producer.Another factor which requiresan increasein the pressuredifferenceis the resistanceto the radial flow of steamaround the injector.Neverthelessthere remainsthe conceptof the continuous steam-assisted gravity drainagewith the productionof oil controlledso that oil is withdrawn at a rate equalto that of the drainagearound the perimeterof the chamberwithout allowinglive steam to bypassin excessivequantities.This can also be looked upon as the productionof oil from below an expandingsteam (gas) cap without allowing the coning or, perhapsmore accurately,cresting of steam.
330
Steam-AssistedGravity Drainage
Chap.7
LloydminslerTy;r o = 0Gtr
o
(9
9ro
Heat Penetr
Figure7.39: a casein\.ol ure 7.12.it $ what lower.1 The rez is lower thar '-
I hls lt
the initial renr
Avoidingthe
2oooc 2tc
oC C o l dL a k eC r u d e ;l o o c s a t l o o o C ; 6 c s a t 2 o o oC q = o.oo9m2/day; ReservoirTemperature 12 Parameteris kh in darcymetres
20 (f)
(D (!)
=
*=tF^"'* 100
200
300
oC SteamTemperature
Figure 7.37 Effect of SteamTemperature and kh on Bs
ed by van Lookeren's e phenomenon shown evidentif the valueof tially the entireVertiThe flow of draining
il q i
tl ltl
tI
20
[,
ill
tf
(9 dl
of steamtemperature ll valuesof a and Z1q. from thesediagrams
at a higher pressurethan rductionwell more rapidly ure within the production rnageheadavailablemore immediatevicinity of the t*een the injectorand the :renceis the resistance to heconceptof the continuso that oil is withdrawnat ithout allowinglive steam rductionof oil from below more accurately,cresting
y Drainage
Chap.7
lt
r{
Lloydminster TypeCrude; 30cs at 1OOo C; 3.5 at 2OO oC "s o = 0.069m27day;ReservoirTemperature= 12oC
nB,
Ir
9ro
ltl
ru r( rr --10
il! rd
Parameteris kh in darcymetres
I i{
ril
200 oC SteamTemperature
300
Figure 7.38 Effect of SteamTemperature and kh on Bz
Heat Penetration as a Function of Distance Along Interface Figure 7.39 showsthe interfacepositionscalculatedusing the sameapproachfor a caseinvolvinga confinedwell. Although the curvesare similar to thoseof Figure 7.12,it will be found, on carefulexamination,that the productionrate is somewhat lower, particularlyinitially. The reasonfor the lower rate is that the heatpenetrationbeyondthe interface is lower than that correspondingto the steadystate.l2The fraction of the steadyr2Thisis particularly true near the start where it is assumedthat the reservoiris cold beyond the initial verticalhot olane.
Avoidingthe Steady-stateHeat-distributionAssumption
331
o .G
a a CE o
0-8
o
tG o t, G ()
(}r -g
0.6
a
o a a
0.4
! C o
E o
a g a
E o 0
0,2
0.4 0.8 1.0 0.6 Horizontaldistance fuh
1.2
1.4
Figure 7.39 Positionof Interfacefor a Confined Well
stateheatpenetrationthat is achievedis plottedagainstthe verticalpositionon the interfacefor a dimensionless time of 0.3 and for l, = 8 in Figure 7.40. The fraction of the steady-state heat penetrationachievedis above0.8 over most of the interfaceand is muchlower near the well. It is this deviationfrom the steady-state heat penetrationthat makesthe drainagerate somewhatlessthan that predictedby the earlier equations. Figure 7.41 comparesthe drainageratespredicted from the earlier equations with thosecalculatedfrom the curvesin Figure 7.39.The three dotted curves in this diagramare the sameas thosein Figure 7.13.The solid curve showsthe rate
E 100 o tr
1. The hea 2. The hea p€ratun This as actuall3. The hea calcula 4. The hc method
t80 .U
o r60 o IE
@+o t t6 o
620
332
Predicted Ol
The steamcc matedusingt In gena
tr o
o bs0
from the nen 7.34.After th exceedsthe n ized that duri drainagerate curve for the r larities in thc calculation.
0 0.2 0.4 0.6 0.8 1.0 Vertical Height Along Interface y/h
Figure 7.40 Heat Penetration Along the Interface as Percent of Steady State:,* : 0.3; 83 : 8
Steam-AssistedGravity Drainage
Chap.7
ttlt is rc|l (T^ Tn)/lTs' with the oil bcy
Avoiding the S
* Originaltheory Q :,/Z
a
TandrainQ* : y't.s _----*_ \'----
o (U E o
ED{ ^
\r..
E G
Tandrainwith depletion
o o v, o c
Nonsteady-state theory withB, : A
-9 v, c o
-E o 0 12
1.4
0
0.5 DimensionlessTime
1.0
+ rl
{
Figure 7.41 Comparisonof PredictedProductionRates
lr tical positionon the ure 7.40. rd is above0.8 over ; deviationfrom the en'hatlessthan that he earlierequations reedotted curvesin urve showsthe rate
from the newer theory. It startsmuch lower and then reachesthe level predictedby 7.34. After this, it fallsbecauseof depletion.Although the solidcurvein Fig,neT.41 exceedsthe rate predictedby equation7.35aoverpart of the range,it shouldbe realized that during this period,the reservoiris lessdepletedbecauseof the earlierlow drainage rate. If the curves had been plotted againstthe fractional recovery, the curvefor the new theorywould havefallen belowthe other throughout.The irregularities in the curve from the new theory are due to instabilitiesin the methodof calculation. PredictedOil-Steam Ratios The steamconsumptionfor the processesdescribedin this chaptermay be estimatedusingthe equationsdevelopedin Chapter2. In general,steamis required to provide the following: 1. The heat to raise the steamchamberfrom Ta to Ts. 2. The heat required to raise the produced oil from Zn to the production temperature. It may be assumedthat this is the sameas the steamtemperature. This assumptionis somewhatpessimisticbecausethe oil leavingthe systemis actuallybelow the steamtemperature.13 3. The heat lossesto the overburdenabove the steamchamber.These may be calculatedusingequation2.28. 4. The heat in the reservoir beyond the advancing front. An approximate method of evaluatingthis is to assumethat it is equal to the heat loss to the
eat Penetration Along s Percent of Steady B.=8
Drainage
Chap.7
13Itis relatively simple to show that the mixing temperatureof the draining oil is given by (T^ Til/Qs - D : ml@ + L). It seemslikely that the draining condensatewill also intermingle with the oil beyondthe interfaceand reachthis sametemperature.
Avoidingthe Steady-stateHeat-distributionAssumption
333
I
I q r l
(
,l
x
d
q r{
I!
ri i
overburden.Alternatively,equation2.48 can be employedusing an average valuefor U. A more accuratemethodinvolvesthe useof the heat-penetration function describedby Butler (1984).It will be found that whicheverof the The heat to the reservoirincreasesrapidly at first as heat penetratesthe side approximatelythe same.
o ! a
The heatlossesfor the unconfinedwell of Figure7.34 areplottedagainsttime in Figure 7.42. In this diagramthe cumulativeheatrequirementsare convertedto dimensionlessvaluesby meansof the following equation:
qi=
u.
a a !g
9 a
c a
E cl
(7.s0)
h2pC(75 - Tp)
In usingthis equation,the value of pC shouldbe for the reservoiror for the overburden, as appropriate.In Figure 7.39 the curve for the cumulativeheat to the chambergivesthe total heatto the chamberplusthe producedoil if the valueof pC is for the fully saturatedreservoir. The curvefor the chambermay alsobe lookedon asa curvefor the cumulative producedoil in appropriateunits. It is the integralof the production-ratecurve. The heat to the reservoirincreasesrapidly at first as heat penetratesthe side of the initial hot plane.The rate of heat supplyto the reservoirdecreases after this initial period and then growsas the extentof the heatedinterfaceincreases. The heat requirementsfor the confinedwell of Figure 7.39 areshownin Figure 7.43 as thinner lines; the thicker lines are for the unconfinedwell and are taken from Figure 7.42. Lines for the confined well deviate starting at the point where the steam chambermeetsthe one growingfrom the neighboringwell. At this point the rates of increaseof the heat loss to the overburdenand to the reservoirdecreasevery
tl3rrr Thrc\c Srstel
markedll' and chamber.Thc increases. A comp ure 7.44. In this fi that is usedto for the confin Effect of Ste
Table7.-lshor performanceI o
=
F t'o o o .9 tr o o tr
E o.s
o
OJ NA F Lrl
F
tr n4 Q)
o ' )p
na
v,z
= :l
DimensionlessTime Figure7.42 Production HeatDistribution RateandCumulative
334
Steam-AssistedGravity Drainage
D Chap.7
Avoiding the Stl
d using an average he heat-penetration *'hicheverof the penetratesthe side
o : F 1.0
plottedagainsttime
o o g c
.9
ertedto dimension-
ao c
o.t -E o
(7.s0) 'oir or for the overulative heat to the ril if the valueof pC : for the cumulative rction-ratecurve. penetratesthe side decreases after this ace increases. 9 are shownin Figrfined well and are rt where the steam this point the rates rvoir decreasevery
0
0.5 1.0 Dimensionless Time Figure 7.43 Effect of Well Confinement on Cumulative Heat Requirements Thicker Lines are for Unconfined Systemand Thinner Lines are for Confined System.
markedly and proportionatelymore so than the decreasein the growth of the chamber.The net result is that the thermal efficiencyfor the confined well case increases. A comparisonof the thermal efficiencyfor the two casesis shown in Figure 7.44. In this figure the thermal efficiency representsthe fraction of the steamheat that is usedto heat the steamchamberand product.The efficiencyis much larger for the confinedcase;the effect is very significant. Effect of Steam Pressure Table7.4 showsthe effect of varying the operatingsteampressureon the predicted performance.In eachof the three calculationsshown,the reservoirwasassumedto
I
I
I
o c
)
.Q)
.9
I
Heatin I erburdenl
a-
Confined w:2h
LrJ
-41I
E E 0.4
Unconfined
L Q)
II
,l
B3:8
u.o
F
c)
II
.F
o
o .2
E 1.0
0
bution Drainage
00.5 Dimensionless Time %a t /h2
Chap.7
1
Figure 7.44 Effect of Well Confinement on Thermal Efficiency
Avoidingthe Steady-stateHeat-distributionAssumption
33s
TABLE 7,4 Effectof Steam Pressureon the Performanceand ThermalEfficiencyof an Unconfined HorizontalWell Steampressure,MPa Steamtemperature,"C
0.45 148
8.7 0.029 0.37 0.37 4
Yearsto produce 92 m3fm Averagerate, m3/m D Thermal efficiency Oil-steamratio Bz
2.0 213
3.8 0.068 0.49 0.36 8
5.7 272 1A
0.104 0.56 0.34 1,2
(from Butler 1985)
havethe propertiesshown at the bottom of the table;thesepropertiescorrespond to a reservoirsimilar to that at Cold Lake. The effect of operatingat higher steampressuresis to raisethe temperatureof the steamchamber;this allowsthe oil to drain morerapidly.Becauseof the shorter time involvedin the operationat the highestpressure,the thermal efficiencyis also highest,i.e., a smallerfraction of the injectedheat is lost to the overburdenand reservoirbeyondthe steamchamber. There is, however,a counteractingeffect that offsets the improved efficiency at high pressure.This resultsfrom the increasedheatneededto raisethe systemto steamtemperature;this is higher simplybecausethe steamtemperatureis higher. The net result is that the overall oil-steamratios in Table7.4 are almostindependent of the steampressureemployed.There may, however,be significant economic advantagesin operating at higher pressuresbecauseof the faster production that is obtained. Calculationswere basedon following parameters:
3.55MPa (t steadystatc I Cold Lr senso that tl quirementn field. In or& meability'pr field pressun In ttrc I Figure 7.4fl lowed.Durin Figure 7.{6 s ment for c within the rq in Figure 7.{ photograpts ure 7.46 is so the fingering The wavy nI which drew t and is not si It was fr preheatingrl adjustmentit rate and thc 1 mentaldata.
P,""= 2040kgl^'
SteamQuality = 9.7
Tn = 6"C
Crock= 963J/kg"C
H =22m d = 0.35
Cor: 2093Jlkg'C Kot : 1.73J/s m"C
AS, = 9.61
pos : 2400kg/-'
k : 0.5 x 10-12m2 K,", = 1.3 /s m "C
Coa: 837J/kg"C z = 100cs at 99"C
SAGD RESULTSFROM SCALED LABORATORYRESERVOIRMODELS OPERATING AT BOTH HIGH AND LOW PRESSURES Chung and Butler (1989b)describeexperimentalstudiesof the Steam-Assisted verticallaboGravity DrainageProcesswhich were carriedout in two-dimensional ratory scaledmodels.Someof the experimentswere carried out with steampressuresnear to atmosphericand others,using a strongerapparatus,with a pressureof 336
Steam-AssistedGravity Drainage
Chap.7
SAGD Res.*ts
Eiencvof an Unconfined 5.7 272
2.4 0.104 0.56 0.34 l2
ropertiescorrespond e the temperatureof rcauseof the shorter malefficiencyis also the overburdenand improved efficiency o raisethe systemto mperatureis higher. are almostindepensignificanteconomic ster production that
3.55 MPa (507 psia). The resultswere comparedwith predictionsfrom the nonsteadystate theory which was describedpreviously (Butler 1985). Cold Lake Bitumen was employedand the experimentalconditionswere chosen so that the value of ,83would be the samein the model as in the field. This requirement meansthat a coarserpacking is required in the model than that in the field. In order to model the samefield conditions it is necessaryto use higher permeability packing for low pressureexperimentsthan for ones carried out at the field pressureand temperature. In the first experimentsa preheatedvertical injection well was employed(see Figure 7.45) and steamwas circulated within the well before production was allowed. During the production period steamwas injected at the top of the reservoir. Figure 7.46 showsphotographsof the steamchamberat various stagesof development for one of the experimentsand Figure 7.47 showsthe position of isotherms within the reservoirfor the sametimes. It is interestingto comparethe photographs in Figure 7.46 for a steamchamberspreadingfrom a central hot well to the initial photographsin Figure 7.15 which show a rising chamber. The interface in Figure 7.46 is stableand advancesin a steadyand systematicmanner as contrastedto the fingering displacementwhich occurs above the rising chamberin Figure 7.15. The wavy nature of the isothermsin Figure 7.47is causedby the computerprogram which drew the contours from the limited temperaturemeasurementinformation and is not significant. It was found necessaryto modify the theory slightly to allow for the reservoir preheatingwhich occurred during the initial steamcirculationperiod. With this adjustmentit was found that the theoretical predictions of both the oil production rate and the position of the interface were in excellentagreementwith the experimentaldata.
/kg'C
;'{
r{
,
i lff
"i
fkg'c I/sm'C kgl^' lkg"C s at 99'C )ELS OPERATING '
y Drainage Chap.7
4
i l-l
kg/m'
the Steam-Assisted nsionalvertical laboout with steampresus,with a pressureof
/, {
HORIZONTAL PRODUCTION WELL
Figure 7.45 PreheatedVertical Steam Injector usedin Model Experiments (from Chung and Butler 1989b)
SAGD Resultsfrom ScaledLaboratoryReservoirModels
*S min.
60 mln*
9S nin.
1P0min.
Figurt 7f Figurc 7.4 Chungend
Figure 7.46 Photographsof SteamChamberDevelopingAbout a PreheatedVertical IniectionWell in a Low PressureExperimentwith a TransparentCell Wall (from Chungand Butler 1989b)
The oil production rate is compared to the theoretical predictions in Figure7.48.Two theoreticalcurvesare shown.The dottedcurve is the theoretical curve which is obtainedif it is assumedthat the reservoiris all at the initial temperatureat the start of production.The solid curve makes an allowancefor the preheatingbeforeproduction.Figure 7.49 shows,for the sameexperiment,a comparisonof the position of the interfaceas determinedfrom photographswith the predictedvalues.The agreementwith the measureddata is satisfactory. In experimentsof this type the oil-steamratiosare far lower than thosewhich would be found in the field becauseof the excessiveheatlossesfrom the largevertical surfacesof the two-dimensionalmodel.It is howeverquite practicableto predict the oil-steamratiosfor the field situationand examplesof this are given in the paper(Chungand Butler 1989b). A similar agreementbetweentheoreticalpredictionsand experimentaldata was alsofound for the high pressureexperiments.Figure 7.50showsa comparison for a high pressurerun. Experimentswere also conductedusing multi-well modelsat both high and pressures and againthe resultswere similar.Figure 7.51showsisothermsfrom low pressure model experimentin which five parallelhorizontalwell pairs were a high representsa two-dimensionalsectionthroughthe reservoir.In The model modeled. the steamwas injectedfrom five injectionwells eachof which theseexperiments was locatedimmediatelyabovea producer. 338
Steam-AssistedGravity Drainage
Chap.7
This ga pilot at AG facility consis In the steam wards from tl well in eachp o1:
o, qt
e,200 c o o !t o tt
100
Co5 tr.-r
o
SAGD Reglte
lO min.
20 min.
60 min.
t
T {1
120min.
90 min.
h
tr
Scaled time, years
.r
o
5
300
P.sdicled and expetimental resulls tot a preheated v€rtical inleclor
tt\.oor'
ot t
.15
C E E
a
gt
c
.9 o T' 'loo o
o
..?
200
.i\ i ;
j
.9
o'..
,' \
'
\
cold f.acture
\'..... o
... \ oN'
CI
a
a
o
!
t - \ - - - . _ .
\
o o.o5 E o t -9 (! o(h
2
Time,hours
ity Drainage ChaP.7
ll
This geometricarrangementis similar to that employedin the steamchamber pilot at AOSTRA's UndergroundTest Facility (Edmundset al. 1987).This test facility consistsof tunnelsimmediatelybelow a sectionof the Athabascareservoir. In the steamchamberpilot three pairs of parallel deviatedwells are drilled, upwards from the tunnels and then horizontallyinto the reservoir.The production well in eachpair lies near to the baseof the reservoirand its steaminjectionwell is
etical predictions in urve is the theoretical all at the initial teman allowancefor the re experiment,a comwith the photographs ,atisfactory. ru'er than thosewhich sesfrom the largeverrite practicableto prerf this are given in the
rdelsat both high and showsisothermsfrom izontalwell pairs were roughthe reservoir.In rn wells eachof which
r
Figure 7,47 Temperature Distribution within the Reservoir for the Experiment of Figure 7.42. Isotherms are Labelled in "C. Cell Dimensionsare Marked in cm (from Chung and Butler 1989b)
reheatedVerticalInlall (from Chungand
rnd experimentaldata i0 showsa comparison
H q
l2O min
I
Figure 7.48 Predicted and Experimental Oil Production Rates for a Low Pressure Experiment (from Chung and Butler 1989b)
SAGD Resultsfrom ScaledLaboratoryReservoirModels
339
c
:u 1 t
ft ll
E o +i E
.9 ro o I
Figure 7.49 A Comparisonof the Predicted and ExperimentalPositionsof the Interface (from Chung and Butler 1989b)
51015
Half well spacing,cm
parallel and slightly above.The project was adoptedby an industry steeringcommittee following a proposalmadeby the author to AOSTRA in 1984(Butler 1984). The project has been constructed and operated and it has been very successful; there are plans to developan expandedproject. One of the factors studied in the laboratorywork was the effect of the steam chambersinterfering with each other before they grew to the top of the reservoir. This can happenif the wellsare locatedwith a closehorizontalspacing.The ability to drill closelyspacedwells economicallymight possiblybe the majorjustification for a commercialtunnel-basedbitumen recoveryproject. Projectswith large spacingswould be more economicalusingwells drilled from the surface.la
o 19 zoo G
a
.9 o
a
a aaaa-
.\. t
=
t.\.' a
loo
€
o-.o
o
o 123
Time,hours
Figure 7.50 A Comparison of the Predicted and ExperimentalOil Production Ratesfor a High Pressure Experiment (from Chung and Butler 1989b)
Figurr m e n t .! Separe Steam Chamb Exccp (from (
toThereis doubt as to whether the cost of developingundergroundmine-workingsas a base for the constructionof horizontal wells is economicallyjustifiable. A significant part of the mine cost is the provisionof safeworking conditions,escaperoutesand the like, for the undergroundfacility in the event of a well failure or of a steamor hot oil leak. At the AOSTRA projectthere are
two alternate es refugeroom to br the mine approsurfacewhich ha
Chap.7
Oil Production t
340
Steam-AssistedGravity Drainage
10min.
, Comparisonof the Prerrimental Positionsof from Chung and Butler
; {
dustry steeringcomn 1984(Butler 1984). ,€en very successful; e effect of the steam top of the reservoir. I spacing.The ability re major justification pcts with large spacurface.to
I{ {
r
ill
h s n
60 min.
i I i q
I
\ Comparisonof the PreperimentalOil Produca High Pressure rom Chung and Butler
. 90 min. Figure 7.51 TemperatureDistribution for a High Pressure5 Well-pair Experiment. Steamis InjectedJustAbove Each of the Five ProductionWellsThrough SeparateInjectors.The Upper Part of the Figure ShowsFive SeparateRising Steam Chambers.At 60 Minutes These Have CoalescedTo Form a Separate Chamber.By 90 Minutes EssentiallyAll of the Model is Saturatedwith Steam Except for Colder SpotsBetweenthe ProductionWellsand the Ends of the Cell (from Chung and Butler 1989b).
mine-workingsas a base nificant part of the mine :. for the undergroundfaOSTRA project there are
two alternate escaperoutes throughout; these are based upon dual mine shafts. There is also a refugeroom to be occupiedby personneltrappedwithin the mine. A major factor that detractsfrom the mine approachis the substantialimprovementin the cost of drilling horizontalwells from the surfacewhich has occurred during recentyears.
ry Drainage Chap.7
Oil Productionafter StoppingSteam lnjection
341
Scaled time, years
OIL PRODUCTION A
12
200
E o
3
)'a'
) rso
..A^ 6_ A
at S roo
ot
A ; .^a
ix_r
. ,,
^ \i^
rL
e---r
" . t ] ] . _ort -a-, - -
.9 o
" a. r .
Aa
a a
[-
a t -''!
3uo o
^
70
Well spacing 11.7 cm
.9 o o.os!
=
,a."o,, ..
"
a.o.!
o
|E
u !
'a'a-rr_e. sO
Time,hours
E
-g o
Figure 7.52 Oil ProductionRatesfor High PressureExperimentswith Varied Horizontal SpacingsBetween AdjacentWells.The Curve for 11.'7cm Spacingis for the Experimentwhich is Depictedin Figure7.47(from Chung and Butler 1989b)
Formatlon lleight 2O m
In the steamof the prodtjt1 this operation the rocks u ith steam is produ boundaries.11 The pru that in a confi mately the tim the adjacent r lowing the ces fore, altho,'gh production ral of 60, 90. and Curvesshor tl bers interming
o .} ,oo
E
Wsll Spacing 67 m
.9 150
(,
!
9 roo
IL
o
.z -g
50
tr
o
4
Time, years
1
i
\
Figure 7.53 PredictedCumulative Oil Productionfor the Field at AOSTRA's UTF Site for VariousHorizontal Well Spacings;FormationHeight 20 m (from Chung and Butler 1989b)
-._Q?tq!9rnce*a|llgjlgamrchimbers occurred in the experiment depicted in Figure7.51.This coalescence did not resultin a reducedrateof productionper well ashad beenfeared.In fact the experimentindicateda higherrate of productionper well after the interferencethan from wells which were more widely separatedfor the sametime in the experiment. Figure7.52showsthe rate of productionas a function of time for variouswell spacings. In eachexperimentit took aboutoneyearof time (scaledto the Athabasca reservoirconditions)for the steamchamberto reachthe top of the reservoir.Howby the solid circlesthe rate was ever for the most closelyspacedwells represented somewhathigher and the peak rate which correspondsto the chambersreaching the top of the reservoirwas achievedearlierthan in the other experiments. The cumulativeproductionfor the Athabascafield conditionswhich would be predictedfrom theseexperimentsis shownin Figure 7.53.This diagramcorrespondsto a steamtemperatureof 200"C (i.e. steamat 1.6 MPa or 232 psia). 342
Steam-AssistedGravity Drainage
Chap.7
Recovervof Hg
OIL PRODUCTION AFTERSTOPPINGSTEAM INJECTION In the steam-assisted gravity drainageprocess,it is possible,toward the latter part of the productivelife, to continueproductionof oil without steaminjection.During this operation,the pressurein the steamchamberfalls as the systemcools.Heat in the rockswithin the steamchamberis transferredto waterin the pores,and further steamis produced.This heat is transferredfrom within the steamchamberto the boundaries,whereit heatsthe oil and promotesgravity drainage. The processhas been studiedby Fergusonand Butler (198s).They showed that in a confineddevelopment,the steaminjectionshouldbe stoppedat approximatelythe time that the adjacentsteamchambersmeeteachother halfwaybetween the adjacentwells.Under thesecircumstances, the productionof oil obtainedfollowing the cessationof steaminjectionis approximately507oof that producedbefore, although the rate drops off fairly rapidly. Figure 7.54 showsthe predicted productionrate as a function of time for a Cold Lake reservoirwith half-spacings of 60, 90, and 120m. The rate risesrapidly and rhenfalls off with time. The three curvesshowthe rate predictedif the steamis shut off at the time the steamchambers intermingle (the confinement time).
I ProductionRatesfor .xperiments with al Spacings Between The Curve for 11.7cm LeExperimentwhich is tre 7.47 (from Chung DI
;
tl 0
200
5
150
;u ll
rt
IJ F
:dictedCumulativeOil he Field at AOSTRA's rious Horizontal Well rtion Height 20 m (from :r 1989b)
F r{
(r 100 z I
I
\w= 120m 90\
F
:)
50
E
o12 16 YEARS
)erimentdepictedin f productionper well ateof productionper widely separatedfor
20
y Drainage Chap.7
28
o
o.z+ Q E
W=60m
= o.20 lrj
time for variouswell rledto the Athabasca f the reservoir.HowI circlesthe rate was e chambersreaching r experiments. rditionswhich would This diagramcorrea or 232psia).
?4
Figure 7.54 Predictedproduction Rate for ParallelHorizontal Wells in Cold Lake Reservoir Well Length 1000m; ReservoirHeight 30 m; Injectionto Time of Confinement; ParameterW : Well HalfSpacingin Meters (from Fergusonand Butler 1988)
120
fi o.re J
o o.lz trJ
P o.oe E j o.oe l (J
oo'
8121620 TIME (yeors)
Recoveryof Heavy Oil above Water
?4
28
Figure 7.55 Predicted Oil-Steam Ratio for Parallel Horizontal Wells in Cold Lake Reservoir Reservoir Height 30 m; Injection to Time of Confinement; Parameter W : Well Half-Spacing in Meters (from Ferguson and Butler 1988)
343
$t
ilrt il
fr ll
I
0.3
J
6 9F
IInjectionfl
ifl
E =o . e =Ft )a
STEAMINJECTION OMPo P R E S S U RI E
()
0.1
o
23
75 50 ( % R E C O V E R Y o f m o b i l eo i l )
100
Figure 7.56 Cumulative Oil-Steam Ratio versusRecoveryfor Parallel Horizontal Wells in Cold Lake Reservoir ReservoirHeight 30 m; Parameters: Injection Time as Percentof /., Half-well Spacingin Meters (from Fergusonand Butler 1988)
The cumulative oil-steam ratio is shown for the same three cases in Figure7.55.In eachcase,the COSR increases rapidlyafter the steamis shutoff; oil is producedduring this period without the further consumptionof steam.Higher oil-steamratiosare obtainedwith the closerwell spacingsbecauseof the morerapid production and reducedtime for heat loss. The generallylow level of oil-to-steam ratiosthat are shownin Figure 7.55and 7.56reflect the choiceof conditionsused pressure(10 MPa) ' for the case-in particular, an extremelyhigh steam-injection with its associated extremetemperaturei:fftl. It is thoughtthit muchmore economic OSRswould have beenfound if a lower injectiontemperaturehad been assumed.Nevertheless, similar trendswould be expected. In Figure7.56 the cumulativeoil-steamratio is plottedagainstthe percentrecoveryof mobile oil (the mobile oil lying abovethe productionwells).Curves are shown for the samethree well spacingsand also for the time at which the steam injectionwas stopped.This time is expressedas a percentageof the time of confinement.For eachwell spacing,the overallrecoveryincreases asthe time of steaming increases, and the cumulativeoil-steamratio risesto rather flat maxima in the vicinity of t" = 1; at this point the recoveryof the mobile oil is about75Vo.
o
1(( \ Produlr
ry
>
u
Y,/,/, -<<
3.
ry
Figrrt 1 an Aclit
The thicker conventionalheavy oil reservoirsin Saskatchewan and Alberta frequentlycontainsubstantialaquifersat the base.This water tendsto limit the applicabilityof conventionalsteamrecoverytechniquesbecauseof the extra heatload it creates.If steam is introduced above reservoir pressureit tends to flow into the water layer and excessiveheat can be lost. Similarly cold water may be drawn towards the production well and consumevaluableheat. Conventionalcold production in thesereservoirsis usually not economicalbecauseconing of water to the production wells results rapidly in excessivewater-oil ratios. The use of SAGD to produce these reservoirscan be attractive becauseof the possibilityof controllingthe pressurewithin the productionwell to be almost equal to that within the aquifer. Under these conditions the oil can be produced without drawing much water, other than the condensatefrom the steam,into the producingwell. The processis shownschematicallyin Figure 7.57. As is shown in the first diagram of Figure 7.57, (or as was discussedon pages322 to 325 for an intermediateelevation)steamis injected into a well at the
top of the f a growiry t higherthan throttling t The s gramsin Fi after a tirr Up until t[ chamberhr ids have bo As th producedfl allow oil al be controll aquifer.uo the genera aroundthc its radialfl trol stratq longer eco
34
Recoveryd
RECOVERYOF HEAVY OIL ABOVE WATER
Steam-AssistedGravity Drainage
Chap.7
Overburden InjectionWell 'umulative Oil-Steam .ecoveryfor Parallel lls in Cold Lake ReserHeight30 m; ParameTrme as Percentof 1., ing in Meters(from Butler1988)
1.
ame three cases in : steam is shut off; oil
Stream Lines
Underburden
ion of steam.Higher ruseof the more rapid , level of oil-to-steam ce of conditionsused )n pressure(10 MPa) that muchmore eco)€raturehad been asgainstthe percentreon wells).Curves are e at which the steam e of the time of con' asthe time of steamer flat maximain the is about 75Vo.
I Figure 7.57 Diagram ShowingProductionof ConventionalHeavy Oil which Lies above an Active Aquifer using Downward Steamfloodingand SteamAssistedGravity Drainage
lh not economicalbein excessive water-oil attractivebecauseof :ion well to be almost : oil can be produced m the steam,into the = 7. 5 7 . as was discussedon :ted into a well at the
top of the formation.In the first phaseof the processoil is displaceddownwardsby a growing steamchamber.During this phasethe steampressureis substantially higherthan the reservoirpressureand the productionwell pressureis controlledby throttling to preventwater from the aquiferflowing to the well. The steamzone advancesdownwardsas shown in the secondand third diagramsin Figure 7.57. It advancesmore quickly alongthe central streamline, and after a time of perhapsoneyear steamarrivesin the vicinity of the productionwell. Up until this the producedoil and the accompanyingcondensatefrom the steam chamberhavebeenflowing throughrelativelycold reservoirand the producedfluids havebeencold. As the steamchamberapproachesthe production well the temperatureof the producedfluid risesrapidly.At this point the productionwell shouldbe throttled to allow oil and water to be producedwithout steam.The steaminjectionrate should be controlledso that the pressurewithin the steamchamberbalancesthat of the aquifer.Under theseconditions,the injectionwell pressurewill be somewhatabove the general steamchamber pressurebecauseof the near well bore pressuredrop around the injectionwell, and the productionwell pressurewill be lower becauseof its radialflow pressuredrop. The SAGD processphaseis continued,usingthis control strategy,as shown in the fourth diagramof the figure, until the OSR is no lonsereconomic.
ry Drainage Chap.7
Recoveryof Heavy Oil above Water
r.an and Alberta frendsto limit the applithe extra heatload it :nds to flow into the ter may be drawn to-
345
*' a)a E:6
E}; coc
F;$
o
Aa
x.:
i
rr.l > 9 =-s :ot
€E9
I I= =Xts QE
V
';o:
=\.,
-od* ,a7
aH y.g a
=o.I
-r'.v Fi p
-q oray < rFF tFgo oo y/.: ii.f,^
346
Jtd
F}
9rf
v)J6
F O
>a E : o€
;t6
dJa U)E
u
!EC)
E}:
\ =!-l :F:
?r
CQ
:E^
ll
h!=
lt
6zd
il
E e U
a
Aa
x.: tr Et;g -;:r!
€ eg Z'-
oXb
F
9 TB =xh oH q It
v
F.vt 'Eoa
t, l ]-
Y 9,= sco d
=15 -o{!oF
rI I
99; q3Q= cB
F Ll tl
x-
o
:*
}
@ , Q -
o RoP :Htrt
i{
= 33
5< E ooE
; E.E
i
=x
-J.Y
'Ev
-r t 9 < oo EJ1 i: S(€oo Eo9.g i:/Fn
FO
fir 9J r;{ o d.^ t=2 u! i:s
d *
].
t-
4
347
rtl
i l
!t
IT
t
{
The processhasbeenstudiedin a seriesof 12 scaledlaboratorymodelexperimentsby Sugiantoand Butler (1989)and encouragingresultswere obtaineO.Higtr recoveriesof oil with little water productionother than that of the steamcondensatewere achieved. The extrapolatedresults indicated that a typical Lloydminster formation (14 m thick) shouldproduce over 1.60m3/d (1000B/d) from a horizontal well 500 m in length. Studiesof the effectofvarying the verticalelevationof the horizontalproduction well showedthat satisfactoryoperationcould be achievedwith the welllocated somewhatabovethe water interface. Howeverwhen this strategyis adoptedthe oil locatedbetweenthe well and the aquifer can not be producedbecauseit cannot drain by gravity.[n someexperimentsthe well was locateddeliberatelyat the bottom of the formation and thus at the baseof the aquifer.This arrangementwas found to give good resultswith little productionfrom the aquiferif the initial productionwas throttled to allow displacementof water from around the production well as oil was forced downwardsby the advancingsteamfront. In this mode of operationthere is little heatingof the aquiferby injectedsteam. Figures7.58 and 7.59 show the temperaturedistributionsmeasuredduring two companionexperiments,one without a bottom water layer (seethe left-hand diagramsin eachof the figures)and one with an activewater level (seethe righthand diagrams).In the experimentswith bottomwater,watercould flow freelyinto and out of the bottom of the model through tubesconnectedto an externalconstantpressurevesselcontainingcold water.By adjustingthe injectionpressurein the reservoirit was possibleto operatewith little flow of water to or from the model. It is apparentfrom the position of the isothermsin the two figuresthat the operationwith bottom water was conductedwith very little heat passinginto the bottom water zone. An oil recovery of 87VoOOIP was the highestwhich was achievedin experimentswithout bottom water. The recoveryachievablewith a waterzonepresentwassomewhatlessthan that obtainablewith a waterfree system but satisfactory;the highestrecoveryobtainedwith a bottom waterlayer was797o. The reasonfor the lower oil recoveriesin the experimentswith bottom water was that someoil was forcedinto the water layer.
Fi3rrr 1 Half of Yang et
slopeis neo reservoir-P this type. The e ler to depa that shoc.n
EFFECTSOF RESERVOIR HETEROGENEITIES Scaledmodel studiesof the effect of some reservoir heterogeneitieson the SAGD processhavebeenreportedby Yangand Butler (1939).They investigated the effects of reservoirscontaining horizontal layersof material of different permeabilitiesand also the effect of horizontalshalebarriers. When a higherpermeabilitylayer lies near the baseof the reservoirthere is a tendencyfor the steamchamberto underminethe layer above as by the photographsin Figure 7.60.Howeverheat is transferredupwardsinto the lower permeability layer as the process proceeds and this tend to limit the 'degreeof undermining. When a layer of lower permeability lies at the baseof the reservoir then the interface curves become steeperin the lower permeabilitysection;this steeper 348
Steam-AssistedGravity Drainage
Chap.7
Effects d R
torv model experire obtained. High lhe steam condenminster formation izontal well 500 m horizontal producth the well located is adopted the oil becauseit cannot €rately at the botarrangementwas r if the initial prond the production n this mode of opmeasured during rsee the left-hand r el (seethe rightld flow freely into r an external conion pressurein the : from the model. o figures that the t passinginto the riehestwhich was achievablewith a \\ ater free system ter layer was 79Va. bottom water was
It
ll it
{t il
I It
Figure 7.60 Positionsof Interface During ScaledVisual Model Experiment with Upper Half of Model Packedwith 2 mm GlassBeadsand Lower Half with 3 mm Beads(from Yang and Butler 1989)
ll
u
the higherflow from the upperpart of the slopeis neededin orderto accommodate reservoir.Positionsof the interfaceare shownin Figure 7.67for an experimentof this type. The effectof horizontalbarriersin the reservoirwasfound by Yangand Butler to dependupon the geometryof the particular situation.Shortbarrierssuchas that shown in the photographsin Figure 7.62 had relativelysmall effects.As the
ties on the SAGD tisatedthe effects rermeabilities and eservoirthereis a as by the photothe lower permeit the degree of reservoirthen the 'tion: this steeper 'ainage
Chap. 7
Lowpermeability belowbrokenline and highpermeability above.
0
20 10 Horizontal distancein cm.
Effects of Reservoir Heterogeneities
Figure 7.61 Positions of Interface During Scaled Visual Model Experiment with Upper Half of Model Packed with 3 mm Glass Beads and Lower Half with 2 mm Beads (from Yang and Butler 1989)
349
ll t
il ,t t
(c)
-.Lr Figure zontai B:r:x
(d)
Figure 7.62 Positions of Interface during Scaled Model Experiment with a short Horizontal Barrier in the Left-Hand Side of the Reservoir (from yang and Butler 19g9)
steamchamberreachedthe barrier it spreadunderneath,but heat was also transferred through the barrier to the reservoirabove;becauseof this transferredheat the oil abovecould continueto drain and the barrier had no long term effect. Long barriersin somelocations,such as that shown in the photographsin Figure 7.63,had only a limited effect. In this experimentboth the oil abovethe barrier and that belowwereproduced.An importanteffectwasthat heatwastransferred through the baffle and as a result only a small inclinationof the interface abovethe baffle was sufficientto allow productionfrom above.Nevertheless, as may be seenfrom Figure 7.64,the overallproductionwas retardedas comparedto that in a companionrun without a barrier. Different resultswere obtainedwith the geometryshown in Figure 7.65 and 7.66. rn this experimenta long barrier extendedacrossmost of the width of the model abovethe injectionand productionwells.A normal steamchamberrose to the undersideof the barrier and then spreadsidewaysas if the barrierwerethe top of the reservoir.when it reachedthe end of the barrier howeverthe drainageprocessstalledand no steamchamberformed in the upper half of the model.The oil above,although it graduallybecameheated,could not fall downwardsbecause
350
GravityDrainage Steam-Assisted
Chap.7
there qas t drainage p from a ner the produ dou nr'rard 800 E
3 soo 8 +oo : { zoo E
o
Formation t
(d)
(c)
u ||
Figure 7.63 Positions of Interface during Scaled Model Experiment with a Long Horizontal Barrier in the Right-Hand Side of the Reservoir (from Y4ng and Butler 19_89)
I ShortHorir 1989)
therewasno continuoussteamchamberand no densitydifferenceto allow a gravity drainageprocess.The oil abovethe barrier could be producedby injectingsteam from a new well locatedin the upper zoneat the top of the reservoirdirectly above the producer.With this arrangementthe injectedsteamcould sweepthe heatedoil downwardsrelativelyeasily.
Leat was also trans-
ris transferredheat ,ngterm effect. the photographsin r the oil abovethe hat heatwastranson of the interface e. Nevertheless, as led as comparedto in Figure 7.65 and rf the width of the m chamberrose to ,arrierwere the top r the drainageprothe model.The oil ownwardsbecause
)rainage
Chap.7
= 3 ooo 8 qoo
r Withoutbarrier a Withbarrier
o
zoo E E o 2 Timein hours
Formationof WO Emulsionswithin the Reservoir
Figure 7.64 Cumulative Recoveryof Oil from the Experimentof Figure 7.63 Comparedto that from an Experiment without a Barrier (from Yang and Butler 1989)
351
i I
h I
Id
ir
FORMATIONOF WA
..t
*a HE oF
F.] b
.E; od) o +E
srE
I
So X=
=# -9X =v =v 9E o'.
3F oo
Htr
oo oo
2e loF
\o= F;X 5!
.90F frF
oo
352
The formatir tions.The m cussedbl" Jar emulsionfan steamis the o tumen to sprc by the condcl For snrd small radiusc supersaturat abovethe vq this supersat degreeof sry water to csrd there is consi densewithort emulsion forn coolerbiturnc din and Butla dispersewatcr they are watd Experim portedby'Cho (1988).Jamal stronglyoil-*r ratios of emut mentswhich e The measure Measurg Butler (1988ar at both low ar when there crl ing. This is co sincethere is r rise into the cr Figure 7. ucts from tr*'o of 153kPa (2 both experinr connater*'ate that the packi pressureruns tively high dur the steamcha Formation of |l
FORMATION OFWO EMULSIONS WITHINTHERESERVOIR
99P oF
rb >! o60
ha *E
aE -9o != 9Q
>= 3- - 3E boo
e2 o'.
HF oo :c oo = e
.Y;
2e h'F
9H rm
O_
=|€
.10 F EN
The formation of water-in-oil emulsionsis very commonin thermal recoveryoperations.The mechanismof formationof emulsionswithin the reservoirhasbeendiscussedby Jamaluddinand Butler (1988).They considerthat the main causeof emulsionformationwithin the reservoirduring recoveryprocesses which involve steamis the condensationof steamon cooler bitumen surfaces.The tendencyof bitumen to spreadon water surfacescausessmall dropletsof water which are created by the condensation of steamto becomeburied within the bulk of the bitumen. For small water droplets to form it is necessary,becauseof the effect of the small radius of curvature of the droplet on vapour pressure,for the steam to be (i.e. the partial pressureof the water vapor needsto be somewhat supersaturated abovethe vapor pressureof liquid water at the temperatureof the condensate).It is this supersaturation which providesthe driving force for the emulsification.The degreeof supersaturationwhich can be achieveddependsupon how easyit is for water to condenseelsewhere.In particular if the reservoir rock is water-wet then there is considerablewater availablewith a flat surface on which steamcan condensewithout droplet formation. From this reasoningit would be expectedthat emulsionformation would be greatestin circumstances where steamcan contact coolerbitumensurfaceswithout contactingrelativelyflat water surfaces.Jamaluddin and Butler show from a thermodynamic argument that the work required to dispersewaterwithin circular capillariesis lessif the capillariesare oil wet than if they are water-wet. Experimentaldata which are in support of the above ideas have been reported by Chungand Butler (1988and 1989a)as well as by Jamaluddinand Butler (1988).Jamaluddinand Butler showedthat when oil is displacedby steamfrom a stronglyoil-wet packedbed (Teflon beadsor toluene-washed, dried sand)higher ratios of emulsifiedwater to oil were found in the productthan in similar experimentswhich employedwater-wetsand (sandwashedprior to run with detergent). The measuredratiosfor theseexperimentsare shownin Figure 7.67. Measurementsof the emulsified-wateroil ratio were reported by Chung and Butler (1988and 1989a)for the productsfrom scaledSAGD experimentscarried out at both low and high pressures.It was found that more emulsificationwas found when there was a rising steamchamberthan when the steamchamberwas spreading. This is consistentwith the theoreticalideaswhich were describedpreviously sincethere is more opportunity for steamto contactbitumen as the steamfingers rise into the cold reservoir. Figure 7.68showsa comparisonof the emulsified-water oil ratiosfor the products from two companionexperiments;one was carried out with a steampressure of 153kPa (22 psia)and the other with a steampressureof 790 kPa (115psia).In both experimentsthe modelwas saturatedinitially with bitumenand therewas no connatewater.It wasfilled by upwardsflooding of the dry packingand it is likely that the packingwas oil-wet initially. The resultsfrom the high pressureand low pressureruns were very similar. In both, the emulsifiedwater-oil ratio was relatively high during the period when the steamchamberwas rising and then it fell as the steamchamberspreadsidewards.The low initial valuesof the ratio are the reFormationof $O
Emulsionswithin the Reservoir
o o b
o a
3
g
a I
:
E o o -9 a
tr
Fi3rrt p€ruE tained
(c) Figure 7.66 1989)
sult of rhe po experiments The resu run in which I
(d)
Photographs of Experiment Shown in Figure 7.65 (from Yang and Butler
'6 1.0
C
o b 0.8 3
E a E o g
1o
1A
1' 0.6 o '6
WATER-WET .-tI AA
II.
b
ta
+
I
E o.z
o A
o
I
Teflonpacking Toluene-washed sand Detergent-washed
IE
4
Water-saturated sand
E0
t
OIL-WET
G
= o.4 E o
o !
50 100 Time in minutes
t G
150
Figrrc i perirncr menttL Saruret
Figure 7.67 The Effect of SandPretreatmenton the Ratio of EmulsifiedWater to Oil in the Productfrom SAGD Experimentswith Cold Lake Crude Bitumen (from Jamaluddinand Butler 1988)
354
' o .9
Gravity Drainage Steam-Assisted
Chap.7
Well Bore ResB
Steam Grain pressuresize kPa mm o 153 2.0 r 790 0.85
o 0.8
L o (E
=
rr 0.6
o 6
= o.4
E
o
o o.2
o (u
0
2 4 Time in hours Figure 7.68 Ratio of Emulsified Water to Oil in the product from SAGD Experimentswith SteamInjectedJust abovethe production well. Reservoircontained No water at the start of the Experiments(from chung and Butler 19g9a)
sult of the productionof the bitumenwhich waswithin the well at the start of the experiments. The resultsfrom run 1 of Figure7.68 arecomparedwith thosefrom a similar run in which the packinghad a saturationof 12.5%of connatewater at the start
Yang and Butler
l-Ft
I
5 1.0 I
f
E 0.8 o
s =(J 0.6 o b 0.4
I
o =
I
-----=l!r----1r..r
rrrll
. \I
\
i.. .t1
'
r irr-rl!-r-.r.i
.
E 0.2 o
Eo 150
Figure 7.69 Ratio of Emulsified Water to Oil in the Product from SAGD Experimentswith SteamInjectedJustAbove the ProductionWell. In One Experiment the ReservoirwasDry Initially and in the Other It Contained72.5VoWater Saturation(from Chung and Butler 1989a)
Emulsified Water e Crude Bitumen
ity Drainage
24 Time in hours
Chap.7
Well Bore Resistance
1.0 o
+o
0.8
o o =
0.6
Hatschek's Equation u o l l re : 1 - " 1 / 3 wherex is the volume fractionof water
r.
applications/ bore has been, as occurringil
a I
i) Gravitr r has been ii) Flo* of hereis tt iii) The pres to achie the *ell-
(E !,
o
0.4
f
aD (U
q)
=
o.2 0
Figure 7.70 Comparisonof Viscosities of Cold Lake EmulsionsPredictedus-
0
0.2 0.4 0.6 predicted vatue of
0.9
1.0
It ollr e
ing Hatschek's Equationwith Measand Jamaluddin ;'r",Ln*:l(rrom
(seeFigure 7.69).Although the resultsof this secondexperimentshow the same trends the connatewater had alarge effect and much lower levelsof emulsification wereobserved.This is in agreement with the theoreticalideaswhich werediscussed previously.l5 The viscositiesof water-in-oilemulsionsare higherthan thoseof the baseoil. A convenient,approximateequationto predict the viscosityis that of Hatschek (1911);this is given below, tt": tt,/(l-
xll3)
(7.s1)
Ong and Butk slopein the h pressurediffer smallunlessth cold then then An inter sider the well havingrelativ sure gradient( laboratorvrno( simplegeome
coNcLUsroNs
15Inthe experiment with a high permeabilityreservoirlayer below a lower permeabilitylayer that wasdescribedon page348 and illustratedin Figure 7.60,morewater emulsificationand a lower drainagerate were found than in the experimentwith the high permeabilitylayer at the top. It is thoughtthat this differencewascausedby the greatercontactof steamwith bitumenwhich occurred becauseof the underminins effect.
In this chapte This processir near to the bor jectionwells.lt productionratc The proc of the improva tal wells, much operateat satr manceand he[ The proo oils. Although promising indk promisingfield area,havejoin In Athatx is believedtha ning stages. Th steamfloodinr
356
Conclusions
where ;.r,, is the viscosityof the emulsion is the viscosityof the pure oil at the sametemperature Po and x is the volumefraction of water in the emulsion. Emulsionviscositiespredictedfrom this equationare comparedto measuredvalues for Cold Lake crude emulsionsin Figure 7.70.In Chapter8, Figure 8.25,which is taken from Chung and Butler 1989,showsmeasuredvaluesof viscositiesof Cold Lake crude emulsionsas a function of temoerature. WELL BORERESISTANCE Although in the analysisin this chapterit is assumedthat the pressurewithin the horizontalproductionwell is constantthere is a need to considerthis in practical
Steam-AssistedGravity Drainage
Chap.7
applications.An analysisof the effect of pressuredrop along the horizontal well bore hasbeendescribedby Ong and Butler (1989).They consideredthree processes as occurringin series:
Comparisonof Viscosities EmulsionsPredictedus's Equationwith Measfrom Jamaluddinand
:iment show the same evelsof emulsification ; whichwerediscussed
i) Gravity drainagearound the steamchamber.The rate at which this occurs hasbeendiscussedpreviously. ii) Flow of oil from below the chamberto the productionwell. The resistance here is that due to the radial convergingflow. iii) The pressuredrop along the length of the well bore. The pressuregradient to achievethis increasesfrom zero at one end to a maximum at the outlet of the well. . ong and Butler show that the effect of the well bore pressuredrop is to causea slopein the bottom of the steamchamberalongthe well. This slopereflectsthe pressuredifferencealongthe well. In practicalfield situationsthe effect is relatively small unlessthe oil viscositywithin the well is high becauseit is cold. If the well is cold then there is an advantagein heatingit by circulatingsteamor otherwise. An interestingfinding in their paperis that it is particularlyimportantto consider the well bore pressuredrop in three-dimensionalscaledlaboratorymodels having relatively long horizontal wells.A well scaledto have the samerelative pressure gradient(measuredas the slopeof the bottom of the steamchamber)in the laboratorymodel should have a diameter larger than that which would come from simplegeometricscaling.
emperature ,ion. 'ed to measuredvalues , Figure 8.25,which is of viscositiesof Cold
[e pressurewithin the rsiderthis in practical a lower permeabilitylayer emulsification and a lower bility layerat the top. It is th bitumenwhichoccurred ity Drainage
Chap. 7
l
rl
rl
1 'i
1 {l
r thoseof the baseoil. y is that of Hatschek
(7.s1)
r
4
il f
CONCLUSIONS
,l
In this chapterthe SteamAssistedGravity DrainageProcesshas been described. This processinvolvesthe use of one or more horizontalproductionwells located near to the bottom of the reservoirwith steamintroducedabovefrom separateinjection wells. It hasbeen shown that suchan arrangementcan lead to satisfactory productionrateswith good recoveryand oil-to-steamratios. The processis a logicalextensionof conventionalsteamfloodingbut, because of the improvedcontactwith the reservoirwhich is achievedby the useof horizontal wells, much higher ratesper productionwell can be obtained.It is possibleto operateat satisfactoryrateswithout steam-coning.Becauseof this, better conformanceand hencerecoverycan be obtainedthuswith conventionalsteamflooding. The processcan be usedfor the productionof bitumenor conventionalheavy oils. Although extensivefield demonstrationdata are not yet available there are promisingindicationsof success which are in line with expectations.Recentlytwo promisingfield demonstrations, one in Athabascaand one in the Lloydminster area,havejoined the long-standingEssopilots which are at Cold Lake. In AthabascaAOSTRA hasbeentestingthe processat their UTF site and it is believedthat the resultsare successful. An expansionis said to be in the planning stages.The AOSTRA demonstrationis believedto be the most promisingfield steamfloodingoperationthat hasbeenconductedyet in the Athabascafield. Conclusions
357
ff
:
1
The SceptreResourcesprojectin the Tangleflagsfield near Lloydminsteris alsovery promising.Very high productionrateshavebeenobtainedwith reasonable waterto oil ratiosand steamrequirements. The resultsare notablenot only because of the very high production rates (up to 1000B/d or more of oil from a producer which is 420m long)but becausethey are obtainedin a field which, with conventional production,is uneconomicbecauseof excessivewater productionfrom the underlyingaquifer.
BIBLIOGRAPHY Bezernn,G. E. and MaRrrw, I. A., "EssoResources HorizontalHole Projectat Cold Lake," CIM 79-30-10, 30th Annual TechnicalMeetingof the PetroleumSocietyof CIM (1979). ButLEn, R. M.: "New Interpretationof the Meaningof the Exponent"m" in the Gravity DrainageTheory for ContinuouslySteamedWells,"AOSTRA J. of Research,2, 67-71 (1985). ButLen, R.M.,'A SteamChamberPilot for AOSTRA's UndergroundTest Facility," presentedat AOSTRA's UTF-IndustryMeetingin the GlenbowMuseumAuditorium, Calgary (May 8, 1984). BurLER,R. M., 'A New Approachto the Modellingof Steam-Assisted Gravity Drainage," JCPT, 42-51.(May-June 1985). Burr-en,R.M., "Rise of InterferingSteamChambers,"JCPT, Yol.26, No. 3, 70-75 (MayJune 1987). ButLen, R. M. and Perela, G., "TheoreticalEstimationof BreakthroughTime and InstantaneousShapeof SteamFront During VerticalSteamflooding,"AOSTRA J. of Research, Vol. 5, No. 4 (1989),pp.359-382. Burr-en,R. M., McNen, G. S., and Lo, H.Y., "TheoreticalStudieson the Gravity Drainage of Heavy Oil During SteamHeatinE,"Can.l. Chem.Eng., 59: 455-460(August1981). ButLrR, R. M. and SrerHeNs,D. J., "The Gravity Drainageof Steam-Heated Heavy Oil to ParallelHorizontalWells,"JCPT, 90-96 (April-June 1981). Burlen, R.M., SrepHeNs, D.J., and Werss,M., "The VerticalGrowth of SteamChambers in the In-Situ Thermal Recoveryof Heavy Oils," Proc. 30th. Can. Chem. Eng. Conf., 4: 1152-1160,(October 19-22, 1980). Burlrn, R. M. and Yee, C.T., 'A TheoreticalStudyof SteamCondensation in the Presence of Non-Condensable Gasesin PorousSolids,".4OSTR A J. of Research,3, no.1: 1-14 (September1986). ButLen, R. M. and Yee, C.T., 'An ExperimentalStudyof SteamCondensation in the Pressureof Non-Condensable A J. of Research, 3, no. 1,:15-24 Gasesin PorousSolids,",4OSZR (September 1986). CaRlwEt-t-,W.T. and PensoNs,R. L., "Gravity Drainage Theory," Trans.AIME 179, t99-2r1 (1949).
Cnurc. K i{ : A s s i s t e ;( i : , : FourthL \ lT V o l .- 1 :I ; : - : : DrerRrcu. -l ii 935-9li \-; Dvxsrn r. ll T 7978). Eptvruro:.\ R . O i l a n dO : v gar!'(19\Fencusor.F R i
^r e-t -i n_o_-F_- ,-.-' . :- ..
Sept.-O.: . -e G n r n p r r .P . , T - ' : ; Drainagc P: ..: FlarscHrx. E . {
JeueLuoo;r. \ W a t e r - i n - O :I :
Josur, S. D -::.1 D r a i n a g eL ' r : : i
ONc, Ter. S ::.. Drainagc. -r( I Pnars,M.. '.{ (':
SucIANTo.S. i:J with Bott,.,:: \ (March--A.pr:.-" TEnwrlrrcrri. P I perimenta: r:i AIME IJ$. ),-
YeNc, Gurn'. i. .r coverv br S:r.: A n n . T e c h .\ l : i
CnuNc,K. H. and Burr-en,R. M., "GeometricalEffect of SteamInjectionon the Formation of Emulsionsin the Steam-Assisted Gravity DrainageProcess,"JCPT, Yol. 27, No. 1 (January-February 1988). CHuNc,K. H. and BurLEn, R. M., "In-Situ Emulsificationby the Condensation of Steamin (1989). Contactwith Bitumen,"ICPT, Vol. 28, No. 1 (January-February 358
GravityDrainage Steam-Assisted
Chap.7
Bibliography
near Lloydminster is ained with reasonable able not only because I oil from a producer x'hich, with convenproduction from the
r Projectat Cold Lake," iociety of CIM (1979). ent "m" in the Gravity of Research, 2,67-71 ,undTest Facility," prerseumAuditorium, CalstedGravity Drainage," 16, No. 3, 70-75 (MayroughTime and InstanIOSTRA J. of Research, rn the Gravity Drainage ;5-450(August1981). rm-HeatedHeavy Oil to wth of SteamChambers )an. Chem. Eng. Conf,
CHuNc,K.H. and Burlrn, R.M.,'A Theoreticaland ExperimentalStudy of SteamAssistedGravity DrainageProcess,"in R. F. Meyersand E. J. wiggins (Editors),The Fourth UNITAR/UNDP International Conferenceon Heavy Crude and Tar Sands, Vol. 4: In-Situ Recovery,AOSTRA, Edmonton,(1989b),pp. 191-210. Drrrnrcu, J. K., "The Kern River Horizontalwell SteamPilot," spE ReservoirEngineering, 935-944 (August 1988). DyrsrRA, H., "The Predictionof Oil Recoveryby Gravity Drainage,""fp?l 818-830(May 1978). Eorr.ruNos, N. R., WoNc,A., McConrr.recr, M. E. and Succrrr, J.C., "Fourth Annual Heavy Oil and Oil SandsTechnicalSymposium,"Universityof Calgary,February18, 1987,Calgary (1987). FeRcusoN,F. R. S. and Burr-nn, R. M., "Steam-Assisted Gravity DrainageModel Incorporating Energy Recoveryfrom a Cooling SteamChamber,"JCPT, Yol.27, No.5,75-83, Sept.-Oct.,1988. GRInrtN,P. J. and Tnontvnwrorr, P. N., "LaboratoryStudiesof the Steam-Assisted Gravity Drainage Process,"AOSTRA J. of Research,2, no. 4: 197-203(1986). HanscuEr,E., Kolloid-Z.,8, 34 (1911). JeuaLUDDrN,A.K.M. and BurLen, R.M., "Factors Affecting the Formation of Water-in-OilEmulsionsDuring Thermal Recovery,",4OSTRA J. of Research(May, 1988). Josru, S.D. and Tnnnr-relo, C. B., "Laboratory Studies of Thermally Aided Gravity DrainageUsingHorizontalWells,",4OSTRAJ. of Research,2, no. 1: 11-19(1985). ONc, Tne, S. and Burr-pn, R. M., "Wellbore Flow Resistancein Steam-Assisted Gravity Drainage,"JCPT,YoL29, No. 2 (March-April 1990). Pnars,M., 'A CurrentAppraisalof Thermal Recovery,"JPT, \129-1136(August1978). Suct,lNto, S. and BurleR, R. M., "The Productionof ConventionalHeavy Oil Reservoirs with Bottom Water Using Steam-Assisted Gravity Drainage,"JCPT, YoL. 29, No. 2 (March-April 1990). TrnwrLLrceR,P.L., Wrlsny, L. E., Halr-, H. N., Bnroces,P. M., and MorsE,R. A., 'An Experimental and Theoretical Investigationof Gravity Drainage Performance,"Trans. AIME 146,28-53(1951). YaNG,GurHua,and Burlen, R.M., "Effectsof ReservoirHeterogeneities on HeavyOil Recoveryby Steam-Assisted Gravity Drainage,"PaperNo. 89-40-72,presentedat the 40th Ann. Tech.Mtg. of the PetroleumSocietyof CIM (May 28-31 1989).
ensationin the Presence v c h , 3 , n o . 1 : 1 - 1 4( S e p in the Presondensation ?.esearch, 3, no.l: 15-24 ry." Trans. AIME 179, iectionon the Formation " JCPT, Vol. 27, No. 1 .ondensation of Steamin (1989). ty Drainage
Chap.7
Bibliography
359
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:if
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n
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fit
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It s.-,..n extended hca I n g e n e r a l ": r
Sfeqm Recovery Equipment
snd Focilifies
INTRODUCTION In this chapterthe equipmentand surfacefacilitiesneededfor thermalrecoveryare discussed-the equipmentfor steamgenerationand steamdistribution,the wells, the facilitiesfor treatingthe crude,and, finally, the processes involvedin treating producedwater to make it suitablefor recyclingto steamgenerators. In a typical steamrecoveryoperation,the volumeof producedwater may be aboutthree to five times largerthan the volumeof producedoil. As a result,tlere are very significantcapital and operatingcostsfor the water-treatingand waterhandlingfacilities.Sincethe performanceand servicefactor of the whole project dependsupon the satisfactoryhandlingof water and generationof steam,lt i, uital to developgood designsand operatingprocedures. For thesereasons,a goodunderstandingof the water reuseprocessis essentialif oil recoveryis to be successful technicallyand economically.
1. Fire tub that are fuel arc flou thr In scrme throu€:h 2. \t\ater tr
f lou ins the outs
Fire tub i n s t a l l a t i o n :e are limited rr fire tube:. F i g u r e: i n 1 8 7 7 .\ a t u inclined tulre from the liqu boiler in orJe N{odern shown in Fre water tube tr
STEAM GENERATION The main roots of the industrialrevolutionare to be found in the discoveryand developmentof practicalsteampower in England at the end of the seventeenth century. Early steamboilerssuchas the one shownin Figure8.1wereof simpledesign and were limited in capacityand pressureby the small sizeof the steelplatesavailable.There were many explosionsand accidentsas a result of improperoperating practicesand design.
360
Steam Gerpra
It soon becameapparentto boiler designersthat it was necessaryto provide extendedheat-transfersurface area in order to build boilers of increasedcapacity. In general,two approacheswere followed:
ment
r thermalrecoveryare listribution, the wells, esinvolvedin treating nerators. roducedwater may be Loil. As a result,there er-treatingand waterr of the whole project ion of steam,it is vital reasons,a goodunder:ry is to be successful
1. Fire tubes.in which combustionoccurswithin the insideof one or moretubes belowthe surfaceof the waterin the boilervessel.Air and that are submerged fuel are introduced into one end of thesetubes,and the combustionproducts flow throughthe remainderof the tube; this providesadditionalheattransfer. \n sornecases,ttre convectirretreat tranrsteris extended,b; passirrgthe t\ue gas through the boiler within a set of parallelsmallerdiametertubes. 2. Water tube boilers in which the water is heatedand boiled with the water flowing insidetubesthat are exposedto the fire and combustionproductson the outside. Fire tube boilersare usedfor smallerinstallations,particularlylower-pressure installationsand for portableusessuchas railway locomotives.Their applications are limited by the needto build a high-pressure vessellargeenoughto contain the fire tubes. Figure8.2 showsa crosssectionof an earlywatertube boiler,which wasbuilt in 1877.Natural convectioncausedwater to circulateto the bottom of the bank of inclined tubesand the boiling mixture of water and steamto rise. Steamseparated from the liquid water in the upper drum. Blowdownwaterwas removedfrom the boiler in order to limit the concentrationof dissolvedsolids. Modern, large,high-pressure boilers are of the water tube type. The boiler shown in Figure 8.3 showsthe type of constructionemployedin a large,modern water tube boiler. This boiler seneratessteamwithin vertical tubesthat form the
Lin the discoveryand nd of the seventeenth rn'ereof simpledesign f the steelplatesavailof improperoperating
Figure 8.1 HaycockBoiler (1720) (from Babcockand Wilcox 1972)
Steam Generation
361
a t a
o c E o
Fi3rn $'ikq Figure 8.2 coal-Fired, Babcock and wircox water Tube Boiler (1g77)(from Babcockand Wilcox 1972)
Tempering
362
Figure 8.3 Stirling Boiler for 925 psi and 900"FSteamTemperature.This Boiler Is Fired By PulverizedCoal. The Walls of the CombustionChamber Are Lined With Water Tubes Which Absorb Radiation from rhe Flames.SensibleHeat from the Combustion Gas Product Is AbsorbedIn ConvectionTube Banks (from Babcock and Wilcox 1972)
Steam RecoveryEquipmentand Facilities
Chap.g
wall of the c steamis supe Heat is ation from tl may be caus atedby purq Water tr and they'can The dir externalll'ry scale repres steam.The q The three up different lera Near th ing point. th is being heat and a largert larger heat flt ference betlr transfer coef As bdU mechanism d form at the b by a layer of 'The
rcq the liquid is gsr are formed colb b e p o s s i b l et o b r of the liquid hrl
Steam Gersl
.
i+ll
o I a!
o
CL
E o
Practical tubeoutletconditions Tubewalltemperature
-ll9!I"-1t-rlYl--i-----i*j-- onQ i \. i -__i/ -lte_d-I'_e_aJjl:u]--j-__-______ Low heatflu5- - -i- - - - - - - - - - - - - - - - - - - - - - -., -\ |
\-
FluidTemperature
100 SteamQuality7o (afterBabcock Figure8,4 BoilerTubeFluidandTubeWallTemperatures and Wilcox1972) 0
1877)(from
ng Boilerfor 925 psi Temperature. This ; PulverizedCoal. CombustionChamith Water Tubes :diationfrom the Heatfrom the Comuct Is AbsorbedIn Banks(from Babcock
Facilities
Chap.8
wall of the combustionchamberand also in an independentbank of tubes.The in a separatesectionof tubes. steamis superheated Heat is transferredthroughthe surfaceof the boiler tubesboth by direct radiation from the fire and by convectionfrom the hot gases.Flow through the tubes may be causedby naturalcirculation,as in the designshownhere,or it may be createdby pumping. Watertube boilersare fired usingany of the commonfuels-gas, oil, or coal; and they can alsobe adaptedfor specialfuels suchas refinerycoke. The diagramin Figure 8.4 showsthe temperaturealonga tube that is heated externallyby a furnace;wateris flowing insidethe tube and boiling.The horizontal scale representsthe cumulativeheat transfer representedby the quality of the steam.The ordinatedepictsthe temperatureof the tube wall and alsoof the fluid. The three upper broken curvesshow the metal temperatureof the tube for three different levelsof heat flux. Near the entranceto the tube, assumingthat the water entersbelow its boiling point, the temperatureof the tube risesalongwith that of the liquid water that is being heated.The temperatureof the tube wall is higher than that of the fluid, and a larger temperaturedifferencebetweenthe wall and the fluid is requiredfor a largerheat flux. At the point wherethe water beginsto boil,r the temperaturedifbecauseof the increasedheatferencebetweenthe wall and the fluid decreases due to the boiling. transfer coefficient that resultsfrom the agitation the tube where the boiling point along As boiling continues,there comesa where separatebubblesof vapor mechanismchangesfrom that of nucleateboiling, the surfacebecomescovered form at the hot surface,to that of film boiling, where by a layer of vapor through which the heat must be transferred.At this point a lThe temperaturegradientat the heatingsurfacecausesthe liquid to boil at the surfacebefore the liquid is generallyheatedto the boiling point. At moderateheat fluxes, the bubblesof vapor that are formed collapseas they rnix with the bulk of the liquid. At extremelyhigh heat fluxes, it would be possibleto havea completefilm of vapor coveringthe inner wall of the tube eventhough the bulk of the liquid has not reachedthe boiling point; this is not a desirablecondition.
Steam Generation
363
I
tr
I I
E
( {
!t
E
H P d
f
r{
o
qt t (!
Practical tubeoutletconditions Tubewalltemoerature
+f
o
CL
E o
F
100 Steam Quality 7o Figure 8,4 Boiler Tube Fluid and Tube Wall Temperatures(after Babcockand Wilcox 1972)
r1877)(from
ng Boilerfor 925psi Temperature. This ; PulverizedCoal. CombustionChamrth Water Tubes rdiationfrom the Heat from the Comuct Is AbsorbedIn Banks(from Babcock
Facilities
Chap.8
wall of the combustionchamberand also in an independentbank of tubes.The in a separatesectionof tubes. steamis superheated Heat is transferredthroughthe surfaceof the boiler tubesboth by direct radiation from the fire and by convectionfrom the hot gases.Flow through the tubes may be causedby naturalcirculation,as in the designshownhere,or it may be createdby pumping. Watertube boilersare fired usingany of the commonfuels-gas, oil, or coal; and they can also be adaptedfor specialfuels such as refinery coke. The diagramin Figure 8.4 showsthe temperaturealonga tube that is heated externallyby a furnace;wateris flowing insidethe tube and boiling.The horizontal scale representsthe cumulativeheat transfer representedby the quality of the steam.The ordinatedepictsthe temperatureof the tube wall and alsoof the fluid. The three upper broken curves show the metal temperatureof the tube for three different levelsof heat flux. Near the entranceto the tube, assumingthat the water entersbelow its boiling point, the temperatureof the tube risesalongwith that of the liquid water that is being heated.The temperatureof the tube wall is higher than that of the fluid, and a larger temperaturedifferencebetweenthe wall and the fluid is requiredfor a largerheat flux. At the point wherethe waterbeginsto boil,l the temperaturedifbecauseof the increasedheatferencebetweenthe wall and the fluid decreases due to the boiling. agitation transfer coefficient that resultsfrom the point the tube where the boiling along As boiling continues,there comesa where separatebubblesof vapor mechanismchangesfrom that of nucleateboiling, the surfacebecomescovered form at the hot surface,to that of film boiling, where by a layer of vapor through which the heat must be transferred.At this point a lThe temperaturegradientat the heatingsurfacecausesthe liquid to boil at the surfacebefore the liquid is generallyheatedto the boiling point. At moderateheat fluxes, the bubblesofvapor that are formed collapseas they rnix with the bulk of the liquid. At extremelyhigh heat f luxes,it would be possibleto havea completefilm of vapor coveringthe inner wall of the tube eventhough the bulk of the liquid has not reachedthe boiling point; this is not a desirablecondition.
Steam Generation
363
much larger temperaturedifference is required to maintain the heat flux: as a result, the temperatureof the boiler tube tends to rise rapidly. The film of vapor forms an insulating blanket through which the heat must be tiansferred. The point wherethe boiling mechanismchangesis known as the departure from nucleatiboiling (DNB). Boilers are normally designedto maintain nucleateboiling within the tubesin which evaporationis occurring. For large heat fluxes, this limits the evaporation per passto low values.In once-throughoil field steamgenerators,the evaporation (in one pass)is higher than in typical drum-type boilerJ,but the heat flux is much lower. The expenseof the additional heat-transfersurfacethat is required is offset by the mechanical and operating simplicity. Typical heat fluxes are given in Table8.1. TABLE8.1 Typical
Heat Flux in kBT
High capacitypower boilers Oil field generators
I
t2 h{r)in RadiantSection g0-190(2)
15- 1g(3) (t)1 kBtu6t'h = 3.1546kWm2. of tube wall. Low_ervalue is for pulverized coal firing and upper value is iT* fuel oil :,1 (Blokh H?]::]""*j"t"a for 1988);seealso Delibert (1987). (3)Based on tube area3l-in. oD on 6-in. spacing(Kerby, Kense,and peacheyr9g4).
The lower flux in oil field steamgeneratorsmakes them much more tolerant to the overheatingcausedby the depositionof scaleon the heatingtubes.Scaledeposits due to such causesas water hardness provide a heat-trinsfer resistance betweenthe wall and the water.The heatflux flowing throughthis resistanceproducesan increasedtemperaturedrop that is proportional to the resistanceuni to the flux' Although this effect is lessin oil field generators,it is still very important to soften the feedwaterto minimize scaleformation. There is, however,considerable toleranceto other dissolvedsolids suchas sodium chloride. The feedwaterflow rate to a steamgeneratormust be kept within a certain range.Low velocities,for a givenfiring rate,resultin excessive vaporization,DNB, and tube failure. On the other side, high feed rates result in low-quality steamand tube erosion. EFFECTOF WATERIMPURITIES The quality of feedwateremployedfor conventionalsteamboilers is frequently .the critical to their operation if corrosion and scale formation are to be avoided. Table8.2 gives specificationsfor feedwaterand for the water within the boiler that have been recommendedby the ASME Committee on Water in Thermal power Systems.These recommendationsare for typical water tube boilers; oil field steam generatorsare much more tolerant becauseof the lower heat flux.
364
Steam RecoveryEquipmentand Facilities
Chap.8
TABLEE2
r f
Drum pressure MPat
I | 0.1-2.2 | 2.2-3.2 | 3.242 4.2-5.3 | | 5.3-6.3 | 6.3-7.0 7.0-10.4 | 10.4-13.9 |
tTo converl llt 2Minimumterd regard to silbr 3Atkalinityu aZero in tbccc r amount of tofd treatment uscd
The co When oxyga ferric oxi&; senceof oryl
It is recomn to 3 MPa pr Appr€o in boiler fecd versesolutil poundsdecrt and Mg(OHl heatingsurfi Silica ir depositsco
2A cc are shut do?t a in contact rhl recommendcd 1
Effect of \ir!
e heat flux; as a reThe film of vapor rnsferred.The point zfrom nucleateboillwithin the tubesin rits the evaporation Jrs, the evaporation te heat flux is much is required is offset luxes are given in
iring and uppervalueis r 1984).
TABLE 8,2 RecommendedFeedwaterGuidelinesfor Modern IndustrialWater Tube Boilers for ReliableContinuousOperations(from Kirk-Othmer1978-84) Boiler feedwater
Drum pressure MPal
0.1-2.2 2.21.2 3.24.2 4.2-5.3 5.3-6.3 6.3-'7.0 7.0-10.4 10.4-13.9
Boiler water
lron, ppm Fe
Copper, ppm Cu
Total hardness, ppm CaCO3
Silica ppm SiO2
Total alkalinity2, ppm CaCO3
Specific conductance, pS/cm
0.100 0.050 0.030 0.025 0.020 0.020 0.010 0.010
0.050 0.025 0.020 0.020 0.015 0.015 0.010 0.010
0.300 0.300 0.200 0.200 0.100 0.050 0.000 0.000
150 90 40 30 20 8 2 1
7003 60d 5003 4003 3003 2003 04 04
7000 6000 5000 4000 3000 2000 150 100
1To convert MPa to psi, multiply by 145. 'Minimum level of OH alkalinity in boilers <6.9 MPa (1000psi) mustbe individually specifiedwith regardto silica solubility and other componentsof internal treatment. tAlkalinity not to exceed107oof specificconductance. aZerc in these casesrefers to free sodium or potassiumhydroxide alkalinity. Somesmall variable amountof total alkalinity is presentand measurablewith the assumedcongruentcontrol or volatile treatmentused at thesehigh pressures.
F I
I
much more tolerant ing tubes.Scalede-transfer resistance this resistance proLeresistanceand to still very important however,considerrpt within a certain vaporization,DNB, r-quality steamand
roilers is frequently are to be avoided. ithin the boiler that in Thermal Power Llen;oil field steam ux.
Facilities
Chap.8
The control of dissolved oxygen is necessaryin order to avoid corrosion.2 When oxygen is presentat appreciableconcentrations,it reactswith steel to form ferric oxide; this does not protect the steel; and corrosion is excessive.In the absenceof oxygen,a protective layer of magnetiteis formed. 3Fe*4HzO:Fe:O++4Hz
{ *
ft i
I
Magnetite
4 d
It is recommendedthat the oxygenconcentrationshouldbe kept below 0.04 ppm up to 3 MPa pressureand below 0.007ppm for pressuresup to 14 MPa. Appreciablehardness(dissolvedsaltsof calcium and magnesium)is disastrous in boiler feedwatersbecausethesecompoundsdeposit scaleas a result of their inversesolubilitycurves.The solubilitiesof calcium and magnesiumhardnesscompoundsdecreasewith increasingtemperatureand thesecompounds,notably CaCO3 and Mg(OH)2,tend to precipitatewhere the temperatureis highest-i.e., at the heatingsurface. Silica is undesirablein boiler feedwaterbecauseof its tendencyto form scale depositsconsistingof inorganic silicates.However,with oil field steamgeneratorsit 24 common potential problem is the boiler corrosionthat can occur when steamgenerators are shut down and idle. Precautionsmustbe taken to ensurethat water containingair doesnot come in contactwith the boiler internals during suchperiods.Steamgeneratormanufacturerswill supply recommendedguidelinesfor boiler layup.
Effect of Water lmpurities
I I
36s
{ {
is possibleto tolerate considerabledissolvedsilica provided that the water is soft3 (so that the formation-ofcalcium and magnesiumiilicate compounds is avoided), the pH is alkaline(sothat the silica can remainin solutionas siiicateions), and ttre iron content is very low (so that iron silicatesare not formed). [t is necessary to maintainthe feedwateralkalineand oxygenfree so that iron soiutionis minimized. Iron shouldbe consideredas a hardnession and treatedas such. In conventionalboilers dissolvedsolids becomeconcentratedin the water within the boiler and they are controlledby the blowdownof water.Maximum con_ centrationsof dissolvedand total solidsrecommendedby the ABMA (data from Delibert 1987)are given in the followins table:
Cold water feed
TABLE8.3 Steam
Total solids
pressure Psrg 0-300 301+50 451-600 601-750 751-900 901-1000 1001-1500 1501-2000 2001 +
Suspended solids
ppm
ppm
3500 3000 2500 2000 1500 1250 1000 '750
300
500
2s0 150 100 60 40 20 10 5
remainingd stage.This I The re trolledbl th into a harm it is comrm consumedb
I
In once-throughoil field steamgenerators, where the solidsdissolvedin the feedwaterleaveconcentratedin the liquid part of the wet-steamproduct,the concentrationsof dissolvedsolidsare typically much higher than those given in the precedingtable. DEAERATION AND OXYGENCONTROL The oxygenconcentrationin all boiler feedwatermustbe minimized to reducecorrosion.It is usualto do this by first heatingand strippingthe waterwith live steam in a deaeratorto removedissolvedsases. Figure 8.5 showsa schematic-diagram of a spray-traydeaerator.It consistsof a countercurrentscrubbingsystemin which low-pressuresteamcontactsthe feedwater in two stages.Much, but not all, of the steamis condensedin the top spray chamber,wherethe incomingfeedwateris raisedto its boiling point.atvtosiof tne 3The
hardnessshouldbe lessthan 1 ppm and preferablylessthan 0.5 ppm measuredasCaCO:. many boilerhouses,the steamusedin deaerationcomesfrom the exhaustfrom steamturbinesdriving the feed pumpsand other boilerhouseauxiliaries.Using steam-drivenpumps can maKe the boilerhousea dependablesourceof steameven in the event of a failure of the elecirical power supply. oln
366
Steam RecoveryEquipmentand Facilities
Chap.g
At hig sulphitecan sulphurdio residuallert calll' a leve b unsuitable the practic actsu'ith or
This a Hou'ever. lt the hazards handle but I Anoth generator.s
Deaerationa
'lat the water is soft3 npoundsis avoided), ;ilicateions),and the l). It is necessaryto rlution is minimized. ch. rtrated in the water ater.Maximum con: ABMA (data from
Ventsteam andgas Cold water feed
Nearlyall steam condensesto heat waterto B.Pt Risingsteamstnps dissolvedgases from water
rended rlids
Deaeratedwater at B.ft.
pm o0 :50 50 00 aa) {0 :0 l0
Figure8.5 Diagramof a Spray:Tray BoilerFeedwater Deaerator
remainingdissolvedgasis strippedby contactwith the incomingsteamin the lower stage.This sectionoften containstraysor baffles. The residualtracesof oxygenin the watercomingfrom the deaeratorare controlled by the additionof a chemicalthat will reactwith the oxygento convertit boilers(belowabout1000psi, or 7 MPa) into a harmlessproduct.With low-pressure it is commonto employsodium sulphite as the reactivechemical.The oxygenis consumedby the oxidationof this compoundto sodiumsulphate. 2NazSO:* 02 = 2 NazSO+
lids dissolvedin the rm product, the conl those given in the
mizedto reducecor;aterwith live steam rerator.[t consistsof n contactsthe feedsed in the top spray I point.4Most of the rpm measuredasCaCOr. exhaustfrom steamtur-drivenpumpscan make : of the electricalpower
I Facilities
Chap.8
Sodiumsulphite
SodiumsulPhate
(and,hence,highersteamtemperatures) the useof sodium At higherpressures sulphite can presenta problembecauseit decomposesto form hydrogensulfide and sulphur dioxide. In conventionaldrum-type boilers,it is common to maintain a residuallevelof sodiumsulphitein the waterto ensurethe removalof oxygen;typically a levelof about40 ppm is maintained.Above 1000psi (546'F),this practiceis unsuitablebecauseof the decompositionof the sodiumsulphite.In thesecases,it is Hydrazinerethe practiceto use the chemicalhydrazineas the oxygenscavenger. actswith oxygento form nitrogenand water. NzH+* Oz = Nz + 2H2O Hydrazine
This approachcan be and also hasbeenusedwith oil field steamgenerators. However,there is a problembecauseof the carcinogenicnature of hydrazineand the hazardsthat this involves.One solution is to use chemicalsthat are safe to handlebut that liberatehydrazinewithin the boiler. Another approachis to use sodium sulphite by addingit well upstreamof the generator,which alsoprotectsthe water-treatingequipmentfrom corrosion,and to
Deaerationand OxygenControl
367
rs on\1 a -te;r; stsra\\residua\ a&ust t\e quantrg so \\a\ \\ere
'::T]^q:":J:i::'"i: r["-iii"sqi'l Yt|r'l': e"i,?** entersthesteam before.it is ttrermativ h temgeratures' t' ltfie) s$\$t:sssl1$1""0,$
il;;;G;h
onfurrrrouo!c[booo0 t0
Ttrcgl
OIL FIELDSTEAM GENERATORS Figure 8.6 is a diagram of a typical horizontal oil field steamgenerator.Feedwater under pressureis usuallypreheatedin a heatexchangerto a temperaturehigh enough to prevent condensationof water from the flue gas on the exterior of the tubes in the convectionsection. With hot recyclewater feed, preheatingis unnecessary. Condensationis avoidedto prevent corrosion of the tubes. In the convection section,the flue gasesexchangeheat with the water. The partially heatedfeed passesback through the exchangerand then to the heating tube that iurrounds the combustionzone. If the feedwateris preheatedby steam deaerationor otherwise, then the preheatexchangeris usuallyomitted. In the radiant section heat transferred to the water boils about 60 to BTVoof the water to give the steamproduct.The horizontalcylindricalfurnace has,typically,a length-to-diameter ratio of 3:1 to 4:1. The figure also shows a typical heat and material balance for an oil field steamgenerator.A generatorhaving a duty of 50 million Btu/h, suchas that shown, is the largestthat has been employedin oil field practice until recently,when units having about three times this capacitywere placed in service by Esio Resources Canadain their field at Cold Lake (peachey1984). The unit shown in Figure 8.6 has a single 3-in.-diameterboiler tube; the largerunits recentlybuilt by CE-Natcoand Struthers:TlWfor Essohavethree 3-in. FLUEGAS 400 F 204 C
col,tvEcTtoN SECTION
For an cild somewhato 23s Blddl Genca when oil (ur flue gasest sodium cart There is a g mental proG producedrr Bertness (19 sodiumhydl Horiza cutawayvier
STEAM 51.7 k tb/hr 2200 psig 15.3 MPo 75 % quolily
3" dio tube (76 mm) Fe€dlE/
AIR 15 Z XS 9000 cFM
FUEL 254 FOEB/D 40 nf /D FEEDWAIER 51.7 k tb/hr 80F 27C 3547 B/D
447 F 2J1 C
HEATEXCHANGER to preheot woter to ovoid condensotionon convectiontubes
+.sr#7=
to 12000cFM S.t nlTs
STEAMGENEMTOR50 MBtu/hr or _14.65 MW 51,7 k tb/hr = 3547 B/D : sI3 nl /aoy
Figure 8.6 SteamGenerator50 x 10"Btu/h (14.675MW)
368
HeatEx.rr.rlgF
Steam RecoveryEquipmentand Facilities
Figurt t 7
Chap.8
Oil Field Stsr
I amountwithin the is convertedto sullerator,and thus the
lenerator.Feedwater rcraturehigh enough erior of the tubesin g is unnecessary. :s. In the convection rartially heatedfeed e that surroundsthe :rationor otherwise, , about 60 to 80Eoof al furnacehas, typi-
tubesin parallel. Larger units are possible,provided that it is not required to transport the fabricatedequipmentalongnormal highways;it is this transportationlimitation that has determinedthe sizeof the Essounits. The generatorshown in Figure 8.6 produces3547B/d of 75Voquality steam. For an oil-steamratio of 0.3 (a fairly high value),this would be sufficient to produce somewhatover 1000 B/d of oil; the generator requires the equivalent of about 235 B/d of heavy oil as fuel. Generatorsof this generaltype burn either gas or oil as fuel. In California, when oil (usually the produced crude) is employedas fuel, it is usual to scrub the flue gasesto remove sulphur dioxide. Typical installations use caustic soda or sodium carbonatesolutionsfor scrubbing;however,this is costly and troublesome. There is a growing tendencyto use natural gas as fuel as this reducesthe environmental protectionproblems.The removalof Soz from stackgasesby scrubbingwith producedwater (containingaddedalkali if required)is describedby snavelyand Bertness (1975).wendt (1978) has reviewed the operation of a scrubber using sodiumhydroxidesolutions. Horizontal oil field generatorsare the most common types used. A general cutawayview of a typical horizontalgeneratoris given in Figure 8.7.
rnce for an oil field . suchasthat shown, recently,when units : by Esso Resources rter boiler tube; the lsso havethree 3-in.
/nr 1 1 5 . 5M P o lity
-.l]-X-,(
/o /O
AIR 1 5z x s 9000 cFM 43 r# /s to 12000CFM 5.7 nf/s
Figure 8.7 CutawayDiagram of Horizontal SteamGenerator(courtesyNatco)
Facilities
Chap.8
Oil Field Steam Generators
369
Steam (lfl
Figure g.g photographof part of a Natco Horizontal Steam Generatorwith a capacity of 160,000lb/h Being Transported to Bp,s Thermal RecoverySite in the cold Lake o'Field (courtesyof Totr"n ServicesLimited, cargaryand Edmonton)
I
Figure8.8 is a photographof the main sec.tion of a 160,000lb/h -' steamgenera_ tor beingtransportedto a pilot site in the cold Lake oil riia.-
steam. hasbeenreviewed senerators by ;|""j:.1?:Yr;,?1"3,'1::lllough Kirby, tYq5). andpeachey (1e8a)
RX-:::ll
revilwffiHH: .sw('u rll9 means
IlTy], {:lrr, maintainingthe efficierrcv
of o' fieri ,t"ur g.n".atorsin a very
practical :Tjf$;;i:"and paper. needto preventcondensation on the convectionsectiontubesin order to . .The avoid corrosionwas mentionedearlier.The dew point of the combustiongasesde_ pendsupon the sulphurcontentof the fuel-largei sulphu, resurtin higher dew points. "onr"ni, The main reasonfor the effect of fuer sulphur content on the dew point is the presenceof so: in the flue gas.This is extremelysolublein water and forms sul_ phuric acid' In contrast'Soz, which is the main ,llphu, oxide influe gas,is much lesssolubleand has rittre effect on the dew point. The effect of so: on the dew point can be predictedby a correlationgiven by verhoff and Banchero (r974): (l/Toi = 0.002276- 0.00002943 tn(ps,6) - 0.000085g ln(pH,soo) + 0.00000620 ln(pgr6) In(pn,soo)
*h"'"#::jl,:jT
partial pressures,p, arein mmHg. T11|115correlation 1"dlh:. is trrit the distiibuti", :1""R1"::.,i."X between SOr and SOz::r:g-lli: is viriable. "ir".itulphur
The following recommendedminimum wall temperaturesto avoid condensa.. . tion in economizersburning fuel oil have been read from a chart given by Babcock and Wilcox (1972\: Wt% Sulphur in fuel oil: Minimum temperature"F:
370
0.1 240
One of the u is that of thc t is to measurc to analy'zea I used as the tr for analysir 1 sodiumis m In takiq crackedopca water to leatc ration. Tlresct the collectio Anotbcr ploy an orifn For a giveno the qualityd readingand tl A cofirE the control d volvesa ratb flow proporti
Convectkn S
Figure8.1& C a typical stea ally finned ia usuallynot fu tion, overhea perature at th and the elimir The co mining the th heat from th tubesclean.l
u
FTD T
z1 ^J 4 6
240
249
2$
Steam RecoveryEquipmentand Facilities
260
Chap.8
Oil FieldSteen
Steam Ouality
leneratorwith RecoverySite J. Calgaryand
0 lb/h steamgenerabeen reviewed by reviewedthe means generatorsin a very on tubesin order to ombustiongasesdeentsresultin higher the dew point is the rater and forms sulin flue gas,is much of SO: on the dew lanchero(1974): i ln(pursoo) re in mm Hg. tion of fuel sulphur to avoid condensart givenby Babcock
{6 :.i3
260
One of the measurements which shouldbe madein the controlof a steamgenerator is that of the quality of the steambeingproduced.A commonmethodof doingthis is to measurethe chloridecontentof the feedwaterby chemicalanalysisand then to analyzea sampleof the condensate in the steam(seeFigureg.9).Sodiumcan be usedas the tracer elementinsteadof chlorine using atomic absorptiontechniques for analysis.The steamquality is calculatedby assumingthat the chlorideor the sodiumis nonvolatile. In taking a sampleof the liquid associated with the steam,the valveshouldbe crackedopen enoughto maintain a flow at a rate that will allow only condensed waterto leavethe system.It is necessary to cool the collectedsampleto avoidevaporation.Thesesamplesystemswork bestif they are left to drip continuouslybetween the collectionof samples. Another way to measurethe quality of the steamleavinga generatoris to employ an orifice flowmeter (Palm, Anderson,and Kirkpatrick 196g;wilson 1975). For a given massflow the readingfrom an orifice meter is stronglydependentupon the quality of the steam.The quality of the steammay be deieimined from this reading and the water feed rate to the generator. A common method of adjustingthe quality of the producedsteaminvolves the control of the ratio of fuel flow to feedwaterflow. A practical arrangementinvolves a ratio controller, which measuresthe feedwaterflow and controls the fuel flow proportionally. Convection Section Figure8.10ashowsa schematicdiagramof a convectionsection,or economizer,for a typical steamgenerator.The tubes, exceptfor the lower couple of rows, are usually finned in order to improve the heat-transfercoefficient.The lower tubesare usuallynot finned becausewith the very high gastemperaturesfound in this section, overheatingof the fins would otherwiseoccur.Also becauseof the high temperatureat the bottom of the convectionsection,the gasvelocitytendsto be high, and the eliminationof the fins can be desirablefor pressure-drop reasons. The convectionsection, or economizer,plays a very important role in determining the thermal efficiencyof the steamgenerator.It is the unit that recovers heat from the flue gas on its way to the stack.It is essentialto keep the finned tubes clean. Many early designsof steam generatorshad undersizedeconomizers BOILER FEEDWATER
WETSTEAM PRODUCT
z euority= (1 -plE-q!I!999-)
x r0oz
Figure8.9 SteamQualityfromWaterAnalyses Facilities
Chap.8
Oil FieldSteam Generators
371
equivalentto authorsgiic generatiqtRadiant SG
Figure 8.10 SteamGeneratorConstruction a) Field SteamGenerator-Convection Section A. Convectionbox B. Bare shield tubes C. Finned tubes D. Hog trough E. Flue gas inlet from radiant section F. Stack G . Girder H . Flue gas exit I . One-half tube diameterbetween tube and sidewall. (Courtesyof FosterWheelerFired HeatersLtd., Calgary)
and wastedheat in the flue gas. A well-designedand well-operatedeconomizer should be able to cool the flue gas to about 340'F. Someearly units, after yearsof operation, gave stack gas temperaturesof 650'F to 800'F even though they were producing steam satisfactorily. A decreasein stack gas temperature of 100'F is
Figure8.1ft nally backH chamberwitl tially in a si wherethereI The rd bustionchan receiveconsi The bq which passc cleanand in r its accompa Vertical SE
Another srylr vertical Mit( Wilcox. Thb also usedat I As wdl coal-firedun The rna cally upwar& closely-sprc( diation from chamberare outsideof rba The syn that contrihl rical locatio flame impirg
STEAM DISTRIBUN
It is normal p groupedtogg doingthis is t can be treatq A facta tralized and < worker time i
Figure 8,10 b) Field SteamGenerator-Radiant Section A. Air inlet duct B. Forced draft fan C. Burner D. Radiant coil E. Casingstiffener F. One tube diameterspacingbetweentube and wall insulation. (CourtesyFosterWheelerFired HeatersLtd., Calgary)
372
Steam RecoveryEquipmentand Facilities
Chap.8
Steam Distrh
equivalentto a fuel savingsof about 3Vo(Kerby, Kense, and Peachey1984).These authorsgive an excellentdiscussionof meansfor improving the efficiency of steam generation. Radiant Section
:am GeneratorConienerator- Convection n box d tubes )es rlet from radiant sec-
rlt ube diameter between rdewall. ;ter Wheeler Fired rlgary)
p€rated economizer units, after yearsof n though they were erature of 100'F is
Figure 8.10bshowsa sectionthrough the radiant section.The tubesrun longitudinally backward and forward around the perimeter of the cylindrical combustion chamberwith a spacingbetweencentersof about 6 in. They are connectedsequentially in a single pass (exceptin the new large Natco and Struthers:TlWunits, where there are three or four parallel passes). The tubes are supportedby hangersawayfrom the insulatedwall of the combustion chamber.With this construction,the backsof the tubes awayfrom the fire receiveconsiderableenergyby reflection from the hot insulation. The burner for the generatoris mounted axially and producesa long flame, which passesdown the center of the chamber.It is important to keep the burner cleanand in adjustmentso that direct impingementof the flame on the tubes,with its accompanying high local heat flux, will not occur. Vertical Steam Generators Another style of generatorthat has found popularity, particularly with Shell, is the vertical Mitchell Engineering (ME) generator manufactured by Babcock and Wilcox. This equipmentwas developedfor Shell'soperationsin Venezuelaand is also used at their thermal recoverypilot at PeaceRiver, Alberta. As well as conventionalfluid-fueled units. Babcock and Wilcox also offer a coal-firedunit. The main distinguishingfeaturesof thesegenerators is that the firing is vertically upwardswith a singleburner.The boiler tube is in the form of two concentric, closely-spaced helicalcoils surroundingthe flame. The inner coil absorbsdirect radiation from the flame. The combustion gasesfrom the top of the combustion chamberare directeddownwardbetweenthe two coils and then upward,past the outsideof the outer coil: the outer coil forms the convectionsection. The symmetricaldesignof the verticalsteamgeneratoris an attractivefeature that contributesto evenheatingand stressingof the boilertubes.Also, the symmetrical location of the burner pointing upward gives easieralignmentand reduced flame impingement. STEAM DISTRIBUTION SYSTEM It is normal practicein larger projectsto use a number of oil field steamgenerators groupedtogetherto provide sufficient capacity.In California, one of the reasonsfor doing this is to allow the flue gasfrom severalgeneratorsto be collectedso that it can be treatedin a singlescrubber. A factor of generalsignificanceis that the operationof the systemcan be centralized and combinedwith the operation of central water-treatingfacilities. Less worker time is required to operatea centralizedfacility.
;ulation.
Facilities
Chap.8
Steam DistributionSystem
I i I
il
I
It is normal to provide separateoil and steamlines and to run theseto individual wells or groupsof wells from the centralplant(s). A feature of steamdistribution systemsis the need to allow for the thermal expansionof the pipeline.Figure 8.11showsthe expansionloopsthat were usedin Esso'sLeming pilot and a more recentdesign. The measurementof the flow of wet steamusing orifice or flow nozzlemeters is discussed by Miller (1983). A problemassociated with the distributionof steamin thermalprojectsis that of the division of Iiquid and vapor flow at pipe junctions.There is alwaysa tendencyfor unevendivision;as a result,somewellswill tend to get steamof a differ_ ent quality from others(Hong 1978;Sabaand Lahey 19g4). This problemhas beenwidely recognized,but there are, as yet, no generally acceptedsolutions. Gulf canada developeda dividing system that has been reported to give improved results,but it is complicatedand has not yet found general use. Another systemfor splitting wet steamflows has been describedby Konak (1985and 1986).The principleis shownin Figure g.12. This method dependson the observationthat, under the usual steam-flow conditions,the water tendsto flow as an annulusjust within the perimeterof the pipe' If the pipe is horizontal,this water ring tendsto be thicker ai the bottom. As a result,a line connectedinto the bottom of the main pipe tendsto producewetter steamthan the average,and a top connection,drier steam.In the Konak devicethe two streamsare blendedto give the desiredquality.This can be automatedby using a steam-qualitymeter downstream. A very promisingdevelopmentis the neutron-scattering steam-qualitymeter that was describedby Lim of Esso Resources(Lim 1985).An americium/berylium sourceis placedbesidethe steampipe; this emitsfast neutrons,which penetraiethe pipe. Neutronsare scatteredby hydrogenatomsmuchmorethan by other elements. The scatteredneutronsthat leavethe pipe at right anglesare measured,and their flux is an indicationof the quality of the steam.A largerflux of scatteredneutrons indicatesa higher proton density,i.e., a lower steamquality. Metersoperatingon this principlehavebeen constructed,and Lim describesintlresting and promising results.An instrumentthat dependsupon the sameprinciplehasbJendeJcribedb! Woiceshynet al. (1985). I 6 . 2 mI
l-l
_i EI @l t OriginaiLeming ExpansionLoops - (square)
ModitiedAlyeska zee Expansion LooP configuration
Steam RecoveryEquipmentand Facilities
A grouingr to locaterb was develo the well co wells of ,50 The r Figure8.1reservoir.Tl centersof tl rangedin tr Subse of clustere design. The u above-grou alsoreduce able envirm This is impo Figure drillingcosl relativelviru ing 12rrells
THERMALWELL.C
A ty'picalco is cemente zone is perf
Figure 8.11 Cold Lake SteamLine ExpansionLoops (after peacheyand Nodwell 1981)
374
CLUSTEREDD€V!
Chap.8
ThermalWeA
to run theseto indirllow for the thermal )ps that were usedin
Vapor-richstream
rr flow nozzlemeters ermal projectsis that hereis alwaysa tenget steamof a differ. as yet, no generally stem that has been asnot yet found gen-
Main steam header
Liquid-richstream
Figure 8.12 Esso'sWet SteamSplitter (after Konak 1985)
describedby Konak CLUSTEREDDEVIATEDWELLS he usual steam-flow the perimeterof the ier at the bottom. As rdsto producewetter :heKonak devicethe e automatedby using steam-qualitymeter americium/berylium . *'hich penetratethe rn by other elements. measured,and their of scatteredneutrons \leters operatingon estingand promising Lasbeendescribedby
A growingtrend in steamprojectsis to drill deviatedratherthan verticalwells and to locatethe well headsin groupsin closeproximity to eachother. This practice was developedby EssoResourcesin their Leming pilot at Cold Lake. In this pilot the well completionsformed hexagonalpatterns,with a distancebetweenadjacent wells of 500 to 600ft. The well layout for the original part of the Leming pilot is shown in Figure 8.13.The diagramshowsthe locationof the completionsof the wells in the reservoir.The headsof the wells and the pumpsare locatedin groupsof 7 at the centersof the hexagonalcells(exceptfor the J pattern,which involvedL3wells arrangedin two concentrichexagons). expansionsof the Leming pilot have involvedthe sameprinciple Subsequent of clustered,deviatedwells. Figure 8.14 is a perspectiveview of such a pattern design. The use of clusteredwells greatlyreducesthe length and complexityof the facilities-roads, steamand productionlines, and power lines. This above-ground alsoreducesthe areathat mustbe clearedand thus makesthe projectmore acceptable environmentally.Also, the manifold facilities can be locatedmore flexibly. This is importantin areaswheremuch of the ground is muskeg. Figure8.15showsthe effectof varyingthe numberof wellsper satelliteon the drilling costand on the overallcostof the well facilities.The costswerefound to be relativelyinsensitiveto the numberof wells per satellite,at leastfor satelliteshaving 12 wells or more. THERMALWELL.COMPLETIONS A typical completionfor Cold Lake wells is shownin Figure 8.16.The 7-in. casing is cementedto the surfacewith 50Vosilica flour thermal cement.The producing zone is perforatedwith six shotsper meter; an insert pump and 3]-in. tubing are
rt'hev and Nod-
1 Facilities
Chap.8
ThermalWell-Completions
375
tl tl
ftl d{ 4l
3mJ
LemlngArea
g
c 6
o o
I ax! IJ n|
:q
o ;l(pJ o CL
mlle '
R a h g e 3W 4 M
l
Figure 8.13 Bottom Hole Location for Esso'sLeming Pilot (after Buckles 1979)
employed.A 5-in. slottedliner is placedinsidethe perforationsto keep sandfrom the pump. During injection,steamflows down the annulusbetweenthe casingand tubing. It would be preferableto inject down the tubing to keep the casingcooler, but this is not done by Esso canada becauseof the difficulty presentedby the hightemperaturepackerthat would be requiredto isolatethe casing.one of the problemsin usingthermalpackersin steamstimulationis the needto bypassthe packer
d
o
o
Figrrc tafter I
Pad Limits
Figrrt 1 9 E lI
Figure 8.14 Esso Design for a Cold Lake Steam Stimulation Well Pad (after Peacheyand Nodwell 1981)
376
Steam RecoveryEquipmentand Facilities
Chap.8
ThermalWdl{
300,000 @
i
OL
o
o o I200.000 r.J ol
liftand surfacefacilities
.s
A
.o
A
I100,000 o
Drillingonly
CL
ttom Hole Location for ilot (after Buckles
o o
o 0
; to keep sand from the casingand tube casingcooler,but sentedby the highg. One of the probo bypassthe packer
0102030 Number of Wells Per Satellite
Figure 8.15 Unit Well Cost at Cold Lake. Letters Identify Particular Satellites (after Peacheyand Nodwell 1981)
BASICWELL CONFIGURATION
Limits
Figure 8.16 Cold Lake SteamStimulation Wells (after Peachey and Nodwell 1981)
r'ell Pad (after
Facilities
Chap.8
Thermal Well-Completions
gt7
so that gas can be vented to the annulusduring the pumpingperiod (Gatesand Holmes1967). The coefficient of thermal expansionof steel is about 7 x 10-6per degree Fahrenheitof temperaturechange.Thus,for example,if the temperaturebfu "aiing that is 1500ft (457 m) in length is raisedby 600'F (333'C),then the increase in lengthwould be 6.3 tt (1.92m) if it were unconstrained.There are three possible solutionsto this problem:
I -t
1. Use high-strengthcasingand restrainthe movementby cementingthe well throughoutits length.In this example,the compressive stress*ould b"
t = (*)t
= (#)
{
122,ooo psi es x 106)=
whereE is Young'smodulus.In casessuchas this the yield point of the steel will be exceededand the steelwill yield under the compreisivestress.As a result,if the well is cooledlater, it will be under tension. 2. Prestressthe casingof the well during cementingby applyingan initial tension to offsetthe compressive stresses that will be causedlatei by heating.To do this, a quick-settingcementmixture is placednext to the bottom liVo of the well, with a slower-setting mixture above.Tensionis appliedto the well by pullingwith the rig after the lowercementhassetbut beforethe uppermaterial hardens. 3. Allow the casingto expandand the wellheadto rise. One way of doing this involvescoveringall the pipe exceptfor the lowest10Voof its iengthwiitr Uitumen. The wellheadis allowed to rise abovethe surfaceof the ground bv usingswivelconnections("Chicksans")similar to thoseusedin loajine racks. This techniqueis not usedanymore. Peacheyand Nodwell no longerfavor the use of the extremehigh-strengthsteels that would be necessaryto avoid inelasticyield, since thesematerialsare susceptible to catastrophicfailure due to sulphidestress-corrosion cracking.Insteadthey believethat L-80 or MN-80 casingwith specialcollarsis mostsuitable.The inelastic yield of the casingmaterialthat occurson heatingseemsto be acceptable. It is important that the well cementshouldprovide essentiallycompleteradial supportto the casingto reducethe tendencyof bucklingunder the compressive stress. A surveyof thermalwell completionpractices(FarouqAli and Meldau 1979) is reproducedin Table8.4.A generalreviewof thermalwell tompletionsis givenby Gatesand Holmes(Gatesand Holmes1967). The designof steam-injection wells is discussedin a paperby Willwhite and Dietrich (1967).
=:!i
a: ii
>-':e
i t a
o ,F
d F
-9
E =q) = c
E 0) 3 F
TEMPERATURE LOGGING
a €
Techniquesfor logging the temperatureprofile in thermal recoverywells were discussedby Leschyshynand Seyer(1989).They found that consistentmeasurements 378
Steam RecoveryEquipmentand Facilities
Chap.8
ul J
co
ng period (Gatesand o
t 7 x 10-6per degree :mperatureof a casing , then the increasein ere are three possible
o
^^a^qa
zz9z2zz99
oI)
rv cementingthe well stresswould be
Lrr
FitrFr
9YFFYYFFF Ft--tFF5Fr',h)-nichct)Z;X
>= -o
o
U F
F
F,.
FP
.L-li\Jr,r:.I-
rbd);a>it{ ca
o--
ax
oo
) psi
q
d
(J
-
-=n o n n o 5 o
rl
ield point of the steel npressivestress.As a n. rplying an initial tenrd laterby heating.To to the bottom 10Voof is appliedto the well : beforethe upper ma-
* g P 2JJ262 au) C)
bo o
T bo>
E-E
n
o N
oz) N(h'e
x€x.e9-eg € O\O\€
oo J
per by Willwhite and
o
L-
.=.d69,4
:.q 9ge
N-
-N-
o_^ FOOOOAOOn z+N:*iitc.l
:
4u =i =A
X A
E 5 E ; , E 8' F E
-
^t
# s# 5
I i,89
o)
3 o
z
o
O\alh\OcO.iOhn *idiNOar)O
o q)
{: o
sseiss55g 6 E^ h5., Y (, Y
'5sss5€se
.L
6
; o
-
oX A i-
i 5T F: E: E: ;: :;. ;: =Ed oEF 51= oT U :
'E
g>di:>8oa>
E o
=0t =
g E^ l-.=,,4a^
.;gi H{ €I e= ; t;e =<.j(.,.9
6
:::;o5qH;5
a o
Chap.8
ooooooooo 6*o-vJnooogv?v-i
z
OJ
d Facilities
S nS' *\ ^o X rr € nS n 6S S
O)
!,1
E
:overy wells were dissistent measurements
r ooSo,ciootr-tr-6 l.l9N.lNii-
6\OGiO\OOt\Oci6 NOCI
U)
)ne way of doing this " of its lengthwith biace of the ground by usedin loadingracks. e high-strengthsteels materialsare suscep:racking.Insteadthey suitable.The inelastic e acceptable. It is imrleteradial supportto pressivestress. Ali and Meldau 1979) rmpletionsis givenby
noonnooo
' un Sr €2h nJO,€2€ 2 2 2 I
hh-roOhV)€/ioO
i>a'F>3ou>
q)
Sa b=
iN6+h\Ot'-0Ocl\ ay G
ojr
i- ii =c z.v S=
.< vo'
uJ to
;0 .q -
dNo$h\Ot'-ooo\
^J
Lli
379
can be made if the temperaturemeasuringtool is at the bottom end of the logging string' The designof the roggingtool is discussedin their paper. when they emproyeda conventional,"stackable,'temperature-rogging tool in which the sensingelementwas containedwithin un op"n sectionin the centerof the tool, it was found that the logs obtained were uuriubt. and dependedon the direction of logging (up or down)lnd on the rate of ,n*"-"rrt of the toor. This was causedby the thermal capacityof the fluid that was urong'uy i;:1f# "ur.i"i
I
CONTROLOF HEAT LOSS IN STEAM.INJECTION WELLS The effect of using the tubing for injection of steam with insulation betweenit and the casingwas.discussedin chaptei z. rnl, is desirable from the point of view of reducingheat losses,providing higher-quality steam at the sandfaie and reducing the mechanicalstresseswittrin thi casing.ih, lutt", is a particularly important factor if it is planned to employexistingwills that are not designedr- irr"iiJ-"peration in a thermal project. The current practicesin reducingwell bore heat losses havebeenreviewedby Meldau (1gSg). In manycases'becauseof the complicationof using a thermalpackerand becauseof the need.tovent gasesup the annulusbetweerithe tubing and the casing during cyclic production,operationwith no insulation has been used; the casing must be designedto operateat the steamtemperature. This approachis common in the Cold Lake area. Someoperatorsinject steamdown the tubing and inject a small amount of gas, either natural gasor nitrogen,down the annulus-in order to preventheat transfer by refluxing in the annrrlus-i.e., by liquid waterboiling on ,t hot tubing and con_ densingon the casing.This has blen done uoth witriuare " tubing and, more recently,with insulatedtubing (Meldau 19gg;Cormier l9g7). Insulationby isolatingthe annuluswith a packerand venting the annulusis often usedas a simpleform of insulation in steamfloodr; tt i, is com-"mon pi"fii." in california. If the annurusis vented,any_steam leaking at the packe.oi.oupiing. passesthrough the annuluswithout condensation. The use of insulatedtrrbingis quite practicalas a meansof savingheat and reducingcasingtemperature.Howevei,it is expensive; costsare of the order of $25 to $35 U.S. per foot (Meldau 19gg). The general arrangement for the use of insulated tubing is shown in Figure8.17. As is shownin Figure 8.18,insulatedtubing is constructed with a hollowwall with the annulusfilled with layersof foil (to ,"iu." radiation losses)and ceramic fiber' The insulation spaceis evacuated.A major problem with earlier versionsof in-sulated tubing was the heat lossthat occurrei uittr" couplings betweensections of the insulatedtube. The probrem is aggravate d by reftixing; this involves the boiling of water in contact with the hot ioupling roitowlo by its condensationon the casing.The heatloss.hasbeengreatlyreoucejuy uning thl couprings*ith ;; lation. Typical constructionis shownin Fisure g.lti. 380
Steam RecoveryEquipmentand Facilities
Chap.8
STEATI SELECTIVE
SeveralmeaE specific horia that have bec pack with a o ure 8.19).Thit so the pluggiq The usc of steam duril ARTIFICIALLIFT
Artificial lift i steam prodtd pumping is ru Conveo for lifting cil metal-to-rnet ventional nig practice.The t The c'tt significantpt wear can be t around the pc
tAn inscrt string. It is s..I
Artificial Lift
-^4 ==l
m end of the logging €r. ature-loggingtool in rion in the centerof nd dependedon the :nt of the tool. This wascarried alongby
Thermalpacker joint and expansion
ationbetweenit and the point of view of rdface and reducing rticularly important ;nedfor thermalopwell bore heatlosses rmal packerand berbingand the casing en used;the casing rroachis commonin ;mall amountof gas, revent heat transfer hot tubing and conrbing and, more rexting the annulusis commonpracticein packeror couplings of savingheat and : of the order of 925 ubing is shown in J with a hollowwall losses)and ceramic r earlierversionsof qs betweensections f: this involvesthe its condensationon ;ouplingswith insu-
Facilities
Chap.8
--
Figure 8.17 Use of InsulatedTubing for SteamInjection (after Meldau 1988)
STEAMINJECTION SELECTIVE Severalmeanshave been developedto allow the selectiveinjection of steaminto specifichorizontal layers.Borregales(1977) and Burkill (1977)describemethods that have been usedin Venezuela.These allow the partial pluggingof the gravel pack with a cement material that is forced through a specialport collar (seeFigure 8.19).This equipmentallowsports in a blank sectionof the liner to be opened so the plugging agentcan be squeezedinto the gravel' The use of speciallysized and placedperforationsto allow selectiveinjection of steamdurins a steamfloodis describedby Gates and Brewer (1975). ARTIFICIALLIFT in both steamfloodingand cyclicsteamprojects.In cyclic Artificial lift is necessary steam production, reservoir pressuredrives the fluids up the well initially, but pumping is required when the reservoir pressurefalls' conventional pump jacks with tubing insert pumpst are generally employed for lifting oil from ihermal wells (Peacheyand Nodwell 1981).The pumps have a metal-to-metalpiston sealthat will withstand high temperaturesin placeof the conventional nipple seals.Longer and slower strokes are employed than in normal practice.Thi constructionof a typical pump is shownin the diagramin Figure8.20. The wear of the couplingsusedwith conventionalsuckerrods has presenteda significant problem, partiiularly when pumping deviated wells. The effect of this wear can be reducedby rotating the rods during operation.This spreadsthe wear around the perimeterof the couplingsrather than allowing it to concentrateat one 5An insert pump can be run into the hole as a completeassemblyon the end of the suckerrod string. It is seatedwithin a sealthat is previouslyinstalledin the tubing'
Artificial Lift
381
Buttress c o up li n g
ilti
SrEu SELECTTVE txro rtC Lt8
ragn lltl
Tubing I n s ul a t io n
Insulation
? N
Foil layers Csramicfiber Vacuum
#
I nsert
T H E RM A L P A CK E R
Coupling l i n er
$
I
I
Tubing 27l8"N.80 4 1 / 2 "K - 5 5
Buttress coupling
I
I
I Figure 8.18 Typical InsulatedTubing and Coupling (after Meldau 1988)
tional oil fields the 1500operar
location.The rotationis achievedby a mechanicaldeviceon the pumpjack that imparts a slight rotation during eachstroke. . Another approachto reducingcouplingwear is to usea type of couplingcontaining smallwheelsthat roll on the surfaceof the well tubing.Theseare available with plasticwheelsfor operationbelow250"Fand with steelwheelsand journalsfor high-temperature operation(DDS Calgary). Another meansfor alleviating the problemof suckerrod wear involvesthe use of a continuoussuckerrod without couplings(Corod).6This continuoussuckerrod is suppliedin long lengthsin large-diameter (18-ft)coils, and theseare weldedinto still longerlengthsat the site as the rod is installedinto the well. Figure 8.21illustrates the procedurefor feeding the rod from the transportationreei into the well. Another featureof Corod that reduceswear is that it can be madewith a flattenedratherthan a circular crosssection.If the oval sectionis used,it is chosenso that the flattenedfaceshaveapproximatelythe sameradiusof curvatureasthe tubing in which it is installed;this increasesthe areaof contactand reducesthe wear. Pump maintenanceis a major sourceof expensein many heavyoil projects. Elgert, Chambers,and Suzuki (1989)report that at the Essocyclicsteamprojectin cold Lake, averagepump life was only 200d, as comparedto 1 to 2 y in conven-
Trt
I
oCorod6 is a registeredtrademarkof corod ManufacturingLtd., Nisku, Alberta.
382
Steam RecoveryEquipmentand Facilities
Chap.8
ArtificialLifl
SEL€CTIVE S1EAT INJECTION INTO T}€ t'PPEi ZONE
SELECTIV€ STEAM IIIJECTDI
ftro T|€ LOtrenzoilE
Tubing
THERUAL PACX€R
Figure 8,19 SelectiveInjectionof Steam(after Borregales1977)
tional oil fields.Pump repairsand relatedservicework cost $2 million per year for the 1500operatingwells in the project.
rl
rt
rl tf
Sucker rod
'pe of couplingconTheseare available :els and journals for
lt
Tubing
In
tl Plunger
ear involvesthe use ntinuoussuckerrod ese are welded into ll. Figure8.21illusn reel into the well. rc madewith a flatused,it is chosenso urvatureasthe tubd reducesthe wear. r heavy oil projects. ;lic steamprojectin I to 2 y in conven-
ti
Travellingvalve
j
Barrel
Seal Standingvalve
Rising Plunger Standing valve oPen
(u. Alberta.
Fallmg Plunger Travellmg valve oqen
Figure 8.20 Diagrarnof Tubing Insert Pump
Chap,8
ll !l
) pumpjack that im-
Facilities
lr
ArtificialLift
383
In manl th nificantpm T . R -' Californiar in this field the special1 This p
l. Therc carria 2. The sl contiE enced tects tl 3. The p the flu ing in I diamd 4. The di Huskyl prodrr
SURFACEDROD IN REEL
THECORODSYSTEM Figure 8.21 The Instailation of continuous Sucker Rod (courtesy of corod ManufacturingLtd.)
Their analysisof the problemindicatedthat the primary causesof pump failure were related to the followins: Sand flowing into the wells, particularly during flowback and particularly during the first cycle. 2. ScalescontainingCaCO: and SiOzadheringto pump barrels. Theseproblemshave beenalleviatedby thesemeasures: 1. Throttling the productionduring initial blowbackto reducesandproduction. A choke-operatingguideline has been developedfor well operation in which the well chokeis progressively openedas the AP acrossthe chokedecreases. 2. Using chromium-platedpump barrels.These are resistantto corrosion,and scaledoesnot adhereto the smooth surface.It is not practical to use chromium-platedplungersinside chromium-platedbarrelsbeiausethe two hard materials gall. However, Esso has found that plungers with a sprayednickel coating work effectively with chromium-platedbarrels. Steam RecoveryEquipmentand Facilities
Chap.g
The pl conventiond the smalhr 1 the new pul The sa scaleis the c small and is Small amouo slowlyin thc The ch heavyoil wd the producti< valve. After through ancl by forcinga g plungerpiscr shuttingoff tl rising liquid. In the c ductionand tl cally. The lil chamber.Th Anothcr by downholcI ArtificialLift
In many thermal recoveryprojectsthe production of sandwith the oil is a very significant problem.Somereservoirsare particularlyprone to this problem T. R. vonde (1979)describesthe production or o" apt cai canyon crude in California where the averageproduction contains27 wt% of sand.Someproduction in this field has containedas much as70vo.To handlethis, Husky has developed the specialpump shown inFigure 8.22. This pump has the following features: 1. There are two tubing strings.one carriesdiluent to the pump and the other carriesthe diluted productionto the surface. 2. The suckerrod is containedwithin the diluent tubing and doesnot comeinto contactwith the productionstream.This avoidsthe slow fall that is experiencedwhen the rod must move through the viscousproduct, and it also protects the rod and plunger from the abrasiveaction oi the sand. 3. The pump deliversfluid to the surface on the downstroke(most pumps pull the fluid upward;this one pushesit). In order to minimize compressive loading in the suckerrod, a counterweightconsistingof 2900to 3g5bkg of 2-in.diametersteelbars is fastenedto the end of the suckerrod. 4. The diluent flow is controlled by adjustingthe addition rate atthe surface.In Husky's application at cat canyon, the rate is controlled to give a 12. Apr product.
rrtesyof corod
causesof pump fail,ack and particularly rrrels.
uce sandproduction. ll operationin which the chokedecreases. rnt to corrosion,and rcticalto usechromiusethe two hard maith a sprayednickel
d Facilities Chap.8
The pump is consideredsuccessfur and, althoughits cost is more than for a conventionalpump,the extra is saidto be paid for by the reducedmaintenanceand the smallerpower requirement.It is reportedthat, in one lease,installingfive of the new pumps increasedproduction from 200 to 700 B/d of oil. The sandproblemjust describedis an extremecase.At the other end of the scaleis the experienceof Essoat Cold Lake, wheresandproductionis usuallyvery small and is handledby the small sectionof a slottedliner shown in figure 4.19. Smallamountsof fine solids,which are carriedwith the crude,tend to accumulate slowlyin the separatorsand tanks, and theserequireoccasionalcleaning. The chamber-liftprincipleis anothermeansthat has been usedfor pumping heavyoil wells (Elfarr 1976).rnthis technique,a downholechamberconnectedto the production tubing is allowed to fill with produced fluid through a nonreturn valve. After the chamber has filled, the fluid contents are displacedupward through anothernonreturn valve, through the productiontubing, and to the surface by forcing a gasinto the top of the chamber.The gasthus repla-esthe conventional plungerpiston.After the dischargecycle,the pressureis reducedin the chamberby shutting off the gas supply and allowing excessgas to blow to the surfacewith thl rising liquid. In the chamberlift systemtwo tubing strings are employed:one for the production and the other to transfer the lifting gasdown to the pump chamberperi^oaically. The lift is assistedby the buoyant effect of the eihauited gas from the chamber.The pump has beenusedsuccessfully in the slocum field in Texas. Another lifting techniquewhich has been tried is the use of pumps operated by downholehydraulicmotors.The CanterralTennecoin situ pilot in Athabascahas ArtificialLift
385
t ll il
ril
'1 tt Il
ri
Itr & ri
CONVENTIONAL DILUENTPUMP
T Y P EY
TYPE X orlr.rfrt lxf,cl|or tI'O PUIP o[Utrr liJ€cllor nto lozlLt
t
a
; =
H0(L0f
sucrtl Portr stRn6
a
HEP unit.r the Hrdrabc An irq the dor.r'nal ductionnbcr the needto t casesthereh very cold*c
J
toLLol s\JcxtR f,00 srnlrc
IMPROVINGWELL I
In cyclicsea Keelirq peratureand cyclicsteam1 As prod surefall as in reservoirpre$ ing this perb nulusof the r afterthis rhe flowing b1 irs gasis separat ratelyup thc the pumping maintained-
sPRil€ CHECTY LVE
I rA't0,!01 tuLL lult
rn'_ TUBIIG
PI,IP SEAI 6 SE L
sPirs Loltf,o vllvE
clfct
2' PUIP EARi€L
HOLLOI PULL R00
XI OILU€
cH^r6€R 0rLrftl PORIS I !/{. PUIP urffL
2tE PUIP tl
ryt'
C ?t rt. ttttfL
E intL c|{cr VALYT
2 Va' PLUIGEi
I
orLUErl PORT
txtt YALY€
gr
sTAr0n6 vrlv€ ttTirxct YALYE
'll' t/
\l t\
ll
0nouL sPtY tozzlt
tr rLrtlrt0t F'Si---\]
Figure 8.22 Husky Diluent Pump (from Vonde 1977)
used Kobe downhole hydraulic pumps; these have also been used at the Suncor World Wide Energy pilot at Fort Kent. Another developmentof interest is the use of drivers, driven by hydraulic cylinders,in place of conventionalcrank-drivenpump jacks. One of theseis the 386
Steam RecoveryEquipmentand Facilities
Chap.8
Figrrr I LakcR
lmproving Wel I
IVEIITIONAL IENT PUMP
HEP unit, which is manufacturedin Calgaryby ForemostEngineering;another is the Hydrabeamunit; a third is the curtis Hoover Hydraulic Fump raik. An importantpotentialadvantageof this type of driver is its ability to adjust the down- and upstroketiming independently. This is imporrantwith heavyoil ductionwherethe speedof the downstroke,due to the viscousnatureof the oil iroand the needto avoidcompressive bucklingof the rod, can be a limiting factor.In some casesthere havebeenproblemswith hydraulicallyoperatedpumpingequipment in very cold weather. IMPROVINGWELL PERFORMANCE In cyclic steamprojects,eachwell is subjectedto a seriesof changinqconditions. Keeling (1985)has discussedmeansfor improving well perfor-ma-nce. The temperatureand pressureof a typical well during the productioncycle in the Esso cyclic steamprojectat Cold Lake are shownin Figure g.23. As production continues,the wellheadtemperatureand the bottom hole pressurefall as indicated.Initially, the entire productionfrom the well flows, driven bv reservoirpressure,throughthe tubing and a choketo the productionflowline. Duiing this period, there is considerable steamin the produit. At somepoint the annulusof the well is connectedto the flowline, and the gasflows separitely.Shortly after this the productionpump is seatedand pumpingsiarts.At thii point th" gu, i, flowing by itself to the productionline, and the oit ir ueinglifted by ir,. purnpltn" gasis separatedfrom the producedliquidsat the bottom of the weli and ilowi separately up the annulus.This separationof the gas at the bottom of the well makes the pumping much more efficient and allows a lower bottom hole pressureto be maintained. MPa 9auge
k-
II
t:
ll
ll
WellheadTemperature \i
1
i\
100 Bottom hole - lressure
:acilities Chap.8
:1 tl'
Vent gas compressionstarted
\!i
it \l
riven by hydraulic )ne of theseis the
ru
i{
\i i
,sedat the Suncor
til
!tl
oc
Oil pumpingstarted
j.iT-
\ 2
Vent gas divertedto flow line from annulus
l#-
i il
Flow I
Oitpumped
Time (up to 250 days total) Figure8.23 well remperature andpressure Duringproductioncyclefor cold LakeReservoir (fromKeeling1985) lmprovingWell Performance
387
When the wellheadpressurefalls to the point where gasflow into the producsystemis startedand the tion line is no longerpossible,the vent gas-compression gas is compressedseParatelY. A flow plan showingthe compressionsystememployedby Esso at Cold Lake is shown in Figure 8.24; it is the result of considerabledevelopment. The casinghead product from the wells flows to the vent gas separator.The liquid that separatesis pumped to the product line. The gas from the separatoris cooled,and someof the liquid is condensedin an exchanger.The cooledstream passesto anotherseparator.The liquid from this separatoris pumpedto join the plant product stream. The gas from the secondseparatorpassesto a liquid ring gas,after passingthrough a knockoutdrum to remove the compressed compressor; joins the remainderof the productstream' liquid, the compressor facility such as this Oni of the problemsin designinga well-gas-compression from the wells. feed stream well gas in the is the variability of the amount of of time. as a function plant a in such Figure8.25showsthe flow of gasto be treated compresfor two calls design In order to handle the variability of flow, Esso's sors.Both compressorsare used in the first two cycles;after that, the secondcompressorbecomesan on-line sPare.
the oil. A rar ply oil field r what worksr Whrerof demulsifi
FLUIDS TREATINGPRODUCED The productionfrom steamedheavyoil wells is usually a mixture of hot oil and water with somegas.In many casesit containssubstantialportionsof solidssuchas clay and sand. The production is nearly always emulsified; some of the water is emulsifiedin the oil and someof the oil is emulsifiedin the water. Figure 8.26 showsa typical schemeof the treatmentof the productionfrom thermal recoveryoPerations. A demulsifieichemical is addedbefore the production streamfrom the wells reachesthe treatment plant; this promotesthe separationof dropletsof water from
_
]J J-_--i-
J-
FEE)
+
Pi
c{
fi3rrc and \o
J
lEmulsrm
Figure 8.24 Esso'sCold Lake Casing Scheme(from KeelGas-Compression ing 1985)
388
Steam RecoveryEquipmentand Facilities
Chap.8
in-oil emulsionr. oil, and oil-in-re water. Attemp{r l flow by the addrt d i s c u s s e di n C h q allow pipelinc tn
Treating ftodr
# into the producis startedand the Essoat Cold Lake lent.
Figure 8.25 Expected Flow of Vent Vapor in Esso'sCold Lake Commercial Project (from Keeling 1985). The Diagram Showsthe Vapor Flow from a Gas CompressionFacility Serving a Pad of 20 Wells.The Wells are Steamed10 at a Time. The Numbers abovethe PeaksRefer to the Production Cycle.There Are Two Peaksfor Each Cycle, Correspondingto the Two Batchesof l0 Wells Goins on Production
3asseparator.The m the separatoris fhe cooledstream umpedto join the :s to a liquid ring rt drum to remove t.
acility suchas this m from the wells. a functionof time. s for two comprest, the secondcom-
YEARS
the oil. A variety of demulsifierchemicalsis availablefrom the companiesthat supply oil field additives.There is an art in selectingthe bestone, and it is found that what works well in one location is unsuitablein another. Water-in-oil emulsionsare more viscousthan the oil itself,Tand the addition of demulsifier at the wells can reduce the pressuredrop in the gathering lines as
: of hot oil and wars of solids such as me of the water is
t;
it
rll
rt€f .
rfl
,r
re production from
'1 gamfrom the wells plets of water from
r!l I I I
i
ELECTROSTATIC TRFATER
Figure 8.26 ProductionTreatmentUsed by Esso at Cold Lake (after Peachey and Nodwell 1981)
so'sCold Lake Casing n Scheme(from Keel-
Facilities
Chap. 8
TEmulsions are dispersionsof one liquid in another.There is a largedifferencebetweenwaterin-oil emulsions,where the oil is the continuousphaseand which have higher viscositiesthan the oil, and oil-in-wateremulsions,which are lessviscousthan the oil althoughmgre viscousthan the water. Attempts have been made to createoil-in-water emulsionswithin the rbservoirto promote flow by the addition of chemicalssuch as causticsoda to the steam(Doscheret al. 1963).As was discussedin Chapter1, there is currently interestin making concentratedoil-in-wateremulsionsto allow pipeline transportationof very heavyoils.
TreatingProducedFluids
389
well as allowingpremixingof the demulsifier.Premixingalsogivesthe demulsifier more time to act. Figure 8.27 showsthe measuredviscositiesof Cold Lake crude containing various fractions of emulsifiedwater as functions of temperature. At the plant, the streamis cooled and introducedinto a baffled horizontal separatorvessel.The oil, which still containsemulsifiedwater(about3Va),is cooled further and treatedin an electrostatictreaterto producethe final bitumenproduct (0.5%BS & W) and morewater,which can be sentto the recycleplant or disposed of otherwise.Figure 8.28 is a diagramof a modern electrostatictreater.Electrostatictreatersare often combinedwith a fired heater(it is then a "heatertreater") to raise the temperatureof the oil. This is required for conventionalproduction which is cold. In thermal projects,it is more commonfor the oil to be cooled. Electrostatictreatersutilize an electricalfield betweenimmersedelectrode water droplets.The role of the coagrids to promotecoalescence of the suspended lescershouldbe confinedto removingsmallresidualamountsof waterfrom the oil ratherthan largequantities.The separationdependsupon the effect of the electrical field in causinga motionof the waterdroplets.Althoughboth AC and DC fields have been used,AC is more popular becauseit is simpler,althoughperhapsnot quite so effective.More recenttechnologyusesboth AC and DC fieldsin the same unit-the so-calleddual polarity treater such as that shown in Figure 8.28. The electrodesin this equipmentare connectedto the electricalpower in the manner shownin Figure8.28. Electrostaticfields promotedropletcoalescingbecause in the elec1. The waterdropletsbecomepolarizedand tend to alignthemselves trical field, with one sideof the dropletpositivelychargedand the other,negatively charged.There is thus a tendencyfor dropletsto attracteachother; this promotescoalescence. woter/Oilvolumerotio Emulsjfied 0.015.(cold.Lokebitumen) 0.19(R'un1) 2 0.30'(Run2) 0.30'(Run
0.70Gun frun 2)
i
l= o
8 .q
toooo
\ l.-
FEr
Eu
\
:-:\l
Fior natc Sra r rth
2. The dr electr droplc
Temperoture,'C Figure 8.27 Effect of Emulsifiedwater on the viscosity of cold Lake Bitumen (from Chung and Butler 1988)
390
Steam RecoveryEquipmentand Facilities
Chap.8
Treatirpftoc
ivesthe demulsifier e crude containing 'e. r baffled horizontal tbout3Vo),is cooled ral bitumenproduct le plant or disposed tic treater.Electrot a "heatertreater") entionalproduction il to be cooled. immersedelectrode fhe role of the coarf water from the oil effectof the electrirh AC and DC fields though perhapsnot C fieldsin the same in Figure8.28.The o*,er in the manner DUAL POLARITYDESALTER
in the elecemselves and the other,negatracteachother: this
WATEROUT
E M U L S I O NI N
Figure 8.28 Diagram of a Dual-Polarity ElectrostaticTreater. Water in Oil Emulsion Feed Is Introduced Beneaththe Inverted Distributor Trough and It Flows Upwards Between the Vertical Electrodes.These are Charged Alternately + and - by the Electrical SystemShown in the Lower Right. At the SameTime an Alternating Voltageis Applied to the Whole Electrode System with Respectto Ground (CourtesyNatco)
2. The dropletstend to have electricalchargesinitially and to migrate in the electricalfield. However,there is a differencein the velocitywith which large dropletsand smaller onesmigrate, and there is an increasedtendencyfor col-
J Lake Bitumen
d Facilities
ChaP.8
TreatingProducedFluids
391
whereI
->ioperotingl
Pr P.
i Ronge I
o
Leming Produced Woter
Leming
L
I
lL'
(J
\20 t./
q)
o (n
o APt Oil
i
\
i
\
0.9
Other r SI units shor For the dropletsintcr by a factr fi
I I I I I I I
\
I I I I
I
200
100 Temperotureo C
0
Figure 8.29 Densitiesof Cold Lake Oil and Water (after Peacheyand Nodwell 1981)
lision. Also, particularly in a DC field, dropletshaving oppositeelectrical chargesmove in oppositedirectionsand tend to collidewith eachother. 3. The electrical field may weaken the film of emulsifier on the surface of the upon collision. droplets.This promotescoalescence If there is too much water suspendedin the oil, then the dropletsmay form chains betweenthe electrodesand producea short circuit. Adjustmentsthat can be made to the operationof an electrostatictreater include the spacingof the grids and the appliedvoltage. The temperatureof operationof the separatingfacilities is important as it controlsthe densitydifferencebetweenthe oil and the water(Figure8.29)and also the oil viscosity(Figure8.30).Both of theseaffect the rate of settling' The rate at which water droplets settle from oil is determinedby Stokeslaw. This may be written for a singlesphericalwater droplet as: 2 R2(p,- p)g (8.1) Y == 9
l"o
where F = 6 As rhc t to increasett maximum,:lt settlingrareBoth fr This is parriq If the addirir be dilutedro r add diluenrlo formance {cq pipelinecorry than 0.5%in r the pipelines
PRODUCTIONTREA
Figure8.31sh at Cat Canlu Somewhatorr which is firred out periodiceX emulsiontre-
3% BS& \r. 6 o
MAKEUPWATERSII
o
Evenif rhefir 100 Temperatureo g
392
200
Figure 830 Viscosity of Cold Lake Oil (after Peacheyand Nodwell 1981)
Steam RecoveryEquipmentand Facilities
Chap.8
907a),there ri that has beeo I ume. There ri and cooling p
Maker.p WaE !
where V pw po g po
is falling viscosity of water droplets (m/s) is density of water (kg/m') is density of oil (kg/m3) is accelerationdue to gravity (9.81m/s'z) is oil viscosity(Pa . s)
Other sets of dimensionallyconsistentunits can be used in place of the SI units shown. For the caseof an actual emulsion, the velocity is lower becausethe falling dropletsinterfere with eachother. The effect may be calculatedby multiplying 8.1 by a factor f'5 (Steinour 1944).
sitiesof Cold Lake ter Peacheyand Nod-
oppositeelectrical ith eachother. the surfaceof the ts may form chains s that can be made rf the grids and the ; is important as it igure8.29)and also €ttling. ined by Stokeslaw.
v : +R2(P' P)EF, 9
(8.2)
l"o
rztt-a;and e : volume whereF5 : 62119-i fractionof oil in the emulsion. As the temperatureis raised,the viscosityof the oil decreases, and this tends to increasethe settling velocity. However, the density difference passesthrough a maximum, and there is thus an optimum temperaturethat provides the maximum settlingrate. Both factorsjust mentionedcan be improvedby addingdiluent to the system. This is particularlyvaluableif the densitiesof the bitumenand waterarevery close. If the addition of diluent is practicable,as it is, for example,when the bitumen is to be diluted to transport it eventually through a pipeline, then it is very desirableto add diluent to the mixture before separatingthe water. This will increasethe performance (capacity and/or product quality) of the separation equipment. Most pipeline companiesrequire BS & W to be less than lVo by volume and usually less than 0.5Voin order to prevent corrosion and to reducethe frequencyof pigging in the pipelines. PRODUCTION TREATMENTWITH HIGHSAND PRODUCTION
(8.1)
Figure 8.31showsthe facilities used by Husky in the treatment of their production at Cat Canyon. The averageproduction from this project contains 27 wtTo sand. Somewhatover half of the sand is separatedin the direct-fired desandervessel, which is fitted with a conicalbottom and containshydraulicjets to flush the sand out periodically. The remainder of the sand is removed from the bottom of the emulsiontreater.The producedoil containslessthan 0.2 wtVosand and lessthan 3VoBS &W. MAKEUP WATERSUPPLY
icosity of Cold Lake et and Nodwell1981) I Facilities
ChaP. 8
Even if the fraction of the producedwater that is recycledis very high (greaterthan 907o),there will still be a need for makeup water supply.In the reservoir, the oil that has been removedis normally replacedby injectedwater of an equivalentvolume. There will alsobe a need for additional water in a recoveryprojectfor service and coolingpurposes. MakeupWater Supply
393
Produced U TAX€-UP PROCESS WA'ER I
L._
_.- _ _.
E:
l1 Al 8 ! Gl dl
sl;
tl
iJ
I 1..'-
I
lr r.., !
3 r tl
L[€
4'rEsr Lrir€
PRESCJR€ }tGE
PROqffIOTT
-
-
TDS SS
I UAPHRAil I ArRACTUATED ar-r Sxlll
RJHP
MANIFOLO
so.
HCO, Sulphrd
sio:
wAtER r{JECTrOr,r IO REOUCE LINE
BROOKSZONE A TREATING FAcrury C'ATHERING
\{g CI
Tempcil
PNESSLRE
pH
'tF El..trut ( 2 ) K"ro n a k and Gr (3)Suspende d ol as total organt
*'."B.rI63Ii*
Figure E.31 Processfor TreatingHigh-Sand-ContentHeavy Crude (from Vonde 1979)
Conventional sourcesof water supply such as from undergroundreservoirs, rivers,and lakesare normallyused.However,other water suppliesmay be consideredif thereis a shortageof waterin the area.For exampleSuncor,in their thermal recoveryproject at Bonneville,Alberta, useswastewatereffluent from a nearby municipality. Freshwateris normallytreatedby chlorineoxidation,lime/sodasoftening,filtration, ion exchange,and deaeration(Kloepfer,Card, and Kus i983). RECYCLINGPRODUCEDWATER In the previous section it was shown how the production from steam recovery projects can be separatedinto a marketable oil product and a produced water stream.In manycasesit is desirableto treat this water so that it may be recycledto the steamgenerators. Recyclingwater reducesthe impact of the thermal recoveryprojecton the environment; it not only provides an acceptablemeansfor disposingof the tainted produced-waterstream,but it also greatly reducesthe needfor fresh water. In areas wherewateris scarce,as in California,this reductionin the needfor freshwater is a very significant factor. Another advantageof water recycling is that the heat in the recycledwater reducesthe heat requirementfor steamgenerationsomewhat. 394
Oil and (
Na. K
SANO 8 WATER ' t otJp sYstEM|
{FJ
rcr comt
TABLE 8.5 q
Ca
tfc
't ti tZ
Analy'sesof a correspol once-throrr
Steam RecoveryEquipmentand Facilities
Chap.8
The pn dissolvedsol the water at from the lea material. In the t to removeth ica, althoug iron content Thesecondit vent the foru TableE basca.The a impuritiesan The lor peratures of t Essopilot at It seemslikel concentrali becomemore Recycling ftc
ProducedWater Analyses UAKE-UP PROC€SSWAIER ! _-._l-._
-.-
-
-1
Analysesof a typical producedwater samplefrom the Essopilot at cold Lake and a correspondingtreated produced water sample that is suitable for feeding to a once-through,oil field steamgeneratorare given in Table8.5. TABLE 8.5 Compositionof Producedand TreatedRecycleWater{l)at The LemingCold Lake Pilgt(2)
;;l
-E--- - 1 6 II.ER
^-\. :0 clflr.l
I F
i:
srmra I I rx ---te ll
---r
:tl Fl ;
o:i
IU :F
_15
m Vonde 1979)
dergroundreservoirs, rpliesmay be considncor,in their thermal :luent from a nearby
UNTREATED
ppm
TREATED
Oil and Grease 5,000-10,000 0-100(3) TDS 4,000-10,000 4,000-10,000 SS 10-120 0-5 Ca 4M0 0-1 Mg 4-8 0-1 Na, K 1,000-4,000 1,00H,000 CI 2,00M,000 2,000-6,000 SO+ 4U200 4V200 HCO: 10H00 0-r0 Sulphide 10+0 5-10 sio2 150-300 15-30 Temperature("C) 80=90 80-90 pH 7-8 8-9 (l)From ElectrostaticTreatersand Water RecvclePilot (2)Konak and Grisard(1979). (3)Suspended oil (usuallynear 0). There are alsoabout250 ppm dissolvedorganicmaterialsmeasured as total organic carbon (TOC\.
ery projecton the enposingof the tainted r freshwater.In areas reedfor freshwater is ng is that the heat in nerationsomewhat.
The producedwater containsrelativelylarge quantitiesof dispersedoil. The dissolvedsolidsare largelysodium chloride,arisingfrom the reservoirwater, but the water also containsappreciableamountsof hardnesssalts and silica, arising from the leachingof the reservoirrocks.There is alsosubstantialdissolvedorganic material. In the treatmentof this materialfor feed for steamgeneration,it is necessary to removethe suspended oil and the hardness.It is alsodesirableto reducethe silica, althoughconsiderablesilica can be toleratedif the calcium,magnesium,and iron contentsare kept low and if the wateris alkalinewhenit is fed to the generator. Theseconditionswill tend to keep the silica in solutionas sodiumsilicateand prevent the formationof insolubleiron, magnesium,and calciumsilicatescales. Table8.6 showsan analysisof producedwater from the Texacopilot in Athabasca.The analysisis similar to that from Cold Lake but the concentrations of the impuritiesare lower. The lower silica contentmay reflect the lower solubilityof silica at the temperaturesof the steamedreservoir;the Texacopilot is at a shallowerdepththan the Essopilot at Cold Lake, and one would expectthe injectionpressuresto be lower. It seemslikely that the lower levelof dissolvedsolids(salt)arisesbecauseof a lower concentrationin the reservoirconnatewater-possibly the original seawaterhas becomemore diluted by surfacewater.
d Facilities Chap.8
RecyclingProducedWater
ne,/soda softening,filus 1983).
trom steamrecovery rd a produced water it maybe recycledto
395
l
:l
ii
TABLE 8.6 ProducedWater Analysisfrom TexacoSteamfloodingPilot Near McMurrayAthabasca Qu"ntitutiu" AnulysesofDissolved
u Ptodrr.tion Wut"t"'
Sodium Potassium Calcium Magnesium Chloride Sulfate Aluminium Iron Silicon
529 11 56 20 820 80 <1 <2 47
(t)Milligrams of soluteper liter of solution at 23'C. (Burchfield and Hepler, 1979)
The water analysesshownfrom the Getty plant at Kern River, California,in Table8.7 showevenlessdissolvedsalt but are otherwiserather similar.
TABLE 8.8 Or
TABLE 8.7 Water Analysesfrom Getty's Kern River Operation JUNCTION WATER PLANT (mglkg) PHYSICAL ?LANT PHYSICAL PLANT INLET OUTLET
CONSTITUENTS Bicarbonates,HCO3 Chlorides,Cl Sulfates,SOa Sulfides,S Nitrates,NOa Silica,SiOz Boron, B Sodium,Na Iron, Fe Hardnessas CaCO3 Total dissolvedsolids pH value at25'C Conductivity: micromhos/cmat 25'C Resistivity:ohm-metersat 25"C
185 82 0.0 0.0 125 1.3 190 J.J
tt3 622 7.2 950 10.8
ferencein Ed ing was direo largeutility'ty ties and veqvI The pm treatmentof t the steamin I cussedprevid erabledissolx also remo\'6 t tation *'ith u A sirnpl plant expans summarizedir duction faciliti ing three parr
278 200 65 0.0 0.0 111 1.2 260 0.1 0.3 793 7.4 1150 8.9
cul
IGf, l@ IGF rld lor r
& Tr
sa pl
o
Sr
o (Peachey and llor
The waE OIL AND GREASES Freon extractables(solubleand insoluble) Millipore (insoluble)
50 20
20 0
(Carrell 1979)
Treating RecycledWater Various schemesfor the treatment of recycledwater were investigatedduring the developmentof the design for the large commercial plant at Cold Lake that was proposedby Esso.Thesewere discussed by Whalley and Wilsonat the Unitar Con396
Steam RecoveryEquipmentand Facilities
Chap.8
flotation cell.l pends upoo th located near tl and carn" thc as a foam. TL ter is treated s " I hls pftlc
treatmentof tGC The buildupof H of the facilitbrRecyclir€ ftod
$cMurrav Athabasca on Water(l)
rer, California,in ,imilar.
ferencein Edmontonin 1979(Whalleyand Wilson 1979).Much of this earlythinking was directed toward the developmentof schemesthat would allow the use of Iargeutility-type boilers becauseof the ability to build thesewith very large capacities and very high thermal efficiencies. The processfinally adopted(Figure 8.32)for use at Cold Lake involvesthe treatment of the recycledwater to remove oil and hardnessand the generationof the steam in multiple, once-through,oil field steam generators.As has been discussedpreviously,theseoperatewith low heat flux and are able to tolerateconsiderabledissolvedsolids,provided that the water is soft. The processadoptedby Esso also removesmuch of the silica from the feedwaterby adsorptionand/or coprecipitation with magnesiumhydroxidein the hot lime treater. A simplifiedflowplan of the treatmentsystemusedby Essoin their Leming plant expansionis given in Figure 8.33,and operatingconditionsfor the plant are summarizedin Table8.8. As has been mentionedpreviously,the commercialproduction facilities employedby Esso employonce-throughsteamgeneratorscontaining three paralleltube passes,which generateabout 160,000lb/h of steameach.
TABLE 8.8 OperatingConditionsfor Esso'sLemingWater RecyclePlant -ANT (mg/kg) PHYSICAL PLANT OUTLET
278 200 65 0.0 0.0 111 1.2 260 0.1 0.3 793 7.4 I 150 8.9
20 0
;tigatedduring the old Lake that was at the Unitar Con:acilities Chap.8
CURRENT REUSE PLANT OPERATION IGF inlet rate IGF inlet suspendedoil IGF outlet suspendedoil Hot lime treater inlet suspendedoil Ion exchangereffluent: Rate Total hardness Silica pH Chloride Sulphides Oxygen
fiom3/h 200ppm 21ppm 9 ppm 1oom3lh 0.2ppm 26 ppm 9.1 ppm 1600-2200 20 ppm 5 ppb
(Peacheyand Nodwell 1981;
The water from the primary separationof the oil is treated in an inducedgas flotation cell.8An apparatusof this type is shown in Figure 8.34. Its operation dependsupon the dispersionof small bubblesof gasby meansof centrifugal impellers locatednear the bottom of the contactstages.The bubblesof gasrise to the surface and carry the oil with them as adheringdroplets.At the surfacethey are removed as a foam. The equipmentshown contains four separationstages,in which the water is treatedsuccessivelv. tThis processis commonly referred to as inducedair flotation in other applications.In the treatmentof recyclewater, it is desirableto use a natural gas rather than air to reducecorrosion. The buildup of HzS in the gaswithin the processis a problemthat needsconsiderationin the design of the facilities.
RecyclingProducedWater
397
-: HARON€55 POI,ISHING
srtAM 'oJ,ll,i'lo,Ti^';'tf i,t'lf$'."' Figure 8.32 Conventional Oilfield Steam Generators (from Whallev and Wilson 1979) Figrrl
The water leavingthe inducedgas flotation cell is filtered and treatedin a hot-limetreater.In the hot-limetreatmentprocess,the water is softenedand silica is reducedby adsorptionand coprecipitationwith magnesiumhydroxide.A diagram of a hot-limetreater(of the type usedby Essoresourcesat cold Lake) is shownin Figure 8.35.The equipmentshown softensthe water, removesmuch of the silica. and alsoremovesdissolvedgases;a separatedeaeratoris not required. calcium is removedfrom solution as calcium carbonate,and magnesiumis precipitatedas magnesiumhydroxide.The chemicalreactionsare as follows: Ca(HCOr)z+ Ca(OH), : 2 CaCOt I + zHzO
I
llt
Dependingupt necessar!'to I carbonateor ti as sodaash(so feed, additime Feed----J' Coagulanl-J
Dirtybackwash from secondary filters and ion exchangers Caustic Sodaash
Lime
Mso
Figure E.33 Flowplan for Leming Water RecyclePlant (after peacheyand Nodwell 1981)
398
Steam RecoveryEquipmentand Facilities
Sludge Recyde hn I
Chap.8
RecyclingProdr
t5H ,FTT NI D
Anr
I I I I I I I I
l) iii._l--.
RAMT
-
,.. . IURNET
, {
to7. t ouAllTY SrtAr
LEGEND
FiTil werea orr ffi f-__-l ens
Whalley and
Figure 8.34 Four-StageInducedGas Flotation Cell (CourtesyNatco)
sd and treatedin a softenedand silica 'droxide.A diagram d Lake) is shownin muchof the silica, :quired. and magnesiumis rre as follows:
Mg(HCOr)z+ Ca(OH), : MgCO: * CaCO: I + 2 H2O MgCO3 + Ca(OH)r: Mg(OH), J + CaCO3 J Dependingupon the concentrations of the ionic speciesin the feed,it is sometimes necessaryto add other reactantsbesideslime to the hot-lime treater.lnsufficient carbonateor bicarbonateion in the feed is augmentedby the addition of carbonate as sodaash (sodiumcarbonate).Similarly,if there is insufficientmagnesiumin the feed, additionalmagnesiumoxide may be addedto adsorbsilica. Soda ash Feed
Magnesiumoxide
Coagulant
Gases to vent
Sludge
Watetpumpedfrom dirtybackwashcompt into reactionzone bypump notshovn
+
I Lime Dirtybackwash fromsecondary Recycle
Final deaeation
secondaryfilters Productstorage
Cleanbackwash ct|angers '1 ,esin)
^I-l
niee nte
I rg
tt2
slearn
generalion
:hey and NodSludge Product
Facilities
Chap.8
RecyclingProducedWater
Figure 835 Sludge-ContactHotProcessSoftener(after Bridle 1986)
399
The successfuloperationof a hot-lime treater requiresthe maintenanceof a sludge inventory of a proper consistency.chemicals may be added to promote coagulation. It is also very important to control the amount of oil in the feed to very low levels(lessthan 20 ppm). Failure to do this resultsin a putty-like sludge,which is ineffectiveas a contactingmedium. Followingthe hotJime treatment,the water is filtered to removesludgethat has beencarried over and is then given a "polish," or softeningtreatment,ln two stagesof ion exchangers. Conventionalion exchangetreatmentof water for boiler feed involvescontact with sodium"zeolite"resin.Although this resin is commonlycalledzeolite,it is no longermade from zeolite mineralsbut is usuallya sulphonatedcross-linkedpolystyreneresin.Calciumand magnesiumionsin the water exchangewith the sodium ions in the resin.As a result,the calciumand magnesiumin the waterare replaced by sodium.When the resinis spent,it is regenerated by contactwith a sodiumchloride solution.This is the sameprocessusedin domesticwater softening. With low dissolvedsolidsthe followinereactionsoccur: Softening:
bt
ftr
A reclc 230 individu (equipments ceousearth-( tion of the r (1979)for Ga
2 R - N a * + C a * * : R z - C a * *+ 2 N a + 2 R-Na* * Mg** : Rr-Mg** + 2Na*
R e g e n e r a t i o nR: z - C a * ** 2 N a + : 2 R - N a *
+ Ca**
In theseequationsR- representsthe sulphonateanionsin the polymeric resin material. The zeolite softeningprocesslosesits effect when the water that is to be softenedcontainsa high concentrationof sodiumions. In this circumstancethe equilibrium of the softening reaction is suppressedby the sodium ions already in solution,and the capacityof the sodiumform of the resin to removecalcium and magnesiumions is greatly reduced.This problem preventszeolite softening from beingeffectiveat Cold Lake. The softeningof high-brine-contentwater can be carried out using a weak carboxylic acid resin in which the acidic groups on the resin are carboxyiic rather than sulphonicacid groups.The disadvantage of this resin is that it is much more difficult and costly to regenerate.A two-stageregenerationwith acid and then caustic is requiredrather than the simplereactionwith brine. The processand the regenerationare shown by the following chemical equations: Softening
ProducdH frmgra{ oil ratsscpd
I
--J
I -T
oetra
I
-T
lI Sedin'€fletL
,--_lFbtr'Oa I
-T
2 R-Na* + Ca** : R z - C a * * + 2 N a *
-T I I
2 R-Na* * Mg** = R r - M g * t * 2 N a *
DiatomarA PressueC& F
Regeneration: 1. With acid Rz-Ca** + Z}l+ : 2 R - H * + C a * * 2. With caustic 2 R-H* + 2 NaOH = 2 R N a * + 2 H r O
I
Getty, at Kern River, has a very large water-recycleoperation using the processsequenceshownin Figure 8.36. 400
Steam RecoveryEquipmentand Facilities
Chap.8
Caoon
Steam
EdI't
g6FtE Fe€d
RecyclirgProd
the maintenanceof rc added to promote the feed to very low 'like sludge,which is
Depuralot
) removesludgethat ng treatment,in two leedinvolvescontact ;alledzeolite,it is no :d cross-linkedpolyngewith the sodium rewater are replaced with a sodiumchlosoftening.
r the polymericresin
Oxygen
Chomicals
Fegdwaierto steam
Callon exchangel
Dlatomaceousearth cake fllter
Figure 8.36 Getty's water-Recycleprocessat Kern River (after carrell 1979)
A recyclerate of 80,000tonnesper day is usedand the plant supplieswater to 230 individual steam generators.The processinvolves deoiling with a depurator (equipmentsimilar to an IGF), further flotation, and filtration through diatomaceousearth. Conventionalzeolite softeningis employedbecausethe salt concentration of the water is relatively low. Impurity concentrationsreported by Carrell (1979)for Getty'soperationare shownin Figure 8.37. lnsoluble Oil ppm
ter that is to be softcumstancethe equium ions already in removecalcium and olite softening from
Suspended Solids pPm
Hardness as CaCOa ppm
110
:d out using a weak re carboxylic rather rhat it is much more r acid and then causprocessand the re-
ation using the pro-
I Facilities
Chap.8
Steam generator Feed
RecyclingProducedWater
Figure E37 Compositionof Streams in Getty'sWater-RecycleProcess(after Carrell 1979)
401
Wastewater Management In a large steamrecoveryproject, there is a considerablecomplexityin the handling of the various water streams.The situation for the Esso project at Cold Lake has beendescribedby L.A. Courtnage(1987).Figure 8.38givesan idea of the factors that have to be considered.
Esso'sTtsr
COLD LAKE AREA WATER SALANCE fiESH
FRE3H WATEi
WATEI
FIETH
rTESX WATET
WATET
WAIEi
I I
In gcl sources.Th disposalof 1 scheduliryI equipmentf
ocxctallo]a
Esso hasdcr involveshet lowedby'tL in Figure8J Heatiq surfacesthd hot-limepro that it is des pH of the el Lim and Kq
rtE x PT@UCCD
WAITI
Experimenld0
DrsPoa^t Dl3?o3AL ExcE33 ttooucED
WATER C:
r:t nELO tioDucEo wA?El
REDUCINGTOTAL I
The water-ro and hardnes days of wata solvedsolids up the bulk o normal curdi In its co containing* containing25 out problems
oExEt^noil
tloDucED WATEI DIsFO3AL 3 ld b
a z NELO PRODUCED WA?Ei
I OEXEiATIOX
utrtt Figure 8,38 Water Flows for Esso's Cold Lake Facilities. Leming and May are Esso's Pilot Facilities; Maskwa and Mahihkan are Commercial Facilities (after Courtnage 1987)
402
Steam RecoveryEquipmentand Facilities
Chap.8
ReducingTote
exityin the handling ct at Cold Lake has n idea of the factors
In general, water is supplied from recycle and from various freshwater sources.The systemmust be managedto minimize freshwaterusageand minimize disposalof produced water (in deep disposalwells). There is also a considerable schedulingproblem involved becauseof the necessityat times to shut down major equipmentfor repairs.There can be both planned and unplanned shutdowns. Esso'sThermal Softening Process
',64\ rrFFuvr \
.:;16;-,/ -/
rlfl
I
L_] ?uxT | 3?E v
r'
I oex:rrnol
I noouc:o wattl
l* I
us?oalr.
J
Essohas describeda process(Lim and Konak 1985)for the softeningof water that involvesheatingthe water to a high temperatureby direct mixing with steam,followedby the removalof the precipitatedsolid by filtration. The principleis shown in Figure 8.39. Heating the feedwaterby using direct steamavoidsthe scalingof heat-transfer surfacesthat would occur otherwise.Removalof somesilica alsooccurs,as in the hot-limeprocessby coprecipitationwith magnesiumhydroxide.The inventorsfind that it is desirableto add causticsodaor sodiumcarbonateto the feed to bring the pH of the effluent into the range9 to 10. Someexperimentalresultsreportedby Lim and Konak are given next. ExperimentalData Reportedfor ThermalSofteningProcess AverageData from SevenTests ReactorTemperature211"C;Effluent pH 9.7 Feed ppm Productppm
REDUCING TOTALDISSOLVED SOLIDS The water-recycleprocessthat has been describedremovesoil, dissolvedoxygen, and hardnessbut doesnot reducethe total dissolvedsolids (TDS). From the early days of water recycling, there has been much concern over the level of total dissolvedsolids that can be toleratedin steamgeneratorfeed. Sodium chloride makes up the bulk of thesesolids.This has a high solubilityand will not crystallizeunder normal conditions. In its commercialoperationsat Cold Lake, Essois successfully recyclingwater containingabout 8000ppm of TDS. Thielen et al. (1988)demonstratedthat water containing25,000ppm of total dissolvedsolidscan be usedto generatesteam,without problems,in a test rig that simulatesan oil field steamgenerator.
ng and May are Facilities (after
d Facilities
Figure 8.39 Esso'sThermal Softening Process(from Lim and Konak 1985)
Chap.8
ReducingTotal DissolvedSolids
403
The removal of most of the total dissolvedsolids from water of even higher salinity can be done by methodssuch as evaporation,reverseosmosis,electrodialysis, and freeze desalination. This field has been reviewed by Zaidi, Kok, and Schmidt (1988);they have arrived at the following cost estimatesfor the production of 3000m3/d of once-throughoil field steamgeneratorfeed.
GAS STANT{' BUNilE
I
T
I
I
Vapor compressionevaporation Electrodialysis Freezedesalination
With Capital Depreciation
Without Capital Depreciation
2.07 1.66
1.01 1.05 0.80
I.JJ
-| \ -| coMBUSnOn =
ArR +
I I I !
It
(Zaidi, Kok, and Schmidt 1988)
\ For a water-to-oil ratio of 3 to 5, the costsof desalinationjust given would be $4 to $10per cubic meter of oil product.
I --vvRF-
IL- srr
ALTERNATESTEAM GENERATORS Coal-FiredSteam Generators In areaswhere coal is abundantit may be a more economicfuel for the generation of steamthan gas or oil. There has been considerableinterest in this possibility in Alberta and a number of ongoingjoint industry governmentstudieshave been described (Alberta Energy 1989). Two approachesare being followed. The first approachis the designof a new coal-burning, oil field steam generatorwhich will have a capacity of 180 million BTU/h and which will use feedwatercontaining a high concentrationof dissolved solids.Reactivesolidswill be injected into the furnace to absorb about40Voof the sulphur in the coal fuel. The secondapproachinvolves the designof a coal burner which can be addedto existingoil field steamgeneratorsas a retrofit. This too will involve a reduction of sulphur emissionsby employing a new type of slagging burner in which part of the sulphur is removedin the slag. Both approachesinvolve the useof pulverizedcoal. The first was proposedby CombustionEngineering Canada and would involve the coal being pulverized so that 70Vowould pass through a 200 mesh screen.The secondapproachwas proposedby Struthers:IlW; it would use micronizedcoal (i.e. coal ground so that 90%o of the coal would passthrough a 325 mesh sieve).A new Low NO^/SO, (LNSB) burner that has been developedby Rockwell International will be used.A diagram showinghow this burner would be connectedto a conventionalhorizontal oil-field steamgeneratoris shown in Figure 8.40.A project to demonstratethe operability of the concept has been initiated at the Esso operations at Cold Lake by the TransAlta ResourcesInvestmentCorporation. The project is expectedto be comSteam RecoveryEquipmentand Facilities
Chap.8
(SourcerLNS Ari!
Gr
TransAltaR6or6
t
plete in 1991 phur, are 03 existingemirr Downhole Sl
There has bcr field steamga duction of cd duction in ver There a
1. Low-pra relativdy ini:ctio late the I 2. High-pre rectlywil tion well
An inpo oxygen rath6 that the resuh
AlternateSteor
ater of even higher mosis,electrodialyy Zaidi, Kok, and r for the production
Cubic Meter Without Capital Depreciation 1.01 1.05 0.80
iven wouldbe $4 to
STEAMGENERATOR SKID
{Source:LNS Burneron EOF SteamGeneratorFeasibilityStudy, TransAltaFesourcesInvestmentCorporation,19BB)
:l for the generation in this possibilityin udieshave been dethe designof a new rcity of L80 million rtration of dissolved rb about 40Voof.the ign of a coal burner rtrofit. This too will rw type of slagging int wasproposedby being pulverized so I approachwas proground sothat90Va w NO"/SO" (LNSB) be used.A diagram rl horizontal oil-field atethe operabilityof Cold Lake by the lxpectedto be comI Facilities Chap.8
Figure 8.40 Low NO-/So- Burner Shown Retrofitted to a Horizontal SteamGenerator(from Alberta Energy)
plete in 1991,192. The emissiongoalsfor the programfor coal containing 0.36Vosulphur, are 0.3 lb of Soz and 0.2 lb of No, per million BTU; thesecompareto the existingemissionregulationsof 0.6 SOzand 0.6 NO" (0.2NO" for gasfuel). Downhole Steam Generation There has been a significant effort to develop downhole steam generatorsfor oil field steamgeneration.One of the main advantagesseenfor this approachis the reduction of well bore heat lossesand, becauseof this, improved economicsfor production in very deep deposits. There are two basic approaches: 1. Low-pressurecombustion,in which the downholecombustionis carried out at relatively low pressureand in which the flue gas products are vented up the injection well. This approachrequiresa heat exchangerdown the well to isolate the low-pressurecombustionzone from the high-pressuresteam. 2. High-pressurecombustion,in which the productsof combustionare mixed directly with the steamand passinto the reservoirto be collectedat the production wells. An important possiblevariation of the secondapproachinvolves the use of oxygen rather than air for the combustion.This also has the potential advantage that the resulting high concentrationof carbon dioxide may improve the effect of Alternate Steam Generators
the steamin recoveringoil. Considerations similar to this also apply to the use of oxygenfor in situ combustionand to the wet oxidation steamgenerators,such as the Zimpro equipmentthat is discussedlater. A majoradvantageseenfor the useof downholesteamgenerators with the direct injectionof the flue gasinto the reservoiris that the sulphurand nitrogenoxideswill be absorbedin the reservoir,either as anionsin the water or by the rocks directly; flue gasscrubbingis avoided. Figure 8,41 showsa cross-sectional diagramof the high-pressuredownhole steamgeneratordevelopedby Sandia National Laboratoriesin the DOE "Deep Steam"projectdescribedby B.W. Marshall (1982). The wallsof the generatorare cooledby the feedwaterthat flows from the annulus aroundthe "combustioncan" onto the wall at the lower part of the combustion chamber.Here it evaporates,and the steam mingles with the flue gases. Versionsfor using either air or oxygenhave been studied.Dieselfuel was used as fuel in the prototypemodel.
S e rc : r ; encedT . ::. rr low the ;,':::ir s m a l l - di r r : . u c: face is a i:.*J \ ; - , ,- ; - l
u ( ' F
- - ^
a period r,: .c flame ha: *;c: adding J :.. l( method: u,':i C h e m i c a ,O : T- f - n
r -.' "--"
w h e r ei t i r , : ; ; r c o m p l i c a t c . i:: may bectr::r l tion. rrhert ::r
Orldlror
Fluidized Bed
T h e u s et r : : . u of steam lh,1: : fuel is adcc; : m e a n so i t h . ; c atlon Zona
500 lr c.
o
Coollaj U.lot Flor
L
rroo 3 a t \l
rl
t 3 b
E
F
g
o o 300 -31 E a, o t
ttrExstox , I L D Lc
tt?* etr a!'
a.c' It'
I
E 200 -z 2, a
oryeon
o
o
t-
o
aa' a.t' a'
(l
100 ! t' UJ
o Figure 8.41 Sandia'sHigh PressureDownholeSteamGenerator(from Marshall 1982\
406
Steam RecoveryEquipmentand Facilities
o
Figurt I s h a i .- +
Chap.8
AlternateStea.
applyto the use of generators, such as
Severecorrosionresultingfrom the action of the sulphur dioxideswas experienced.This wascontrolledby the direct additionof causticsodato the producibelow the combustionzone. The causticwas conveyedto the generatorin a separate small-diametertube. The needto install severalseparatetubing stringsto the surface is a disadvantageof the downhole generatorapproach. A downholegeneratorof this type hasoperatedsuccessfully in Californiafor a period of severalmonths;performanceis shown in Figure g.42. Ignition of the flame hasbeenobtainedboth by meansof an electricglow plug or, alternatively,by 'botir addinga hypergolic(self-igniting)liquid, triethyl borane,to the dieselfuel; methods worked. Another high-pressuredownhole generator developed by the ChemicalOil RecoveryCo. (Eson 1982)is shownin Figure 8.43. up until now, downhole steam generation has not advanced to the point whereit is acceptedasa commercialalternative.The equipmentthat hasevolvedis complicatedand not competitive.Although the use of downholesteamgenerators may becomepracticalfor steamflooding,it is unlikely to be so for steamstimulation, wherethe periodicrequirementfor steamwould make it more expensive.
eratorswith the dirr and nitrogenoxrteror by the rocks pressuredownhole n the DOE "Deep f lowsfrom the anrart of the combusrth the flue gases. el fuel was used as
FluidizedBed Combustion Boilers The use of fluidized bed combustionboilers is another approachto the generation of steamthat may be of value in the recoveryof heavyoil. In theseboilers,solid fuel is addedto a bed of solid particles,which are maintainedin a fluid statebv meansof the combustionair stream.
500
TEIPERATURE
lr c
ft roo Et t
e
a b
t
E o
.P
E goo= 3 .l
t
F
€o
to zooo3
J
o
o L a roo C I tu
oAY t-IOYEIBER 30,t08t sTEAI OUAUTY-aOA
o
Figure 8.42 Performanceof Sandia'sDownhole SteamGenerator(from Marshall 1982)
from Marshall
Facilities
Tlmo,dryr to
Chap.8
Alternate Steam Generators
flrt gatar ro ccond a?EAr alo corluallofl rtooucla firo ratttolt
Figure 8.43 ChemicalOil RecoveryCompany'sDownhole Generator(from Eson 1982)
Limestoneis also addedto the combustionzone bed; it reactswith the sulphur oxidesthat resultfrom the combustionof the fuel to yield calciumsulphate, to add limestonein excessof the and this is removedas a byproduct.It is necessary stoichiometricquantity required to react with the sulphur. Three types of fluid bed combustorsare beingdeveloped:
Ftt{ col
1. Atmospheric-pressure combustors,in which the fluidized bed operatesat a pressureslightly aboveatmospheric. combustors, in which the gasesleavingthe combustionfurnace 2. High-pressure are used to drive a gas turbine. Although this approachis attractivefor the generationof increasedpower becauseof its higherpotentialefficiency,there has been trouble in obtaining reliable mechanicalturbine operation because of the entrainedsolidsin the gasstream. 3. A multi-solid fluidized bed generator,which is being developedby Battelle; this equipment is being promoted by Struthers Wells for the generationof steamfor thermal recovery(Berry 1979). A schematicflowplan for a multi-solid fluid bed combustionboiler is shown in Figure 8.44. Fluidized silica particles are usedto conveyheat from the combustion zone to the external boiler. These silica particles circulate from the combustion zone to the external boiler and then back to the construction zone when they become reheated.Separationfrom the fly ash is obtainedbecauseof the considerably higher densityof the silica ascomparedto that of the fly ash.The surpluslimestone and calcium sulphateare removedas a separatestreamfrom the fly-ash collector. Although more lime is used in this processthan would be required for a wet slurry flue gas treatment system,it is simpler to disposeof the dry solid product. Possibleusesfor the wasteinclude agricultural liming, a neutralizing agentfor municipal wastewatertreatment, and aggregatefor construction and road building. Other companiesinvolved in fluidized bed combustion(mostlywith a view to power generation) are Babcock Wilcox, BP, Riley Stoker Corp. (Worcester, Mass.), Foster Wheeler, Fluidyne Engineering, and JohnstonBoiler Co. (Ferrysburg, Mich.). Vapor Therm Steam Generators The Vapor Therm steam generationprocess(Sperry 1981)has been developedby Carmel Energy Inc. The principle is shown in Figure 8.45. An air and fuel mixture under a pressureslightly higher than the required steampressureis burned in an external combustionchamber,and the gasesare di408
Steam RecoveryEquipmentand Facilities
Chap.8
FIF Are I Z*
rectedinto tl directly to d ture of cnd generator(n mended by provide usc somecas€st ventional g! contain a il
AlternateSE
I
Fluc 9a*3 to ?conomirar
H
.?EAI AIO cor!ul'llofl rroDUCla irto flllorr
n Eson 1982)
reactswith the suld calciumsulphate, ionein excessof the
Entraincd bed
Fly-arh collectot
FlyrCr
bed operatesat a combustionfurnace is attractivefor the tial efficiency,there e operationbecause
Extcrnrl boiler
velopedby Battelle; rr the generationof
Distributor plate
r boiler is shown in :romthe combustion rom the combustion zonewhen they bee of the considerably he surpluslimestone rhefly-ashcollector. >erequired for a wet re dry solid product. alizing agentfor murnd road building. (mostlywith a view :r Corp. (Worcester, r Boiler Co. (Ferrys-
Dcnro bod
Air
t Distributor plate
Figure E,44 Battelle'sFluid Bed CombustionBoiler. Fluidized Solids Which Are Retainedwithin the Plant Circulate and Carry Heat from the Combustion Zone to the External Boiler (from Berry 1979)
er than the required and the gasesare di-
rectedinto the pool of boilingwater.The mixture of steamand flue gasis conveyed directly to the wells that are being steamed.The fuel that hasbeenusedis a mixture of crude oil and diesel fuel. There have been severalsuccessfultests of the generatoron a relatively small scale,and it is availablecommercially.It is recommended by Sperry for use where the high-pressureinert gas in the steam can provide useful drive in pressure.depletedreservoirs.Sperry also suggeststhat in somecasesthe output from the generatorcan be combinedwith steamfrom a conventional generatorto give a cheapermixture, which may, for some applications, contain a more optimum amount of inert gas.
I Facilities Chap.8
Alternate Steam Generators
s been developedby
409
F!€.
S- ]*tr
pump walerpump Fuelcontrolvalve orv35\
-ra J
t
Almoilhcdc ir
c0ntr0ller Inioction line Pressirre lo wells conlrol
Alr ry$om Air compressors anddnvers
bypass valve
Timsrconlrolled blorvdownvalve
Code &
Control vatves @ ritters
iryectron* Chemical ,,0.* ur,u* .Q eumos | valves tt Checkvalves & Relief @ Strainers
Figure 8.45 Carmel Energy'sVapor Therm Process(from Sperry 1981)
For the Vapor Therm processto be widely utilized, it will be necessaryto demonstratethat the addedcostof air compression and the usuallymore expensive fuel arejustified by improvedrecoveryperformance.It is an interestingidea. The Zimpro-AECSteam Generator The Zimpro-AEC steamgenerationis anotherprocessin which steammixed with flue gas is producedfor injection into the reservoir.However,unlike the Vapor Therm approach,this can utilize solid and other poor-qualityfuels. Poor-qualityfuels that come to mind for Canadianbitumen projectsinclude coal, petroleumcoke, coker cycle oil, residualcrude, and high-melting-pointasphalt. To be ableto disposeof suchmaterialsin an integratedin situ projectshould allow significantreductionsin the cost of upgrading. The principleof the processis shownin Figure8.46.It is basedupon technology that is well known in the disposalof aqueouseffluentssuchassewageand pulp mill effluents.Many commercialdisposalplantsare in operation.Fuel,water,and oxygen(or air) are introducedcontinuouslyinto a reactormaintainedat the steam pressure. 410
Steam RecoveryEquipmentand Facilities
Chap.8
Tnc ;c w a t e r . r rh : ; h within thc .r callr to ::cr Thc pr types anJ .ri s u l p h a t e :a n duces lt-lF. Di:;r,h; OI OX\9cli
ltr
product. -{h and it ha. itr e x p e n s lc\ . A cr:tx can be shrr\r t h a n s i m i . er o x r ' _ q e nu. h r p r o c e s s c$. h include h:el g e D € f 3i 0 tn
AI-sr R: .'.L r , R e c c t;r: i ,
(19re BAts( (x \ i:.:
(19-: B e n n r .R I Bttz Ha,:;tt
BroxH. .{ G . B O R R L Ti.:: : r . I irc--:.i.; Bibliog.ao. '
I
Flow so*r
tc tlrso0sAl
to wells ;. 5mosro -5.-N:D+>
;JH,, |"ils
controlvalve
' mntr0lle{t 0100wn valve
/Fr Frlters
.\ bi ta
Pumps valves Check
:r 1981)
ll be necessary to lv moreexpensive ;restingidea.
steammixedwith unlike the Vapor els. 'n projectsinclude -melting-pointassitu projectshould isedupon technols sewageand pulp r. Fuel,water,and iined at the steam acilities
C h a p .8
Figure 8.46 Zimpro'sWet-Air Oxidation Process(from AEC/Zimpro)
The conditionswithin the reactor are such that it is largely full of liquid water, which boils as a result of the oxidationof the fuel. The heat is liberated within the liquid phase.Unreactivesolidsand somewater are blown down periodically to preventaccumulation. The processhas the advantageof beingableto consumea wide rangeof fuel types and of avoidingpollution by sulphuroxides;the sulphurleavesas dissolved sulphatesand sulphiteswithin the water.The processcan useuntreatedwater,prodtces I00Voquality steam,and is potentiallyvery energyefficient. Disadvantages of the processare the needto compressall the combustionair or oxygento the steampressureand the corrosivityof the steam-carbondioxide product. Also, the reactorhas to be built from specialcorrosion-resistant alloys, and it has to havethick walls to withstandthe high pressure;thesefactorsmake it expensive. A critical factor in determiningthe successof this processwill be whetherit can be shownthat the steam-carbondioxidemixture is moreeffectivefor recovery than simplesteam.Also, it will haveto competewith wet, in situ combustionusing oxygen, which also generatesa mixture of steam and carbon dioxide. Other processes whosesuccessdependslargelyon the effectiveness mixtures of steam-gas include high-pressuredownhole steam generationand Carmel's Vapor Therm generation. BIBLIOGRAPHY Boilerfor SteamInjectionin HeavyOil of a Coal-Fired Ar-BpRra ENencv,"Development PubNo I/293,Edmonton, andTechnology, Recovery," AlbertaOfficeof CoalResearch (1989). andUse,NewYork:BabcoxandWilcoxCo., BescocrandWrlcox,Steam-ItsGeneration (r97D. O 1979SPE. Benny,R. I., "Fluid-BedGetsthe Nod,"Chem.Eng.,60-62(Oct.8,1979). (1980). Trevose, Penn.: Bnrz Handbookof IndustrialWaterConditioning,8th Ed., Hemisphere Pub.Co.(1988). BLoru,A.G., HeatTransfer in Steam BoilerFurnaces, Bonnecares,C. J., "SteamSoakon the BolivarCoast,"in The Oil Sandsof CanadaVenez uela,CIM SpecialVolume17. 56I-583,1977). Bibliography
411
li
ll
fl
I
n rJ I
Bnrole, M. K., "Esso'sExperiencewith Producedand waste water RecycleSystems,"3rd Annual HeavyOil and Oil SandsTechnicalSymposium,Challenges and Innovations,University of Calgary,Calgary,Alberta (February 19, 1986). Buncurtnlo, T. E. and HEPLen,L. G., "SomeChemicaland PhysicalPropertiesof Produced Waterfrom an In Situ Oil SandsPlant,"In Situ 3, no.4:383-390(1979). BUnKILL,G. C. C., "Thermal Well CompletionDesignwith OpenholeGravelPackedLiners and Methods for selective Steam Injection," The oil sands of Canada-venezuela,clM SpecialVolume17, 595-608,(1977). CaRRELL, N.A., "ReclaimingProducedWatersfor SteamGenerationin the Kern River Field," SPE84tL (1979). CHUNG, K. H. and ButLen, R. M., "GeometricalEffect of SteamInjectionon the Formation of Emulsions in the Steam-AssistedGravity Drainage Process,"JCPT, 36 (JanuarylFebruary 1988). Convrnn, K.W., "InsulatedTubing at Shell'sPeaceRiver Project,"4th Annual Heavy Oil and Oil SandsSymposium,Universityof Calgary,Calgary,Alberta (February18, 1987). CountNace,Lisa A., "Water ManagementChallengesat Esso'sCold Lake Operation,"4th Annual Heavy Oil and Oil SandsSymposium,University of Calgary,Calgary,Alberta (February18, 1987). DeLIneRr,J. C., "SteamBoilers," in Marks StandardHandbookfor MechanicalEngineers, gth Edition, McGraw Hill (1987). DoscueR,T.M., LaspLLn,R.W, Sewersrv,L.H., and Zwrcrv, R.W., "Steam-Drive-A Processfor In-Situ Recoveryof Oil from the AthabascaOil Sands,"K.A. ClarkVolume, 123-141,Edmonton,Alberta: ResearchCouncil of Alberta, Information SeriesNo. 45 (1e63). ELrenn, J., "The ChamberPump and its Applicationto Hot Wells,"ASME 76-Pet-91, presentedat Joint PetroleumMechanicalEngineeringand PressureVesselsand PipingConference,Mexico City (September19-24, 1976). ELGERT, B. D., CuerranERs, N. A., and Suzurr, F., "Cold Lake Artificial Lift Optimization," 6th Annual HeavyOil and Oil SandsSymposium,Universityof Calgary,Calgary,Alberta (March 8, 1989). EsoN,Rod L., "DownholeSteamGenerator-Field Tests,"SPE10745(March 1982\.@ 1982 SPE. FINARITIS, J. P. and KruuEL, J. D., "Review of OnceiThroughGenerators,"JPT, 409-416 (April 1965). Fenoue Ar-r, S. M. and MeLDAU,R. F. "Current Steamflood Technology,"IPT, 1332-L342 (october 1979).O 1979SPE. Gerns,C. F. and Bnewen,S.W.,"SteamInjectioninto the D and E Zone,Ttlare Formation, SouthBelridgeField, Kern County,California,"IPT,343-348, (March 1975). GatEs,C. F. and Holt"res,B. G., "Thermal Well Completionsand Operation,"PaperPD1l, 7th World PetroleumCongress,Mexico City (1967). HoNc, K. C., "Two-PhaseFlow Splittingat a Pipe Tee,"JPT, 290-296,(Feb.1978). IN.tpeRtaLOrLLrrvrrreo, "The Cold Lake Project,"Appl. 770866to Alberta EnergyResources ConservationBoard, May 1978. KneI-rNG, L., "Venting Well Casingsat Cold Lake," Heavy Oil and Oil SandsTechnical Symposium,Universityof Calgary,Calgary,Alberta (February20, 1985). Kenny, S.L., Krusn, K. and Peecuey,B. R., "Upgradingof Oilfield SteamGeneratorPerformance,"Heavy Oil and Oil SandsTechnicalSymposium,Universityof Calgary,Calgary, Alberta (February,1984). 412 Steam RecoveryEquipmentand Facilities Chap.8
Kirk-Orhnr t (1978-:r Kroeprri. J ( Oil Pr.rc.r' Petroleun Koxex. .{ R 5 2 2 .l 1 : l q Kox.rx. A R 5 7 1 .E : - i ! Koxer. A R ft 80-31-1"'.
LESCHIsi:-.r. HeavvO:- i
Lru, G. B .5t Scatterrr.tI Alberta Ftt Ltv. G. B ":, SPE.
MansH.c::-B 107-1.:,\l::, Meloer-. R F Complel:.r: Sands L'\l the Caia.:i Mrlrrn. R \*
Pelrt. J.\\ . .{ :-^
lllEl
^^ dll
n--f. v.
-1J
PracHrr. B I No. t-l--:i-r 198-lr.
PEecurr.B I Semrnar..r 24-16. :q.1 p"rs916.. rr E ing Oii F:tu
Saea. \ .ir:.: I Conduit:. Snevrrr Jn . I with Oill:e Spennr'.J. S . Region." f)
Srrrsour,. ll 901-9{r- :. Tirrelrr. \\ . Using Hrrl: ence on He
V E n H o n r .F l Progress.' Bibliograpf-y
cycle Systems,"3rd d Innovations,Unirpertiesof Produced 79). ravel PackedLiners rda-Venezuela, CIM in the Kern River )n on the Formation ' ICPT, 36 (JanuAnnual Heavy Oil kbruary 18, 1987). rke Operation,"4th y, Calgary,Alberta chanical Engineers, .. 'Steam-Drive-A K. A. Clark Volume, ation SeriesNo. 45 preSME TGPet-91, cls and Piping ConLift Optimization," qv, Calgary,Alberta March 1982).O 1982 uon," /P?i 409-416 gy," JPT,1332-L342 e, TulareFormation, ch 1975). ration," PaperPD11, (Feb.1978). ta Energy Resources oil SandsTechnical
ts5). team GeneratorPersity of Calgary, Calracilities
Chap. 8
Kirk-Othmer Encyclopediaof Chernical Technology3rd Ed., Volume 24,369 (1984),Wiley (1978-84). KLoerrun, J.G., CaRo, R., and Kus, J., "ProcessDesign for the Re-Useof Wastewaterfor Oil Production," Presented at AOSTRA's 4th Annual Conferenceson Advances in PetroleumTechnology,Calgary,Alberta (May, 1983). KoNlr, A. R., "Method and Apparatusfor Splitting Two-PhaseFlow at Pipe Tees," US, 4, 522,2t8 (1985). KoNar, A. R., 'Method and Apparatusfor Splitting Two-PhaseFlow at Pipe Tees," US, 4, 574,827(t986). KoNer, A. R. and Gnlseno, P. J., "Deoiling of ProducedWaterby Acidification," PaperNo. 80-31-30,PetroleumSocietyof CIM, Annual Technical Meeting, Calgary,Alberta (1980). LescuysHyN, T. and Seyen, W., "In Situ Oilsands Temperature Logging," 6th Annual Heavy Oil and Oil SandsTechnical Symposium,Calgary,Alberta (March 8, 1989). Lrru,G. B., "SteamQuality Surveyat Esso'sCold Lake Pilots Using a Non-IntrusiveNeutron ScatteringDevice," Heavy Oil and Oil SandsSymposium,University of Calgary, Calgary, Alberta (February20, L985). Lru, G.B. and KoNar, A.R., "Thermal SofteningProcess,"US 4,518,505 (1985).O 1985 SPE. MensHnLL, BrLlv W., "Operational Experiencesof a Downhole Steam Generator," SPE 10744(March 1982). MELDAU,R.F., "Reducing Well Bore Heat Loss," Reprints of papersin the Thermal Well CompletionsSeminarheld at the 4th International Conferenceon Heavy Crudes and Tar Sands(UNITAR), Edmonton, Alberta (August 7-12, 1988).Presentedand publishedby the CanadianHeavy Oil Association. MrLren, R.W., F/ow MeasurementEngineeringHandbook, McGraw Hill (1983). Pelrra,J.W., ANoersoN,W. H. and KtnrretRtcr, J.W., "Determination of SteamQuality Using an Orifice Meter," JPT, 587(June 1968). PeacHry, B. R., "Design Conditions for Very Large Oilfield Steam Generators," Paper No. 84-35-81,PetroleumSocietyof CIM, Annual TechnicalMeeting, Calgary(June 10-13, 1984). for Heavy Oil In Situ Pilots," Peecuey,B.R. and NoowerL, J.A., "DesignConsiderations and Upgrading, Calgary, Alberta (March in Petroleum Recovery Advances Seminar on 24-26,1981). Organizedby AOSTRA and CANPET. Pr,rnolrull ExrnxsroNSenvrcr, University of Texasand API Division of Production, Treating Oil Field Emulsions,3d Ed. (1974). Sasa,N. and Lenr,y Jn., R.T., "The Analysis of PhaseSeparationPhenomenain Branching Conduits," Int. J. MultiphaseFlow, 10, No. I p l-20, (1984). SNavelvJn., E. S. and BEntNnss,T. A., "Removal of Sulfur Dioxide Emissionsby Scrubbing with Oilfield-ProducedWater,"IPT,227-232 (Feb.1975). SrEnRv,J. S., "Heavy-Oil RecoverySystemCompletesThree Field Testsin Mid-Continent Region,"OiI GasJ., 225-237(htly 27, 1981).O 1981SPE. SrrrNoun, H.H., "The Rate of Sedimentation,"Ind. Eng. Chem., 36,6L8-624,840-847, 901-907 (1944). F., "SteamGeneration Tnrer-eN,W., Walorr.teNN,H., MontceL, M., PADnoN,and CarraacHo, Using High TDS Water and Heavy Fuels," Paper183,4th UNITAR International Conference on Heavy Crudes and Tar Sands,Edmonton, Alberta (August7-12, 1988)' VrnHorE, F. H. and BaNcueno, J.T., "Predicting Dew Points of Flue Gases,"Chem. Eng. Progress,70,No. 8,71-72, (Aug. 1974). 413 Bibliography
VoNor, T. R., "SpecializedPumpingTechniquesApplied to a Very Low Gravity Sand-Laden Crude, Cat Canyon Field, California," 1st UNITAR Conference,Edmonton, Alberta (June 4-L2, 1979),rcported h The Future of Heavy Crudes and Tar Sands, New York: McGraw-Hill (1981),574-585. Weuor, R. E., "Review of StackGas ScrubberOperatingExperiencein an Oil-Fired Steam Generator," SPE,7125(1978). WuaLLev, M. J. and WILSoN,T. M., "Water Conservationin a SteamStimulationProject," 1stUNITAR Conference,Edmonton,Alberta (June4-12, 1979),reportedin The Future of Heavy Crudesand Tar Sandq New York: McGraw-Hill (1981),734-738. WtLLwHItr, G. P. and DIetnIcu, W. K., "DesignCriteria for Completionof SteamInjection Wells,"JPT, 15-22 (January1967). WILsoN,T. M., "SteamQuality and Metering," Preprint 26th Ann. Tech. Mtg. of the Pet. Soc.of CIM, Banff, Alberta, June 11-13,(1975). WorcesHyN,G., ManrrN,W., MoNrrN,J., YueN,P., and MeNzeNo,J., "SteamQuality Measurementsby NeutronTransmission,"3rd UNITAR/UNDP InternationalConferenceon HeavyCrude and Tar Sands,Long Beach,Calif, July22-31, 1985.pub. by AOSTRA, Edmonton (July 1988). WoIcesHvN,G. E., YueN, P. S., JosN,H., and M,qNzaNo-Rurs, J. J., "Measurement of Steam Quality, Mass Flow Rate and Enthalpy Using CombinedDensitometerand Nozzle," SPEI DOE 14907(re86). Zxor, A., Kor, S. and Scsrurpr,J.W.,"ProcessOptionsfor Recycleof High TDS Produced Waterduring In Situ Recoveryof HeavyOil," in R. F. Meyersand E. J. Wiggins(Editors), The Fourth UNITAR/UNDP InternationalConferenceon Heavy Crude and Tar Sands, Vol3: Mining, Drilling, AOSTRA, Edmonton,(1989),pp 449-465.
In Si
INTRODUCTrc)
In steamfl without prr erator,in tl A significa and overbu depleted. Estim heat losses and from th in the fuel i
TABLE 9.1 !
SteamGencn Transmissio Flow do,rn r, Flow in rescr condensa (trl-oss =
l-Ct
\\'ithi steam temp front. Beca the front hi 414
Steam RecoveryEquipmentand Facilities
Chap.8
r.Gravity Sand-Laden , Edmonton,Alberta 'ar Sands,New York: in an Oil-Fired Steam StimulationProject," rportedin The Future f738. ion of SteamInjection ech. Mtg. of the Pet.
In Siru Combustion
, "SteamQuality Meattional Conferenceon ub. by AOSTRA, Ed'{easurementof Steam ter and Nozzle," SPEI f High TDS Produced .-J. Wiggins(Editors), Crude and Tar Sands,
INTRODUCTION In steamflooding,a considerableamount of the energygeneratedby the fuel is lost without providinguseful heat in the reservoir.There are lossesin the steamgenerator,in the steamtransmissionlines,from the well bore, and to the overburden. A significantfactor is that in steamflooding,it is necessaryto keep the reservoir and overburdenheatedbehind the condensationfront even after the oil has been depleted. Estimatesof the rangesof the variousheatlossesare shownin Table9.1.The heat lossesfrom the steam-generation facilities, from the steam distribution lines, and from the well borewithin the overburdencan amountto over half of the energy in the fuel and even in favorablecircumstances,to about one-quarterof the energy. TABLE 9.1 Steamflooding-ThermalEfficiencyBasisHeatingValueof Fuel = 100
SteamGenerator Transmissionto well(t) Flow down well to reservoir Flow in reservoirto condensationfront (r)Loss270 Btulh ft of insulated6-in. pipe.
VoEf.ficiency of Step
ApproximateRange Cumulative
75-85 75-95 80-95
75-85 56-81 45-77
25-75
I 1-58
Within the reservoir, it is necessaryfor the steam-sweptregion to remain at steamtemperatureso that the steamcan condenseat the advancingcondensation front. Becauseof this, the heat lossesfrom the steam-sweptregion continue after the front has passed. Facilities
Chap.8
415
With in situ combustionthe situation is different in that there are no heat lossesuntil the oxygenin the injectedgasreactswith the fuel at the fire front. Heat behind the front preheatsthe advancingair, and there is thus someconservationof heat. This effect is enhancedin wet combustionby the addition of water to the injected air. The water coolsthe sweptreservoirbehind the front, boils, and then supplies steamthat passesthrough the combustionfront and condensesfarther along, where it preheatsthe reservoir aheadof the front. In situ combustionthus has featuresthat give it the potential for being more efficient and economical.The fuel for in situ combustioncomesfrom the residual material in the reservoir and there is no need to supplycombustionfuel. However, it is necessaryto provide energyto compressthe air and if oxygenis used,to separate the oxygenfrom the air:.This energyfor compressionor, in the caseof oxygen, for separationand compressionis much lessthan that requiredfor steamgeneration. In Table 9.2, the fuel requirements(excludingthe in situ combustionfuel) for in situ combustionwith air or with pure oxygenare comparedto that for thermal recovery using steam. The basis for the comparisonis the supply of a constant amount of heat, 1 million Btu, to the reservoir.The quantity of steamgeneration fuel is comparedto that required to compressthe air or to separateand compress the oxygen. It is assumedthat the compressedair or oxygen must be supplied at 1000psig. The column headedefficiency in the table relatesthe amount of heat supplied to the reservoirto the amount of energy,assumedto be suppliedas natural gasfuel
TABLE 9.2 Fuel Requirementsto Supply 1 Million Btu to Sand Faceat 1000psig EFFICIENCY Vo
FUEL REQUIRED Millions of Btu
ENERGY COST $/Million Btu in Res.a
Steam(r) 45-:77 L.J-Z.Z 2.6-4.4 Air in situ combustion(2) 190 0.5 1.0 Oz in situ combustion(3) 315 U.J 0.6 (l)Based on Table 9.1. (2Assuming compressordriven by gas engine: o Engine efficiency 34Vobasedon LHV of 908 Btu/SCF for CH+; o Compressordrive requirement6.35 HP h/1000SCF; o Heat of combustion100Btu/SCF of air (476Btu/SCF of 02). (3)The rnechanicalenergyrequiredto separate1000SCF of air is approximately2.9 HP-h. 02 requiredto generate1 million Btu is 2101SCF. This can be producedby separating210U0.21= 10,004SCF air.
Work HPh Air separation 02 compression
to fire the bd the oxygen-O the steamofl 23% to 39%o For oq6 air injectim.l be compresr liquificatim I small compo Inamd to about lfr) p (Newton 1979 to that for sct Thecd to $1 for in rl bersdo not tJ In qic widely used d production ir In lHl of 6525 !fl.
qo (101,000
California. In situ q in controlliq steamfronts, t thelessth€rc I
,m
x
Equivalent Fuel Btu
29.0 13.3
2r7,t60 99,904 317,064
(a)Fuel cost assumedto be $2/Million Btu. Capital costsare not included.
416
ln Situ Combustion
Chap.9
Introductiqt
here are no heat refire front. Heat reconservationof rf waterto the inils, and then supsesfarther along, ial for being more from the residual on fuel. However, n is used,to separe caseof oxygen, steamgeneration. mbustionfuel) for ) that for thermal ply of a constant 'steam generation rate and compress ust be supplied at nt of heat supplied as natural gasfuel
psig ENERGY COST S/MillionBtu in Res.a
to fire the boiler, to fuel an engineto compressthe air or to separateand compress the oxygen.On this basis,the in situ combustionoptions comparevery favorablyto the steam option. In this comparison air in situ combustionrequires only about 23Voto 39Voof the fuel neededfor steam' For oxygeninjection, the potential fuel savingsare evengreaterthan thosefor air injection. The reasonfor this is that only about one-fifth as much gas needsto be compressedto 1000psig. Although it is also necessaryto separatethe air by liquification and distillation, the energy requirementsfor doing this are relatively small comparedto those for high-pressurecompression' In a modern tonnageair separationplant, the air feed needsto be compressed to about 100psia, and this work suppliesessentiallyall of the energyfor separation (Newton 1979).Acomparisonof the energyrequiredfor the compressionof the Oz to that for separationis shown in the footnotesto the table. The cosi of the energyfor supplying1 million Btu to the reservoiris only $0.60 to $1 for in situ combustionas comparedto $2.60to $4.40for steam.Thesenumbers do not take into accounteither the capital costsor the nonfuel operatingcosts. In spite of the potential advantagesfor in situ combustion, it is much less widely used than steam.Figure 9.1 showsthe resultsof a survey of thermal EOR production in the USA. In 1988there were nine commercialU.S. ISC projects,having a total capacity of 6525 B/d. The largest U.s. steam projects were those of Shell, Belridge (101,000B/d) and Texaco Kern River (87,600 B/d), both in Kern county, California. In situ combustionhas found lesssuccessthan steambecauseof the difficulty in controlling the process.Fire fronts tend to advancemuch more erratically than steamfronts, and it is much harder to obtain an even sweepof the reservoir.Neverthelessthere are successfulin situ combustionprojects'
2.6-4.4 1.0 0.6
T H E R M AE L O RI N U S A kB/D
Doto 3ource Oil ond Gos J' Apill 18' 19EE
ISC I 77 Sleom :lv 2.9 HP-h.
Equivalent FuelBtu ?17,160 99,904
1980 1982 1984 1986 Yeor
317.064
'1988
Figure 9.1 Oil ProductionUsing Thermal EOR in USA
nbustion
Chap.9
lntroduction
417
In the i perature Flril
DRY COMBUSTION Description of Phenomena
illOI€ prO0trul
Figure 9.2 showstypical temperatureand saturationprofilesfor a dry combustion processcarriedout in a laboratorycombustiontube.The term dry meansthat water is not introducedintentionallyinto the reservoir.The gassaturationat a distance aheadof the front is high enoughto allow the combustiongasesto flow to the production end without undue pressuredrop. This is frequentlyalreadythe casein laboratoryexperimentswhere the tube has been filled by packing.Somedistance beyondthe front, water is condensing,and the oil is sweptforward by the gasand steam.If the initial gas saturationis high, the oil displacessomeof the gas and forms an oil bank. If there is a low gassaturation,the initial gasflow tendsto displace oil and build gas saturation.Under these circumstances, injectivity for air may be very low. Immediatelybeyondthe combustionzone,residualoil losesvolatile material nonvolatiledeposit,coke.It is and cracksthermally,leavingbehinda carbonaceous, this coke that providesthe fuel to reactwith the injectedair. At the fire front, the temperatureis at maximum. Upstreamof the front, the temperaturefalls because of the coolingeffectof the injectedair. Downstreambeyondthe front, the temperature falls as the heat carried forward by the flowing gasis consumedheatingthe reservoirand residualoil and by supplyingthe heatsof crackingand evaporation.
almost at'.ca The rr other po:.:hi Parrish ,19r] (see,for cr.'r I n r c re t same manner reversed. -..-.t can be comp then carrr l::i The com'ouq Such .: ; v i s c o u st ' i t u n does not h.rrr Ther* : SAGD prNi! SAGD prrxc' w h e r e a si r ; i ber has tr.rLtl
TgVEfS€ CON:]I f hp T€mp€rature profile
I I
nrnri.,.---
cold reserr.': Un fo;l u u s u a l l v p r o re near to lhc :r i s d e s c r i b e ii ; for oil sand..
Propagation of tho tront
Combustisr c
., .; I
o
ttl
6
Saturalion profil6
lll
There harc b bustion tuhct In oriicr of the comi"u with reier\ rli
I 6
B
t
Figure 9.2 Temperature and Saturation Profiles in Dry Forward Combustion (from Latil 1980)
418
In Situ Combustion
Chap.9
DryCombrs:
for a dry combustion dry meansthat water :uration at a distance es to flow to the proi already the case in ;king. Somedistance rward by the gas and some of the gas and gasflow tends to dises, injectivity for air osesvolatile material ile deposit,coke.It is At the fire front. the )€rature falls because lrefront, the temperaonsumedheating the ing and evaporation.
...............,..---...__..--x
6 d
In the condensationregion beyond the fire front, there is frequently a temperature plateauthat correspondsto the condensationof the steam.This is much more pronouncedwhen considerablewater is present;in dry combustionit may be almostabsent. The processshown in Figure 9.2 is known asforward dry combustion.Another possibilitycalled reversecombustion(Tranthamand Marx (1966;Berry and Parrish (1960) has received attention and has been investigatedexperimentally (see,for example,the laboratory studiesdescribedin Wilson et al. 1963). In reversecombustion,as shown in Figure 9.3, the processis startedin the samemanner as for forward combustion,and then the direction of air injection is reversed,so that the original injector becomesthe producerand vice versa.This can be comparedto smokinga cigaretteby lighting it in the normal manner and then carryingon the combustionby blowinginto the cigaretteratherthan sucking. The combustionzone movesup the cigarettebut againstthe flow of air. Sucha processwasthoughtto be particularlysuitedfor the productionofvery viscousbitumensand tar becausethe producedfluid remainsmuch hotter and it doesnot haveto be forcedthrough the unheatedreservoiras in Figure 9.2. There is an analogybetween the reversecombustiondescribedhere and the SAGD process(seechapter 7), in which the injectoris closeto the producer.In the SAGD process,the produced oil remains hot as it flows to the production well, whereasin conventionalsteamflooding,oil that is displacedfrom the steamchamber hasto flow througha coolerreservoirto reachthe productionwell. Similarly,in reversecombustion,the displacedoil flows through the hot burned zone to reach the producer. In forward combustion,the displacedoil must be forced through a cold reservoirto reachthe productionwell. This is very difficult in cold tar sands. Unfortunately, practical attemptsto use the reversecombustionprocesshave usually proven to be unsuccessfulbecauseof the formation of new flame fronts nearto the injector.Theseare ignitedby spontaneous combustionin a mannerthat is describedlater.Reversecombustionis an ingeniousideawith attractiveincentives for oil sands,but it has turned out to be unsuccessful (Dietz and weijdema 1968). Gombustion Tubes There have beenmany studiesof in situ combustionin the laboratoryusing combustiontubes.A recentdesignis shownin Figure 9.4 (Moore et al. 1987). In order to minimize the effect of the heatcapacityand thermal conductivity of the combustiontube, it is constructedwith a very thin wall. The tube is filled with reservoirmaterial, and air or oxygen is passedthrough it. Combustionis Produced fiu fluids
Figure 9.3 The ReverseCombustion ConceDt
d Combustion (from
lombustion
Chap. 9
Dry Combustion
419
I
f
l!
f3 N N lr
L
WATER STORAGE BURETTE
2 . W A T E RP U M P 3. C O M B U S T I O NT U B E 4. 5. 6.
PRESSUREJACKET HIGH PRESSURESEPARATOR T E U P E R A T U R EC O N T R O L L E D LOW PRESSURESEPARATOR CONDENSER GAS SAMPLINGVALVE PROCESS GAS CHROTATOGRAPH WET TEST METER
*ro o ()
g lt
:.
!
o o !
ir E o 6
REGULATOR L+{ PRESSURE olucg O pRessune -{ CONTROLVALVE] MASS E SENSOR J FLOW
S cnEcxvlwE O FILTER --FN HoKE vALvE
I caeuuanv t reEole vluve Figure 9.4 University of Calgary in Situ CombustionApparatus (from Moore et al. 1987)
started from one end, and the progressof the combustion is followed by means of thermocouplesand produced gas analyses.Ignition is usually accomplishedby meansof an electricresistanceheater. The thin-walled combustion tube is contained within a strong outer vessel that can withstandthe desiredoperatingpressure.The annularspacebetweenthe tube and the pressurevesselis filled with insulationand with a gasunder a pressure high enoughto support the weak inner tube. A major considerationis the minimization of heat loss from the tube so that the adiabaticconditions within a large reservoir can be simulated.In some tubes this heat lossis minimizedby insulationalone;in others,short compensating electrical heatersare placedoutsidethe inner tube and controlledin order to minimize the temperaturedifferences.A problem with this sort of systemis causedby the possibilityof leading,or "helping," the combustionif the externalheatersget too hot. Sincethe axial temperaturegradientscan be quite steep,it is desirable,if external heatersare to be employed,to use numeroussmall heatersso that the internal gradient can be duplicated. The designof the adiabaticcompensatingheatershas been studiedby Leaute and Collyer (1984).They haveshownthat it is important to use a high gradeof insulationbetweenthe heatersand the tube and to employnarrow heaters.The large effects of thesevariablesare shown in Figure 9.5, which is taken from their paper. It is usually found desirableto employhigher front velocitiesin the laboratory than would be found in the field so that the heat lossproblem in the laboratoryapparatuscan be minimized. It is customaryto operatecombustiontubesin a vertical position so that gravity will not causeoveride.Another approachthat has beenusedis to make the tube horizontalbut to rotateit so that the effectsofgravity are canceledout (Latil 1980). 420 In Situ Combustion Chap.9
o cl
-E. o o. I
o ;2.
t' 3
g
a
E
titr.r ancco Usin3 t Lcogr MINT Matcr
Figures obtainedin e 21'API oil. Figure 9 very sharp gn istic. A tempe tion of water, r the steampla ally to the air. As may I rate movesal slowlythan th The prod main point of ing of the dl ahead of thc r creasedoil sat voir were nea gas saturatio tion end. [n tl the gas flood I beyond a stea Dry Comhrstir
O R A G EB U R E T T E IP ,X TUBE .IACKET iSURE SEPARATOR URE CONTROLLED SURE SEPARATOR R .ING VALVE 6A5 CHROTATOGRAPH ' HETER
N 100 0)
EBo 6 6
o
*60 E c, tt,
o
RESSUREREGULATOR RESSUREGAUGE O}ITROLVALVEI MASS ENSOR J FLOTY I€CK VALVE ILTER OKE VALVE
.E 40 o
a
3ro E
APILLARY EEOLE VALVE
ls (from Moore
s followed by means ally accomplishedby a strong outer vessel ar spacebetweenthe r gasunder a pressure rromthe tube so that rlated.In sometubes rt compensatingelecin order to minimize tem is causedby the ternalheatersget too , it is desirable,if exters so that the inter:enstudiedby Leaute se a high gradeof inow heaters.The large ken from their paper. itiesin the laboratory in the laboratoryappositionso that gravd is to makethe tube ;eledout (Latil 1980). )ombustion Chap.9
0.05
0.'l 0.2 0.3 0.4 Combustion Front Velocity (ftlh)
0.5
Figure 9.5 CalculatedEffect of Heater Width and Insulationon the Performance of an Electrically Heated 3-in. Diameter Adiabatic Combustion Tube. Using a MathematicalModel the Authors Investigatedthe Effect of Varying the Length of the HeatedZones and of Using a SuperiorInsulation(Johns-Manville MINK) Which Has One-Thirdof the Thermal Conductivityof the Standard Material (after Leaute and Collyer 1984).
Figures 9.6 through 9.10 from Penberthyand Ramey (1966)show results obtainedin a classiccombustiontube experimentusing a 5-darcysandpackand a 21'API oil. Figure 9.6 showstemperaturemeasurements from a typical experiment.The very sharp gradient aheadof the advancingcombustionfront is a notablecharacteristic.A temperatureplateauaheadof the front, which corresponds to the condensation of water,can alsobe seen.This is causedby the connatewater in the sample; the steamplateaubecomesvery much more pronouncedif water is addedintentionally to the air. As may be seenfrom Figure 9.7, the burning front for a constantair injection rate moves at a steadyand essentiallyconstant rate down the tube; it movesmore slowlythan the steamfront. The producedgasrate and the injectionpressureare shownin Figure9.8.The main point of interesthere is the buildup in pressuregradientcausedby the banking of the oil aheadof the combustionfront. In this example,the gas saturation ahead of the combustionzone decreasesas oil is forced down the tube. The increasedoil saturationrepresents a "bank." If the initial gassaturationin the reservoir were nearly zero, then the pressuregradientwould be high initially, and the gas saturationwould increaseto accommodatethe flow of flue gas to the production end. [n this case,oil would flow almost immediately,reflecting the effect of the gasflood beyond the combustionfront. This is analogousto the waterflooding beyond a steam-condensation front that was discussedin Chapter 5. Dry Combustion 421
|tltct
oft lt
'lK'.-_t\ rf
I I I I I
2.aa xlt.
Hlg''llilt "!ff 1*."ig6.'i1iff*' E a
\Fd
\ al Eol
'l
I I
r.l
o hl I IJ
.t | a ^l <.-
'l
.
a
Ll
,x.Ecrrc FnE33Jrt
r
I 'h*--
al
5 tG tt
u-^r
=|
s'
ll*
I
t E
oll'
I
td
o a
! x
I
3Y[/II 'LATEru
\
I
I I I
uST itc€ FRot 9Ata0FACE,tlcltEs Figure 9.6 Temperaturesalong Axis of Combustion Tube at Various Times (from Penberthyand Ramey 1966)
sult for onedil of problemsce The cuu is a considera build a bank br mostly upon ri this has to be I delay in produ discussedlater
Alexande/s Fl Figure 9.9 showsthe producedgasanalysesfor the sameexperiments.Once combustionis underway,the compositiondoesnot changevery much.Only a small amountof unreactedoxygenis presentin the producedgases.This is a commonre-
Another type o the firef lood p< In this 4 insertedin a h rate by an eloc
= U-
f, o z
:. E
z L o
Figure 9.7 Positionof Burning and SteamFronts (from Penberthyand Ramey 1966)
422
In Situ Combustion
Chap. 9
Dry Combustirt
PROOUCED OAS RATE G
r I 6
9,
I
tG o I
!t
G t o 6 U G c
PRESSURE \
J.r5 RI.[I TITE. HR3
Figure 9.8 Gas ProductionRate and Injection and ProductionPressures versusTime (from Penberthyand Ramev 1966)
sult for one-dimensional combustiontubes,but in the field there can be a number of problemscausedby the bypassingof unreactedair to the production wells. The cumulativeproductionsof oil and water are shownin Figure 9.10.There is a considerable delaybeforeoil appearsat the outlet.This is causedby the needto build a bank beforethe oil can flow to the productionwell. The delayis dependent mostly upon the amount of gas saturationpresentin the original reservoir,since this has to be filled beforeappreciableflow to the producercan be achieved.This delayin productioncan alsooccur in field projectsand shouldbe anticipated;it is discussedlater in this chapter.
rious Times (from
Alexander's Fireflood Pot I experiments.once much.Only a small l-hisis a commonre-
Another type of apparatusthat has proved useful in in situ combustionresearchis the fireflood pol shown in Figure 9.11. In this apparatus,air flows radially inward through a core sampleto a tube insertedin a hole drilled in its center.The whole apparatusis heatedat a controlled rate by an electrical resistanceelementwound around the external pressurecon-
F
z U E a U t o
; E q
G
t
8 q
sition of Burningand from Penberthyand
0
a56 RUN I r M E , H O U R S
rmbustion
Chap.9
Dry Combustion
Figure 9.9 ProducedGas Composition (from Penberthvand Ramev 1966)
423
)t
c .<
)
z g15
5 J
6
6
or0 o a o
rt
2a
[-.-
d F a
l
F
G
e 6
Figure 9.10 Liquid Productionand Oil Gravity (from Penberthyand Ramey 1966)
=
tainmentvessel.A typical experimentinvolvesraisingthis temperatureat 200"F/h up to a maximum combustiontemperatureof 800"F.Resulting gas analysesfor an experimentare plotted in Figure 9.12. Calculationof H/C Ratio for Fuel Stoichiometriccalculationscan providethe H/C atomicratio for the fuel that is being consumedin combustiontubes.lTo do this we proceedas follows: Supposethat the balancedchemicalequationfor the combustionprocesscan be representedby: C H , + S ( O ,+ 3 . 7 6 N r ): a C O z + b C O * c H z O + d O 2 * e N z Fuel
Air
V
There are sg ever,the!'an be written frt analysisof tt on a dr1'bas providethrec tions from tb simpleto do
Exampleof S
The flue gas
Carbm Carbm Oxygso Nitroge
Find the ap1 fed per kilog reaction.
1. Obtain
Figure 9.11 Fireflood Pot (from Alexander,Martin, and Dew 1962) lThis technique can be applied usefully to other combustionareas-for example,for the analysesof the operationsof steamgeneratorsor processfurnaces.Such studiesare frequentlydiof air introducedinto a rectedtoward the estimationof the excesscombustionair. Large excesses furnace result in low thermal efficiencybecauseof the heat carried from the furnace by the heated excessair.
424
In Situ Combustion
Chap.9
2. Calcula
tcas aar water vapor Hr on a dry basir. Dry Comh.rsti
tf
)
o
U 600 r
2
F
F-
o I
t o
:
ro
400 I
z
9 2ooE
o o U o
o o
o G
o rquidProductionand cm Penberthyand
nPeratureat 200'F/h I gasanalysesfor an
rr the fuel that is befollows: nbustionprocesscan dO:+eN2
0
stot520?5TIME -
HOURS
Figure 9.12 Temperatureand Gas Analysis for an Experiment Using a Fireflood Pot (from Alexander, Martin. and Dew 1962)
the precedingequation:n) S, Q,b, c, d, and e. HowThere are qqvenunkno=rylls-in ever,they are not all unrelated.Four algebraicequationsinvolvingthe variablescan be written from the materialbalancesfor eachof the four elements.In addition,an analysisof the flue gasfor COz,CO, and Oz is normally available.This is usually on a dry basis-i.e., the concentrationof water is excluded.Thesethree analyses can be solvedtogetherwith the equaprovidethree morealgebraicequations,which tions from the materialbalancesto give all sevenof the unknownvariables.This is simpleto do in practicalcases;an exampleis given next. Exampleof StoichiometricCalculationfor CombustionProcess for a combustionprocessis The flue gasanalysis2 Carbondioxide Carbonmonoxide Oxygen Nitrogen (by diff)
14.0% 3.0Vo 0.2Vo 82.8Vo
Find the apparent H/C ratio n and the number of standard cubic meters of air fed per kilogram of fuel burned. Write an overall stoichiometricequationfor the reaction. 1. Obtain S from ratio of C:N in feed and productsby settingtheseequal: r 0.14+ 0.03 = 0328 3365 S :1..2954 rireflood Pot (from rrtin. and Dew 1962) as-for example, for the studies are frequently dir of air introduced into a hc furnace by the heated
ornbustion
Chap.9
2. Calculatee from nitrogenbalance: e:3.76x1.2954 : 4.8706 2Gasanalysesare usuallyreportedon a volumebasis.This is the sameas a mole basis.Since water vapor normally condenses,it is usuallynot includedin the analysis.The analysisis said to be on a dry basis.
Dry Combustion
425
3. Calculatea, b, and d from ratios of gascomponentsto N2:
0.r4 o= 'mx
The arr factors that il
= 0.8235 4.8706
l. The pro cracked til r,rittx lrith in paraffin
0.03 . ,:0f2g x4.8706=0.1765 . 0.002 = 0.0118 o= 4.8706 Ug2gx
2. The cm pores irs tlon arr thar is n tion in t is also d the frrl
4. Writea materialbalancefor oxygenandsolvefor c: 1.2954=
0.8235 + 0.1765 c +r+0.0118 2
- 0.8235- 0.0118) - 0.1765 c = 2(1..2954 = 0.7437 5. obtain n from the hydrogenbalanceand completethe problem: n = 2c = 1.4874= 1.49 kg moles air/kgfuel :
(for example)
L2954x .=O''9 = t2 + ].49
: 0.451 Volumeof air/kg fuel = 0.457 x 22.4m3 at NTp : 10.24 The overallstoichiometricequationmay be written: CHr.on+ 1.2954(02 + 3.76Nz) = 0.8235CO2 + 0.t765CO + 0.7437H,O + 0.0119 02 + 4.9706N2 The Alberta ERCB definesstandardconditionsas 1 atmosphereand 15.c. Volume of air at standardconditionsper kilogram of fuel are
10.24x 288 273
In summan'. also bv the cr Figures upon fuel ara Figure 9 reservoir mat( ing the initial tively clean O the improved also be seen I plotted *'ith a the steam pla Figure 9 more fuel trec This is a against the G
rE rm,
.+:=
= 10.80m3
|
In the former British system,standardtemperaturewas 60.F; 15"c is equivalent to 59'F.
?o
Fuel Deposition
The most importantmeasurement that comesfrom a combustiontube or fireflood pot run is that of the fuel production.This is frequentlyexpressedas the weightof fuel per unit volume of reservoiror, alternatively,as the weight of fuel pei unit weightof reservoirrock. It is calculatedfrom a materialbalanie.
;<
426
JA
i:
In Situ Combustion
.ln
l-' s
>c
Chap.9
d J
rf'J
l-*
FV
l-
odr-Jool
Drv Combustr
The availableexperimentaldata can be largelyexplainedby consideringtwo factorsthat influencethe fuel availability: 1. The propensityof the particular crudeoil to depositcoke as it is heatedand cracked.Light crudescontainlargerproportionsof volatilematerialsthat distil without forming coke.As a result,thesecrude oils give relativelylessfuel with in situ combustionthan do heavy crudes. Also, the residuesfrom paraffiniccrudestend to give higheryieldsof crackedproductsand lesscoke. 2. The conditionsthat affect the saturationof the crudeoil within the reservoir poresas the combustionfrcint advances.Theseincludethe initial oil saturation and the effect of steammoving oil aheadof the coke-formingzone.Oil that is movedaheadby the flood doesnot contributeto the fuel (coke)formation in the crackingzone.The movementof oil aheadof the combustionfront is also dependentupon the nature of the reservoirmatrix, so this too affects the fuel production.
i_5
oblem: example)
+ 0.7437H2O
In summary,the formation of fuel is determinedby the nature of the crude and alsoby the conditionsunder which the fuel is formed. Figures9.13through 9.16showthe effect of someof the significantvariables upon fuel availabilityas measuredby Alexander,Martin, and Dew (1962). Figure 9.13showsthe effect of initial oil saturationfor a numberof different reservoirmaterials(both coresand crushedcores)usinga2L.8'API crude.Increasing the initial oil saturationtends,in general,to raisethe fuel availability.The relatively clean Ottawa sandgivesmuch lessfuel at the higher saturationsbecauseof of the crude aheadof the combustionfront. This may the improveddisplacement also be seenfrom Figure 9.14,where data for the sameseriesof experimentsare plottedwith an abscissa equalto the residualoil saturationthat was left behind by the steamplateauaheadof the combustionfront. Figure9.15showsthe effectof the crudeoil type. Low'API crudesgive much more fuel becauseof their greatertendencyto form coke. This is alsoshownin Figure 9.L6,wherethe fuel availabilityhasbeenplotted asainstthe Conradsoncarbonfor the different crude oils. Conradsoncarbon is a
s and 15'C.Volume cRuo€orl - 2t.B'APl P O R O UM S E O I U M8 E O U I P M E N T
i i!!ii:H{{1"{i:,iit\:mmm, ^./
o o >E
l5'C is equivalent
6 OYTAIA SATO - FFP ) a 8ER€A sAtDsroilE-LorGTUaE a orTAw sANo-Lorc tuBE
iqi
o//
ot-
-/" ooto
ts 3:
rn tube or fireflood sed as the weight of lht of fuel per unit
nhrustion
Chap.9
3 lO.O 10 60 8.O 2.O WT. PERCEI{T INITIALOIL SATURATIOT{,
Dry Combustion
Figure 9,13 Effect'of Initial Oil Saturationon Fuel Availability (from Alexander,Martin, and Dew 1962)
427
0Ru0E otl - 2t.fi'aPl P O R O U SM E O I U M 8 E O U I P M E N T O 8€REA SAI{DSTONE- FFP o cuRIIs coR€ rAT.L- FFP 6 OITASA gAI{D - FFP a aEREA sAitoslof{E - uollc tuge . I OTTAWA SAI{D - LOI{G TUSE
o o >E F
J3 €o
i9
t<\
EP
a<
ta
o.o
2.o 40 6.0 8.O tO.O RESIOUALOIL SATURATION. WT. PERCENT
tz.O
Figure 9.14 Effect of ResidualOil Saturationon Fuel Availability (from Alexander,Martin, and Dew 1962)
direct measureof the percentageof coke that is laid down by the crude oil in a standardhigh-temperature cokingtest(ASTM 1985).This testis usedextensivelyin the designof petroleumrefining equipmentsuchas cokers.High Conradsoncarbon crudesgive high fuel availabilities. Low-TemperatureOxidation when crude oils are contactedat high temperatures with oxygen,the productsare mostly carbon oxides and water. However, at low temperatures,reactionsoccur in which the oxygentendsto combineand remainwith the crude and alsoto causeit to polymerizeby oxidativedehydrogenation type reactions.A particularlyundesirableresultof thesereactionsis that they increasethe viscosityof the crude oil. Figure 9.17showsthe effectof preoxidizingthe crudeat a lower temperature beforemeasuringthe fuel availability by combustionat 800'F. There is a very strong effect with a maximum at about 425"F.Above this, the fuel availability (measured in the subsequent oxidationat 800'F)dropsoff becausethe fuel is alreadypartially converted to gaseousproducts in the preoxidation. At 425"F the polymerization causedby the preoxidationgreatlyincreasesthe fuel availability. 3.0
3 zs7-6l
OTTAIVA SAND
\
. LONGTUBE RESULTS
sE Z^z o|l
\
-z >g
B ; I NI
\o
fat -J
Y: x^
ao jo <\ >z
The or, (total from p At the peat Previc from the ane of the ox1'gr not true. Pa can react aff Alexao of experimc resultsare pl ent H/C ratk High q combustionI within the n With ct is a real indi correlationd normalhigh
.o LO
J(J
\ o\
b : r oll r=
o
:
.\{ o
o
r c- ll -
J @
|
=E
I
36 o'l-
o--$
J
eq
I
>J
o'o6
428
to 20 30 CRUOEo r L G R A V | T Y' A , Pl
Figure 9.15 Fuel Availability versus "API (from Alexander,Martin, and Dew 1962) In Situ Combustion
Chap,
I
{l J
O OL--L-
E0@
Dry Combust
-z >t
,/
l- a i J
/o
?e a \ >z JY
or/"
U< fo L o J
n, the productsare , reactionsoccur in and alsoto causeit articularlyundesirof the crude oil. lower temperature lere is a very strong illability (measured is alreadypartially the polymerization
^ot/ O T T A W AS A N D
o5r015 @NRADSOI{ RE9IOUE, WT.1 CAREON
:ct of ResidualOil el Availability (from rn. and Dew 1962)
' the crude oil in a usedextensivelyin t Conradsoncarbon
-ev6'
Figure 9.16 Fuel Availability versus CCR (from Alexander,Martin and Dew 1962)
The overall effect is shown in Figure 9.18,where the grossfuel availability (total from pre and final oxidations)is plotted againstthe preoxidationtemperature. At the peak condition, the availabiilty of fuel is increasedabout three times. Previouslyit was shown how the H/C ratio for the fuel could be determined product.In this calculation,it wasassumedthat all from the analysisof the gaseous of the oxygennot in the product as COz and CO had reactedto form water. This is not true, particularly for low-temperatureoxidations, becausepart of the oxygen can reactand remainwith the crude and coke. Alexander, Martin, and Dew measuredthe "apparent" H/C ratio for a series of experimentscarried out with a range of maximum reactiontemperatures;the resultsare plotted in Figure 9.19.For reactiontemperaturesbelow 650'4 the apparentHlC ratio for the fuel is even larger than the ratio for the whole original crude. High apparentHlC ratios(i.e., low COz in flue gas)are an indicationof a low combustion temperature and may be used as an indicator of what is happening within the reservoir. With combustiontemperaturesof the order of 800'F, the apparentH/C ratio is a real indicationof the type of fuel that is beingconsumed.Figure 9.20 showsa correlation of the total air requirementsagainstfuel availability for a wide rangeof normal high-temperaturecombustions.The averageis 189SCF/lb of carbonburned. : 6 -9zo 6< UO N. :6 =J
X - oo o\ >z f6
=G q-j <
fa
ae .fuailability versus nder.Martin, and
rhrstion
Chap.9
J
too
200 300 400 500 6@ . F700 O X I O A T I OTNE M P E R A T U. R E
Dry Combustion
800 900
Figure 9.17 Effect of Low TemperatureOxidation on Fuel Availability (from Alexander,Martin, and Dew 1962)
429
r- <9
It ;o = o >G
J6
:'s
o
HE
r-8
:E
J-
qz
\-oo_
.-G
F
cro E@ (9J
o
oo 2oo 3oo 4oo 5oo 600 7oo Boo goo roo iioo O X I O A T I O NT E M P E R A T U R E . ' F
Figure 9.18 Effect of Preoxidation on Gross Fuel Availability (from Alexander,Martin, and Dew 1962)
Figure9.2f is typical of a numberof resultsthat havebeenpublishedby workers at IFP. Theseresultswere obtainedin an experimentin which a sampleof the reservoirmaterial was heatedat a 100"C/h in a laboratoryapparatuswith air passing throughit. The markeddifferencebetweenthe oxygenconsumedand thaiproduced as CO2 and CO indicates the prevalence of low-temperatureoxidation around 250"C. A significantdifferencebetweenlaboratoryand field resultsis that the concentrationof CO found in the field is much lessthan that in the laboratory.This has the effect of increasing,somewhat,the air requirementsneededin the field.
voir in produd 2. The fir tempen
These t that havebcr
In Situ Combustion Experiments Using Oil Sands Leaute and Collyer (1984)have studiedthe effect of initial reservoirtemperaturein a seriesof combustiontube experimentsusing Cold Lake bitumen and dry conditions. From this work there are two very interestingfindings: 1. With low reservoirtemperatureswhere the unheatedbitumen is essentially immobile,there is little mingling of the mobilizedbitumenwith the bitumen downstreamof the combustionfront; insteadit movesthroush the cold resero F G
o
J t!
3 t!
9 = o F F
z U t
fc
200 400 600 800 tooo oF coMBUSTt0N TEMPERATURE,
430
t200
Figure 9,19 Apparent H/C Ratio of Fuel (from Alexander,Martin, and Dew 1962)
In Situ Combustion
Chap.9
Figurt iI of019SG Dry Comh.rst
O FFP RESULTS r LONG TUEE RESULTS
-.5 = P o
Hg qo -9 J\
<E FA
I
oo F
I
I
t of Preoxidation lability(from and Dew 1962)
,rblished by workh a sampleof the tus with air passnedand that prorrature oxidation s is that the conlaboratory.This ed in the field.
I
F U E L A V A I L A B I L I T Y , L B , C A R B O N/ I O O L 8 . R O C X
Figure 9.20 Effect of Fuel Availability on Air Requirements.LaboratoryTests above650'F (from Alexander,Martin, and Dew 1962)
of the viscosityof the voir in fingers.This was found from measurements productwith time. The data are shownin Figure 9.22. 2. The fuel load is very dependentupon the initial reservoirtemperature;higher resultin lessfuel laydown.This is shownin Figure 9.23. temperatures These resultsindicate that better resultsshouldbe obtainedfrom oil sands that havebeenpreheated.The workersfrom Essoconcludethat in situ combustion
Tcmpcrolurc
,ir temperaturein n and dry condiren is essentially rith the bitumen th the cold reser-
htvtoryjz;/
/.
!
I
a
$ ,o
T
02 Contumad --- COe producrd -- CO producrd
(o
-\\ Timr.hq|n ent H/C Ratio of ler. Martin, and
Chap.9
Figure 9.21 Comparisonof oz consumed and coz and co ProducedDuring oxidation of 0.89 SG Crude Oil (from Burger and Sahuquet1972) Dry Combustion
431
() ut (o
. Decreas o Rise in tr . Decrect delaf in I absorpti
800
'= 600 o E
.= 400 @
\1
o o o 200 oo
0
o (, o
-1 -5 0- o/C\ 7oo
0
100 200 300 400 Cumulative Productionof Bitumenin g
soo
Figure 9.22 Effect of Preheat Temperatureon Viscosity of Produced Bitumen (after Leaute and Collyer 1984).Parameteris the Preheat Temoerature.
should be employedin oil sand reservoirsthat have been first produced and preheatedby steaming.Later in this chapter field projectsare disiussed in which in situ combustionis used to produce bitumen from reservoirsthat have been producedinitially by cyclic steamstimulation. lgnition The combustionprocessis frequentlyinitiated by heatingthe reservoiraroundthe injection well by meansof an external source of heat. Both electrical and gas heatershave been employed,and each method is successful.lnformation on ignition methodsis given in a paperby J.T. Moss,who is one of the pioneersin itris area(Moss 1965).Also seeWhite and Moss (1983). In electricalignition, a heatingelementwith a power capacityof 10 to 40 kw . is lowered into the well on the end of an armored power supply cable through a pressureseal.Means should be provided for measuringthe downhole temperaiure in the vicinity of the heater.Air injectionis commencedat a low rate,and power is suppliedto the heateruntil ignition is obtained.Mossdiscusses variousmeins that can be usedto determinewhetherignition has occurred: o Rise in temperatureof the air abovethat expectedfor the given input of electrical power. 35 ro) 30
whereK A
.9 o
n
Fru
o G
9zo o lt
15
40
432
Moss ah within a c)cli! ers themsehG large Rumani (Aldea, Turta' Anottrcr The oxidatio and the hear1 reservoir grad and eventuall This rr 1920suhen ai that causedth The autc reservoiris el it and then to ample.Counil tion in the fd secondar)'cf Alrhor4i there are exa! project in Scl lots usinga gl patternslhat t depletionof tl The kiu and Weillemr surementsof I The;-rq
80 120 160 200 og FormationBase Temperature
Figure 9.23 Effect of Formation Temperatureon Fuel Load for Cold Lake Crude (after Leaute and Collyer 1984) In Situ Combustion
Chap. 9
By relatingtb the reserroir the time reqtr propertiesd
Dry Comhsri
r Decreasedair injectivity. o Rise in temperaturedetectedin observationwell(s) near to the injector. . Decreasein oxygencontent of gasproducedfrom producers.There is often a delayin the correspondingrise in carbon dioxide contentbecauseof reservoir absorptioneffects.
'fect of Preheat r Viscosityof Produced Leauteand Collyer :r is the Preheat
;t produced and preiscussedin which in that have been pro-
reservoiraroundthe h electrical and gas Informationon ignithe pioneersin this racityof 10 to 40 kW rply cablethrough a rwnholetemperature rw rate,and power is s variousmeansthat : giveninput of elec-
Moss alsodescribesgasburnersusedfor ignition. The burnersare contained within a cyclindricalheatshieldto protectthe well from direct radiation.The burners themselvesmay be ignited using a chemical which flames spontaneously.The large Rumanian in situ combustionprojects employ electrical heatersfor ignition (Aldea, Turta, and Zamfir 1988). Another meansof achievingignition is to rely upon the autoignitionof the oil. The oxidation rate of an oil is often significant at the original reservoirtemperature, and the heat produced by this low-temperatureoxidation is sufficient to heat the reservoir gradually.As the temperaturerises the oxidation reaction rate increases and eventually the temperatureruns away to give high temperaturecombustion. This mechanismcausedthe accidentalignition of oil reservoirsduring the 1920swhen air was being injectedfor pressuremaintenance.[t is theseaccidents that causedthe discoveryof the in situ combustionprocess(Ramey1971). The autooxidationprocessis much more rapid if the initial temperatureof the reservoir is elevated.One way of doing this is to steamthe reservoir first to heat it and then to inject air. This is a reliablemeansfor achievingignition (see,for example,Counihan 1977).As wasmentionedearlier,attemptsto usereversecombusignition that occurs;this resultsin tion in the field fail becauseof the spontaneous fronts near injection well. secondarycombustion to the generally Although ignition can be achieved in a straightforward manner, where it has there are examples beenvery difficult to achieve.In the GoldenLake projectin Saskatchewan, Husky Oil had little difficulty in igniting their initial pilots using a gas heater.However, they subsequentlyfailed to ignite two additional patternsthat borderedon the originalones.They ascribethe difficulty to the partial depletionof the patterns before ignition was attempted(Miller and Jacques1987). The kinetics of the spontaneousignition processhavebeenstudiedby Tadema and Weijdemaof Shell (Tademaand Weijdema1970).Figure 9.24 showstheir measurementsof the oxidation rate of severalcrude oils as a function of temperature. They representthe straightlines that are shownby the Arrhenius equation9.1. K = AoPle-B/r
whereK Ao, B, n P,
lfect of Formation r Fuel Load for Cold ter Leauteand Collyer rmbustion
Chap. 9
(e.1)
is mass 02 consumed per unit time per mass of oil
are constantsthat dependon oil and sand is 02 partial pressure
By relating the rate of heat releaseto the heat neededto raise the temperatureof the reservoir,they were able to derive the approximateequation9.2. This predicts the time required for the spontaneousignition of the reservoiras a function of the propertiesof the oil and reservoir and of the initial reservoir temperature. tt=
Dry Combustion
p(1o(.
+ zTofB)eBffo QS"p.HAoPiB/To
(e.2) 433
TABLE9.. Sr
o,
6-s
-5
CD -v
Crude oil mixed with sand at 100 atm air pressure
o 9e
Formationtc+c Formation Frert O1 partial prcrcr
D
N
€
do
E
tt
o
n
6
E c -9 -7
H, kCalrkgO; Porositl'.d Oil saturauo. S. Water saturetn p',kg/mt p r C r ,k C a l ' m !t
-7
6 E
x
o
o
-8 _r -8
€t
olJ
!-
0.0024 0.0026 0.0028
0.0030
€ 0.0024 0.0026 0.qt28
0.0030
Reciprocalof Absolute Temperaturein K'l Figure 9.24 Oxidation Rate of Various Oils as a Function of Temperature (after Tadema and Weijdema 1970)
where /i ptCt Ts As, B, n H O S, po
The agrr from Table 9.{ temperatufes
is ignition time in seconds is heat capacity/unitvolume formation is absoluteinitial formation temperature are as in (9.1) is heat of reaction per unit massof Oz is porosity is oil saturation is oil density
Effect of Reserw
Temperaturc.'C Ignitiontimc. dr!
Typical valuesof the constants-40,B, and n for different crude oil-sand mixtures are given in Table 9.3. A comparisonof the ignition time that was measuredin two field testswith those predicted from equation 9.2 is given in Table 9.4. TABLE9.3 Values of.4o,B, andn CRUDE A
B
c D E F
434
Ao
3,080 925 498 84,800 I,2TO 7,380
8,860 8,640 8,880 10,270 8,680 9,480
Ignition tirncs rr Calculated Observed
0.46 0.57 0.79 0.48 0.45 0.31
ln Situ Combustion
Chap.9
It is appr time requircdt
Temperatur r
One of the im the combustirr erated.This bc bustion tempc front both aba The folh flux is very larl of the total. an perature.In th just be equal t rise is given b1 Dry Comhrsfb
TABLE 9.4 SpontaneouslgnitionTimes for Two Oilfields SOUTH BELRIDGE FormationtemperatureIe, 'K Formationpressure,atm 02 partial pressure,atm Ao B n H, kCal/kg 02 Porosity,f Oil saturation,5, Water saturation,S, p-kg/m'
303.8 15.3 3.20 3080 8860 0.46 2940 0.37 0.60 0.37 970 553
orCr,kCalfm3'C
0.0028
0.0030
il K'l
VENEZUELA
Ignition times in days Calculated Observed
312.2 29.6 6.18 l2t0 8680 0.45 2940 0.34 0.66 0.34 980 5Z'7
99 106
49 35
perature(after
The agreementis very satisfactory.Using the data for the Venezuelancase from Table9.4, the ignition time has been calculatedassumingdifferent reservoir temperatures, with the following results. Effect of ReservoirTemperatureon AutoignitionTime Temperature,"C Ignition time, days
(Samepropertiesas for Venezuelacase) 10 20 30 40 706 266 r07 46
50 21,
60 10
crude oil-sand mix-
It is apparentthat a small amount of reservoirheatingwill greatly reducethe time required to obtain autoignition.
two field testswith
Temperatureat the Gombustion Front
0.46 0.57 0.79 0.48 0.45 0.31 mbustion
Chap.9
One of the important variablesin an in situ combustionprocessis the air flux at the combustionfront. Air arriving at the front reactswith the fuel, and heat is generated.This heat raisesthe rocks in the vicinity of the combustionfront to the combustion temperature and also suppliesthe heat that is conducted away from the front both aheadand also vertically. The following discussionis based upon a paper by Ramey (1959).If the air flux is very large, then the heat lost by conductionwill be a relatively small fraction of the total, and the combustionfront temperaturewill approachthe adiabatictemperature.In this circumstancethe heat of reactionper unit volume of reservoirwill just be equal to the sensibleheat gained by the rocks. This adiabatictemperature rise is given by equation9.3. Dry Combustion
435
- f,=Y ?in"" where 2,"" Ti LH pC W
(e.3)
r T.l'ilr -
is adiabaticmaximum temperature is initial temperature is heat of combustionof fuel is reservoir heat capacityper unit of volume is fuel concentrationper unit volume
It is important to note that, other thingsbeing equal,the temperaturerise is proportional to the fuel concentration.This implies that if the fuel concentrationis too low, it may not be possibleto raisethe rock to the requiredcombustiontemperature evenif all of the other conditionsare adequate.This can be a problemin attempts to use in situ combustion to produce oil from reservoirs having low oil saturation.Calculatedvaluesof ?lnu"- Ti are given in Table 9.5. TABLE 9.5 TypicalValuesol T^", - Ti AssumeAtI = 18000Btu/lb and pC : 35 Btuft3 'F Fuel Load 7 T^^" - Ti .F lbft3
0 0.5 1.0 r.l7 1.5 2.0
tion 9.3)is pl the front frcx and t is the tr T*.o cu
0 257 514 600 771 1029
Effect of Conductive Cooling upon the Combustion Temperature
1. The bn i . e . .V vances front rt air-inje 2. The so proximr constan spondin
In general,the temperaturerise will be lower than calculatedfrom equation9.3 becauseof the effect of the conductiveheat losses.If the rate of heat generationis low becauseof a low air flux, then the relative effect of the heat loss will be greater, and the temperature of the combustion front will be lower. If the flux is low enough,the temperatureof the front will fall to the point where vigorouscombustion can no longerbe sustainedand only low temperatureoxidation will occur. The "fire" will be extinguished.This effect can be analyzedmathematicallyby writing a differential equationthat equatesthe heat conductionfrom the front plus the heat used to raise the front temperatureto the heat evolvedby combustion. Ramey consideredtwo cases.[n both, the combustionfront is consideredto be growing radially from a vertical injector. In the first case,the flame front is consideredto be an infinite vertical cylinder (i.e., vertical conductionlossesare ignored);in the second,the vertical lossesare included. Figure 9.25 showscalculatedresultsfor the infinite vertical case.The temperature rise at the front (as a fraction of the adiabaticrise calculatedfrom equa-
Figures the effectsof perature rise ofvertical trc the reservoi temperatureI ter. Also. the differentvert This res outward frort the reservoir guishedin th
436
Dry Combust
In Situ Combustion
Chap.9
(e.3)
T -I
1.0 Constont front vefocity i.e. r1/t
Tmor-T
0.5 r temperaturerise is luel concentrationis :ombustiontemperabe a problem in atroirs having low oil
Constontrr2l t i.e. oir rote
For infinitely high front 0 0. 2
10
1000
100
\'ht Figure 9.25 Temperatureat Fire-Front(after Ramey 1959)
tion 9.3)is plottedagainsta dimensionless number,r| fat, wherer1is the distanceof the front from the startinglocation, a is the thermal diffusivity of the reservoir, and I is the time from the start. Two curvesare shown:
rom equation9.3 beeat generationis low losswill be greater, . If the flux is low rre vigorouscombusrtion will occur.The :maticallyby writing re front plus the heat nbustion. ront is consideredto reflame front is conuction lossesare ig-
L. The broken curve is for the casewhere the velocity of the front is constant; i.e., V = rsft is constant.In this casethe abscissais Vr1fa.As the front advances, the temperature approaches7,"". In order to achieve the constant front velocity,which is assumedin this case,it would be necessary to raisethe air-injection rate in proportion to /. 2, The solid curve in Figure 9.25 is for a constant value of rflt. This is approxirnatelyequivalentto the casewhere the air-injection rate is maintained constant. In this case the flame-front temperatureremains constant correspondingto the value of the ordinatewhich is determinedbyr|/at.
tical case.The temalculatedfrom equa-
Figures9.26-9.29showthe resultsof Ramey'scalculationsfor the casewhere the effectsof vertical conductionare included.The figures give the calculatedtemperaturerise for four different horizontal planesin the reservoir.The largesteffect of vertical heat lossis for the casecorrespondingto the top (and also the bottom) of the reservoir;the resultsfor this caseare shown in Figure 9.29.The calculated temperaturerise is much smallerfor this casethan for the planesnearerto the center. Also, the curvesfor the other planesare very similar to eachother (note the differentvertical scales). This resultintroducesthe importantpossibilitythat as the flame front moves outward from the injection well, the vertical heat lossesat the top and bottom of the reservoirmay causethe combustionto be extinguishedthere beforeit is extinguishedin the center.
rmbustion
Dry Combustion
Chap.9
437
DASHEOLINES ARE LINES OF CONSTANT Ar V\k
ID L.INES ARE LINES OF CONSTANT AB . V'al<
CONSTANT VEL
ITY SOURqE, l-O
rgd - a-t Figure 9.26 DimensionlessTemperatureRise for a Heat Sourceof Finite Height Moving at ConstantVelocity-Temperatureat Center PlaneEdge (z = 0). (from Ramey 1959)
Figrnll at Coocr to thc E{
o1ffi
LINE3 ARE LINES OF CONSTANT
A' vQ /<
lLtlc! lA'Y
o.t ttoj.?-'l:-
e1p
I
il,t
I
D LIN€S ARE LINES OF CONSTANT AB - Vlrx.
CONSTANT VE LOCITY S O U R C . E ,l -
O.5
%
0/4 - s-r Figure 9.27 DimensionlessTemperatureRise for a Heat Sourceof Finite Height Moving at Constant Velocity-Temperature Halfway Between Center Plane and Edge (z = 0.5) (from Ramey 1959)
438
"l T "Y
In Situ Combustion
Chap.9
Figrnf! at Cmir
Dry Cornhrcli
LINES ARE CONSTANT
IES ARE CONSTANT
souRcF,Z' 0.75
E' Z.-O
Y{r ! inite Height Moving rm Ramev 1959)
Figure 9,28 DimensionlessTemperatureRise for a Heat Sourceof Finite Height Moving at ConstantVelocity-TemperatureThree-Quartersof the Distancefrom the CenterPlane to the Edge (z -- 0.75)(from Ramey 1959)
OASHEDLINES ARE LINES OF CONSTANT Ar VQ l<-
INES ARE )F @NSTANT
:\
'{9
SOLID LINES ARE LINES OF CONSTANT AB . V:llx'
k,
I T Y S O U B C E ,l -
Finite Height Moving : and Edge (z = 0.5)
bmbustion
ChaP.9
|
96 ' a-' Figure 9.29 DimensionlessTemperatureRise for a Heat Sourceof Finite Height Moving at ConstantVelocity-Temperatureat the Edge (z = 1) (from Ramey 1959)
Dry Combustion
439
Examplesof the Useof Ramey'sSolutions Figure 9.30 showsthe combustion-fronttemperaturescalculatedby Rameyfor the advance,at a constant rate, of an infinitely high, cylindrical combustionfront for the conditionsshown.As the front advancesthe temperatureincreasesbecauseof the decreasingheat flux loss in front of the cylinder; the cylinder curvature is decreasing,and an increasingtemperatureis required to conduct the heat away. In eachcasethe front approachesZru" as an asymptote. Curves are drawn for severalfuel loads.The higher the fuel load, the higher is the temperatureof the front. For the front to advanceat all, it is necessaryfor it to reachthe ignition temperature. For example, if it is assumedthat the temperature has to be greater than 400'F for ignition to occur, then, as shownby the dotted line on the diagram,the front would have to have a radius of greaterthan 0.9 ft in order for it to be able to advanceif the fuel load is 1..5lblft3.External heat would have to be applied to "kindle the fire" in order to move the 400"Fisotherm0.9 ft from the well. The curves in Figure 9.30 do not allow for the effect of convection on the temperatureof the combustionfront. The reader is referred to Ramey'spaper for an analysisof this. The effect is to reducethe amountof fuel requiredto attain a particular front temperature.For the caseshownin Figure 9.30,Rameycalculates that the fuel concentrationcould be reducedby 78%. The curvesjust discussedare for an infinite well with a constantrate of advanceof the combustionfront. In order to sustainthe constantradial velocity,the air-injectionratewould haveto be increasedcontinuously.If the air-injectionrate is
maintainedco stant as th€ fn For a frnt it is lowesrat I Figure9tion of the ad effect of vertic abscissa is thc the front ten? highestat the r minesr;:;t: it i
The hai (it would be at the limit at nt the combusriq a radiusof abo declinenearer combustionbe In practi becauseof the causesandbla beingstudied
F l.,
I
LJ
E, t F g LJ
aH - rtooo tTu/Ll c - o.30tTurg6-r7 | - r20 Lt/cu FT
o :
n -. too'r
|lJ
F
Y - -
O.5 FIIDAY O.5 SCI iTl0AY
tO to R A D ] A L L O C A T I O N O F HEAT SOURCET F E E T
440
Figure 9.30 Effect of Fuel Concentrationon the Temperatureof a CombustionFront of Infinite Height Moving Radially at a ConstantVelocity (from Ramey 1959)
ln Situ Combustion
Chap.9
Temper heat sqrt inversely b Dry Combustir
d by Rameyfor the ombustionfront for ncreases becauseof der curvatureis dert the heat away.In uel load, the higher it is necessary for it to be greaterthan on the diagram,the r for it to be able to ve to be applied to rm the well. f convectionon the r Rameyb paper for requiredto attain a 0, Rameycalculates constant rate of adt radialvelocity,the : air-iniectionrate is
maintained constant,then the front temperaturefor an infinite front remainsconstant as the front advances. For a finite front, the temperaturefalls with a constantair-injection rate, and it is lowestat the top and bottom of the reservoir. Figure 9.31showsthe calculatedtemperatureof the front (expressedas a fraction of the adiabatic temperaturerise) for such a case.This diagram includes the effect of vertical heat losses,and it may be seenthat, at any particular radius (the abscissais the ratio of the radius from the well to the half-reservoirheight a), the front temperatureis lowest at the very top and bottom (i.e., where Z : 1) and highestat the center plane. [n this figure the parameterU is a constantthat determinesrj /t; it is defined by equation9.4. r1= (2Ut)112
(e.4)
The horizontaldotted line in Figure 9.31indicates,for a particular example (it would be at a different vertical location if the fuel concentrationwere different), the limit at which hightemperaturecombustioncould continue.[n the caseshown, the combustionprocesswould declineat the very top and bottomof the reservoirat a radiusof abouteight times the reservoirhalf-height,and at largerradii, it would declinenearerto the centerof the reservoir.In orderto maintainhigh temperature combustionbeyondthis, it would be necessaryto increasethe air-supplyrate. ln practicalcasesthere may be difficulty in increasingthe air-injectionrate becauseof the excessive gasvelocitythat is createdat the productionwells;this can causesandblast-type erosiondamage.Another solution,and one that is increasingly beingstudied,is to use enrichedair or oxygen.This allowshigher heat-generation
Ar{rP
oilGngloxL:3s OIST^NCE FIOY
C O N S T A N TF U E L CONCEI{TRATION
fect of Fuel rn the Temperatureof :ront of Infinite Height y at a ConstantVelocity )59) rnbustion
Chap. 9
_E_- E - l a Temperaturerise ratio at a moving heat sourceof finite heightand velocity inverselyproportionalto radial source locationand U/a of 10. Dry Combustion
Figure 9.31 Effect of Vertical Height on the Temperatureof a Combustion Front of Finite Height Moving with a Velocity InverselyProportionalto the Radius (from Ramey 1959)
441
rates at the combustioninterface and, as a result, allows larger spacingbetween wells without excessivegas production rates. Figure9.32is similar to Figure9.30,exceptthat it includesthe effectof vertical heat conductionand is drawn for a constantfuel load of 1.5 lbft3; the front velocity is assumedconstantat 0.5 ft/d. In this caseit would be necessaryto, in some manneror other, raisethe upper and lower boundariesof the reservoirto abovethe ignition temperature(400'F) at a radius of 7 ft in order to have the front extend vertically through the reservoir. Properties of ProducedOil One of the featuresof in situ combustionis that there is someimprovementin the propertiesof the oil. The material that is burned is essentiallycoke, whereasthe oil producedconsistsof unchangedoil that has been displacedfrom the reservoir diluted with distilled and crackedmaterials.This mixture usuallyhas a significantly lower density(higher API gravity) and a lower viscositythan the original oil; it contains a smallerproportionof high boiling materials. Inspectionson producedoils from firefloods are comparedwith those for the original oil in Table9.6.
TABLE 9.6 Changg h O FIELD. LOCATION Operator South Belridge,Califanir GeneralPetroleum West Newport, Califonir GeneralCrude East Venezuela Mene Grande Kyrock, Kentucky Gulf Oil South Oklahoma Magnolia
Asphalt Ridge,Utah U.S. DOE(') (t)Changes in other propcr!
WET COMBUSTION In the previous discussion,it has been shown how in situ combustioncan be used to produce a combustionfront, which, as it advancesthrough the reservoir,drives the oil aheadof it and consumesthe residualcoke that is laid down as fuel. One of the main parametersin this processis the fuel concentration,which is determinedby the natureof the crudeoil and by the conditions.Oil that hasbeen driven forward or convertedto crackedvolatile material cannot remain as coke to be burned. ^or^a.t rc corraut?ro.. n",3-.j1g1-:r._3 a d 3
t
3 U I
t |. tor.tttrt.^ru.t /,-r.{r -" - " "'-c6*b1tr(ttrt"' 3- !l!!-: a o 3 a
CO.t. - Ll LarCU ,t t COra - tFlrU/|'l I YlL. - C.l rtlo^t aAL Oltt-Otrt'rD^V tt - rao !a/cu tl . - o.lO |tvrLl tttlCtt ttt - lOtt "
aAoraL orSt^rcc
?lov
riJgctrox
wELL. ?Et?
Temperaturesat the combustion front, sampleproblem.
42
Figure 9.32 Temperaturesfor CombustionFront within a Finite ReservoirWhich Is Advancingwith a ConstantVelocity (from Ramey 1959) In Situ Combustion
Chap. 9
(Chu 1982)
In the d need for heat I to be more fir generatedrco pletely depleA The t*o for dry con$r much heat is I There is a smr from combrrd tion front, co In wet cc tinuous or, wil wells are used Somed Without watcr evaporatedin liquid water fl combustionfn the combusir the front whca
Wet Combusti
rger spacingbetween
TABLE 9.6 Changesin Oil Propertiesafter Firefloods .API
FIELD, LOCATION
les the effectofverti.5 lbft3; the front venecessary to, in some neservoirto abovethe tave the front extend
e improvementin the coke. whereasthe oil irom the reservoir dilly has a significantly be originaloil; it conred with those for the
TEMPERAIURE
Operator
Before
South Belridge,California GeneralPetroleum
t2.9
1/
West Newport, California GeneralCrude
15.2
20.0
.F
After
Before
87 L20 160 60 100 2t0
a
VISCOSITYcp
2,700 540 1,20 4 5R5
777 32
After
800 200 54 269 7l 10
9.5
East Venezuela Mene Grande Kyrock, Kentucky Gulf Oil South Oklahoma Magnolia
t2.2 Then10.5 10.4 1,4.5 15.4
20.4
Asphalt Ridge, Utah
14.2
20.3
60 210 66
90,000 2,000 r20 27 800 5,000 After 1 month 5,000
u.s.DoE(') (t)Changes in other properties: Pour point, 'F 1000+ 'F wtTo
nbustion can be used t the reservoir,drives d down as fuel. mcentration,which is )ns.Oil that hasbeen rct remain as coke to
Temperaturesfor Frontwithin a Finite hich ls Advancingwith a ocitl' (from Ramey 1959)
lombustion
Chap.9
Before r40 62
After 25 35
(Chu 1982)
ln the dry combustionprocess,the air requirementis not determinedby the needfor heat but ratherby the availabilityof fuel. With heavycrudes,there tends to be morefuel than is requiredsimplyto heatthe reservoir.Also, muchof the heat generatedremainsbehind the combustionfront in the rocks that have been completelydepleted. The two diagramsin the upperleft part of Figure9.33showidealizedprofiles for dry combustion.The temperatureis high behind the combustionfront, and much heat is being left behind. No water vaporizesbehind the combustionfront. There is a small temperatureplateauaheadof the front, where somewater products from combustion,togetherwith connatewatervaporizedbythe advancingcombustion front. condense. In wet combustion,water is addedto the air. This additioncan be either continuousor, with essentiallythe sameresult, intermittent. [n somecases,separate wells are used for water injection. Someof the addedwater remains in the burned zone as water saturation. Without water addition,the burned rockswould be dry, sincethe connatewater is evaporatedin front of the combustionzone. If sufficient water is addedto the air, the liquid water flows toward the combustionfront, and as the water approaches combustionfront, it evaporates;this cools the rocks. Heat is transported through the combustionfront by the steam,largely as latent heat. Heat is releasedaheadof the front when the steamcondenses. Wet Combustion
443
extendsfar bg of the effecro sumedin th l If the I diagramin tL combustim et Someunburq temperatureq Wheos the processb ratios, liquid t describedrtr Figure 9 wet combustir for dry cofi
q "o
Distonce ----l> Combustion&
/ z- Evooorotion
NORMAL
Laboratory F Figure 9.33 Effect of Water Addition
Normal wet combustionis shown by the two diagramsin the upper right part of the figure. Steampassesthrough the front and later condenses.The steammoves oil aheadof the combustionfront as well as movinq heat. There are thus two beneficial effects:
Figure9.35sh was injected ir were measutca
o The rocks are preheatedbefore the combustionfront reachesthem, and this tends to increasethe temperature of the combustion front ([ is higher in equation9.3). o The steamreducesthe concentrationof residualoil remainingin the path of the advancingcombustionfront. This resultsin a substantialreduction in the fuel concentrationand reducesthe air required to burn through a given volume of reservoir.This effect tends to lower the temperatureof the combustion front (Ifzis lower in equation9.3). Also, becauseof the displacementcausedby the steamaheadof the front, it may not be necessaryto burn all the way through the reservoirin order to achieveeffective recovery.In the extreme,wet combustioncan be looked upon as a meansof generatingsteam within the reservoir rather than in a surface steam generator. When sufficient fuel has beenburned to generatethe steamrequired for the recovery, then the processcan be terminated,leavingthe remainingresidualoil uncoked and unburned. The lower left diagramsin Figure 9.33 show the condition obtained if the amount of water is increasedto the point where the evaporationfront just trails the combustionfront. [n this condition the maximum amount of steam is generated without liquid water reachingthe combustionzone. The combustionzone is not itself being cooled by the direct evaporationof water. The steamcondensationzone 4M
ln Situ Combustion
Chap.9
I
u
Itt.
0 I'[ut'l Latil lll Wet Comhstb
rStron nsotion l-
T] gJ, OUENCHEDI
extendsfar beyondthe combustionfront, and the fuel laydownis decreasedbecause of the effect of the steamin reducingthe residual.Essentiallyall the oxygenis consumedin the high-temperaturecombustionprocessat the front. lf the water-to-airratio is increasedstill further, the situationshown in the diagramin the lower right-handcorneris produced.Now liquid watercan enterthe combustionzone, and this zone is cooled below the levels found with lesswater. Someunburnedfuel is left behind. In this condition there can be excessivelowtemperaturecombustionand production of viscoustars. When someliquid water entersthe combustionzone and vaporizescompletely, the processis describedaspartially quenchedcombustion.At higher water-to-air ratios, liquid water passesright through the oxidation zone, and the operationis describedasquenchedcombustion,or superwetcombustion. Figure 9.34 showstypical temperatureand saturationprofiles for a normal wet combustionprocess.It may be comparedwith the similar diagramgiven earlier for dry combustion(Figure9.1). Laboratory Results
-91-
r the upper right part ses.The steammoves re are thus two bene-
Figure9.35showstemperatures measuredin a combustiontube run in which water was injectedinto the air feed partway through the experiment.The temperatures were measuredby a seriesof thermocouplesplaced along the path of the combus-
nchesthem, and this front (4 is higher in rainingin the path of ntial reductionin the through a given volature of the combusd of the front, it may rrderto achieveeffecI upon as a meansof iace steam generator. equiredfor the recovg residualoil uncoked
t E
t
'-6
E ig
t
E 3 o
lition obtainedif the on front just trails the rf steam is generated bustionzone is not itrm condensationzone bmbustion
Chap.9
s
t
Figure 9.34 Temperature and Saturation Profiles for Wet Combustion (from Latil 1980) Wet Combustion
445
Rua !2 l,. t.ot raL. |.Fd}l
I I
llrmni .rala?
d cailnrara lalach-
r) .a
I ta a
t
lraa.tn|.|
Figure 935 Tcq (from Burger ll t
Figure 9.35 Temperaturesas a Function of Time for Various Locations along CombustionTube (from Burger and Sahuquet1973)
tion. As the combustionfront approachedeachmeasurementpoint, the temperature increased,reacheda maximum,and then fell as the front passedalong. Severalfeaturesshouldbe noticed: o The width of the high-temperaturezone decreasedmarkedly when the water was added. o Water addition did not greatly affect the peak temperature.Presumably,the two effectsof water on the combustionfront temperaturethat were discussed previouslyalmost compensatedeachother. o A distinct steamplateauformed when the water was added. The sametemperaturemeasurements are plotted as instantaneoustemperatureprofiles in Figure 9.36, and the sameobservationscan be made from an examination of this diagram. Figure 9.37showsanalytical data for the producedgasfrom the sameexperiment. The gas composition showed no change as a result of the water addition. This indicatesthat the fuel was of the samecompositionwith water addition as it waswithout it. Although the composition of the fuel did not changewith the addition of water,there was a large changein the quantity of fuel. This is shown in Figure 9.38, wherethe positionsof the combustionfront, the condensationfront, and the vaporization front are plotted againsttime. At the point where the water was added,the 46
In Situ Combustion
Chap,9
I
i
I
E
IT Figure 937 Cq Sahuquet1973) Wet Comh.stin
lnr.rrrer
rns along
l. gll
Figure 9.36 Temperatures as a Function of the Distance along the CombustionTube (from Burger and Sahuquet1973)
fnt, the temperature ed along. edly when the water ure. Presumably,the ) that were discussed led. oustemperatureprotom an examination om the sameexperii the water addition. t water addition as it with the addition of rhownin Figure9.38, front, and the vaporiwaterwas added,the ornbustion Chap.9
Tha.lnll Figure 937 Composition of Produced Gas from CombustionTube (from Burger and Sahuquet1973) Wet Combustion
47
Brsrnninsof I rotrinircfion I
I
|
tlt
t50 E ct a c o
li
roo
o
o o-
R u n8 2
// coodrnrolion fmnf
ll
o E o c .9
i
/ / / /
comburlion fnonl voporirotion front
and materia the rocks ld addedis abo of air). The ct Chiu (l988f. the poresbd tion zoneby mum $aterestimatedfn pies 8ff2 of t
wherc/ I I
I
I
//'/
Timr,houn 60
70
Figure 9.38 Effect of WaterAddition upon the Velocitiesof the Condensation, Combustion,and VaporizationFronts (from Burger and Sahuquet1972)
condensationfront acceleratedas more heat was transported ahead of the front. The additional steamhad the effect of reducingthe residualoil left in the path of the combustionfront, and, as this decreasedthe availablefuel, the burn could movefastereventhough the air rate was kept constant. Similar resultshave been reported by Josephand Pusch(1980)for a field pilot studyin the Bellevuefield in Louisiana.The test, carriedout by Cities Serviceinfive-spotpatterns.One of thesepatternswas operateddry volvedtwo side-by-side and the other, wet. Someresultsfrom this paperare shownin Figure 9.39,where the heated reservoirvolumes are comparedas a function of the volume of air injected.[t wasconcludedthat with wet combustion,higherrecoveriesof oil could be expectedbecauseof better volumetric sweep,that the air volume required to processa given reservoirvolume was reducedby 63%, and that lesstime would be required becauseof the lower air requirement.
Chiu also ce steamzoneplus the hea jectedwater percentageo so doesthis percentage b
I
:
6 3
o I o o
o
Water-to-Air Ratio
!
The ratio of water to air that shouldbe usedin wet combustiondependsupon such factorsas the fuel concentration,the water content alreadypresentin the reservoir, and the possibility of water intruding into the combustionregion from outside the pattern. In principle, the amount of water to be addedcan be calculatedfrom heat
M8
In Situ Combustion
Chap.9
e
Wet Cornhrsl
Brglnningof woftn injtction
I
I ! !
R u n8 2
,l
t50 E a, , C
condanrction fr!|rf
o c
conburlion front voporirotion fFonf
o
o c .9
and materi the rocksI addedi; ah of airr. The c Chiu r l9EE the poresh tion zone ! mum \r'ate estimatedfi pies 8{r? o{
roo
6 o
ii/
o
xherc
/ Timl,hounr 40
50
60
70
{)
Figure 9.38 Effect of WaterAddition upon the Velocitiesof the Condensation, Combustion,and VaporizationFronts (from Burger and Sahuquet1972)
condensationfront acceleratedas more heat was transported ahead of the front. The additionalsteamhad the effect of reducingthe residualoil left in the path of the combustionfront, and, as this decreasedthe availablefuel, the burn could movefastereventhough the air rate was kept constant. Similar resultshavebeenreportedby Josephand Pusch(1980)for a field pilot studyin the Bellevuefield in Louisiana.The test,carriedout by Cities Serviceinvolvedtwo side-by-side five-spotpatterns.One of thesepatternswas operateddry and the other, wet. Someresultsfrom this paper are shownin Figure 9.39,where the heatedreservoirvolumesare comparedas a function of the volume of air injected.It wasconcludedthat with wet combustion,higherrecoveriesof oil could be expectedbecauseof better volumetricsweep,that the air volume requiredto processa given reservoirvolumewasreducedby 63Vo,and that lesstime would be requiredbecauseof the lower air requirement.
Chiu also c steam zon€. plus the trca jected$atcf percenlage ( so does thb percentaeet
t I
Water-to-Air Ratio
t
The ratio of water to air that shouldbe usedin wet combustiondependsupon such factorsas the fuel concentration,the water content alreadypresentin the reservoir, and the possibilityof water intruding into the combustionregionfrom outsidethe pattern. In principle, the amount of water to be addedcan be calculatedfrom heat
448
In Situ Combustion
Chap.9
-
Wet Comhrst
and material balancesusing the objectiveof removingmost of the excessheat from the rocks left behind the combustionfront. In many cases,the amount of water addedis about200Io 250B per million SCF of air (0.92to 1.15lb waterper pound of air). The choice of the water-to-air ratio to be employed has been discussedby Chiu (1988).If low water-additionratesare employed,the addedwaterpartially fills the poresbehind the combustionfront and doesnot removeheat from the combustion zone by forming steamto condensebeyondthe combustionfront. The minimum water-to-air ratio required for water to be available for evaporationcan be estimatedfrom the followingequation;this assumesthat, at the limit, water occupies 80Voof the pore volume behind the front.
n-"= uffi6 whereR,o Ro, 6 Bs pw
Condensation, | 1972)
aheadof the front. ril left in the path of uel, the burn could 1980)for a field pilot by Cities Serviceinrnswas operateddry n Figure 9.39,where he volumeof air inveriesof oil could be rme required to pro:sstime would be re-
(chiu 1e88)
(e.s)
is the massof water per unit volumeof air is the volumeof air requiredto burn a unit volumeof reservoir is the porosity is the formation volume factor of the air behind the front is the densityof water.
Chiu also calculatesthe heat carried forward from the combustionfront into the steamzone.This is equalto the heatin the dry gasat the combustiontemperature plus the heat in the watervapor-both the vapor from the vaporizationof the injectedwater and that from the water formed by combustion.He expressesthis as a percentageof the heat of combustion.As the quantity of injected water increases, so doesthis percentage. At the limiting conditionfor normalwet combustion,this percentagebecomeslffiVo.This is an absoluteupper limit. Chiu recommendsthat
1o' 30
I
o
'o
F
= o U F u
t0
o
: F
n dependsupon such :sentin the reservoir. lion from outsidethe calculatedfrom heat
cmbustion
Chap.9
U
UMSC'
lo 20 CUMULATIVE AIR IT{JECTEO
Wet Combustion
Figure 9.39 Comparisonof Heated Volumes for Side-by-SideWet and Dry Five-SpotPatterns(from Josephand Pusch 1980)
449
the percentageof the heat of combustioncarried forward to the steamzone should not exceed85% and that combustiontube experimentsshould be conductedto showthat this is workablefor a particular reservoirsituation. Figures9.40 and 9.41show the resultsof Chiu'scalculationsof the water-toair ratio requiredto carry variouspercentages of the heat of combustionforward for typical reservoirconditions.Figure 9.40showsthe water-oilratio as a function of the air requirementfor air ISC. Figure 9.41showsthe effect of using enriched air for a particularreservoir. IN SITU COMBUSTIONIN TAR SANDS A processfor utilizing in situ combustionwithin tar sanddepositsmust overcome two fundamentalobstacles: o There is little or no initial injectivity in tar sanddeposits. o The low volatility of bitumen, togetherwith its asphalticnature, makesthe fuel depositionload very high. The depositioncan amountto Z to 3 lbft3 of reservoir,whereast lb/ft3 would be sufficientto raisethe reservoirto 500'F. There havebeensomeattemptsto producebitumenfrom tar sandsby in situ combustionwithout prior heating.AMOCO operatedseveralpilots at GregoireLake in Athabasca.Their processis describedin a paperby Jenkinsand Kirkpatrick (1979). lt involvedthe injectionof air into wellslocatedwithin invertedfive-spots.The formation was ignited by first injectingsteamand then air. The processwas carried out in three phases. In the first phaseof the process,the objectivewas to heat the reservoirby combustion.Injection was continueduntil the combustionfront approachedthe productionwells.Relativelylittle bitumenwasproducedduring this phase. In the secondphase,air injectionwas stoppedand the reservoirpressurewas loweredby allowing productionat the productionwells. It was thought that this productionwasassistedby the flashingof connatewaterto steamwithin the heated reservoir.
'i\*: \NIi. l\
-€ g16 v
kt
SupaNot Combudion
3oo
E
200
ai
t
: 6
s
"."-"t :
,
i Dry Comburrion
;
loo
i , :
: I
r6{,
200
250
300
m aeouneuerr h.(sn/m'l
450
360
400
Figure 9.40 Effect of Air Requirementupon the Water-Air Ratio Requiredto Achieve Various Percentages of Carry Forward of Heat of Combustion.The ParameterIs the Percentof Heat of CombustionThat Is Carried Forward to the SteamZone (from Chiu 1988). In Situ Combustion
Chap. 9
In the f producebitu Apart I information , AOSTRA. h When r reservoir.tlt may alrea$tion, combud front advanc front adranc may fall. Lr from the nm in the cased tial availablc This pn usingin situ meansof pro cyclic steamr nomic produ ing the reser This co Companvin 11.5'APIcrr Westernpill waspredicte than 30cZ.Tl ing designprt cessful.and i possibleb1 o as high as tlu was conclud
In Situ Corrb.
eam zone should be conducted to ; of the water-tonbustion forward rtio as a function rf using enriched
1200
ro
5 E. t !
|m c
l(n !o0
G E
aoo
2
m
is must overcome
o
m
,ro
60
tO
oxtcCl{ Mou PEaCEiIT
ature,makesthe to 2 to 3 lbft3 of :servoirto 500'F. ls by in situ comGregoireLake in ,irkpatrick(1979). !'e-spots. The forlcesswas carried : the reservoirby t approachedthe his phase. 'l'oir pressurewas thought that this *'ithin the heated
:t of Air I the Water-Air Ratio :r e Various rr.r Forwardof Heat ne ParameterIs the iCombustionThat Is o the SteamZone
x.rstion
Chap. 9
=I
E
+ o ()o
g
Figure 9.41 Effect of OxygenUpon the Water-Air Ratio Requiredto Carry ForwardVarious Percentages of the Heat of Combustion.The ParameterIs the Percentof Heat of Combustion That Is Carried Forward to the Steam Zone (from Chiu 1988)
In the final stageof the process,air and waterwereinjectedsimultaneously to producebitumenby wet combustion. Apart from the paper just referred to, there appearsto be little published information on the AMOCO project. An expandedpilot was built jointly with AOSTRA, but it was apparentlyunsuccessful. When in situ combustionoccurs in an initially cold, bitumen-containing reservoir,the gas presumablyflows along relativelythin permeablepaths.These may alreadyexist in the reservoir,or they may be formedby fracturing.With ignition, combustioncan occur alongthe surfacesof thesepaths,with a combustion front advancingat right anglesto the direction of flow. However,as the combustion front advances, the supplyof air to it will tend to decline,and the front temperature may fall. Under these circumstances,low-temperatureoxidation may take over from the normalcombustionprocesswith little mobilizationof the oil. Also, just as in the caseof steamfloodingalonga fracture,there may be little pressuredifferential availableto drive the oil toward the producer. This problemmay be overcomeby preheatingthe reservoirwith steambefore using in situ combustion.It appearsto be practicalto use in situ combustionas a meansof producingadditionaloil from a reservoirthat has been producedusing cyclic steamstimulation.Cyclic steamingcan thus serveas a meansfor the economicproductionof perhaps15%of the oil in placeaswell as a meansfor preheating the reservoirto allow the productionof further oil by combustion. This combination of processeswas pioneeredby the Chanslor-WesternOil Companyin the Midway Sunsetfield in California. This reservoircontains an 11.5"API crude oil, which can be producedby cyclic steaming.In the ChanslorWesternpilot, about I5Voof the oil in placewas producedby cyclic steaming,and it waspredictedthat the ultimate recoverywithout combustionwould havebeenless than 30Vo.The projectwas convertedto dry in situ combustionusing the engineering designproceduresdescribedby Nelsonand McNeil (1961).The project was successful,and it was concludedthat oil was producedmore economicallythan was possibleby continuing the cyclic steamrecovery.The production rate was at least as high as that which could be obtainedby steamdrive in the samepattern,and it was concluded that the in situ combustion processwas more economic in this In Situ Combustionin Tar Sands
451
instance.An expandedproject involving 10 injection and 40 productionwells is operatedby SanteFe Energy on the samelease.The project is describedas promising and is producing 1000B/d of oil, of which 800 is enhancedrecovery production (Aalund 1988). BP ResourcesCanada (Donnelly, Hallam, and Duckett 1985; Nzekwu, Hallam, and Williams 1988)is following a similar approachat its combustionpilot at MargueriteLake in the Cold Lake oil sandsdepositin Alberta. [n its process, BP first producedoil from the tar sandsby steamstimulation; this required the initial steaminjection to be at abovefracturing pressure.After a number of cyclesof steamstimulation,the operationwas convertedto in situ combustion.Initially, BP used air in situ combustion,as in its original plans.Subsequently they converted from the use of air to oxygenand have now had considerableexperiencewith pure oxygeninjection. BP found that the combustionzone overridesthe reservoirand movesrapidly along the fracture paths opened during cyclic steaming.To avoid production well damage,they developedcyclic techniquesin which the injection of oxygenis interrupted. Water injection, either as slugsor intermittently, is important in controlling the temperatures and in distributingthe heat(Nzekwu,Hallam, and Williams1988). The cyclic steamingphaseof the processrequires 5 to 7 y to produce 15 to 20Voof the original bitumen in place.It is anticipatedthat with combustion,the recoverywill be doubledto about 30 to 50Vo.BP startedpilot operationsat Marguerite Lake in 1977 and carried out cyclic steamexperiments,wet-air combustion,and, since March 1983,enriched air and high-purity oxygencombustion. A larger semicommercialoperation was built in 1983at nearby Wolf Lake; this started operationsin early 1985.This project has L92start-up wells that were directionally drilled from 10 satellites;it is designedto produce 1100m3/d of bitumen. After the cyclic steamphase,it is planned to incorporatecomtustion (probably using oxygen)in the early 1990s. Wet combustionhas considerablepotential and many advantageswhen used with tar sands.It provides a meansfor reducingthe quantity of injected air that would be neededto consumethe very high fuel load that arisesbecauseof the composition of the bitumen. Wet combustionproducesa steamfloodaheadof the combustion front that drives oil ahead,and this reducesthe fuel load. [n addition, it is probablypractical to look upon the wet in situ combustionmechanismas an in situ steamgenerator.This leadsto the concept of not burning completelythrough the reservoir,but stoppingafter adequatesteamfor recoveryhas been generated.Thus, in practical bitumen, in situ combustionprojects,it is probably economicto leave behind considerablevolumesof unburned reservoir. USE OF OXYGEN OR ENRICHEDAIR
Potentid Ar
f. Elinir givea o Fctin tinr.I speiq inirt. for sla couE3| 2. The cq highcr, the a! the vir analyr tively (l
a
li 7 It
l: .t t
{
a a
r5
a
a (:'
I rlgr
One of the most interestingcurrent areasof developmentin in situ combustionis the use of enriched air or oxygenin place of air. This possibility was suggestedby H. Ramey (1954). For the useof oxygento becomean economic,commercialreality, it is necessary for its advantagesto outweigh its disadvantages. As it is seenat present,the following are the major advantagesand disadvantages. In Situ Combustion
Chap.9
and C
3one SCt reservoir.Slcinjectionof l([
0.7x ld SCE may reducctha
Useof Oxtga
luctionwellsis opribed aspromising covery production :t 1985; Nzekwu, s combustionpilot rta. In its process, s requiredthe iniumberof cyclesof stion.Initially, BP lly they converted rcriencewith pure and movesrapidly id productionwell of oxygenis intertant in controlling nd Williams1988). r to produce 15 to ombustion,the reions at Marguerite combustion,and,
Potential Advantages for the Use of Oxygen 1. Elimination of nitrogen reducesthe gasvelocity at the producingwells for a given oxygen-injectionrate. This in turn can allow a higher rate of oxygeninjection and can give much more rapid heat production and shortenproduction time. As has been mentioned previously,it is also possibleto use larger well spacing.With air, the rate of production of heat within the reservoirfrom an injection well is frequently lessthan can be achievedby using the samewell for steam injection. with oxygen injection, the rate of heat production becomesapproximatelyequal to that which is achievablewith steam.3 2. The concentrationof carbon dioxide in the gaswithin the reservoir is much higher, and it hasbeen suggestedthat this will improve recoveryby increasing the amountof carbondioxidedissolvingin the crude;this will tend to lower the viscosityand causeswelling.Figures9.42 and 9.43 comparethe flue gas analysesfound in combustiontube experimentsusing air and oxygen,respectively (Mossand Cady 1982).
o I
ton.
rearby Wolf Lake; up wells that were 1100m3/dof bituombustion(probalntageswhen used rf injectedair that ecauseof the comaheadof the comJ. In addition,it is anismas an in situ rletelythrough the n generated.Thus, economicto leave
{
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78
h |!
(, I
35 o
aa
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it
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-f
6
o q
o it
(,
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llne, situ combustionis y was suggestedby reality,it is necesgen at present,the rbustion
Chap.9
hours
Figure 9.42 CombustionTube Run with Air 12' Lindbergh Crude (from Moss and Cady 1982) 3OneSCF air generates of about 100Btu when the oxygenwithin it reactswith the fuel in the reservoir.Steaminjection gives about 1000Btu per pound of steam.Thus, to be equivalentto the injection_of1000B/d of steam(350 x 106Btu/d), one would have to inject 3.5 x 106scF)/dof air, or 0.7 x 10"SCF/dof 02. In practice,the higher efficiencyof utilization of the heat from combustion may reducetheserequirements.
Use of Oxygenor EnrichedAir
100
I coz -..r
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r-
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+, 6
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o >r ?l a { |l
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58 hours flno,
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3. The heatingvalue of the producedgaswill be much higher becauseit is not diluted with nitrogen. Also, the high concentrationof carbon dioxide may makethe gasusefulasa sourceof carbondioxide.It is possible,then, that the producedgas may have a positivOrather than a negativeeconomicvalue. It could, for example,be possibleto separatethe COz for sale and utilize the resultanthigh-heating-value tail gas as a fuel. The combustionof the tail gas from conventional in' situ combustion is difficult and requires special equipment. 4. Theremaybe lessoverridethan with air for the sameoxygen-injection ratebecauseof the reducedvolumeof gasand perhapsbecauseof its higherdensity. PossibleDisadvantagesof the Use of Oxygen 1. There is a hazard in using high-pressure, high-concentrationoxygenin cirwhereit can be mixedwith hydrocarbons. cumstances A particularconcernis to eliminatemixing of oxygenwith oil in the injectionwell. This can occur if the pressurein the injectionwell is allowedto fall during operationand thus allow oil to back up into the well. A likely causefor suchan eventwould be the failure of the oxygensupply.Precautionsthat can be usedto preventthis includethe provisionof backupoxygenand meansfor injectingwaterinto the In Situ Combustion
Precr tro& nece lociri l9&l: minil tion i 3. The ir air ct the n 4. As is with r
The Cost t
Figure 9.43 CombustionTube Run with 02 12" Lindbergh Crude (from Moss and Cady 1982)
454
well r wirb For c able I nelly 2. Spec riqls tisr r
Chap.9
There is al The mosl c practicalf(t and fractio Coolingis r batic expa comes fro0 90 psig is s pressure(se for air liqu O*r-g in insulate by BritishP by Arco ar Roberts1S The li provide a s oxygen and startup.arx Systemsfu Duckerr(19 The o fifth of rhc
Useof Oxyg
o
..1
+, a &
c
r3 l{
rt (, I c
rso l.
B T 0t o l{ a o o
I
well in the event of failure of the oxygen supply. The mechanicalproblems with oxygen in situ combustionhave been largely solved in pilot operations. For example,BP in their Cold Lake pilot has injected oxygenfor a considerable period and are contemplatingits use on a large commercialscale(Donnelly, Hallam, and Duckett 1985). 2. Specialprecautionsare also necessaryto handle oxygen.For example,precautions must be taken to avoid sourcesof ignition that could causethe combustion of ordinary steel pipe carrying high-pressureoxygen. Although these precautionsare well known in the conventionalhandling of oxygen,they introduce a new degreeof complexityinto oil field operations.It is, for example, necessaryto minimize dust particlesand to stay within maximum line velocities to avoid ignition from static electricity (Henningson and Duckett 1984;Hvizdos,Howard, and Roberts1983).The choiceof materialsthat will minimize corrosion problemsand be compatiblewith oxygenin situ combustion is discussedby Zawieruchaet al. (1988). 3. The investmentcostfor oxygen-separation plantsis higherthan that for simple air compressors. This is partially-and in somecasescompletely-offset by the reducedpower requirementto compressthe smallervolume of oxygen. 4. As is discussedlater, low-temperature oxidationseemsto occur more readily with oxygenthan with air-particularly at higherpressures. The Cost of Orygen
: tfrom Moss
er becauseit is not arbon dioxide may sible,then, that the economicvalue. It saleand utilize the rbustionof the tail nd requiresspecial en-injectionrateberf its higherdensity.
ltion oxygenin cirrarticularconcernis ll. This can occurif r operationand thus r an eventwould be usedto preventthis :ctingwaterinto the mbustion
Chap.9
There is alreadya vast experiencein the manufactureof oxygen on a large scale. The most economicmethod for manufacture,and the only developedone that is practical for considerationfor large-scaleoperations,involvesthe liquefactionof air and fractional distillation to separatethe oxygen.The processis very efficient. Cooling is achievedby countercurrentheat exchangewith the products and adiabatic expansionof the compressedfeed. The free energy to operate the process comes from the compressionof the feed. An input air pressureof about 75 to 90 psig is sufficient to drive the processand produce pure oxygen at atmospheric pressure(seeTable9.2).Newton(1979)givesa concisedescriptionof the technology for air liquefaction and fractionation. Oxygenfor small combustionpilots is usuallytransportedto the site as liquid in insulatedtrailers.Productionpilots of this type have been operatedin Canada by British Petroleum,by Husky Oil, and by Dome Petroleum.There havebeentests by Arco and by the GreenwichOil Companyin Texas(Hvizdos, Howard, and Roberts1983). The liquid oxygenis pumpedunderpressurethrough avaporizer.Itis usualto provide a similar facility for the vaporizationof liquid nitrogen so that a blend of oxygen and nitrogen can be injected. A blend correspondingto air is used for startup, and the oxygenconcentrationis increasedgraduallyas the burn progresses. Systemsfor the supply of oxygen to fire floods are discussedby Henningsonand Duckett (1984).Figure 9.44 showsa systemsuitablefor a field pilot. The compressionof the oxygenfrom a separationplant requiresonly about a fifth of the energythat would be required for the compressionof the sameamount Use of Oxygenor EnrichedAir
455
YsrsrEr uqro orvB€xarPzL -5 ,
:: l\
z! s<
: I
.- ' {
Ornur OryDart 8la.e.
=z ou .0 6>
fui
sqxt
9Y
36
;< s
:i
; t
...
.!'.. :i >r
{ :c
l/lgodt
FbrComola
tqhlrtg
Figure 9.44 Liquid Oxygen Vaporization Systemfor In Situ Pilot Operations (from Henningsonand Duckett 1984)
of oxygenas air. This savingin compression work can offset the work neededto separatethe oxygenfrom air. Whetherthe overallenergyis lower or higherdependsupon the final delivery pressure.Figure 9.45 (Hvizdos,Howard, and Roberts1983)showsa comparison of the power requirementsto produce4 million SCF/dof oxygenas air and as pure oxygen.At pressuresabove about 175 psia, the production of oxygen requires lesspower. The costsfrom the samereferencearecomparedin Figure9.46.Which source of oxygenis cheaperdependsnot only upon the pressurerequiredbut also on the volume.This is becauseof the very substantialeconomyin scalein the manufacture of oxygen;largeplantsare more economicalthan small ones.This is a significant problemwhen it is desiredto experimenton a small pilot scalewith oxygento developthe method. The discontinuitiesin the curves of Figure 9.46 reflect the by switchingfrom recipeconomiesthat can be madein the costof air compression rocatingto turbocompressors if the requirementis large enough.
Rathr-: l e a s t ,i n u s : ; l ima in the.c other factr.n r tration.It:ce pureox\qen. An inte is given br k c o m b u s t i o nr s c o m p a r et h c I o r e n r i c h e d:
The Effect o{ with Oxygen
The precedrn fected bv dc'g by Moore an'J case (Nloorc tube, ther ra: I t}_
i I
\ RELAT IVE OXYGEN COST
nvvGEN
40 60 100 200 O E L I V E RPYR E S S UP RS EI A
456
Figure 9.45 Electrical Energy to Produce4MSCF/dof Oz or Air Containing4MSCF/dof 02 (from Hvizdos, Howard and Roberts1983)
ln Situ Combustion
Chap.9
' lrri I I
: I-+tc
Use of Oxvgre.
r s[
F;EI
;fi hi
EgHI t ;l Figure 9.46 Differential Cost for Oxygen Comparedto Air (from Hvizdos, Howard, and Roberts1983)
M M S C F DO F C O N T A I N E DO X Y G E N
)perations (from
re work neededto n the final delivery ows a comparison as air and aspure rf oxygen requires l.tl6. Which source ed but also on the in the manufacture 'his is a significant ile with oxygen to re 9.46 reflect the from recipltchine
Rather than produce pure oxygen there is some economy,in oxygen cost at least,in usingenrichedair. This is shownin Figure 9.47.Although there are minima in these curves,the differencesare not very great, and it seemslikely that other factorssuchas reservoirperformancewill determinethe best oxygenconcentration. It seemsreasonable to expectthat this will likely turn out to be essentially pure oxygen. An interestingdiscussionof the potential for in situ combustionusing oxygen is given by Fairfield and White (1982).A state-of-the-artreview of oxygen in situ combustionis presentedby Garon, Kumar, and Cala (1986).[n their review,they comparethe physicalcharacteristicsof nine different field projectsthat use oxygen or enrichedair. The Effect of Pressureon Combustion Performance with Oxygen The precedingdiscussionof oxygencostspresumesthat burn performanceis unaffected by degreeof oxygen enrichment. Combustiontube experimentsperformed by Moore and Bennion at the University of Calgarysuggestthat this may not be the case (Moore et al. 1987).Using a 4-in.-diameter,6-ft-long adiabaticcombustion tube, they ran a seriesof dry combustiontube testsusing95%oxygen-enriched air LI
s
RELATIVE OXYGEN
cosT
:clricalEnergyto ,d of 02 or Air CFld of Oz (from d and Roberts1983) nbustion
Chap.
60
70
80
90
% O X Y G E NI N P R O D U C T
Use of Oxygenor EnrichedAir
t00
Figure 9.47 Effect of OxygenPurity on Cost (from Hvizdos, Howard, and Roberts1983)
457
Effect of Pressureon Oxygenand FuelRequirements
Nelsm follo*'ing: 120
o Total ei o Rate aa r Total I
(D
E B ro .Y
110 #
c o
100E '=
c o
=(o
Eoo o
Total RrC Lr
soe s
.: = ct o tr' 20 o
The fuel load ent porositf i
L
6s
so Itr X-:
o 70E
5 IL i:
. Rate d ' OPeratir
E
where ll F
o
10
19
a
a
60o
o
The acre-fod tional petrolcr
50 024681012
TotalPressure(MPa) Figure 9.48 Effect of Pressureon Oxygen and Fuel Requirements-Combustion and Tube Experimentswith AthabascaSandCore and95VaOz (from Moore et al. 1987)
Air Retpircrn
and Athabascaoil sandcore.Figure9.48showsthat the overalloxygenand fuel requirementsappearedto increaselinearly with operating pressure,nearly doubling over the rangeof 2700to 10,300kPa (400-1500psi). They attributedthis increase to the preoxidizingeffect causedby the high oxygenpartial pressures. This is consistent with the observationsof Alexander, Martin, and Dew (1962)already presented (see Figure 9.17). Both Moore and Alexander noted that oxygen partial pressurehad a much smallereffect on normal air (21%oxygen)combustionparameters. Further observationson the relative performanceof oxygenand air in situ combinationin a large number of combustiontube testsare summarizedby Moore, Bennion,and Ursenbach(1988). DESIGNOF IN SITU COMBUSTIONPROJECTS The practical design and sizing of facilities for in situ combustion projects have beendiscussedby Nelsonand McNeil (1961)and by Gatesand Ramey(1980).These are two excellentpapersthat will be of considerableassistanceto an engineerfaced with the planningand designof a new project.Chiu (1988)discusses a relatedanalytical model that extendsthe theory. In Situ Combustion
Chap.9
The air consu and this is pn volume of res
where z{
u w
The total air r per unit r-oluo volumeis egu sweepefficiea of 62.6%strm
AN Air
Designof h 9t
Nelson and McNeil describe means for making simple following:
110 #
c o
E
100E '=
r . r o r
of the
Total air requirements. Rate and pressureat which the air must be supplied. Total amountof oil that will be produced. Rate at which the oil will be produced. Operatingexpense.
=(o
Total Fuel Load
60
The fuel load measuredin a combustiontube test is adjustedto allow for the different porosityin the reservoiras comparedto the laboratorysandpack.
eoes oo Itc
lb fuel/acre-ft burned = 43,560WF
X-
o 70E o
ooo 50
whereW
F
(e.6)
is lb fuelft3lab test
is (1 - 6il1$ - 6,)
0^ is reservoirporosity 6o is sand-packporosity The acre-footmeasureof reservoirvolume is often used when employing conventional petroleum-measuring units. 1 acre-ft = 43,560ft3
rents-Combus02 (from Moore
rll oxygenand fuel re;sure,nearly doubling tributed this increase rressures. This is conw (1962)already preI that oxygenpartial ) combustionparamexygenand air in situ rmmarizedby Moore,
rbustionprojects have I Ramey(1980).These e to an engineerfaced iscusses a relatedana)ombustion Chap.9
Air Requirement The air consumptionin the laboratorytube is expressedas SCF per pound of fuel, and this is proratedas shown in equation9.6 to give the air requirementper unit volume of reservoir. V^ t=fiwF
(e.7)
whereA is SCF airlCF reservoir V, is SCF air in lab test We is total lb of fuel burned in lab test The total air requiredfor the project is estimatedby multiplying the requirement per unit volumeby the estimatedvolumeof the reservoirthat will be burned.This volumeis equalto the volumeof the patternmultipliedby an estimatedvolumetric sweepefficiency.For a five-spot,Nelsonand McNeil suggestthat a sweepefficiency of 62.6Voshouldbe employed;this leadsto equation9.8. MScF/acre-ft burned Air per acre-ft burned : 43,56041106 Air per acre-ft pattern = 0.626 x 43,560A/106
(e.8)
= 27,269A/106MscF/acre-ft pattern Designof In Situ Combustion Projects
459
Air Rate and Pressure The rate at which air is introduced controls the burning rate.
(e.e)
U=Au where U is air flux SCFft'z d A is SCF air/CF reservoir z is burning front advance,ftfd
As hasbeen discussedpreviously,avery low burning rate is insufficient to maintain combustion,and a very high rate causeserosionproblemsat the production wells. The practical maximum gas rate at a production well seemsto be about 500,000to 600,000SCF/day. It is commonto choosean injectionrate that will maintain, initially, a constant burning front velocity. A velocity of 0.5 ft/d is recommendedby Nelson and McNeil. As the front advances,the air-injectionflow is increasedup to the capacity of the compressor. Followingthis, the injectionis maintainedat the maximumrate. During this main period, the rate of advancedecreasesbecauseof the increasing area of the front. Figure 9'49 shows how the air-injection rate and cumulative injection vary with time. The gradualdecreasein the rate at the end of the production is required to minimize oxygenbypassing.[n a large multiple-patterndevelopment,the air capacity that is madefree during this period can be utilized to start up a new pattern. Nelson and McNeil discussthe schedulingof air for production from a number of staggeredpattern operations. Nelsonand McNeil considerthe lowestburning velocity at which satisfactory combustioncan be obtained is about 0.125tt/d. The methodsof Ramev described earliercan alsobe usedto studythis.
Gat.'. e to gire a n::' this flur iilr reserrc-ri::i The erl tain a rni::nr s i n c ei t r r : 1 .a b e s to b t a : : e c Asarr e q u a t i o nv : i l to the f lou .-l permeat'iiitr abilitl of 5-. Equa:i. the marinut mum value.
*here P D
rl
T j
: t1
c
o .P
(E G tr
.9 .H
o o tr
.9 {
InjectionRate
Oil Displaced
C'
o
A s s u m i n et h a displaced ::ruThis is giren I
E o .z +. (g
E E J
L
o
* here
t' c (g 'T.\s:'::::
Time
w e l la su p c : : : c temnerer,rr.
Figure 9.49 Air Injection Programm(after Nelsonand McNeil 1961)
460
In Situ Combustion
i
-.
( 1 9 7 7r)e 3 . : : sr r :
Chap.9
Design of In ft
(e.e)
ufficient to maintain he production wells. ' be about 500,000to rain, initially, a con:nded by Nelson and ed up to the capacity rt the maximum rate. rse of the increasing Llativeinjection vary roduction is required elopment,the air carrt up a new pattern. rn from a number of at which satisfactory of Ramey described
Gatesand Ramey(1980)considerthat the air capacityshouldbe great enough to give a minimum burning rate of 0.15ft/d or an air flux of 2.15 scF/h ft2, but this flux shouldbe calculatedas if the air were passingthrough only ] to ] of the reservoirthickness.a The existenceof a limiting gas-production rateper well and the needto maintain a minimum burning advancerate tend to make the use of oxygenattractive, sinceit will allow largerratesand wider patterns.The injectionpressurerequiredis best obtained from actual field injection test data. As a means of making a prior estimate, Nelson and McNeil recommended equation9.10.This requiresan estimateof the permeabilityof the cold formation to the flow of gas,i.e., the permeabilityof the formationmultipliedby the relative permeability.If there is no specificinformation, they suggestthat a relative permeability of 5Vocan be used. Equation 9.10gives the pressureat the time the air-injectionrate first reaches the maximum value. This is the point where the pressurereachesits maximum value.
P ? . = P*' zl.i'" p " z t \ f ' | 4 _ \ - 1 . 2 3 8 . l \oro3/.1/ L'n\',,,r,r I where Pi, Pio Ita Tf a ty ks h rw v1
(e.10)
is injection well bottom hole pressure,psia is production well bottom hole pressure,psia is maximum air rate, SCF/d is air viscosityat Ty,cp is absoluteformation temperature,R is well spacingfor the five spot pattern, ft is time to reachmaximumrate, d is effectivepermeabilityto air, mD is formationthickness,ft is production well radius, ft is initial rate of advanceof burning front, ft/d
Oil Displaced Assumingthat there is no oil left in the burned-outzone,then the amountof oil displacedmust be equal to the original oil in place minus that consumedas fuel. This is given by equation9.11. Oil displaced= oil at start - fuel
- y:\ B/acre-rt = n.soo1:9i '"'"""\ -' s.ot 35o l
where So Qo 43,560 5.6r 350
is fractional oil saturation is reservoirporosity, fraction ftz facre ft3/B (assumed) lb fue/B
*The temperature at the firefront for a given rate of advance dependsupon the fuel load as well as upon the air rate. Thus a very heavy oil that gives a high fuel load will give a higher front temperaturefor the samerate of advance.Thus, for example,in the Midway Sunsetfield, Counihan (1977)reports excellentcombustionresultswith a designrate of only 1 in./d.
Neil 1961) omtustion
(e.11)
Chap.9
Design of In Situ Combustion Projects
461
Gatesand Rameypointedout that, at an intermediatetime, the cumulativeamount of oil producedcan be greateror lessthan the amount of oil displacedfrom the burned zonebecauseof two opposingfactors: 1. Oil aheadof the front may be displacedto the productionwell by other mechanisms"includinghot water drive, steamdrive, hot gasdrive, vaporization, misciblephasedisplacement,expansionand gravity drainage."These mechanismsare all made more effective by the elevatedtemperatures. 2. Oil may have to form a bank aheadof the combustionzone in order to fill someof the gassaturationthat is presentinitially in the reservoir. Basedon this conceptand usingexperimentaldatafrom the long-standing and successfulSouthBelridgepilot, Gatesand Rameydevelopedthe chart in Figure 9.50. This correlationpredictsthe cumulativeoil productionas a function of the fraction of the reservoirthat has been burned and the initial gas saturation.It is basedupon considerabledata from cored wells at the pilot and also upon laboratory experimentsthat demonstrated the effect of initial gassaturation. Figure 9.50 predictsthat there is a delayperiod before oil is producedthat corresponds to the formation of the oil bank and that the initial production,when it eventuallyoccurs,is at a muchhigherrate than the average. A delayin the initial productionof oil is shownby the data shownpreviouslyin Figure 9.10. In using the correlationit is necessaryto know the fuel concentration.This may be obtained from combustiontube experimentsor, if these are not available, from the correlationin Figure9.51.Figure 9.52 maybe usedto estimatethe air requirementto burn the fuel. Using the correlationin Figure 9.50,we can measurethe slopeof the appropriate curve and calculate the instantaneousoil rate as a function of the fraction burned.Using this informationand the fuel requirement,we can calculatethe instantaneousair-oil ratio as a function of recovery.The resultsof such a calculation for the SouthBelridgefield are shownin Figure 9.53. The initial current air-oil ratio is muchlower than the averagerate shownby the dottedhorizontalline. The cumulativeratio is also lower than the averageexcept at the end, where it converges.
roo: roo-I
f
?oo-
e 'oo0!
o
In prrti that the prodr uneconomic h the dottedlic The calc the combusir gas,and allorr zone.The eto Gatesand Rel air and that it Figure 9. pared to predi that the sprhc when the prod The rcad verv interesliq centrationfru ll-
t aq-
lrl tilfl4.
J
U 5 L o q J
\
F
3
'/fiI
F J
//V
o o It
/. '/,
G 5 o I ! G J
o
462
t
aas safuRAfloil I at I
a
3
I
I t
/lt
+ I
f
3 : + 3
st
7
3
,/
/,
'/t
/xl
t
o o
Figure 9.50 Chart for Estimating Oil Recoveryas a Function of the Percent of the ReservoirBurned (from Gates and Ramey 1980) ln Situ Combustion
Chap. 9
I a
I
>-
i I I olo
Designof In Sitt
cumulativeamount displacedfrom the
F
U
tion well by other ;as drive, vaporizai drainage."These emperatures. ure in order to fill eservoir. g-standingand sucrart in Figure 9.50. s a function of the gassaturation.It is lso upon laboratory )n. il is producedthat rl production,when ' delayin the initial rre 9.10. ;oncentration.This € are not available, estimatethe air reslope of the approtion of the fraction an calculatethe in,f sucha calculation :ragerate shown by han the averageex-
)
@
z o U E
OIL GRAVTTY. 'API
Figure 9.51 Chart for Predicting Fuel Concentration(from Gates and Ramev 1980)
ln practiceit is likely that the processwould not be taken to the very end but that the production would be terminated when the current air-oil ratio reachedan uneconomiclevel.In this casethe final cumulativeratio would alsobe lower than the dottedline. The calculationso far has assumedthat the oxygenis completelyconsumedin the combustionprocess.In practicethere is someunreactedoxygenin the produced gas, and allowanceshouldbe made for this in estimatingthe size of the burned zone. The excessair requirementsmay be estimatedfrom Figure 9.54; however, Gatesand Rameyconsiderthat this figure may overestimatethe amountof excess air and that it is conservative. Figure 9.55 shows the experimental air-oil ratios from South Belridge compared to predictionsmadeusing the precedingmethod. Gatesand Rameypoint out that the spikesin the experimentaldata in this figure correspondlargely to periods when the production wells at the pilot were partly shut in for mechanicalreasons. The reader is referred to the original paper for further details, including a very interestingdescriptionof severalparallel methodsfor estimatingthe fuel concentrationfrom the field data. F E d
I J 2
o
) J
I
\
J
u 2 E
e 0 o
c. t art for EstimatingOil unction of the Percent 'Burned (from Gates rl mbustion
Chap. 9
o U E
c cRuoE otl GRAYITY,.APt
Designof In Situ CombustionProjects
Figure 9.52 Air Requirementsper Acre-Foot of Reservoir (from Gates and Ramey 1980)
463
.o
a
I
I
t
]o.
;
o F
t
20
G J o
- _DlslLlc_E[ENr_\_ _-z_
;
to
W
_ _
lg.
a <e Figure 9.53 ComputedAir-Oil Ratio for South BelridgeField (from Gates
o l L R E C O V E R Y - ? o OOFI L A T S T A R TL E S S F U E L
and Ramey 1980)
Effect of Water-Air Ratio on Oil Recoveryper Volume Burned The correlationof Gatesand Ramey(Figure9.50)for predictingthe oil recoveryas a function of the burned reservoirfraction and the initial gassaturationis for dry combustionin a particularreservoir.Different correlationsmaybe expectedfor differentsituations.For example,in wet combustion,oil is movedaheadby the steam, and oil production occurs more rapidly. This phenomenonhas been studied by Moore et al. (1988)in a seriesof combustiontube testswith varyingratiosof water to air. Someof their data are shownin Figures9.56-9.59. Figure 9.56 showsthe effect of adding2 kglm3(ST) of water to the combustion air. Oil production starts when a smaller percentageof the core has been burned, and for a given fraction burned, the oil recoveryis larger.Also, because the fuel loadis lessfor wet combustion,lessair is requiredto achievethe samefraction burned.As a result, the curvesof percentoil recoveryversusquantity of air injected(Figure9.57)showan evenlargerdifference. Resultsfrom similar experimentsusingcoresof Athabascareservoirsandand bitumenthat were reconstitutedby flooding are shownin Figures9.58and 9.59.In this seriesof experiments,runs with much higher water-injectionratios are compared to a dry run.
-.-p The periment.::r slightlr hrg:er peak temptera was coolinerl reasonfor rte It can hr causedoil t.. i tage of more ! unburned fuel t e d a g a i n s :l x Furthcrr quantitr of ar problem de:.-n bustion tut'c tr a mathemati!the quantitr o volvesthe calc fication of the
$ g o o g
o x u
roo o 20 40 60 80 OIL RECOVERY.'6OF LESS FIfL OIL AT START ExcEss^ri .mffii**--aer
464
x roo* rcr.ritxyt
Figure 9.54 ExcessAir from South BelridgePilot (from Gates and Ramey 1980) In Situ Combustion
Chap. 9
Designof In Srt
XOITHLY IN.'ECTEOAh . PR'UJC€O OIL RATIO
o a t
9 F c J
o c
Air-OilRatio mputed geField(fromGates
oi.0ro60oo OIL IECOVERY.Tf
€d g the oil recoveryas iaturation is for dry be expectedfor difaheadby the steam, as been studied by l ing ratios of water ater to the combusthe core has been [ger. Also, because hievethe samefrac:ISusquantity of air a reservoirsand and res9.58and 9.59.In tion ratios are com-
roo OIL AT START LESS
FI,EL
Figure 9.55 South BelridgeCurrent Air/Oil Ratio (from Gatesand Ramey 1980)
The "optimal" water-airratio for this seriesof runswas about4.6.In this experiment, the averagepeak combustion front temperaturewas 608"c. This was slightly higher than that for the dry run (569'c). on the other hand, the average peak temperaturefor the run with a ratio of 6.9 was only 225'C.In it, liquid water was cooling the combustionzone,and unburnedfuel was left behind. This is the reasonfor the relatively low final recovery. It can be seenfrom Figure 9.58that, as in Figure 9.56,the additionof water causedoil to be recoveredsooner.However, in the superwetrun, the early advantage of more productionwas not maintained becauseof the material left behind as unburned fuel. The difference is even more pronouncedwhen the recoveryis plotted againstthe cumulativeair injectionin Figure 9.59. Further insight into the factorsthat affect the oil recoveryas a function of the quantity of air injected can be obtained from the mathematical analysis of the problemdescribedby Chiu (1988).In his paper,Chiu showshow the resultsof combustion tube testssuchas those shown in Figures9.56-9.59can be developedfrom a mathematicalmodel involving steamfloodingaheadof the combustionzone,with the quantity of steambeing calculatedfrom a heat balance.The heat balance involvesthe calculationof the vertical heat lossesfrom the steamzone using a modification of the Marx-Langenheimmethoddescribedin Chapter4. 100
t
o o (J o
e o .{ rcessAir from Pilot(fromGates t0) cmbustion
Chap.9
200 PVof Air Iniected
Designof In Situ CombustionProjects
400
Figure 9.56 Effect of Water-Air Ratio on Oil Recovery;CombustionTube Test with Packof AthabascaBitumen and Silica Sand(after Moore et al.)
465
Parameter is Water/Air Ratio xgim3 1s1
o o o o
8so = o o
s 100 S0 c/oof VolumeBurned
Figure 9.57 Effect of WaterAddition upon Oil Recoveryas a Function of CumulativeAir; InjectionTestswith AthabascaBitumen-Silica and Sand Pack(after Moore et al.) TABLE9.7 }:
FIELDPROJECT RESULTS Lloydminster,Golden Lake As Fairfieldand White (1982)havediscussed, the Lloydminsterareacontainsmany reservoirsof heavyoil containedin thin, Lower Cretaceous sands.The oils arevery viscous,and the oil saturationis usuallyhigh; the sandsare very permeable.The reservoirsare estimatedto contain a total of 50 to 70 billion barrelsof oil. The Lloydminsteroils are lessviscousthan thosein the Cold Lake field to the north, and primary productionis possible;well productivitiesof the order of 20 Bld are obtained,but the primary recoveryis only 3 to 8Vo.Becauseof the high viscosityand the fingeringthat occurs,waterfloodingis not very effective;Fairfield and White indicatethat the incrementalrecoveryfrom waterfloodingis of the order of only 2Vo. Figure 9.60 showsthat about 90Voof this oil occurs in sandsthinner than 20 ft, and 50Vooccxrsin sandslessthan 10ft. Becausethe sandsare so thin, steam drive is generallynot applicable.For thermal efficiency reasons,a thicknessof about25 ft or more is necessaryfor steamdrive to be practical. In situ combustionis suitablefor sandsdown to about 10 ft in thicknessand has promisefor allowing efficient recoveryof much of the Lloydminstercrude.It hasthe advantages of usingcheaperenergythan steamrecovery,of not requiringall of the reservoirto be maintainedat the thermal recoverytemperaturethroughout the project,and of removingsomeof the most refractorymaterialas fuel.
( F a i r f i e l da n : \ A
100
wet 4.6 /
lJ ^^
66u tt
E o o o
tso o o
*
.: Suoer Wetb,9 ..
60u
=
1."
o,^
Dryo Parameteris
a
Water/AirRatio
dzo
rg/m31sr1 50 o/oof VolumeBurned
466
100
Figure 9.58 Effect of Water-Air Ratio on Oil RecoveryTestswith ReconstitutedAthabascaTar Sand (after Moore et al.)
In Situ Combustion
Chap.9
: v0
FieldProjectRe
e o o o t
o ;x
iffect of WaterAddition rveryas a Function of ir: InjectionTestswith umen-Silicaand Sand rore et al.)
0
400 200 PVof Alr Iniected
Figure 9.59 Effect of Water Addition upon Oil Recoveryas a Function of CumulativeAir Injection Testswith ReconstitutedAthabascaTar Sand (after Moore et al.)
TABLE 9.7 Propertiesof GoldenLake Reservoir Sand Depth, ft Net sand,ft Original pilot Expansion#1 Porosity, Vo Permeability,md Core data Calculatedfrom productiondata Saturation,7o oil Watcr Originalreservoirpressure. psig Reservoirtemperature,"F Reservoirf luid properties Oil gravity, "API Oil formation volume factor Solutiongas oil ratio, SCF)/B Dead oil viscosityat 70"F.,cp Live oil viscosityat 500psig,cp
'-r areacontarnsmany nds. The oils are very very permeable.The barrelsof oil. te Cold Lake field to vities of the order of ,. Becauseof the high :ry effective; Fairfield Ioodingis of the order n sandsthinner than ndsare so thin, steam asons,a thickness of )al. l0 ft in thicknessand .loydminstercrude. It ry, of not requiring all mperaturethroughout terial as fuel.
Sparky 1600 LJ
20.8 35 1200 8000 82 l8 510 70 t2-13 1.01 45 6300 3500
(Fairfield and White 1982) 100 o
E ao rL o
.z
!:6 0 9+o o o
Ezo Effect of Water-Air Ratio ery Testswith I AthabascaTar Sand et al.) Sombustion
Chap. 9
: v0
0
Field Project Results
48 Sand Thicknessm
12
Figure 9.60 Oil in Placein the Lloydminsterfields as a Function of SandThickness(after Fairfield and white 1982)
467
TABLE 9.8 CombustionCharacteristicsof GoldenLake ReservoirMaterial Molecularweight (unit) Atomic hydrogen- carbon ratio Fuel, lbft3 Fuel, B/acre-ft Unit air requirement at (100% efficiency) SCF/lb carbon SCF/lb fuel scF/ft3 Water formed by combustion, Bfacre-f.t Oil displacedby combustionfront, B/acre-ft TheoreticalAOR, dry combustion,kSCF/B Water-airratio, B/MSCF Residualoil saturation,steamzone: Vo pore space(avg.) B/acre-ft (avg.) Displacement in steam zone, Bfacre-ft
I J.+
1.4 1.93 250 200 t79 345 ))4
t957 7.68 205 22.6 614 1593
(Fairfield and White 1982)
Propertiesof the Golden Lake Reservoir and the combustioncharacteristics are shownin Tables9.7 and 9.8.The oil hasa viscosityof 3500cp at reservoirconditions. There is a large difference between the permeabilitiesmeasuredon core samplesand those calculated from production data. This is thought to be due to "worm holes" in the reservoir,possiblyformed as a result of sand production. The well layout for the Golden Lake projectis shown in Figure 9.61.The original five-spotpattern aroundwell 815-11was ignited in July 1969and expansion1, consistingof two seven-spotpatterns,was ignited in 1974.Water injection was startedat a designrate of 205 B per million SCF in 1972in the original pattern and in July 1976in the expansionpattern. Productionresultsare shown in Figure 9.62 and are summarizedin Table 9.9. An analysisof the producedgasis given in Table9.10.
tfuur Fairfid
TABLE 9.9 GoldenLake Injectionand Production(81-09-30)
Pattern
Cumulative Air Million SCF
Cumulative Water KB
Burned Volume Percent(1)
oil Recovered KB
TABLE9.10 G(
Recovery Percent OOIP
t7.1 39.8 1240 165 567 Original Pattern Expansion1 438 18.3 4.4 D7 Pattern r07 507 J.t 378 t9.7 116 B9 Pattern 562 19.0 5.0 816 Total Expansion1 1069 223 (t)It was anticipated that it would be economic to continue the burn until the burned volume was about 20Vo.There are thus quite a few yearsof production aheadof even the original pattern (Fairfieldand white 1982).
Gffffi !
468
In Situ Combustion
Chap.9
I
I
Field Project Rc
1 0 1. 2 5a c 2329 ac-n
13.4
Primarydrainagearea
l.+
c-15
1.93 :,50 100 179
20 ac .7 B-15 t 460 ac-fl
A-147
_u5 17d
A-15
98.75ac 2049 ac-ft
1 9 57 7.68
D-9
r05 c-10 30 ac
)2.6 611 1,s93
B-10
\
A . 1O T
o-
,
< a_v
623 ac-ft u-d
rustioncharacteristics 0 cp at reservoirconies measuredon core thought to be due to sandproduction. Figure9.61.The orig,969and expansion1, \later injection was e originalpatternand rmarizedin Table9.9.
oil Recovered KB
Recovery Percent OOIP
567
39.8
{38 378 816
18.3 t9.7 19.0
,
.115 acres 2386 ac-tt O--'--
Figure 9.61 Well Arrangementfor Husky'sPilot Projectsat Golden Lake (from Fairfield and White 1982)
TABLE 9.10 GoldenLake ProducedGas Analvsis Component Carbon dioxide Carbon monoxide Methane Nitrogen Oxygen Argon
until the burned volume eren rhe originalpattern
Volume Percent
16.0 0.4 t.2 81.4 0.0 1.0 100.0
(Fairfield and White 1982)
lornbr.rstion
Chap.9
Field Project Results
469
TABLE 9.8 combustion characteristicsof GoldenLake ReservoirMateriar Molecular weight (unit) Atomic hydrogen-carbon ratio Fuel, lbft3 Fuel, B/acre-ft Unit air requirement at (100Voefficiencv) SCVIb carbon SCF/lb fuel
13.4 1.4 1.93 250 200 179 345
scFrt3 Water formed by combustion, B/acre-ft Oil displacedby combustionfront, B/acre-ft TheoreticalAOR, dry combustion,kSCF/B Water-airratio, B/MSCF Residualoil saturation,steamzone: Vo pore space(avg.) B/acre-ft (avg.) Displacement in steam zone, B/acre-ft
laA
1957 7.68 205 22.6 614 1593
(Fairfield and White 1982)
Propertiesof the Golden Lake Reservoir and the combustioncharacteristics are shownin Tables9.7 and9.g.The oil hasa viscosityof 3500cp at reservoir con_ ditions. There is a large difference between the permeabilitiesmeasured on core samplesand those calculated from production data. This is thought to be due to "worm holes" in the reservoir,possiblyformed as a result of sand production. The well layout for the Golden Lake project is shown in Figuri 9.61.The orig_ , inal five-spotpattern aroundweil 815-11wasignited in July p(9 andexpansion i, consisting of two seven-spotpatterns, was ignited in r9i4. water injection was started at a designrate of 205B per million SCF in 7972|n the original pattern and in July 1976in the expansionpattern. Productionresultsare shown in Figure 9.62 and are summarizedin Table 9.9. An analysisof the producedgasis given in Table9.10.
Ftrc F.irfi
TABLE 9.9 GoldenLake Injectionand production(81-09-301
Pattern
Cumulative Air Million SCF
Cumulative Water KB
Burned Volume Percent(l)
oil Recovered KB
Recovery Percent OOIP
Original Pattern 1240 165 L7.l 561 39.8 Expansion1 D7 Pattern 507 107 4.4 438 18.3 89 Pattern 562 116 5.7 318 19.7 Total Expansion1 1069 223 5.0 816 19.0 (t)It was anticipated that it would be economic to continue the burn until the burned volume was about 20Vo.There are thus quite a few yearsof production aheadof even the original pattern (Fairfield and White 1982).
468
In Situ Combustion
Chap.9
TABTT 9.IO C
(Fairficld
eod tl
Fa*t Prqsr ft
Sparkyformationoriginalpattern
E
E i .o
E
E
1000=
C'
=
p
c o
e o
E
:tr
o
66 67 68 69 7A 71 72 79
. Lo*er g r Enharro o Aserof! and its s A series Mehrotn bitumeo o Rapid co o Valuable o Lessorg
75 76 T7 78 7g 80 81
Sparkyformationexpansion#1 10000 5000 E
I
E
i o
,rffi
E
t I'
e CL
1000 !E
h'v'1
500
i o
E
.:E
o 100 50 wet combustlon Drv ' l combustlonI
10 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 Figure 9.62 Productionfrom Golden Lake In Situ CombustionPilots. The Air Injection Is In kSCVd. (from Fairfield and White 1982)
470
In Situ Combustion
TrouHc permeabilit;-t drillingof a u waterlaversh be verl' prmi Sandco the oil to be p heavy rods an Ven'hig ployed.and tb The pc Fairfieldand I
Chap.9
It appea minstercrudei ideal type of n the top of a di1 of 30 to 5ff'r o More reo Miller and Jr scribedb1'Fair which were igr culty in ignitiq was shut dovo encounteredh Getty's B€tr
This project is t original pilot b may be seenft about 350 well The rese is broken up b There is vertic
FieldProjectRa
10000
so00 T'
E
1000 s00
c o
E
F
o Lower gasvelocities o Enhancedoil mobility (seeFigure 9.63) o A set of generalizedcorrelationsfor predicting the solubility of carbon dioxide and its effect on swellingand viscosityis given by simon and Grave (1965). A series of papers by Mehrotra and Svrcek (Svrcek and Mehrotn 1982; Mehrotra and Svrcek 1984, 1985a,1985b,1985c)contain measurementsfor bitumen-carbondioxide systems. o Rapid contactwith carbondioxide and swelling o Valuableproducedgas o Lessoverride
100 50 10 7A 80 81
-t ----1oooo ___15000 At |rl|A
I
E E
I
i .9
---*-Jtooo ,r
I
;T=*
E
.F
fl
___-l100
--ls0 rbn ,
'
It appearsthat the in situ combustionapproachto the production of Lloydminstercrudeis successfuland that the useof oxygenmay be very promising.The ideal type of reservoirfor this processis one in which oxygencould be injectedat the top of a dipping reservoir,and the authorsconsiderthat recoveriesof the order of 30 to 50Voof the oil in placeshouldbe practicable. More recent experienceat the Golden Lake fireflood project is describedby Miller and Jacques(1987).The pilot was expanded from the three patterns describedby Fairfield and White by adding two further inverted seven-spotpatterns, which were ignited in 7982,and three adjacentpatterns in 1985.There was difficulty in igniting the lastthreepatterns,and this wasnot solvedby the time the pilot was shut down in 1986becauseof the low price of oil. There were also problems encounteredbecauseof the encroachmentof water into the pilot area. Getty's BellevueField in Louisiana
I
lto
79 80 81 ;. The Air Injection
rnbustion
Trouble was found with air short-circuiting from the injector through a high permeabilitythief zone in the original pattern, and this eventuallyrequiredthe drilling of a new injection well. Severalwell workoversand squeezejobs to shut off water layershave also been required.Nevertheless,the operationhasbeen found to be very promising,and a secondexpansionhasbeencompleted. Sandcontrol is a continuing problem, and Husky has found it better to allow the oil to be producedrather than to try to restrict it from the well bore. They use heavyrods and large(3.5-in.)tubing. Very high permeability channelsform when high injection pressuresare employed,and they limit the pressurein order to preventthese. The possibleadvantagesof using oxygen rather than air are emphasizedby Fairfield and White:
Chap.9
This project is the largestin situ combustionproject in the United States.Sincethe original pilot beganoperationsin 1963,it has been expandednumeroustimes, as may be seenfrom Figure 9.64.In 1978about 2900 B/d of oil was produced from about 350 wells (most of it from 223 fireflooded wells). The reservoiris shallow (depth is 300-420 ft) and relatively thin (20-90 ft). It is broken up by numerousfaults and by a 4-ft layer of noncontinuouslimestone. There is vertical communicationbetweenthe upper and lower zones. Field ProjectResults
IJts f-]1967expansionA rrpans,m B @ 1970 1972 expanso tr f-l Ii973 exoans'u'tr
g
Remaining areassci€dra for futuredeveloprr|?n
I
O Location
3
a Producing weli
t
1ma O:e e
126 O,e
0.9
3. : \'"i \l
F
-"
1.",
20
rF
o nnr.
0
!F
{F
I
sn
pl
Figure 9.63 Effect of COz on Viscosity of Lloydminster Crude (from Fairfield and White 1982)
Figrrc lJ ana. U-S Cop;-ril
Field Exp.l Although the project is very successful,it requires a very high air-to-oil ratio-about 19,000SCF per barrel. The high air-to-oil ratio is believed to be due to the crude depositingan abnormalamountof fuel, to the relatively low oil saturation (about 52%\, and to the difficulty in moving all the heatedoil to the production wells becauseof the reservoir heterogeneities.
472
In Situ Combustion
ChaP.9
1963: 1967: 1970: I9T2:
FieldPrciqr
Legsnd !
1962expansion A$74
Q 19zoexpansion Q$ts f| t9z2exoansion Qfi76 flt973 expansion n
expansion exgansion expansion
tg77expansion
QlgTB rrp ntion Remaining areas scheduled forfuturedevelopment O Location a Producing well
well @ Injection well t Abandoned
Cities Service Co.
Co, Service Cities
Figure 9.64 Getty'sIn Situ CombustionProjectin BellevueField, BossierParish,Louisiana, U.S.A. (from Bleakely 1978).Reprinted by permissionof Edgell Communications. Copyright @ November,1978,PETROLEUM ENGINEER INTERNAIIONAL.
rfrom Fairfield
FieldExpansions at Bellevue a very high air-to-oil r is believedto be due lativelylow oil saturaIted oil to the produc-
Combustion
Chap.9
1963: 1967: 1970: 1972:
Pilot 1.-4 5-8 9-24
Field ProjectResults
1973: 25-28 1974: 29-31, 1975: 36-47
1976: 1977: 1978: 1979:
32 60-73 & 12I-123,except64 85-88 52-55
473
A major factor in the economicsuccessof the projectis the shallowdepth of the reservoirand the low reservoirpressure.This makeswells cheapto driil and reducescompression costs;the dischargepressureof the compressors is only about 100psi. Although the air consumptionis large,the compressed air is cheap. The wells are drilled on inverted nine-spotpatterns.originally, the pattern sizeswerechosento give reservoirvolumesof 185acre-ftper pattern;i.e., the wells were spacedfarther apart wherethe reservoirwas thinner. Somepatternswere as small as 2.2 acresand others,as largeas 8.5 acres.slow responsewas found in the large patterns,and thesewere infilled with additionalproducers.This gavemuch better results. Originally dry injection was used; then, after about50Voof the theoretical burn was achieved,air injectionwas stoppedand waterfloodingwas usedto scavengeand utilize the residualheat.This procedurehasnow beenmodifiedto include a period of simultaneous water and air injectionafter the dry operationand before the waterflood. Getty expectsto recover60Voof the originaloil in placein the Bellevuefield usingin situ combustion.To do this will requirethe combustionto 6 of 15Voof the oil in placeas fuel. Cities ServiceCompanyhas a wet combustionprojectsimilar to that developedby Getty on their leasein the Bellevuefield; this leaselies directly to the east of the Getty lease(Figure9.64).Josephand Pusch(1982)report that Cities Service expectsto recovernearly 40Voof the oil in place.Well productivity is about20 to 30 B/d. [n their paperJosephand Puschalsoprovide an interestingbreakdownof the operatingcostsfor the field, which, exclusiveof taxes,were$17.2j/B in 19g0-1.
The lin of the count a 2000-cpri are shownT A prh 1967.This h injectedand bustionin tl Oil pn 1974 to Effi Figure 9.66. The in capacitvard 1979this*a The rl During this m3/d1te.+n operationis I
In Situ Combustion Projects in Rumania There are somevery interestingand largein situ combustionprojectsbeingcarried out in Rumania (Gadelleet al. 1981;Turta and pantazi 1982;Carcoanar9g2:Aldea. Turta, and Zamfir 1988).These four papersalso contain many related references. TABLE 9.11 Suplacude BarcauReservoirProperties Sandcharacter Depth Effective thickness Dip Initial reservoirpressure Reservoirtemperature Porosity Absolute permeability Initial oil saturation Oil specificgravity Oil viscosity at 18'C (heavyasphalt-base crude oil)
Unconsolidated 35-220 m 4-24 m 5"-8. 0.4-2.2MPa 18"C(at a depth of 80 m) 0.32 1.7 p.m2 0.85 0.96(16'APr) 1.8-2Pa . s
16
(Turta and Zamfir 1988).
474
In Situ Combustion
Chap,9
Field ProjectF
shallowdepth of heapto drill and sorsis only about ir is cheap. rally, the pattern rrn; i.e.,the wells patternswere as wasfound in the This gavemuch rf the theoretical *'asusedto scavrdified to include ration and before :he Bellevuefield o 6 of.l5Vo of the lar to that develirectly to the east rat Cities Service ity is about 20 to ing breakdownof 7.27/Bin 1980-1.
The largestprojectis in the Suplacude Barcaufield, which is in the northwest of the country.The reservoirconsistsof a high-quality,shallowsandsaturatedwith a 2000-cpoil; the reservoirdips at 5 to 8'toward the south. Reservoirproperties are shownTable9.11.Figure 9.65showsa map of the field. A pilot testwasinitiated in 1964,and semi-industrialoperationwasstartedin 1967.This has sincebeen expandedto the point where "given the amountsof air injectedand oil produced,this projectmay be consideredthe mostimportantcombustionin the world" (Gadelleet al. 1981). Oil production due to combustionhas increasedfrom 340 tld, (2200 B/d) in 1974to 800 t/d in 1977and to 1000t/d in 1979.Productionrates are plotted in Figure 9.66. The increasein productionwas achievedby the additionof air-compression capacityand by the extensionof the length of the combustionfront; at the end of 1979this was more than 4 km long. The numberof injectionwells was increasedfrom 11 in 1974to 38 in 1979. During this period the air-compression capacityrose from 0.55 million standard m3lagS.+ million SCF/d)to 1.8million. The air-to-oil ratio achievedin long-term operationis between1500and 2000std m3/t (8.4 andlL2 kSCF/B)of oil.
'r,:i/
o
tr!
o
o
ato
a
204
?a
aa(,
o
at2
o
o
O
o
l0a
o
!al 0
.ri
tl
att
||t
o
atl
6
t0
o
o
9!
o
aaa
Itl
o
lcts beingcarried nna 1982;Aldea, llatedreferences.
o
!tt
a
l?a
o
ta
!rI o\
20t org
l?lt
||l
o
,
I!
@ o
'.
.)\
o
o
!T
It
ed
o
_9_: l.
@
a;-:--j
E0m)
PtlotArco
?\ _
..a 0t
o
att
ll
t,
7/1,, ti..
6+'",d
o I
€8
o
to o
0| I
IA
llt
lioboth
rl)
@
Arr or wotsr npction u.ll in Oct.1977
lOOn
o
ftodtttidr
nll
an Oct.B77
Figure 9.65 Suplacude Barcau Field (from Gadelleet al. 1981)
rustion
Chap.9
Field Project Results
475
START x gTU COIE Srbx
Ttr€sc l. 2. 3. 4.
€c t
r<
E a
U F
c
-
3
o F ()
J
o
I C,
t
o An cil o Profr 3to4 o Acid I air i{ . Prodt
B
a a 6 l,
t
G
r !m co5,t!ttDr: fr' llil96
I
Figure 9.66 Suplacude BarcauField Performance(from Carcoana1982)
Productionhistoryup to 1981is shownin Figure 9.66.In a more recentpaper (Aldea,Turta, andzamfir 1988),resultsup to 1985are described.At that time, the oil production was 1400 tld, with an air-to-oil ratio of about 2250 m31Sf;/m3 (12,645SCF/B).In 1988,air injectionwas 3.5 million m31Sf;74into 120wells, and production was from 600 wells. The combustionfront was 7.5 km long, and recovery in the combustionfront areawas greater than 50vo.The project has many interestingfeatures: o The operationis a line drive with air injectedat the upperedgeof the sloping reservoir;this is boundedby a fault, which forms the trap. o Wateris injectedinto wellsbehind the combustionfront: 6-10 water injectors with about 50 t/d per well. The paper containssomeinterestingcombustion tube data,which showthat the air requirementis reducedby aboutone-third for wet combustionas comparedto dry. o Stableemulsionformation was associatedwith water injection,but this has beenovercomeby a thermalchemicaltreatmentwith a final strippingdistillation (Aldea,Turta, and Zamfir 1988). o The position of the combustionfront in the field is determinedby plotting isothermalcontourmapsof the well headproductiontemperatures. A second method involves the analysis of such data as oil and gas rates, 02 content of produced gas, and downhole temperaturesfrom north-south rows of production wells, i.e., for rows of wells approximatelynormal to the combustion front. o Various methodsare used to control the developmentof the front. 476
In Situ Combustion
Decrc Stirrd Creat CorS
Chap.9
Other largr describedir Of pet oped for thr schemethd 18 km in lc required(2t eration.thc The R situ comhr
I
U
c
There Rumania.
Aaluso. L.l Aorcsrrlsture-Oxid Res.Eng.. Alor.e- G, H tion of \ Me1-ersao
Bibliography
These 1. 2. 3. 4.
Decreasingthe gas flow by throttling production Stimulating specificwells using steam Creating secondarycombustionfronts perpendicularto the main front Combining air and water injection.
o An oil-based,weighted killing fluid is used for well workover. o Productionwells are cooled as the combustionfront approachesby injecting 3 to 4 t/d of water. o Acid treatment and prolongedwater injection have been used to restore the air injectivity of partially pluggedinjection wells. o Productiongasescontaining carbon monoxideare ventedthrough high stacks.
)ana 1982)
more recentpaper l. At that time,the x 2250 m{Sr;/m3 into 120wells,and m long, and recovEcthasmanyinteredgeof the sloping r-10water injectors restingcombustion b,vabout one-third
Other large Rumaniancombustionoperations,in variousstagesof development,are describedin the paperscited. Of particular interest is the enormousin situ combustionproject being developed for the Videle field in Rumania (Turta and Pantazi 1982).This is a line-drive schemethat will burn downdip and that will have a combustionfront more than 18 km in length; an air-compressioncapacityof about 7 million std. m3/d will be required (247,203,000SCF/d).It is forecastthat, after about 45 to 50 years of operation, the ultimate oil recoverywill be about 38 to 40Vo. The Rumanian Suplacude Barcau project is very large comparedto EOR in situ combustionprojectselsewhere.
1988Capacity, B/d Surplacude Barcau U.S. total (9 projects) Canadatotal (8 projects)
There are also nine other commercial in situ combustion operations in Rumania.
ction, but this has al strippingdistillarmined by plotting )eratures. A second 5 rates,02 content south rows of proral to the combushe front. rblstion
Chap.9
9200(Aldea,Turta,andZamfir, 1988) 652s(oil G.J, April 18,1988) 8133
BIBLIOGRAPHY Aar-uNo, L. R., 'Annual Production Report," Oil & Gas L, 33-73 (April 18, 1988). AoncnnseN,K.O., DoNNELLy,J.K., Moone, R.G., and BnNNIoN,D.W., "Low:Temperature-Oxidation Kinetic Parametersfor In-Situ Combustion:Numerical Simulation." SPE Res.Eng., 573-582(November1987). ALoEe,G. H., Tunre, A. L., and Znurrn, M., "The In-Situ CombustionIndustrialExploitation of Suplacude Barcau PanonianField, The SocialistRepublic of Rumania," in R. F. Meyers and E. J. Wiggins (Editors), The Fourth UNITAR/UNDP International ConferBibliography
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ence on Heavy Crude and Tar Sands,Vol 4: In Situ Recovery, AOSTRA, Edmonton, (1989),pp. 841-848. AtnxeNoen, J. D., ManuN, w L., and Dnw, J. N., "FactorsAffecting Fuel Availability and composition during In-Situ combustion," JPT, 1154-1162(october 1962).@ 1962spE. ASTM, "ConradsonCarbon Residueof PetroleumProducts.D189-81" in Annual Book of ASTM Standards05.01,p. L3t-I37 (1985)or in other Annual Books. Barta, L. and HnrLEn, L.G., "Kinetics and Energeticsof Oxidation of Athabasca Bitumen," I Energyand Fuels,2: 309-316(1988). BEnRy,v. J., Jr.. and P.lnnrsn,D. R., 'A TheoreticalAnalysis of Heat Flow in Reversecombustion," Trans.AIME, 219: I24-13t (L960). Brearer-v, w. B. (Ed.), "Getty's BellevueField Still Going and Growing," pet. Eng. International, 54-68 (November 1978). BuRGen,J.G. and Sanueurr, 8.c., "chemical Aspectsof In-Situ combustion-Heat of Combustionand Kinetics," SPEJ,4L0-422, (October 1972).@ I97Z SpE. Buncnn, J. G, and snuueuer, B. c., "Laboratory Researchon wet combustion," Jpr, lr3711.46,Oct 1973and also SPE 4144(1972). CancoaNe,A. N., "Enhanced Oil Recoveryin Rumania," SPE 10699(April 1982). cnru, K.w., 'Analytical Analysis of Air/oxygen wet combustion by Energy Balance," in R. F. Meyers and E. J. Wiggins (Editors). The Fourth UNITAR/UNDp International conference on Heavy crude and rar Sands.vol 4: In Situ Recovery,AOSTRA, Edmonton, (1989),pp. 807-825. cuu, c., "State-of-the-Art Review of Fireflood Field Projects:' Ipr, 19-36 (January l9g2). @ 1982SPE. CouNtuAN,T. M.,'A SuccessfulIn-Situ CombustionPilot in the Midway-SunsetField," SPE 6s25 (1977). Dtnrz, D. N., "Wet Underground Combustion,State of the Art," JPT, 605-617(May 1970). Dtarz, D. N. and weuoeua, J., "Reversecombustion SeldomFeasible,"producersMonthly, 32, No. 5: 10 (1968). DoNNELLy,J.K., Hellarra, R.J. and Ducxerr, J.A.,'An Oil SandsOxygenIn-Situ Combustion Project," 3rd Unitar conference on Heavy crude and rar Sands,Long Beach, California (1985). FatRnteto, W. H. and Wutrn, P. D., "Lloydminster Fireflood Performance,Modifications PromiseGood Recoveries,"Oil Gas J., I0l-112 (February8, 1982). Faneun.rnsoN,R. G. and TuonNroN, R. W., "Lessonsfrom Eyehill," IC?T, 47-53 (MarchApril 1986). GeonLLe, C.P., Buncnn, J.G., BAnooN, C.P., MacueDoN, V., CancoaNe, A., and Prtcovtcl, V., "Heavy-Oil Recovery by In-Situ Combustion-ifwo Field Casesin Rumania," JPT,2057-2066 (November 1981).O 1981SPE. GeRoN,A.M., Kuuan, M., and Cara, G.C., "The Stateof theArt of OxygenFireflooding," In-Situ, 1.0,no. 1: l-26 (1986). GanES,C. F. and RAIrany,H. J.,'A Method for EngineeringIn-Situ CombustionOil-Recovery Projects,"IPT,285-294 (February1980).@ 1980SPE. IIALLaM, R. J,, Moonn, R. G., Knouse,H. R. and BeNNroN,D.W., "Carbon IsotopeAnalysis: A New Tool for Monitoring and Interpreting the In-Situ CombustionProcess,"SPE L74I8 (1e88). HeNNTNGSoN, C.J. and Ducrerr, J.A., "Oxygen Fireflooding for In-Situ production of Heavy Oils and Tar Sands,"5th Annual AOSTRA Conferenceon Advancesin Petroleum Recoveryand Upgrading Technology,Calgary,Alberta (June 14-15, 1984). 478
In Situ Combustion
Chap.9
Hvrzpc, I Enrk'bcd l06l-lm
Jexzusr G" Proi:ct,Joserur C1523-lt
Josrrn C- r Proj€t.' Venezud
Kave, S.E Enhas Lenu M.. / Lreurr- R Lake Cn Upgradrf MrHnonA I Ras.,l: 83-93 (D Mtlr-rn, lL flood Pit CIM. Crl
Moonr, Rt "Nes toc Moolr, R( Merhenirr
Interoatit AOSTRA
Moone R( basis fq c tion.'rCI
Moss.J.T-.
Moss. J.T. r for Heavy
Nrlsor. T-t Gas1.. I
Nrwror. C. ed,..7'?Z
Nzexwt-. B. servatio
Prxaenrxy, Tubes.- S
Ravrr. H-. covery'.-i Rave'r'.H- J
Bibliograpfq
6TRA,
Edmonton,
HvrzDos, L.J., Howeno, J.V., and Ronrnrs, G.W., "Enhanced Oil Recoveryvia OxygenEnriched In-Situ Combustion: Test Results from the Forest Hill Field in Texas," JPI 1061-1070(June 1983).@ 1983SPE.
Rrl Availability and 1962).@ 1962SPE. " in Annual Book of
Jrnnlvs, G. R. and Krmrernrcx, J.W., "Twenty Years'Operation of an In-Situ Combustion Project," L Can. Pet. Tech.,60-66 (January-March1979).
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Joseru, C. and Pr-rscn,W.,'A Field Comparisonof Wet and Dry.Combustion," fPT, 1523-1528(September1980).O 1980SPE.
bw in ReverseCom-
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Kavr, S.E., TINc. V. C., and Farn, J. C., "pevelopment of a Systemto Utilize Flue Gas from Enhanced Oil RecoveryCombustionProjects,""fP4 181-188(January1982). Lartq M., Enhanced Oil Recovery,Paris, Editions Technip (1980). LEAUre, R. P. and CoLLynn, C. J., "Laboratory Studiesof In-Situ Combustionwith Cold Lake Crude," 5th Annual AOSTRA Conferenceon Advancesin PetroleumRecovervand UpgradingTechnology,Calgary,Alberta (June 14-15, 1984).
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App
Symb
(1e83). WtLsoN,L.A,, Rnno, R. L., Reno, D.W., CLev,R. R., and HARRrsoN, N. H., "SomeEffects of Pressureon Forward and ReverseCombustion,"SPEI, 127-137(June 1963). Zawlenucne, R., DnNnvrcn, R.F., McILnov, K., and KNecur, P., "Material Compatibility and SystemsConsiderationsin Thermal EOR Environments Containing High-Pressure Oxygen," JPT, t477-t483 (November1988).
Except where consistentand siredset of cq In rhe fd by the srmbot L M T H 0
hogr m:rst tinr hear terry
Definirkr they are defir cases,suchst*t LOWERCASE a,b.c f L
JL
480
ln Situ Combustion
Chap.9
[e Cylindrical Heat IIIIIE,216: ll5-122 Swelling Sffdlity, 1%5). hary rity Measurements
AppendixI
? Oil Gas 1.,77-N h
by Counterflow
r hocess on an In-
Symbols
b-: Fennwell Books ItlL,'Some Effects re 1%3). rEial Compatibility iing High-Pressure
Except where indicated otherwise, the equationsin this book are dimensionally consistentand they may be used by substitutingvaluesfor the variablesin any desired set of consistentunits. The table on page2l lists somepossibleunit systems. In the following list, the dimensionsof the quantities which are represented by the symbolsare indicated using the following letters: L M T H 0
length mass time heat temperature
Definitions of somevariablesthat occur only locally are not included here if they are defined in the text adjacentto the equationwhere they appear.In some cases,such symbolsmay have specialmeaningsand require particular units. LOWER CASE a,b,c c
f f,. ft *ustion
Chap.9
Arbitrary constants -1 CompressibilityPressure-1- LT2M Dimensionlessfunction of time Ratio of injected latent heat to injected total heat Fractional flow at .L 481
f, f. f"r I 8c h
il,, ho,hc k kokr, ks k,o, k,,, krg
k:",kk m n p q 4, Qo,Q", Qs Qt
r r ,s t tp
t' , t", and t* u Xt!,2 X,I,Z xy 7
Steamquality Fractionalflow of water (dimensionless) Fractionalflow of water just upstreamof front Accelerationdue to gravity LT-2 (standardvalue is 9.80665ms-2) Geothermal temperaturegradient 0L-1 Reservoirheight L Averagethicknessof steamchamberL Heat transfer coefficientsfor radiation and convection. -1 -1 respectivelyHL-2T 0 PermeabilityL2 EffectivepermeabilitiesL2 Relative permeabilities(dimensionless) End point relative permeabilities(dimensionless) Parameterwhich dependson oil viscosity temperaturecurve Tn and Zs Exponent(dimensionless) Temporaryvariable, also used as arbitrary constant Flow rate L3T-1 Cumulativevolumeof displacedoil L3 Oil, water and gasflow ratesL3T-1 Total flow rate L3T-1 Radius L Thermal resistance0TlH Interwell distanceL Time T Dimensionless time Dimensionless times usedin gravity drainagetheory Heat flux vector HL 2T-1 DistanceL also used as temporaryvariables Position of front L Dimensionless distancedefinedby equation2.8
UPPER CASE A
A AR
482
Area L2 Rate of increaseof areaL2T-1 van Lookeren'sdimensionlesssteaminjection number for radial flow Symbols
Apoendix 1
B B, C Cr C,C, Cr CCR E Et, Ex
F Ho
H^ K L L N NR"
osR APt P P, Po, Pn. Pq
h,, P.,
o
Q, Q. Q' Q,, Qn Q,, R R R,, RO Rrr, R.r
s Symbols
AC
lfront
nd convection,
sionless) f'temperaturecurve
r!'constant
nagetheory
:ion 2'8
on numberfor
iymbols
Apoendix1
B Bi C Cr C,Ct Cn CCR E E6 En,
Dimensionlessheat factor (Equation 2.52) Dimensionless constantsBr, Bz,. . ., etc. Heat capacityHM-tg-r Heat capacityat constantpressureHM-19-1 Arbitrary constants Chuoke'sconstant(dimensionless) ConradsonCarbon Residue(ASTM Standardtest D 189) Young'smodulusML-1T-2 Fractionof injectedheatwhich remainsin the reservoir Fractionof injectedheatwhich remainswithin the steam-saturated zone F Function Ho Total heat injectionrate HT-l Ht Latent heat injectionrate HT 1 K ThermalConductivityHT 1L-10-1 L Distancebetweenwell centresin equations4.I5 through4.32 L Length L N Number NR, Rayleighnumber OSR Oil steamratio APs Pressuredrop acrossskin ML-1T-2 -2 P PressureforcelareaML-IT P, CapillarypressureML-1T-2 Po,Po;,Pop Constantpressuresin equations4.10et seq. P*uP*p Pressures at injector and producerML-IT-2 Heat flow rate H/T O Cumulativeheat flow H e, Cumulativeinjectedheat H Q,i Dimensionless oil drainagerate in SAGD definedin Figure 7.13 Q* Cumulative heat lossH Qt, Cumulativeheat in steamchamberH Qn Cumulativetotal heat injectedH Qrc R Ratio of volumetricwater flow to steamflow, equation5.63 et seq. R Radius L Ri, Ro Distance from injector and producer L R*u R,p Radii of injector and producerwell boresL S Skin factor (dimensionless) Symbols
Appendix1
483
So So. SOR
Fractional oil saturation(dimensionless) Residualoil saturation(dimensionless) Steamoil ratio
p
AS,
SO -
p
S" S,r .1,/ S-, $r Ss S" S-,,S-o T fs TR T* U U V V Vc W X
It
a
SO'
Fractionalwater saturation(dimensionless) Irreducible water saturation(dimensionless) Water saturationjust upstreamof water flood front Averagewater saturationbehind front Averagewater saturationbehind front at breakthroush Fractionalgas saturation(dimensionless) Fractional steamsaturation Averagewater and oil saturations Temperature0 Steamtemperature0 Undisturbed reservoir temperatureg Dimensionless temperature Advancevelocityof movingfront LT-1 Overall heat transfercoefficientHT-1L-20-1 VelocityLT-l Volume L3 Volume of steamchamber Massflow per unit area MT rL-2 Dimensionless variableusedby Marx and Langenheim
Enthalpies H H, h U V H. H* Ho H,
Enthalpy per unit massHM-1 Enthalpy of steamand of water HM-l Internal energyper unit massHM I Volumeper unit massL3M-1 Enthalpy of steamper unit volume(of steam)HL-3 Enthalpy of water per unit volume HL 3
a o o' p
€ i u Vg vR
0 0 0 s 5
6 4r Subscripts abs
ab
BT
br
cco c
ctl
conv
co
cum
cu
DD}i ep.
Enthalpy of oil per unit volume HL-3 Enthalpy of rock per unit volume HL-3
eff
ef1
ffn 8ga hln H.r/ ho iiu inj ini Lhg
Greek d Thermal diffusivity L2T-1 (r1,d2,. . . constantsin someexpressions Gravity term B Coefficientof thermal expansiond-1 B 484
a
Symbols
Appendix 1
Symbols
Ap
p ,lt
0 p o o o
d front
a
akthrough
It e i v VS Up
0 0 0
t €* D ,lt
Density ML-' Dimensionlessfunction of exponentrn Fractionalporosity Density ML-3 InterfacialtensionMT-: -4 Stefan-Boltzmann constantHT-rL 29 Stefan-Boltzmann constantHT tL-29-4 Effective interfacial tension MT 2 DynamicviscosityML 'T-t Emissivity(dimensionless) Latent heat of evaporationHM t -t KinematicviscosityL2T Kinematicviscosityof oil at steamtemperatureL2T 1 Kinematicviscosityof oil at initial reservoirtemperatureL2T-' Angle betweeninterfaceand horizontalradians Ratio of volumetricheat capacities Reservoirdip in Table4.2 and in equation5.1 et seq. Distancefrom front L Dimensionless distancefrom front Gap L Dimensionless function definedin equation2.28
Subscripts angenheim
abs BT c c conv cum D e
4f {
J
o
6
h H,V i inj L
rnbols
Appendix 1
Symbols
absolute(temperature) breakthrough cold critical convective cumulative Dimensionless perimeter effective fronl gas hot horizontaland vertical inside injected liquid Appendix 1
485
L o r R .t J
s t w w
loss oil and outside rock reservoir skin stored steam total water well
Appe
Densi
Units and Conversion Factors atm B Btu cp CS OC OF
d
D ft o
b
h ha HP K kg lb lb m md p Pa psi "R st J
w y 486
Illster
atmosphere(760mm = 1,4.696 psia : I0l325Pa) barrel (42 USG : 34.97IG = 0.15899m3) Britishthermalunit (1.055kJ = 778ft. lb.) centipoise(0.01poise: 0.01g cm-' s-' : L mPa.s: -r 2.419lbft-l h-1 : 58.06lb f d-1) centistoke(0.01stoke: 0.01cm's-t : 1 x 10-6m' s-t) degreeCelsiusor Centigrade degreeFahrenheit day (86,400s) darcy (0.9869p^' = 0.9869x 10-12m2) feet (0.3048m) gram (0.00220462lb) hour (3600s) hectare(10,000m2 : 2.47I acres) horsepower(550ft lb/s = 0.7457kW) degreeKelvin ('C + 273.15) kilogram (2.20462lb) pound (mass)Q. $59237 kg) pound (force)(4.448222N or kg ms-2) meter (3.2808ft) millidarcy (0.001D) poise(g cm-' s-t) pascal(Nm-' :1,.45 x 10-apsi) poundsper squareinch (6.8948kPa) degreeRankin stoke(cm2s-1) tonne (1000kg = 2204.6lb.) watts year Symbols
Water at BoIt
where p.
T SaturatedStr
The specificvol ing accuracyfir slightlygreaterI
In theseequatio ume in ft3/lb. The firsr c and Fiori 1987) Brine Solrtkn
The specificgn S.G.zorzo:l+ in ppm by weig Appendix1
Appendix2 Densities of Oif Reservoir I$sterisls S=
*t
t-t)
Water at Boiling Point p*: where p, T
7C[1.7- 0.1616f- 0.00262T'z
is water density in kg/m3 at saturationpressure is temperaturein'C (10to 290'C).
Saturated Steam The specificvolume of saturatedsteamcan be estimatedwith satisfactoryengineering accuracy from the following correlations. The maximum absolute error is slightly greater than lVo. 50 < P < 500 5 0 0< P < 1 5 0 0 1500< P < 2500
V,=363'9P-o'es88 [email protected]/P)-0.04703 4:(551.741P\ -0.0887
ln thesee-quations P is the steamsaturationpressurein psia andll is the steamvolume in ft'/lb. The iirst equationis from (Farouq Ali1974) and the others are from (Ejiogu and Fiori 1987). Brine Solutions The specific gravity of aqueoussodium chloride solutions can be estimatedfrom S.G.zorzo:|+ 7.5 x 10-7Wrr 0 <Wpp- < 260,000where Wpp isthesaltcontent in ppm by weight (or mg/L). nbols
Appendix1
487
ReservoirOil
:pt.s \ (p')"",= I |,rrra* .o'i(999)kglmr
1000 -] 'l
The effectof temperatureon the densityof petroleumfractionsand crudeoils can be predictedfrom the nomographshownin Figure A.2.I. A predictionof the effect of temperatureup to temperatures of 260"c can be madefrom the tablesfor petroleummeasurement publishedby ASTM (196g). For oils in the rangeof 0 to 15 "API, thesetablesgive the followingfactors:
TemperatureoF "C p/p15.6 ASTM Tables: FigureA.2.lK:11.3 10 "API
60 15.6 1 1
100 37.8 0.9861
200 93.3 0.9520
300 148.9 0.9187
0.982
0.951
0.920
lj
I l
coo -.{
400 500 204.4 260 0.8864 0.8549
0.88s
0.850
In the precedingtable, the values are comparedwith values read from FigureA.2.I; the agreementis excellent. Thesevaluescan be representedaccuratelyby the equation,
lr - 15\ /r - rsyl p = p $I l l - 0 . 0 6 2 8 5 1 # f + O - " ."o- -o"r\+ z o^l"' ,1 | 1 0 0I ) \ 1 o o/ L or by the simplerbut slightlylessaccurateformula, r.-\'l I
u d
<
e
500
G
:
-oo6m(r#)l a=nrsll
where Z is in degreesCelsius. The variation of the densitiesof four samplesof Athabascabitumen were studiedby Bulkowski and Prill (1978)over the temperaturerange0 to 150"C.They found that the resultswere in reasonable agreementwith the ASTM tablesand developedthe followingcorrelationfor their data. P=Po_0.627 wherep is the densityin kg/m3at T'C po is the densityat 0'C. Gewers(1965)reportedthe densitiesof samplesof Cold Lake and Athabasca crudesover the temperaturerange0 to 150"C.His data can be represented by the equations p = 1024- 0.6457 8.1 'API Athabascacrude p = 1009- 0.6347
10.4'API Cold Lake crude
Again, theseresultsare in reasonableagreementwith the correlationsdescribed previously. 488
of Oil Reservoir Materiais Appendix2 Densities
R Densities of (
1 0 0 01
l
l l coo-]
actions and crude oils tures of 260oCcan be ty'ASTM (1968). he following factors:
l
400 500 204.4 260 0.8864 0.8549 0.885
0.850
th values read from tion,
-- t ll s V l m tl
?
*. g
e f ?
o
qnn
d
u
:
t
F
6
z
U
abascabitumen were rnge0 to 150'C.They ASTM tablesand de-
DEG APi
I Lake and Athabasca be representedby the wATsoN K
S
,
crude
o.55
crude
0,50 0.45 0.40
;orrelationsdescribed Figure.d2.l
laterials
Appendix 2
Density of Petroleum Fractions (from API 1976)
Densities of Oil Reservoir Materials
Appendix 2
t$89
Rocks The following are typical values for the density of the solid rock material in reservoirs.
Appr
kg/^' Sandstone Carbonates
2630 2680
Conversion Factors
Thert
The densitiesin the previoussectionsare expressed in kilogramsper cubicmeters. The valuescan be convertedto other units usingthe follo;ing f*torr.
of oi
1000kg/m3 = 1 glcm' = 62.43 lb/ft3
BIBLIOGRAPHY API, "TechnicalData Book-petroleum Refining," washington,D.c., Americanpetroleum Institute(t976), 6.51.. ASTM' "PetroleumMeasurement Tables,"7th Printing,Philadelphia,AmericanSocietyfor TestingMaterials(1968). Bur-rowsrr, P. and PRTLL,G., "Researchcouncil of Alberta, Internal Report February 1978,"resultsreportedby D. B. Robinsonin "The Thermodynamicand rransport proper_ ties of Bitumensand Heavy Oils,,,AOSTRA, Edmonton(1-9g4). Errocu, G.c. and FroRr,M., "High-pressureSaturatedsteam correlations,,,Ipr, 1,5g5_ 1590,December1987. Fenouq ArI, S.M., "SteamInjection" in Secondaryand krtiary Oil Recoveryprocesses p11blished by the Interstateoil compact commission,oklahoma city, oklahoma (Sepiember 1974). Grwens, c., Imperial oil Limited unpublisheddata from a 1965report quotedby T. c. Boberg,"Thermal Methodsof oil Recovery,"New york: John wile; (19gg).
Unconsolilil
The condrrrir the individua are approrim
The ther In particular. , grains, and. as content. An e given by Cern given next.
490
Densitiesof Oil ReservoirMaterials
Appendix 2
lid rock material in
Appendix3 Thermsl Conductivity ms per cubic meters. g factors.
of Oil Reservoirl$sterisls
. AmericanPetroleum
UnconsolidatedOil Sands American Societyfor rnal Report February and TransportProper-
The conductivityof oil sandmixturesmustfall in the rangeof the conductivitiesof the individualcomponents-sand,water,oil and gas.Theseconductivitiesat 120"F are approximatelyas follows.
relations,"JPT, L585?coveryProcessespubr, Oklahoma (Septemeport quoted by T. C. ry (1988).
Thermal Conductivity
$m "c Sand Water oil Air
2.85to 7.7 0.64 0.093 0.024
The thermal conductivity of the sandgrains dependsupon their composition. In particular, qrrartzhas a much higher thermal conductivity than most other sand grains, and, as a result, the averageconductivity is largelydeterminedby the quartz content. An extensivelisting of the conductivities of a wide range of minerals is given by Cermak (1967)and by Cermak and Ryback (1982);abstractedvalues are given next.
rials
Appendix 2
491
ThermalConductivitiesand SpecificHeatsof Rock-FormingMinerals
.{n :n1 for a girel u r a t i o ni s t : . r r As ":'l have beee n t h e s a n d: . s
Thermal Conductivity at Room Temperarure
$m'c Quartz Chert Flint Vitrous silica Calcite Dolomite Feldspars
7.69 4.53 3.71 1.36 3.57 5.50 2.3-2.5
^,,^-+qudr t4
-
-- i d.ru
-'g Calculatec
(Cermakand Rybach1982)
1A
\ : :-
Somerton,Keese,and Chu (1974)found that the averagethermalconductivity of the sandgrain materialcan be estimatedby using the fblowing equation(thi; has beenconvertedto SI units). Kn,= 2.86+ 4.95G$m"C
(1)
whereG is the volumefraction of quartz in the solid. The thermal conductivityof a porous reservoirsolid is less than that calculatedfrom (1) becausethe pores are filled with fluids having a lower thermal conductivitythan that of the sandgrains.This effect is exaggerated in an unconsolidatedsandbecauseof the poor contactbetweenthe grains in the directionof heatflow. As a result,the effectivethermalconductivityof unconsolidated sandsis dependentupon the thermal conductivityof the fluid in the pores.water, because it has a muchhigherconductivitythan oil or gas,greatlyenhancesthe overallconductivity of an unconsolidated sand.Furthermore,in water-wetsand,a smallwater saturationhas an exaggerated effect becausethe water tendsto bridge the intergranularcontactregions. The effectivethermalconductivityof dry sandsis increasedby a factorof 6 to 8 when they are saturatedwith water or brine; in contrast,the conductivityof consolidatedrocks increasesby a much smallerfactor as a resultof water saturation. Somertonet al. (I974)developedthe followingequationfor predictingthermal conductivityof oil sandsas a functionof the natureof the sandgrains,the porosity, and the water saturation.This equationhas been convertedto give the result in SI units so as to be consistentwith the remainderof the materialin this section. Conversionfactors are given on page 497. Kn = 1.273- 2.250 + 0.390Kr,S,05
Comparisan with hedcl
Scott and Se oil and rr ate and transre Thc- :a:
Pc'tr...;
Quar:r \\'are: Oil -:r Sor::c::
and
e)
is the thermalconductivityof the compositematerialin W/m .C 6 is the fractionalporosity Kn, is the averagethermal conductivityof the grain material estimatedfrom equation 1 is the fractional water saturation
Set t ::rt
where K1
and
s. 492
ThermalConductivityof Oil ReservoirMaterials
Appendix3
ThermalCorx
An important conclusionwhich Somertonet al. draw from their data is that, for a given water saturation,it makes little differencewhether the remaining saturation is oil or gas;equation2 canbe used for either case. As an exampleof the use of equation2, the following thermal conductivities have been predictedfor two oil sands,eachhaving a porosity of.35%. [n one case, the sand is assumedto be pure qtafiz and in the other, a mixture containing30Vo qxartz andT\Vo of other grains such as feldspars.
Mierals
CalculatedThermalConductivityfor Oil Sandswith S = 9.35 Thermal Conductivity
$m'c
Water Saturation
bermalconductivity n'ing equation(this
less than that calng a lower thermal :rated in an unconin the directionof srsolidated sandsis res. Water,because ces the overall consand,a smallwater to bridge the interd by a factor of 6 to ;onductivityof conf water saturation. r predictingthermal grains,the porosity, o give the result in rial in this section.
1.83 2.39 2.81 3.17 3.49
0.2 0.4 0.6 0.8 1.0
(1)
t.24 1.55 t.79 1,.99 2.17
Comparison of Measured Thermal Conductivity of Tar Sand with Prediction from Somerton's Formula Scott and Seto (1986)have reported measurementsof the thermal conductivity of oil and water saturatedcore samplesof Athabascatar sand using both steady-state and transientheatingmethods. The samplethey used had the following properties: Porosity Quartz contentof sand Water saturation Oil saturation
0.35 0.97 0.267 0.733
Somerton'sformulas would predict Kn,= 2.86 + 4.85 x 0.97 = 7.56$m "C and
x 0.3s+ 0.3e0 x 7.s6v0.267
., :t:rt ;;.2s
(2)
Setting S, : 0 and to 1 gives
in $m'C naterial ainmaterial
30VoQuafiz
l00Vo Qtafiz
Kna,y= 0.49$m "C and K,rwet= 3'43 Wm "C
rials
Appendix 3
Thermal Conductivityof Oil ReservoirMaterials
Appendix 3
493
Scott and Seto'smeasurements are comparedto thesepredictionsin the following table. Valuesof ThermalConductivityWm "C Scott and Seto20'C
Dry Oil saturated Watersaturated
0.49 2.01
0.43
0.44 )n
J.+J
4.03(1)
3.47
(r)Thought to be high by scott and Setobecauseof someconvectiveheat transfel
The agreementbetweenthe predictedand experimentalvaluesis excellent. ConsolidatedPorous Rocks The thermal conductivitiesof consolidatedporousrocks are higher than thoseof unconsolidated sandsbecauseof the continuousnature of the rock matrix. Also, consolidatedrocks generallyhave lower porositiesthan sands,and their conductivity is lessinfluencedby the natureof the pore fluids. The thermalconductivities of a large numberof sandstonematerialshave been measuredby cermak (1967). His measurements of the thermalconductivitiesof dried sandstones are shownas a function of porosity in Figure A.3.1. Although the data are scattered,there is a trend for the thermal conductivityto decrease, as might be expected,with increasing porosity.The scatterin the datareflectsthe varyingnaturJof the solid material as well as, the varying geometryof the pores.The interceptfor zero porosity in FigureA.3.1 appearsto be ratherlower than might be expectedfrom equation1.
o
Cerma samplesu he tivitiesrsprk creasein tix trend. u hrch paper or. air
COMPARISON Of
'
AND UNCONSO
In Fieure .{ saturated. u porositr Tb dated sand: , relation prcd the squaren tion fall: ha The:e tivitr of .rxr more nearlr grain thermr d u c t i ri t r r a r Thermal Cq
These mar tt
L i n ei s K = 2 . 5 4 5- 6 . 5 60
o2 E" -
M
.^l
A
t^
t
Al
E z a:, :
A
l
it^^=:*ii
t
i^^ ^
E
o
o -1 o E o.t t F 0L
0
0.05
0.1 0.15 Fractional Porosity
0.2
Figure A.3.1 ThermalConductivityof Dry Sandstones (Data from Cermak 196'7)
494
ThermalConductivityof Oil ReservoirMaterials
Appendix3
F i gr r S::3r
Thermal
Cqrd
predictionsin the fol-
tt and Seto 20'C
Cermak also measuredthe thermal conductivities of the same sandstone sampleswhen saturatedwith water. The ratio of the wet to the dry thermal conductivities is plottedagainstporosityin FigureA.3.2. Eachcomparisonshowedan increasein thermal conductivity with water saturation, and the data show a general trend, which is representedby the exponential curve that comes from Cermak's paper or, almost equally well, by the straight line.
Transient
0.44 2.0 3.47 transfer.
I valuesis excellent.
higher than thoseof re rock matrix. Also, ls, and their conduchermalconductivities d by Cermak (1967). stonesare shown as a scattered,there is a ipected,with increas: of the solid material I for zero porosity in red from equation L.
COMPARISONOF THERMAL CONDUCTIVITIESOF CONSOLIDATED AND UNCONSOLIDATEDSANDSTONES In Figure A.3.3, predicted curves for the thermal conductivitiesof dry and water saturated, unconsolidated,and consolidatedsands are plotted as a function of porosity. The larger effect of water saturation on the conductivity of unconsolidated sandsas comparedto that on consolidatedsandscan be seen.Somerton'scorrelation predicts that the conductivity of unconsolidatedsandsvaries linearly with the squareroot of the water saturation.As a result, the line for 25Vowater saturation falls halfway betweenthat for the dry sand the fully water-saturatedsand. There are few data on the effect of partial water saturation on the conductivity of consolidatedsands.It is reasonableto assumethat this effect would be more nearly linear than for unconsolidatedsandsbecauseof the absenceof grain to grain thermal resistance.A reasonableassumptionmight be that the thermal conductivity varieslinearlywith water saturation. Thermal Gonductivity of Hydrocarbon Liquids Thesemay be estimatedfrom the followingcorrelation(Bland and Davidson1967)
x, =Y(1 - o.ooos4z) 1.6
L
'L
L
^ )i1
-o l.o o
B Y
.....
..,^
4t
€(u 1 . 2 tr
t
^--{-
I A
to^
0.05
A
^^
r^ f
-Rario=1+2.580 ............ Ratio= expp.ae)
0.1
0.15
0.2
Fractional Porosity r from Cermak
terials
Appendix 3
FigureA.3.2 Effect of WaterSaturationon ThermalConductivity(Data for fromCermak1967) Sandstones
Thermal Conductivityof Oil ReservoirMaterials
Appendix 3
o 3 o
CONSOLIDATED
Kt
UNCONSOLIDATED
K.
E g
Wet
2
LFSTq
.e
Dry
o
W e tS = . 1 . 0
J !t
Sw=oz5
tr
o o 1
E
Kn" = 2'545Wm oC
o
F
A.
D r yS * = 0
(g
g
l("
oo'
0.1
A't uror.
SI{ALE
0.2
0.3
0.4
Fractional Porosity
Figure A.3.3 Comparisonof CorrelatedThermal Conductivitiesfor Consolidated and UnconsolidatedSandstones
t(.
K, TherrnalCor
whereKr, is thermal conductivity, $m "C d is specificgravity,60160.F T is temperature,oC. Hldrol
Bland and Davidsonlist their sourceof data as u.s. Bur. std. Misc. pub. 97.
Helrur
Thermal Conductivity of Liquid Water
\:trogt r*atct
The thermal conductivityof liquid water at its boiling point can be estimatedfrom Kn = 0.57 + 1.69x 10-3f - 6.01x 10-6Z2
Copp31
AIumrr
For example,if T : t50, Kh : 0.69$m "C. The thermalconductivityof liquid waterreachesa maximumat a temperature of about 140'C.
The thermal conductivitiesof overburdenmaterialsin Wm oC mav be estimated from the following:
l
K n * . , =2 . 0 - 0 . 5 i l 496
CONVERSI
/r^-_^r^r Correlations
basedon data from Cermak(1967),6= 0 to 0.2
SILTSTONES
Knd'v= 2'0 - 4'2OI
Roch
G l a r s rI
I
CLAYSTONES ANDCONSOLIDATED CLAYS I Kh*",= 2.2 - 1.56)
Stecl \l'clod
Insulllr 'Scc
Thermal Conductivity of Over- and UnderburdenMaterials
5.56)
Proper Tolrn S il t q 1
whereKa is in W/m'C T is in'C (f : 0 to 300)
Knd,y = 2.2 -
\lcrhrt
Br-aNo,t\. F. ar Hill (1%'r CEnuax.\1. -Cr densitvand q
correlationsbasedon data from
C e r m a (k1 9 6 7 ) ,=d 0 t o 0 . 2 4
Thermal Conductivityof Oil ReservoirMaterials
Appendix 3
ThermalCondr
-l
K66,y= 0.7
I
Kh*s1= 2.6 t".tlJ
FarouqAli (1974)'Q = 0'r9
LIMESTONE
,1ol
K n = 2 . 6 6 = 0 (from Cermak 1967) = l.7l Kna,,
fl
Kn*o= 3'5)
-]
FarouqAli (1974)d = 0.19
SHALE Kr,ory= 1.01
0.4
K^*o:
s for Consoli-
L1J
FarouqAli (1974)
Thermal Conductivities of MiscellaneousMaterials W/m'c Gas (1 atm.)
Misc. Pub. 97.
n be estimatedfrom I
rumat a temperature
C may be estimated
Hydrogen Helium Nitrogen Water Methane Propane Toluene Silver Copper Aluminium Steel Wood Rock Glass(Pyrex) InsulatingMaterials (SeeAppendix 8)
Liquid
0.t79 0.r43 0.024 0.024 0.033 0.017
Solid
0.60
2.22
0.08 0.14 419 389
20r 46
0.r-0.2 1.8 1.1 0.02-0.12
CONVERSIONFACTORS 1 $m "C = 0.5778Btu/h ft oF = 0.002388cal/s cm "C
a from 1.2
BIBLIOGRAPHY BLANo, W F. and DavrosoN,R.L., PetroleumProcessingHandbook, New York: McGrawHill (1967).
r from l-24 rials
Cnnvar, V., "Coefficient of thermal conductivity of somesediments,its dependenceon the density and on water-contentof rocks," Chemieder Erde, 26:271-278 (1967). Appendix 3
Thermal Conductivityof Oil ReservoirMaterials
Appendix 3
497
o
b
CERtrleK,V. and RyBecH, L., "Thermal Conductivity and specific heat of minerals and rocks," in Landolt-Bornstein,Numerical Data and FunctionalRelationshipsin Scienceand Technology,New Series,vol. 4, New York: Springer-Verlag (1982),305 ff. FARoueAu, s.M., "Steam Injection," in secondaryand krtiary oil Recovery processes, Oklahoma City, Okla.: InterstateOil CompactCommission,(1974). HoucrN, O. A. and WersoN, K.M., ChemicalProcessPrinciples,vol. 1, 2d printing, New York: John Wiley (1950),334. 'Scorr, J. D. and Sero, A. C., "Thermal Property Measurementson Oil Sands,,, JCpT, 70-77 (November-December1986). SolrenroN,w. H., Kmse, J.A., and cuu, S.L., "Thermal Behaviour of unconsolidatedoil Sands,"SPEJ, 513-521(October 1974). /
v
n*t .1"+-.{o
App
Heol g/nd I
SandstqE
wherc € This cq for the indivi Carbonatc
This eq carbonate ro FigureA.4.1. Clays
Curves for e r brokenlines il line for the fil The diff variationin ti
498
Thermal Conductivityof Oil ReservoirMaterials
Appendix 3
; heat of minerals and rionshipsin Scienceand !05 ff. 7il Recovery Processes, ). ol. 1, 2d printing, New
Appendix4
)il Sands,"/CPT, 70-77 r of UnconsolidatedOil
Hest Copocifies oind Enlholpies
Sandstones c, : 0.7't5+ 0.ffi17077- 1.909x t0-6T2 where C" is the heat capacity of rock material at T"C (0-300) measuredin k{kg "C. This equationrepresentsthe averagecurve shown in Figure A.4.1. The data for the individual sandstonesshown are taken from Cassiset al. 1985. Carbonate - 1.438x 10-672 C" = 0.823+ 0.001511T This equationis basedon that given by Cassiset al. (1985)for a sampleof the carbonate rock from the Grosmount reservoir in Alberta. It is plotted in FigureA.4.1, Clays Curves for a rangeof clay materialsare shown in Figure A.4.2 including some(the broken lines in the figure) for dehydratedclays.Also shownin the figure is a dotted line for the fine material that was separatedfrom a sampleof Athabascatar sand. The differencesbetweenthe various clay samplesis probablydue largely to a variation in their water contents.
aterials
Appendix 3
499
For t1'gi Linefor Grosmontcarbonate Cs = 0.823+ 0.001511 T - 1.438e-6 I
C)
--
1'2
\\ \ \
x I ,5
0.3
---.-
f
b E1
0.21
G CL .E
o
Broken lines are for 7 ditferent reseruoirs. Solid line
E o.a
lJ-
o It
o.2
o E
(,
G CL o o au a)
This e$r Experim menshave bct linesin Figure
-
I
0
100
200
3oo
Temperature o C FigureA.4.1 Heatcapacities of Reservoir Solids(Datafromcassiset al r985)
f,- =
The ag:r zffi'C. Abore I mental data gi (: *0.03 kJ/k
Oils Water The heat capacityof hydrocarbonoils dependsupon the nature of the oil and upon temperature. A useful correlation for predicting the heat capacityof oils is1 + 0.0s5(K_11.7)ll(2.961_ 1.3315)+ (0.00614 _ 0.00231s)rl whereCo is the heat capacityof the oil, k/kg "C K is the Watson characterizationfactoi of the oil .S is the specificgravity at 60160.F T is the temperature,oC
The heat capa excellentaccu C.=
c,=lr
-
Normal
og
J .? J
gt
(!
t!
3
5
1
i=
o
G CL
a. (! C)
(u o o o I
E o.e
-
0
C" = lll
C, is givenin I The spec equationover !
Athabasca Fines
o o- 1'2
'6
and
100
200 oC Temperature
o
o o !
7z o a
e a c, a a
300
r
r_
Figure A.4.2 Heat Capacitiesof Clays(Data from Cassiset al. 19g5) rThis correlationis due to Hougenand Watson(1950).The algebraicrepresentationaboveis basedupon the equationgiven in British units in Bland and Davidson '1967).
Heat Capacitiesand Enthalpies
Appendix 4
Figun Ar et al. lS Heat Capacities r
For typical heavycrude oils,K = 11.3.Also, by definition, '.e
I4I.5 ^ J=13G+'API
l!
o ll
=3 This equationpredicts the heat capacityas a linear function of temperature. Experimental data for the heat capacitiesof 13 different heavy oils and bitumenshave been publishedby Cassiset al. (1985).They are plotted as fine dotted lines in FigureA.4.3. The averageof thesedata is given by
gl
.25 >, =o 6 CL 6 o
t.2 E
- 4.046x10-672 C,=1.605 + 0.004361T
I
0"C < Z < 300.C
The agreementwith the Hougen and Watsoncorrelation is good up to about 200"C.Above this, the experimentaldata deviatebelow the correlation.The experimental data given by Cassiset al. are stated to have an accuracy of. about -+5Vo ssiset al. 1985)
(= *0.03 krykg)at 300'C. Water
e of the oil andupon rils is' - 0.00231s)zl
The heatcapacityof liquid waterat saturationconditionscanbe represented, with excellentaccuracy, by the equations C, = 4.182- 1.5x 10-47+ 3.44x 10-772+ 4.26x 10-8f3. 10'c
il
c, = 11.550- 0.0645187 + 1.5097x10'472,
240"C< r <300"C
C, is givenin k{kg'C. The specific heat of water cannot be representedaccuratelyby a quadratic equationover a wide range of temperature.
fEs
lr
. - 0 . 3 oo I = -3 /}
"----S'zs @
l r1
I
-'.0.2 2
o.7
o
.=
o ct)
IL
J
o (u
3 2.5
CL IE I
6
'6
o
5 q)
(s o I
0.4 1.5
0
ct al. 1985) ric representationaboveis 167). Appendix 4
f
6 -u.5 s
()
300
-o =. d)
IU CL E2
o o I
II
rhdpies
^^ tl fi ''-
100 200 o Temperature C
I
300
Figure A.4.3 Heat Capacitiesof Bitumens and Heavy Oils (Data from Cassis et al. 1985) Heat Capacities and Enthalpies
Appendix 4
501
HeatCapacitiesof CommonGases
Volumetrie ll
Thesemaybe predictedby the followingequation:
t
The las r
Cp=a+br+#
Conversirxr R where Co is in k{kg K T is in K = /oC * 273.1,5
1 Btu/lb "F
and the coefficientsa, b, and c' (if used)are read from the following table.
Molecular Weight
Name
Hydrogen Oxygen Nitrogen Air Carbon dioxide Carbon monoxide Methane
2.0158 31.9988 28.0134 28.8s 44.00955 28.01055 16.04275
Applicable TemperatureRangeK
13.75 1.08 0.97 1.00 0.98 0.99 1.39
0.001682 0.000034 -24,560 0.000149 0.000123 - \ 1 ) l 0.000261 - 18,600 0.000179 0.003001
273-2,500 300-5,000 300-3,000 300-3,000 273-t,200 273-2,500 273-t,200
BI-aNo,W. F. r Hill (l%7r.
Cassrs,R., Fr lu YeN, H.. -Sg Clays,De@ 163-173(lSS) HouceN, O. A. r (1e50). Pennv, R. H. al Hill, New Ycl
The valuesof the coefficients are basedupon the data summarizedin Perry and Chilton (1973). Average Heat Capacities between T1 and 72. If C:
a * bT + cT2,then
e=a+b(!+r,) *,( T ? + T r r r + r 3 \L/\
If c = a -f uT + c'fT2, then
e =a. r(L#).** Change in Enthalpy between Tt and Tz
LH=ol"ro, =a(rzn)+,(Uf) . ,(ry) r,H= a(rz- n + b(A;!) s02
., (H)
Heat Capacitiesand Enthalpies
Appendix 4
Heat Capacitiesr
Volumetric Heat Capacitiesof ReservoirMaterial pC = (I - 6)p,C, I gSnp.C, * QS"p"C"+ |Sspssg The last term is usuallynegligible. ConversionFactors 1 Btu/lb oF = 1 calfg"C = 1 kcaVkg oC = L CHU/lb .C = 4.t87 k/kg "C o*'ins table.
Applicable Temperature RangeK 2'73-2,500 300-5,000 300-3,000 300-3,000 2'73-t,200 273-2,500 2"t3-1.200
BIBLIOGRAPHY BLaNo, w. F. and DevrosoN,R.L., PetroleumProcessingHandbook, New york: McGrawHill (1967). Cassrs, R., Fur-Let,N., HerLER,L. G., McLeaN,R. J.C., Sreucr, A., SnrNrvasex, N. S., and YeN, H., "Specific Heat capacities of Bitumens and Heavy oils, Reservoir Minerals, Clays, Dehydrated Clays, Asphaltenesand Cokes," AOSTRA J. of Research,l, no. 3: 163-173(1985). HoucrN, o.A. and wansoN, K.M., Chemical Processprinciples, New york: John wiley (1950). Pennv, R. H. and cHrLroN, c.H., chemical EngineersHandbook, 5th Edition, McGrawHill, New York (1973).
rmmarizedin Perrv
rj - ri\ 3)
L)
dpres
Appendix4
Heat Capacitiesand Enthalpies
Appendix 4
503
Appendix5
If oola predictio Ir freq straishrlirE d r a u nb 1 ' n Atrho stokes.it hl tipoise.Fa t a rangeof ti
Viscosities
I
Viscosity of Crude Oil The viscosityof crude oils can be representedas a function of temperaturewith accuracyby the equationl logrologio(z+ 0.7)] : mlogn(T + 273) + b is the kinematicviscosity,cs is the temperature,oC m 2 and b, are constantswhich are characteristicof the oil
where z T
graphpaper, This equationforms the basisof the ASTM viscosity-temperature on which viscosity-temperaturecurves of hydrocarbonliquids plot as straight lines (ASTM 1989).It has been used frequently to correlate,interpolate and extrapolate experimentaldata for the viscosityof heavycrudesand bitumens. In order to define a line for a particular crude, it is necessaryto fix two parameters,suchas two points on the line or a singlepoint togetherwith the slope of the line.
For rne peratureand the viscositv viscositv.Flo of typical vi givesthe bcr There r 150'C.and d to the terryc The bn than thar fc data plorcd i.e.,
Examie from relatird catesthat ril creasefor cil The correlad United Srarc oils can be er
whereD n
tThe history of this equationis describedby Wright (1968).Walther (1928)describedthe idea of plotting viscosityversustemperatureon a plot of log log(z)againstlog T.ln 1932,he modified this to a plot of log log(z + 0.8) versuslog ?. The first ASTM chart issuedin 1932also used0.8 in the ordinatefunction. Although this equationwas identicalto the Walther formula, the ASTM committee credited its introduction to the work of MacCoull, who introduced the idea of plotting log log(z + const.)againstlog 7 in a TexasCompanypublicationin 1921.Variousconstantsand adjustableconstantshave been used in the subsequentversionsof the ASTM paper. The work by Wright, which forms the basis for the current ASTM chart, uses 0.7 for viscositiesdown to y = 1.3 cs. Below that viscosity,a more complexexpressionis substitutedfor the constant0.7.
tThe a"tr papers describ,r ica. The papcrl cally. For eacb centipoiseor r r h i g h d e g r e eo f o constitution o( t
504
Viscosities
If only one measuredvalue is availablefor the viscosityof a heavycrude,then a predictioncan be madeif the slopeof the viscosityline can be estimated. It frequently happensthat the lines for a family of oils fall as nearly parallel straightlines-i.e., have a commonvalue of m. This allows a viscosityline to be drawn by making it parallel to lines for similar crude oils. Although the ASTM graph paper refers to kinematic viscosities in centistokes,it hasalsobeenusedby someauthorsto correlatedynamicviscositiesin centipoise.For example,Svrcekand Mehrotra (1938)have shown that the viscositiesof a rangeof bitumenscan be representedfor temperaturesup to 130'Cby the relation + 273) + 0.7)] : b' - 3.63029lo9ro(T logro[logro(& oC where Z is the temPerature, b' is a constantfor eachoil
ItemPeraturewith acrb
c of the oil rperature graPhP19er, ts plot as straight lines 'polate and extraPolate lmens. s necessaryto fix two togetherwith the sloPe rcr t1928)describedthe idea r T. In 1932,he modifiedthis in 1932alsoused0'8 in the formula,the ASTM commitdrred the idea of Plotting !1. Variousconstantsand adASTM PaPer.The work bY 0.7 for viscosities down to rrcd for the constant0'7'
For mathematicalreasons,if the densityof the oil is a linear function of temperature and the dynamic viscosity of the oil follows the precedingequation,then ihe viscositycannot also plot as a straight line on the ASTM paper using kinematic viscosity.However, the curve will be almost straight and, becauseof the precision of typiial viscosity measurements,it is usually difficult to determinewhich graph givesthe best straightline. There are essentiallyno measuredviscosity data for heavy crude oils above 150"C,and this makesthe useof any correlationfor the extrapolationof viscosities to the temperaturesused in thermal recoverysomewhatquestionable. The beststraightline drawn on the kinematicviscositybasiswill be lesssteep than that for the dynamic viscosity plot. The value of m for the Svrcek-Mehrotra -3.5556; data plotted as kinematic viscosity would be about 2Vo smaller,or m : i.e., + 0'7)] - b - 3.5556logro(7+ 273) logroflogro(z Examination of the data for a wide range of asphalticheavy crudes ranging from relatively fluid conventionalheavy oils to the most viscousof bitumens indi catesthat ratirer than being constant, the absolutevalue of the slope tends to increasefor oils of lower viscosity' The correlation of rn with b fot a wide range of heavy crudes from Canada, the United States,and SouthAmerica in FigureA.5.1 showsthat the viscosityof these oils can be estimatedfrom2 + 0.7)] = mlogrc(T + 273) + b logro[logro(z where b is a constantfor any particular oil m is given bYm : 0'3249- 0.4106b 2The data shown in these plots were obtainedby using the crude oil viscositiesreported in papersdescribingvariousthermai recoveryprojectsin Canada,the United Statesand SouthAmerspecifii.". 1.n" pup.r. *.r" thosethat happenedtobe in the author'slibrary and were not selected to from centistokes converted were These chosen. points *"re viscosity two cally. Foi each oil, The ceniipoiseor vice versa,with an ull6t"n"" beingmadefor the effect of temperatureon density' similar high iegree of correlationfound betweenb andm is surprising;this presumablyref lectsthe constitutionof theseparticular heavyoils.
Viscosities
Appendix 5
505
-2.5
E
high temperrr cationof thc 1 is for a relalir If the m convertedto I lations in Ag ureA.5.2['it similar plot to
m = 0.3249- 0.4106b
o o
E-3
o o o.
t -ss
-9 o
e-4 = (E
! Canada o UnitedStates SouthAmerica
= -4.5; 7
where m ard 8
9 10 Walther Inlercept b
11
FigureA.5.1 Correlation Between WaltherParameters for HeavyCrudeOils
Theserelationsdefine a family of straightlines, which passthrough a common pole on an ASTM plot; seeFigureA.5.2. The tendencyfor lines for oils from a commonfamily to passthrough a particularpole hasbeenusedin lubricatingoil technology,particularlyin Europe,wherethe positionof the pole hasbeenusedas a correlating factor to representthe type of oil. This systemis comparableto the viscosityindex classification,which is more commonlyused(seeBondi (1951)for a discussionof Waltherand Ubbelohde'spole height (Ubbelohde1940)). The viscosity-temperature line for a given crudeoil can be estimatedby joining this pole (at -1'C, 1.5 x 106cs) to a point representinga measuredviscosityof the oil. For bestaccuracyfor thermal recoverystudies,this measuredpoint should be at a temperatureas high aspossible.This will minimize the degreeof extrapolation which is requiredin the utilization of the data. Becauseit is the viscositiesat
In suchr suitablefor tL
Effect of pru While the effi Mehrotn bitumenvaric
wherep is tbe of P, (MPa). This can
rc,l
100,000,000 1,000,000 '| 00,000
r.t r.
10,000
I
(,' 1000
()
'-E
100
Fso
o o c
8ro .9 ro (,
a
o
o e a
F5 a!
E
o tr Y
1
TemperatureDegrees Celsius FigureA.5.2 ViscosityrTemperature Chart for Heavy Crudes KineTat_icViscosity
506
Viscosities
Appendix5
Fi3rnr Viscosities
I
high temperaturesthat are of interestin thermal recoverycalculations,the exactlocation of the pole is not of great importance,particularly if the measuredviscosity is for a relatively high temperature. If the measuredviscosity data are given as dynamic viscosities,they may be convertedto kinematic viscosityby utilizing oil densitiesestimatedfrom the correlations in Appendix 2. It is possible to plot dynamic viscosity directly on Figure A.5.2 by interpretingthe units of the verticalscaleascentipoise.tn this case,a similar plot to that of FigureA.5.1 yieldsa best straightline of m'=0.3464-0.4127b' wherem' and b' refer to the equation 11
logroflogio(r+ 0.7)] = m' logrc(T+ 273) + b'
Crude Oils
ln sucha plot, the pole shouldbe at the position(-8'C, 8.1 x 106cp). A chart suitablefor this applicationis given in FigureA.5.3.
ss through a comlines for oils from d in lubricatingoil le has been usedas comparableto the r Bondi (1951)for a le40)). I estimatedby joinasured viscosity of sured point should bgree of extrapolais the viscositiesat
Effect of pressure Increasingthe pressureon a liquid also increasesthe viscosity. While the effect is generallysmall,it can be significant. Mehrotra and Svrcek(1986)show that the viscosity of a sampleof Athabasca bitumen varied accordingto the following correlation. ln ln(pc)= 22.8515- 3.5784In(T) + 0.00511938& where ;r.is the viscosityin centipoiseat a temperatureof ? (K) and a gaugepressure of P, (MPa). This can be written usingcommonlogarithmsas log log(pc)= 9.56204- 3.57841og(?)+ 0.002223Pg
O. t00
oso C
5 '6 r o to o o 95
0
reric Viscosity sities
Appendix
200 100 TemperatureDegreesCelsius
300
Chartfor HeavyCrudesDylggrgYiscositl FigureA.53 Viscosity:Temperature Viscosities
Appendix 5
In the temperaturerange they investigate,p. would be relativelylarge and log log(pr)would be nearly equal to log log(pc+ 0.7). The effectof pressureis thus to raisethe viscositytemperatureline on a chart suchas that in Figure A.5.3 by a distanceof 0.002223p". The positionof the pole in Figure A.5.3 is thus a function of pressure.
Pressure,MPa Pole position, cP x 106
0.1 8.1
5 12.1
10 28.3
The data in the following table show that the effect of pressureis larger at higherviscosities (i.e.,at lower temperatures).
Viscosity of oil at atmosphericpressure (cp)
ViscosiryDivided by Viscosity at 1 atmosphere 5 MPa
10MPa
8 . 1x 106
1.5
100
r.+z
3.5 3.0
105
r.34
2.s
104
1.26 1 .1 9 t,12 1.06
2.1 1.7
103 102 l0
if. fo plot such a
willbe ccn of the livc r T h i si that logrlrto p. theni The d rangeof ten the solidnr crudes.It m more consr That r Figure..\.5. trationof di samepressu
where -r is t approx. r.
1A
1,.2
At temperatureswhere the oil becomesreasonablymobile-e.g., where p < 100cp-the effect of pressureis relativelysmall. Effect of dissolved methane In the reservoir,the oil is typicallynearlysaturated with naturalgasat the reservoirpressure,Under thesecondiiions,thereare two effectsupon viscosity: 1. The dissolvedgasactslike a solventand tendsto reducethe viscosity. 2. The pressuretendsto increasethe viscosity. The dilution effect is larger than the pressureone, and there is an overall lower viscosity. Mehrotra and Svrcekhave measuredthe viscositiesof severalbitumensthat have beensaturatedwith methaneover a temperaturerangeof about 20"Cto r20"C and at pressuresup to 10 MPa. The effectof the dissolvedmethaneupon the viscosityof three differentbitumensover this rangeof conditionsis shownin Figure A.5.4.
508
Viscosities
Appendix5
[igrc Ctlr:C!
Vtstsr \lerhr
Viscosities
rtively large and
lf, for a constantconcentrationof dissolvedmethane,the viscosity line on a plot such as that in Figure A.5.3 movesdown by a constantvertical distance,then
le line on a chart log log(p, + 0.7) - log log(p + 0.7)
f pressure.
10 28.3
ssure is larger at
I atmosphere )MPa
35 3.0 2.5
will be constant;po representsthe viscosityof the gas-free(or deadoil) and p, that of the live oil. This is the sameas sayingthat logflog(p," + 0.7)llog(g. + 0.7)] is constant,or that log(9,, + O.7)/log(tt + 0.7) is constant.If the term 0.7 is neglectedcompared to p, then it can be seenthat this ratio is the sameas the ordinatein FigureA.5.4. The data in Figure A.5.4 are from measurementscarried out over the whole rangeof temperatures.It is interestingthat the data for Cold Lake crude,which are the solid circlesin Figure A.5.4, correlatebetter than the earlier data for the other crudes.It may be that this reducedscatterfor the Cold Lake crude is indicative of more consistentmeasurements. That the experimental data can be correlated in the manner shown in Figure A.5.4 indicatesthat the viscosityof a bitumen containinga constantconcentration of dissolvedmethanewill fall below the line for the gas-freebitumen at the samepressureby a distance (1)
t=l+O.Wllx
?l
t.7 1.4 t.?
where x is the concentration of methane in SCF/B (89 SCF/B :'1, wtVo CHa, approx.). 0.8
1.2
1.6
1.3
bile-e.g., where
Y : 1 + 0 . 0 0 2 1X
CL
(, E
3 1.2
ly nearly saturated there are two ef"
! _
ct) o
a l
CL
o
[e viscosity.
.E o g
[ree different bitu-
ities
Appendix 5
'*o !
CD
o
.hereis an overall eral bitumensthat )out 20'C to 120"C
1.1
to'
A
. Cold Lake 30- 120 oC oC : Peace River54 - 114 o ^ Wabasca 23 111 C
40 80 Dissolved Methane
120 SCF/B
160
Figure A.5.4 Effect of Dissolved Methane upon the Viscosity of Bitumens. CorrelationofData from Mehrotra and Svrcek(1988,1985aand 1985b).po is the Viscosityof Bitumen in cp with No DissolvedMethane; p is the Viscositywith Methane.
Viscosities
Appendix 5
509
The solubility of the methane in the same bitumens has been correlated againsttemperatureand pressureby the equation
| 343\ scF/B=Pexn(1.50*l)
= 4.66P*r(#) where Z is in K P is the absolutepressurein MPa The data are comparedwith this correlationin FigureA.5.5. Although there is considerable scatterin this diagram,the vertical scaleis relativelylarge,and it will be seenthat all but one experimentalpoint fall within +20Voof the predicted solubilities.Again, the more recent data for the cold Lake bitumen appear more consistent. The methane concentration can be eliminated from equations 1 and 2 to provide a correlation that predictsthe viscosityof the live oil as a function of pressure and the viscosityof the deadoil at the sametemperatureand pressure.This correlation is p =
exp(34317) ""p[ 1 + 0.0093P ^
. 6
o
Viscosity I
ln l"o
-vAUt-/
- 0.1)ll lln pooexpf0.00511938(P
t
Cold lake 1988
(3)
1 + 0.0093P exp(343/T) ) !
Peace River 1985
Pred the resuls Figure .{ j within abo consisten Thc c oils a-sa fur a bitumcrr go€sthrcr,4 viscositl.s becomesm bitumenth
a
Wabasca 1985
2.8
The dr nam ted in Fieu greatertha approacha Figun ted aeainE steamis rn
= E
oo lI-
o
o .E g .ct f
o o \t I
o tr
J
0.0026
0.0028 0.003 0.0032 1/T with T in degrees Kelvin
0.0034
Figure A-5.5 Solubility of Methane in Bitumens. Correlation of Data from Mehrotra and Svrcek (1988,1985aand 1985b).The Thick Line is Given By Y : 1.54 + 343/7. The Thinner Lines CorrespondTo SolubilitiesWhich Are 20VoHigher and 20VoLower Than Those Given By the Above Equation.
510
Viscosities
Appendix5
F4r f rt-l
Viscosities
ns been correlated
where trc Po ltoo
P T
5.5.Although there ativelylarge,and it )oZof the predicted lumen appear more uationsland2to i a function of presand pressure.This
is the live oil viscosityin cp is the dead oil viscosity in cp is the dead oil viscosity in cp at the sametemperatureand atmosphericpressure is the pressurein MPa is the absolutetemperaturein K
Predictionswere made using this equation for each of the data points, and the results are shown as ratios to the corresponding measured viscosities in Figure 4.5.6. The correlation appears to be able to predict the viscosities to within about +20vo. Again it will be noted that the cold Lake data appear more consistent. The curvesin FigureA.5.7 showthe ratio of the viscositiesfor live and dead oils as a function of temperatureand pressurecalculatedby meansof equation3 for a bitumen having a viscosity of 120 cp at 100'C and a dead-oil viscosity line that goesthrough the pole of Figure A.5.4. The effect of dissolvedmethaneon the oil viscosity is indicated to decreasemarkedly as the temperatureis raised and the oil becomesmore fluid. It is also very dependentupon the pressure.This graph is for bitumen that is saturatedwith methane. Viscosity of Water and Steam
(3)
Gca
1985
The dynamicviscositiesof saturatedsteamand of water at its boiling point are plotted in FigureA.5.8. At lower temperatures, the dynamicviscosityof water is much gteaterthan that of steam,but, as the temperatureis increased,the two viscosities approacheachother and becomeequalat the critical point. FigureA.5.9 showsthe kinematicviscosityof saturatedsteamand waterplotted againsttemperature.Becauseof its lower density,the kinematicviscosityof steamis much higher than that of liquid water at lower temperatures.Again, the '-o o o .!2
p = exp{Ln(llo)/(1 + 0.0093p exp(3a3fD)} p is the viscosity ol the live oil in cp /-lo is the viscosity o{ the dead oil in cp T is the temoeraturein K
It o o
.E
o
=
'-o o o o tt o .9 t o o.
o.oo34
L
of Data from r is Given By :s Which Are pation. sities
Appendix 5
o3
0.03
0.1
0.3 1 3 10 Predicted Viscosity in Pa.s
30
Figure A.5,6 Ratio of Predictedand MeasuredViscositiesof Bitumens.Data from Mehrotra and Svrcek(1988,1985aand 1985b) Viscosities
Appendix 5
511
1.2
't
!t
E1 cr
a (t
-9o.s
5
I$ o.s
o
r,
I a
tr .iat, 0.4
s
Bitumenviscosityat 100o C = 'l2Ocp
o
8 o.z
a
E a c
RMa 8S831
o
0
100 200 Temperature degrees Celsius
=
3oo
Figure A.5.7 Effect of Temperatureand Pressureon the CalculatedViscosities of Methane-Saturated Bitumen
viscositiesconvergeat the critical point. Becauseof the higherkinematicviscosity of steam,a much higherpressuregradientis requiredto achievea given massflux in a porousmediumfor steamthan for liquid water. The dynamicviscositiesof saturatedsteamand liquid water can be estimated from the following correlation equations.
Figrn / Schmrd
Water at bo1o-100 t
Saturated steam s., = 0.00879+ 0.00003547+ lVo
where p.
T
where pc, is in cp
g0.c
o-
100-3{nt
1 where l t .
o c
T
=
o o
Converskrn Fr
.9 E 0.03 o
DYNATr The SI unit of The tradi
.E 0.1
0.01
0
100 200 300 TemperaturedegreesCelsius
400
Thus
Figure A-5.8 Dynamic Viscosity of SaturatedSteam and Water (Data from Schmidt and Grigull 1981)
512
Viscosities
Appendix5
Viscosities
l
o o
.E 1 0 0
1 , ""l rs'
6 o
10
(,
1
o o
(g
E o C
I 300
0.1
Y
100 200 300 Temperaturein degrees Celsius
d !'iscosities
kinematicviscosity : a given massflux
Figure A.5.9 Kinematic Viscosity of SaturatedSteam and Water (Data from Schmidt and Grigull 1981)
Water at boiling point
r can be estimated
10-100 "c L
= o.sqaz + 0.02t1g27 + 0.0000893472-+ lvo
F,
wheretrr,, is in cp T i si n ' C 100-300'c !
- 0.4gg7-+ 7.5Vo = O.O+OO7IT
lL.
where g., is in cp T isin'C
- -
II - _-
ConversionFactors
I
(M/LT) DYNAMTC VTSCOS]TY The SI unit of dynamicviscosityis Pa s, or the equivalentkg m-l s-1. The traditionalunit is the centipoise(cp) : 0.01p, where
:T-r-
I
:--
I I
1 poise = 1 g cm-l s-l = 0.1 kg m-1 s- I
400
Thus 1 cP = 0'001Pa s
' (Data from
=l-mPas ities
Appendix 5
Viscosities
Appendix5
513
If consistentequationsare employedthat use ftlb and days,then dynamic viscositiesshouldbe expressed aslbft d.
.r 'P = 0.01x 86400x 30.48= 58.06lb/tt d 453.6
Appe
K|NEMAT|C VTSCOS|TY (LrlT) By definition, u : p,lp. The SI unit of kinematic viscositv is
Pas
;r\ = m:/s (Kg/m-)
The traditional
is the centistoke (cs) = 0.01 stoke, where
Heofi
1 stoke = I cm2/s = I}-a m2/s
1 cs = 10-6m2ls
BIBLIOGRAPHY ASTI4 "Viscosity TemperatureCharts for Liquid PetroleumProducts,"ASTM Standard D34l-87 in 1989Annual Report of Standards,vol. 05.01,philadelphia:ASTM (19g9). BoNor,A., PhysicalChemistryof Lubricating oils, New york: Reinhold (1951). MecCourr, N., Lubrication, New york: The TexasCo. (June1921),65. MEunorna, A. K. and Svncrr, w.y., "viscosity, Density and Gas SolubilityData for oil Sand Bitumens,Part II: PeaceRiver Bitumen Saturatedwith N2, co, aH4, co2 and CzHoi' AOSTRAJ. of Research,1, no. 4:269-279 (19g5). MnHnorna, A. K. and SvRCnr,w.y., "viscosity, Density and Gas SolubilityData for oil SandBitumens,Part III: wabascaBitumenSaturatedwith N2,co, cH4, cb2 and czHe,,, AOSTRAl. of Research,2, no.2: 83-93 (19g5). MeHnorna,A. K. and Svncex,w.y., "viscosity of compressedAthabasca Bitumen,,,Can. J. Chem.Eng., 64: 844-847 (October 1986). MrHnorna, A. K. and Svncrr, W.Y.,"Propertiesof Cold Lake BitumenSaturatedwith pure Gasesand Gas Mixtures," Can.J. Chem.Eng., 66:656-665(August19gg). Scnuror, E. and GnrcuLL, lJ., Propertiesof Waterand Steamin SI Units, Berlin: Springer_ Verlag(1981). SvRcer,W.Y. and Meunorna, A. K., "One ParameterCorrelationfor Bitumen Viscositv.,' Chem.Eng. Res.Des., 66:323-326(July 1988). Uaneroune,L., "Zur Viskosimetrie,"Leipzig (1940). Wer-rHen,C., EnooluNoTenn, 4: 510(192g). WnLrHeR,C., Enoor-uNo TErn, 7: 382(193I\. WnIcnr, W. A., 'An Improved Viscosity:IemperatureChart for Hydrocarbons," L of Materials, 4, no. l: 19-27 (196$.
Hydrocarbor i The heat of q from the folbr Gross h€rt o, -Ji Net heat o{ q
-r, where -JH, I 15.6"Cand AF Theseeq havingthe foll
.API Wt% S
O :9:
For oils h
514
Viscosities
Appendix5
should be subtr
I days, then dynamic
ld
Appendix6 Heofs of Combustion
drts," ASTM Standard phia:ASTM (1989). rhold (1951).
HydrocarbonLiquids
), 65. l SolubilityData for Oil N:, CO, CHr, COz and
The heat of combustionof typical liquid hydrocarbonstreamscan be estimated from the followingequations(API, 1983).
l SolubilityData for Oil )" CHl, COz and CzHoi'
-aH, = 41,105 - 0.735(APD2 - 0.00326(ApIf + 154.9(API)
Grossheat of combustion
Net heat of combustion babascaBitumen," Can. oen Saturatedwith Pure gusr 1988). I Unis, Berlin: Springer-
- aHn= 39,068 - 0.505(API)'? - 0.00442(APIF + 126.S(API) where-AI/, and -A11, are the grossand net heatsof combustionin k/kg at 15.6'CandAPI is the API gravityof the oil. Theseequations arebasedupona correlationgivenby Maxwell(1950) for oils havingthe followingsulphurcontents.
Lfq BitumenViscosity," .API WtVa S
0 2.95
5 2.35
10 1.80
I)
1.35
20 1.00
25 0.7
30 0.4
35 0.3
drocarbons."J. of Materi-
For oils having different sulphur contents,a quantity given by
- 40.s]as [0.01(-Ar1) rcocities
ApPendix 5
should be subtractedfrom the precedingvalues. 515
where -A^FI is the appropriateuncorrectedheat of combustion AS is the sulphur content of the oil in wtVominus that interpolated from the precedingtable Example: Estimate the heats of combustion of a 10'ApI 4.5wt% S.
heavy crude oil containing
-LHs = 41,105+ 154.9x 10 - 0.735x 100 _ 0.M326 x 1000 = 42,577kJ/kg Correction = (426 - 40.5)(4.5 - 1.8)= 1641 Correctedheat of combustion:
Solid Rrlr
Coel [It-
sd'| LiSj rlbod
Grcq Air X Petr& Cartc
(Data from Perryr
-LH, = 42,577- I04l = 4I,536kJ/kg
ConversimFr lBr For gases
= 17.857 Btu/lb +# 2.326
kI
Similarly -LHn = 39,068+ t^6.g x 10- 0.505x 100- 0.00442x 1000 = 40,281 uncorrected
lHq
The correctednet heatof combustion is then
APl, TechnicalD D.C. (1983),l. MaxwrlL J. B.,i original editir PBnnv. R. H. el McGraw-Hill Q
-LH, = 40,281-1041= 3\240kJ/kg or 16,870 Btu/lb Fuel Gases
Heatsof Combustion Molecular Weight Hydrogen Methane Ethane Propane
2.0 16.0 30.1 44.1,
k{kg Gross
t42,Lrg 55,498 51,870 50,358
Gross
r20,02r 50,009 47,497 46,357
t2.03 37.58 66.07 93.98
(Valuesbasedon data from Maxwell 1968.)
516
Heats of Combustion
Appendix6
Heats of Corrhr
Solid Fuels
nbustion ninusthat
Gross Heat of Combustion k/kg Ash-FreeBasis
rude oil containing
326 x 1000
Coal Bituminous Subbituminous Lignite Wood Green Air Dry PetroleumCoke (delayed) Carbon
27,800-35,400 2r,300-24,000 I7,300 5,500-11,000 12,000-14,000 35,450 1?715
(Data from Perry and Chilton 1973.)
ConversionFactors 1 Btu/lb = 2.326kl/kg For gases
k/m3= kyks(#x)
m'measuredat 15'C and 1 atm
1 Btuft3 = 37.26kJ/m3
t442 x 1000
BIBLIOGRAPHY APl, TechnicalData Book PetroleumRefining, American PetroleumInstitute, Washington, D.C. (1983), 14-11. MaxweLL, J.8., Data Book on Hydrocarbons,New York: van Nostrand(9th printing 1968of original edition 1950). Pennv, R. H. and CullroN, C.H., ChemicalEngineerbHandbook, 5th ed., New York: McGraw-Hill (1973).
m Btu/lb
M/m3
Gross 12.03 37.58 ffi.07 93.98
ustion
Net
10.16 33.86 60.50 86.85
Appendix6
Heats of Combustion
Appendix 6
517
Appendix7
Appe
Air CompressionFuel Reguiremenfs
Thern
Thermal insilr (1981), whichc
EnergyEfficiencyof Gas Engines12)
85-400 440-800 880-3000 >3300
Engine Vo Efficiency(t)
Fuel Requirement SCVHP h
28 32 36 38
10.0 8.8 7.8
(l)Based on LHV of methanefuel (908Btu/SCF). (')Based on Perry, R. H. and Chilton, C.H.., ChemicalEngineerbHandbook,5th ed., New york: McGraw-Hill (1973),24-14.
Basis:Inlet conditions60"F and 1 atmosphere. Discharge Pressure Psia
100 200 400 800 1200
HP h per 1000SCF Compressed Isothermal Compression(r)
2.0s 2.79 3.53 4.28 4.71
(t)Hp = t.o7 tn(p2lp). (')Assuming practicalHP is 40Vogreaterthan isothermal,i.e., HP = 1.5 ln(pz/pt). 518
Practical(2)
2.88 3.92 4.96 6.00 6.60
TABLE A.8.1 TherrnalCor
Material Polyurethane Polystyrene Cellular elastomeric Cork pipe insulation Cellulosefiber board Mineral fiber blanket block board pipe insulation Cellularglass Calciumsilicate block board r('
Diatomaceousearth Diatomaceousearth Expandedperlite Neisel and Verschoor , l95lr
Appendix8 Thermql lnsulstion
Thermal insulationpracticeswere reviewedin an article by Neiseland Verschoor (1981),which contains59 references. SeeTableA.8.1. Fuel Requirement scF/HP h 10.0 8.8 7.8 7.4 5th ed., New York:
I Compressed Practical(2)
2.88 3.92 4.96 6.00 6.60 t(PzlP).
TABLE A.8.1 ThermalConductivitiesof Block,Board,and pipe Insulation Temp range or maximum,'C
Material Polyurethane Polystyrene Cellular elastomeric Cork pipe insulation Cellulosefiber board Mineral fiber blanket block board pipe insulation Cellular glass Calcium silicate block board Diatomaceousearth Diatomaceousearth Expandedperlite
-73 to 110
Thermal Conductivity,m$(m "C)
0'c 1A JI
4l
24'C
100'C
400'c
540'C
25 35 +J
48 55
204 204 982 650 -268 to 427 649 650 (577kg/m3or 36 lbft3) 870 1040 816
37 4l
5t 52
A<
58
60 66 lzJ
7l 83 75 100
1,16
79 126
106
100 108 79
109 r2l 105
ll7
130
Neiseland Verschoor(1981)
519
TABLEA.8.2 Annular Insulationfor Steam InjectionWells Material
ThermalConductivity W/mK
Evacuatedjacket with layers of foil and ceramicfiber Sodium silicate foam
0.07-0.0002(t) 0.029t2)
'uepends gas on remainingwithin jacket.Lowestvaluesobtainedusingkrvpton with a getter to absorbH2. Effective conductivity ijhigher than theseuuru., u."uu*'o"iioiJ", ut rrot spots. (See Meldau1988). (2)From Boberg(1988).Foamedsilicate insulation is formed as a layer over the exterior of the well tubing;the layeris typicallyj to in. thick. I (seeChapters2 and 8)
App
{1)n
BIBLIOGRAPHY BonnRc,^[.C., Thermal Methodsof Oil Recovery,New york: John Wiley (19gg). MeLoau,R.F., "Reducingwell Bore Heat Loss," Reprintsof papers in the Thermal well CompletionsSeminarheld at the 4th International Conferencl on Heavy Crudesand Tar sands(UNITAR), Edmonton,Alberta (August7-r2, rggg).presented and publishedby the CanadianHeavy Oil Association. Neiser-,R. H. and VenscHoon,J. D., ,,InsulationThermal," in Kirk-Othmer Encycbpedia of ChemicalTechnology,3ded., 13:591-605,New york: John Wiley (1981).
Ther
of st
Saturatkn I
The steamsr lated from ti P in MPa rr
logroP
This eq Error li
logroP = 4.{
Error li These r 75'C in tern
'" -
't-- -
520
::--__
ThermalInsulation
Appendix8
-
1r''4&
I Conductivity *7m K
Appendix9
'-0.0002(r) ),029(2) I krypton with a getter to f lossesat hot spots.(See sr the exterior of the well
Thermdl Properfies of Sfesm il'iley (1988). :rs in the Thermal Well I Heavy Crudes and Tar ented and publishedby OthmerEncycbpedia of r (1981).
SaturationPressureand Temperature The steamsaturationpressurecorresponding to a temperature ffC can be calculated from the following correlations: P in MPa and 7 in 'C
-lr.orrr, = 9.8809 rogroP - - - - * =t.'t!^--1', 1 0 0 ' c < T < 2 7 5 . C r+273.1s1' LThis equationis due to SanfordMoss (1903). Error lies in the rangeof +0.6Voto -0.4Voof P and 'oot logroP = 4.4988- (, \. 27s'( \r.an315)''2't5"C
r-r = $ - 2 7 3 .- r s ,
(V9.8809 logroP-2.42223)
0 . 1< P < 6 M P a ,
15in"C
Error +0.24"C
ulation
Appendix 8
521
Ts=
2043 4.4988- logroP
- 273.15
6 < P < 22.12Mpa (critical pressure)
to the rested
Error t0.4'C Theseexpressions are shownconvertedto British units next.
in compurr I
P in psia and 7 in "F
l o g r o= p 1 2 . 0 4 2 4 - ( r . o r r r r *= : t 1 ' : : r = ) ' , r + 459.671 \ logroP = 6.6602Z5=
2 r 2 F< r < s z : " F
3677.3 527"F < 705.6"F (critical temperature) T + 459.67'
Moss.Sr,rrc
587.83
459.67, (V12.0424 - logroP - 2.42223) 14.5psia< P < 870psia
?t=
3677.3 - 459.67, 6.6602- logroP 870 psia < P < 3212psia (critical pressure)
Enthalpiesof Saturated Liquid and Vapor: These may be read from Table 4.6 or Figure 4.2. The following correlationsreproducethe enthalpiesgiven in the steamtables within 0.1.5Vo and are useful in computerprograms. Temperature range I 00-275"C Ht = -14.54 + 4.51967- 0.00277172+ 0.0000092273 _ 0.0000182473 Hv = 2523.43+ 1.35567+ 0.00356112 Hv- Ht=
_ 0.000021q6r3 2537.97- 3.t6407 + 0.00633272
Temperature range 275-357"C Hr. = -3899.18+ 45.0857- 0.1441812 + 0.0001739073 Hv = 9457.68 70.9427 + 0.2551472- 0.0003105g23 Hv - Hr:
13356.86- 116.0277+ 0.3993272- 0.00048448?3
where T is iil "C and H7 and H1 are in k/kg.
522
Thermal Propertiesof Steam
Appendix 9
Thermal ftope
In order to minimize computation,it is desirableto convert polynomialexpressionssuchas l=ao*a1x*a2x2*a3x}
to the nestedform l=ao *[a1 * (a2*a3x)xfx Et.
in computerprograms.
r{l
BIBLIOGRAPHY
iT < 527"F
phys.Rev.16:356-363(1903). Moss,SaNroRoA.,"GeneralLaw for VaporPressures,"
pel temperature)
I
r in the steamtables
l,f,0.y 2273 wtg24T3 ofrn467"3 m7390r3 il(E&r3 n$44813 I
Appendix 9
Thermal Propertiesof Steam
Appendix 9
523
Index
Agnew,H., 279 Air compression, fuel requirements, 5 18 Alexander,Martin and Dew, 424-31 Allen, F. H., 14 Alternate steamgenerators, 404-t1 coal-firedgenerators,404-5 downholesteamgeneration, 405-7 fluidized bed boilers,407-9 Vapor Therm generators, 408-10 Zimpro-AEC steamgeneraror, 410-11 Armento, M. E. and Miller, c.A., 191 Aromatics,in middle distillates, 1 ASME boiler feedwater specifications,365 Athabascasands,9
524
Babcockand Wilcox, 361-63,370 Babcockand Wilcox water tube boiler (1877),362 B e l l e v u eL o u i s i a n aI,S Cp r o j e c r . 471-74 Berry,R. I.,409 Biodegradation,10, 167 Boberg,T. C. and Lantz, R. 8., 244_48 Boltzman'stransformation,33 Borregales,C. 1., 25, 273-7S, 383 B o t t ,R . C . , 2 7 1 - 7 2 Bridle,M. K., 399 Britton, M.W., et al, 167-6g Buckles,R. S., 19, 376 Buckley-Leverett displacement theory, 199-216 breakthrough, 205-7, Zl3-14 diffuse and segregatedflow, 2t3-16 effect of viscosity ratio, 207-8 frontal stabilit y, 2A9-fi numerical problem, 210-12
oil-water ratio,214 pressuregradients,208-10 saturationbehind front, 201-3 upper shockfront, 203-5 velocityof shockfront, 200-l Burgerand Sahuquet,431, 446-48 Burns,J., Californiancyclic steamprojects,255-57, 262 Carcoana,A. N., 476 Cardwell and Parsons,288 C a r r e l lN , .A.,396,401 Carslaw and Jaeger,54 Cassis,R., et al., 500-1 CCR, Conradsoncarbon residue,167,429 Cermak,V.,494-95 Chiu, K.W., 449-50 Chuoke,R. L., 181,187-88 Chu, C., 108-10,11,2-19.443 Chung,K. H.,33642
C l a ym i n e r a i si .t , - l r effect on le;nci(rlrFl Cold Lake. ribcnr. lii Compactiondrirc. 16&< 2't4 Conradsoncarbon rcsaa (ccRi. 16r. 429 Convectiveheatinglr reservoin.Z_lG heat beyondcondctll front. 8,s-86.F-l Lauwerier\ equrrtor-, numericalexampbd Lauweriers c$ti 78-82 simpleconvectircbcl transfer,73-7j steamdrive with cca displacemcntr!c. steamdrive with cil injectionrarc. b1 Convectiveheat tranrftr, well annulus.60-{ Corod manufacrurint.I C o u r t n a g eL ,. A . 4 d - t Cyclic steamstimularirl 241_83 Bobergand L:nrz's I 244_48 Bolivar coasr,Tia r.r Lagunillas,Becl; 272-74 casrnggascomp?crsirl Coalinga field, ?61 compactiondrive, 2tl gravity drainageio, 251 gravity drainagemodcl harmonicdeclinecnrx 259_65,272 history, 3 improvingwell pcrfrr 387_88 in California, 255-57 introduction,24I -.{2 mechanism,A4-59 Midway Sunset,pottct r 26r_62 Niko and Troost! experiments,25G-! Quiriquire (seealn b and Lantz), 2i2-63 San Ardo field,2H simplified analysis,259 272 with cold tlout,242-4 Cyclic steamstimulatio. ir sands,266-70 compactiondnve, ZlL2 fracturing and rescrwir expansion,durir3. 26649, Z't4_El
Index
CIay minerals,l6-18 effecton permeability,1g Cold Lake, Alberta,26-8-70 Compactiondrive, 268-69,272. aat a Il
Conradsoncarbonresidue (ccR), 167,429 Convectiveheatingin reservoirs,72-103 heat beyondcondensation front, 85-86, 95-97 Lauwerier's eqruation,75_77 numericalexampleof Lauwerier'sequation, 78-82 simpleconvectiveheat transfer,73-25 steamdrive with constant displacementrate, g2_g6 steamdrive with constant injectionrate, 86-93 Convectiveheat transfer, across well annulus,60-62 Corod manufacturing,382, 3g4 Courtnage,L. A., 402-3 Cyclic steamstimulation,2, 241-83 Bobergand Lantz,smodel, , 244_48 Bolivar coast,Tia Juana. Lagunillas,Bachquero, aa4
a1
alL-t+
r ratio,214 : gradients,208-10 on behindfront,201-3 rock front, 203-5 of shockfront, 200-1 d Sahuquet, 431, -48 Californian cyclic un projects, 255-57, A- Ii, 476 rnd Panons, 288 .4., 396,401 rd Jaeger,54 , ct al., 500-1 rradsoncarbon dve, 167, 429 v-, 494-95 y-,149-50 t - L . , 1 8 1 ,1 8 7 - 8 8 B-10, 112-19,443 H..33642
casinggascompression,3gg Coalinga field,264 compaction driv e, 242, 272_74 gravity drainagein, 258-59 gravity drainagemodels,265 harmonicdeclinecurves, 259-65,272 history, 3 improvingwell performance, 387_88 in California,Z5S-57 introduction,241-42 mechanism,254-59 Midway Sunset,Potter sand, 26r-62 Niko and Troost's experiments, 250-54 Quiriquire (seealso Boberg and Lantz), 262-63 San Ardo field.264 simplified analysis,259-65, 272 with cold flow,242-44 Cyclic steamstimulation in rar sands,266-70 compaction drive, 242, 269_69 fracturing and reservoir expansion,during. 266-69.274-8r
Index
relativepermeability hysteresis, 268-70 VaccaTar, Oxnard,2i l-72 water fingering,in, 270 Darcy's law and units. 20-21 Darcy's law for two-phaseflow, 192 effect of gravityon fractional flow. 196-97 effect of segregationon fractionalflow, 197-99 fractionalf low equation, 193_96 relativepermeabilitycurves, 192_93 Denbina,Bobergand Rotter, 268 Densitiesof oil reservoir materials,487-90 brine.487 conversionfactors,490 oil.488-89 rocks.490 saturatedsteam,487 water,487 Dietrich,1.K.,269-70 Dimensionalanalvsis. 33 Dimensionsof physical properties,481_85 Displacement of heavyoil, 179_240 concepts,180 effect of condensation on stability,188-91 effectof interfacialtensionon srabitiry,184_88 effect of wettingon stability, 187-88 factors,179 flood interface stability-Muskat'smodel, t82 generalconclusions, 238-39 Hagoortt stabilitycriterion, t84,209 mobility ratio, 183 temperaturegradient stabilization, 191 theoreticalapproaches,lgl Doscher,T. M., 258-59.265 Dusseault,M., 280-81 Dykstra, H., 288,298 Economicexploitation,Z-2S Ejiogu and Fiori, 487 Energy resources(seeFuel resourcesl Enhancedoil recovery,2 EOR,2 Error and complementarverror functionl. 34-3i
Eson,R. L., 406 EssoResourcesCanada(seealso ImperialOit), 3 Expansionloops,for steam lines,374 Fairfield and White, 466-71 FarouqAli, 20,132,157-58,380, 487 Ferguson,F. R. S., 342-44 FosterWheeler,372 Fracturingduring steam injection, 274^79 changeof orientation,280-g1 directionof principle stresses, 27'7,280_81 effect of orientationon productivity,279-90 fracturingpressure,277 ground heave,277 in situ stresses, 276-77 principlestresses, 275-7j Fuel resources,5-7 Canada,5 heavyoil and oil sands deposits,7 world, 5 Gadelle,C. P, et al., 475 Gatesand Ramey,ISC design, 462_65 GoldenLake ISC project, 466_71 Gomaa,E. E., 158-63 Gough and Bell, Z78 Govier, G., 6 Grand Rapidsformation,9, 140 Griffin and Trofimenkoff,30t, 326_27 Gutierrez,F. J., 8 Hatschek'sequation for viscosity of emulsions,356 HaycockBoiler (1720),361 Hearn'stheory, 95-98 averageover temperature raage,502 carbonatereservoir rock, 499 clays,499-500 conversionfactors, 503 enthalpychange,502 gases,502 oils, 500-1 sandstones,499 water, 501 Heat capacitiesand enthalpies, 499-503 Heat conduction,30-71 definition of thermal conductivity,30
525
Ijourier'sequation,3i from spreadingzone,37-39, 41 from steamedfracture,38, 98, 101 into semi-infinitesolid,32-37, 47 spreadingchamberthat stops, 39-41 steady-andunsteady-state, 32 Heat conductionaheadof advancingfront, 43-52 effect of changingvelocity, 50-51 transientstate,47-50 U proportional to l/sqrt(t), 5L-52 Heat integral, 47-49 Heats of combustion,515-17 conversionfactors,517 fuel gases,516 hydrocarbonliquids, 515 solid fuels,517 Henningsonand Duckett, Pilot oxygenfaciliiies,456 Hong, K. C.,113-74 Hopco project, 325 Hot waterflooding, 4, 773*74 Huff and puff (seealso Cycltc steamstimulation).2 Hydraulic diffusivity, 32 Hvizdos, Howard and Roberts, cost of oxygen,455-56
lgnition, of ISC projects,432-35 Imperial Oil, 3, 59, 377,402.-3 hjectivity, 1.44-52 between an isolated pair of vertical wells, 145-47 confinedhorizontalwell pair. 150-51 repeatedfive-spot,151 repeatedseven-spot,152 time for breakthrough, 147-48 well surrounded by circle of wells, 148-50 In situ combustion,415-79 BellevueLouisiana,Gettyt field project,471-74 combustion tubes, 419-23 design of projects, 458-65 dry combustion,418-19 fireflood pot,423-24 fuel deposition, 426-?A fuel requirement,comparison with steamflooding, 416-17 generaldescription,4 H/C ratio of fuel.424-26
526
ignition, 432-35 Lloydminster,Golden Lake field project,466-71 low temperatureoxidation
(Lro),s, 428-30
oil sands,in,430-32, 450-52 oxygen,cost of, 455-56 oxygenor enrichedair, use of, 452-58 pressure,effect on performancewith oxygen, 457-58 properties of produced o1l, 442 reversecombustion,419 Rumanianfield projects, 4'14-77 temperature at combustion front, 435-42 wet combustion,442-50 work for compression, 416 In situ stresses within reservolrs, 276-77 Insulation of steaminjection werls.520 Janisch,;,,12, t4 Jardine,D., 9-10, 12 Jianyi,H., 1i Jones,J., 141-44 Josephand Pusch,449 Joshi and Threlkeld. 327 Keeling,L., 387-89 Konak, 4.R., 374-75,395,403 Kuo, Shain and Phocas,265 Latil, M., 4L8,Us Lauwerier,H.A.,75-77 Leaute and Collyer, effect of preheaton ISC, 430-34 Leverett, M. C., 193,199-21.6 Lim, G.8.,374,403 Lindrain theory, 303, 327 Lo, H.Y.,285,296,3N Lo and Mungan, 129 Lower Mannvillesedimentsin W. Canada.9 Low temperatureoxidation (LTO),5, 428-30 Mandl and Volek'stheory, 95, 100 Maracaibo(Lake), Venezuela,2 Marshall, 8.W., 406-7 Marx and Langenheim'stheory, 86-89 numerical example,90-93 McMurray sands,9 McNab, G. S., 285,296,300 Mehrotra and Svrcek.509-11
h{eldaii,R. F., 380-8i Mene Grandeoil field, Yenezuela,2 Moore, R. G., 420,457-58, 464-66 Moss and Cady,gas analyses, 453-54 Moss,Sanford4., 521-22 Myhill and Stegemeier,129-35, 139-40 Natco,369,391,399 Nelsonand McNeil, ISC design, 458-61 Neutron-scatteringsteamquality meter,374 Niko, H. and Troost, P. J. P. M., 250-54 Nutt, C.W., capillarybundle model,216-20 Oglesby,K. D., 135-37 Oil sandsand heavyoil deposits: Canada,8, 10 clay minerals,16-18 comparisonwith Middle East, LZ
correlationof Canadian,11 Gas, occurrenceand production,19 in the United States,12 magnitudeof Canadian,11 nature of, 14 nature of solids,16 origin of Canadian,10 origin of Chinese,11 Sideritein reservoirmatrix, 1A
Venezuela,8 Ong, T. S., 356-57 Orimulsion,2T OSR, estimationfor steamfloods using simple formulas, 93-94 Override of steam,232-34 Oxygen or enriched air, use of for ISC, 452-58 Peacheyand Nodwell,374, 37(-77,389,392,397 Penberthy and Ramey, 422-24 Permeability, 21 Petela, G., 322-25 Pipeline transportation, 27 Prats,M., 130 Priaciple stresses,275-77 Programmablecalculators and microcomputers,use of, 22
lndex
tlot to vcrtird rd ?2-23 Radial heat coodrrtn (r bore heat lostt Radial heat condrrtir. t buried cylio&r. ll Radiant heat transfsr. gr well annulus.60 Ramey.H. J.. 63.r-i5{1. 458-65 Rayleighnumbcr.6l-61 Refining,I Reservoircommunrcalra sealingoff. { Reservoirfracturing rr 3l steamfloodiog,-
Ldid
Saffman, PG. ud Tttb 1ES Scalingof thermal mo& 248-50,29:-99 Skrabec,J.,26 Solutiongasdrive. effc
o
353-57 exponent m. extcndtrd definition of. ]9a-
lndex
ii F.. _r80-81 ;andeoil field, 2 enezuela, R.G., 420,457-58, >{-66 d Cady.gas analyses, i3--s4 tnf,ordA.,527-22 md Stegemeier,129-35, ,9-40 at,39L,399 rnd McNeii, ISC design, 5E-61 r-scatteringsteamquality rcrer,374 [. and Troost,P.J. P. M., 50-54 "W., capillarybundle rcdel,216-20 , tL D., 135-37 ls and heavyoil cposits: d a , 8 ,1 0 oincrals,16-18 erisonwith Middle East, 1
lation of Canadian,11 occurrence and roduction, 19 : United States,12 itudeof Canadian,11 r of. 14 c of solids,16 l of Canadian,10 l of Chinese,11 ilc in reservoirmatrix, l9 zuela,8
. s.,3s6-57 sion, 27 simation for steamfloods Bsingsimple formulas, 93-94 th of steam,232-34 l or enriched air, use of fq ISC, 452-58 y ud l{odwell,374, tlun,3E9, 392,397 nhy and Ramey, 422-24 rbility, 21 ,G.,322-25 r traNportation, 27 M.,130 plc stresses,275-77 rnms!ls calculators and Eicrocomputers, use of,
n.
Index
Radial flow to vertical well, ?:2-23 Radial heat conduction (seeWell bore heat loss) Radial heat conduction, from buried cylinder,6S-7I Radiant heat transfer. across well annulus. 60 Ramey,H. J., 63, 435-41,452, 458*65 Rayleigh number, 61-62 Refining, 1 Reservoir communication, sealing off, 4 Reservoir fracturing in steamflooding,23L-32 Saffman, P G. and Taylor G.I.' r85-E8 Scaling of thermal models, 248-50,297-99 Skrabec,J., 26 Solution gas drive, effect of viscosity on recovery, 24-25 Sperry,J. S., 410 Steam,thermal properties,11GlL, 120-21.,521 enthalpies of saturated liquid and vapor, lZ0-27, 522-23 saturation pressureand temperature, 120-27, 521-22 gravitYdrainage Steam-assisted (SAGD),28s-3s9 avoiding steady-state assumption,328-36 83. definition of, 297 83, effect on interface shaPe and heat penetration, 329 83, valuesof, 330-31 breakthrough time, 32!, 323-24 dimensional similarity, 297-99 downward displacementfrom upper injector, 321-25 drainage rates for field conditions, 300-2 effect of oil proPerties,314-16 effect of shale barriers, 349-53 effect of steam pressure,335 effect of TS, TR, and oil properties on rates, 3r3-16 emulsions,formation of WO, 353-57 exponent m, extended definition of,294-96
lndex
finger rise theory, 31.2-13 gravity drainage theory and mechanism,287-94 heat balance and oil-steam ratios. 333-36 heat penetration beyond interface.331-32 heterogeneities,effect of reservoir, 348-53 horizontal injection wells, 321-25 introduction, 285-86 Lindrain theory, 303, 327 mixing temperature of draining oil, 330 noncondensablegas, effect in, 299 numerical problem on SAGD, 316-20 pressuredrop along well bore, effect of, 356-57 production after stopping steaminjection, 342-44 recovery above bottom water, 344-48 relationship to conventional steamflooding, 286 residual oil saturation in steam chamber. 288 rising chambers,307-13 scaled models, 296-302, 305-7.336-41 steam-injectionwells (horizontal and vertical), 321-27 Tandrain theory, 299, 302-5 vertical injectors, 325-n, 337 Steamdistributioa, 373-75 Steamfingering, 5 Steamflood analysis using Buckley-Leverett theory, 220-32 effect of shaPeof relative permeability curves, 228-29 effect of steam quality, 234-37 effect of steamviscositY,238 numeric al examPle, 224-28 pressure drop,229-30 Shutler and Boberg, 238 vertical heat losses,238 Steamflooding (seealso, Convective heating), 3' t04-78 additives, 125-26 changesin relative permeabilities,127-29 characteristicsof field projects, II2-19, 135, 137 comparisonwith in situ combustion, 416-17
comparisonwith steam-soak, 139-40 FAST process, 167-68 Farouq Ali's model, 157-58 fingering, 124 Gomaa'scorrelations, 158-63 gravity override, 124-26 Jones'steam drive model, t4l-44 laboratory f loods-Willman, 169-72 multilayer reservoirs, 140 Myhill and Stegemeier's approach, 129-35 other mechanisms,168-73 qualitative introductory discussion. 104-7 qualitative review, 174-7 5 reduction in oil viscositY, t26-27 residual oil,l25,l32 San-Ardo steamflood, 137-39 steam distillation. 168-69 steam distillation drive, 172-73 steam zone shapevan Lookeren, 152-57 suitability of reservoirs, 107-10 temperature distribution' 122 Ten-pattern steamflood, 135-37,157,166 thermal efficiency, 415-16 Vogel'sapproach, 164-66 waterf looding after, 773-74 Steamgeneration: averageheat flux, 364 convection section, 371-73 deaeration and oxygen control, 366-68 DNB (Departure from Nucleate Boiling), 363-64 effect of S in fuel, 370 feedwater requirements, 364-66 history and background, 360-64 horizontal generators,369 oil field steam generators, 368-73 radiant scetion, 373 vertical generators,373 Steam measurement,3 Steamquality measurement,371, 374 Steamrecovery equiPment and facilities. 360-414 Steamstimulation (seeCYclic steam stimulation) Steamvolume, units of measurement,3
527
Stefan-Boltzmann constant,60 :t:qlen!, D. J.. 285, 302_s,307 srlrtrng boiler, 362 Strom and Dunbar. 13 Subsidenceof ground surface, 273 Sugianto,5., 324,344_4g Sulphurin bitumen.10 Suplacu_de B_arcau, ISC project, 474-77 Symbols,list of, 4gl_g6 Syntheticcrude,properties,26 Tademaand Weijdema,433_35 I a k a m u r aK , ., 15_16 Tandraintheory,302_5 Tangleflags,SceptreResources
thermal cement,375 unit well costs,327_7g well pads,376 Tia Juana,cylic steamprojecrs, 114
a,
Transoil,27 Transportation,of bitumen. )\-)1
Transportation, of emulsions, 27 lransverse, E. F. 137_39 Treatingproducedfluids. 388_93 electrostatictreating,390_92 rreewatersettling,399_92 vrsco_sity of WO emulsions, 390 with high solids,393 Turta and Zamfir,474
Temperaturetogging, 37g_g0 r nermatconductivities of oil UTR AOSTRIfs underground reservoirmaterials, demonstrationof SAGD. 491_98 32I,340_42.357 consolidatedporous rocks, Units of measurement, 494_95 20_22 Upgrading.1 conversionfactors,497 hydrocarbonIiquids,495 miscellaneous Vanadiumin bitumen.10 materials.492 over- and underburden, van Lookeren'sequations, 496_97 152_57,330 unconsolidatedoil sands. numericalexample.157 491_94 Viscosities,504-14 water,496 conversionfactors,513_14 Thermalconductivity,insulatins crude oil, effect of dissolved materials,5l9 methane,50g_11 Thermalefficiency,constant crude oil, effect of pressure, displacement 507-8 rate.g4 crude oil, effect of Thermalefficiency,Hearn,99 I hermalefficiency,Marx and temperature,504_7 Langenheim,g6 heavyoil and bitumen, 19_20 Thermalinsulation,519_20 waterand steam,511_13 suckerrod wear,3g1_g7 Vogel,J.V., 164-66 Thermalwell completions. Volek and pryor,172_73 375_78 Volumetricheat capacity,of artificial lift, 381_87 reservoir. 503 continuoussuckerrod, 3g2, Vonde,T. R., 386.394 384 selectivesteaminjection, 3g1 Water,in reservoir. lg Cold^Lakewell configuration, Watertreating, 393-404 377 analysesof producedwater, control of heat loss,3g0_g1 395_96
Esso,sthermal softenine process,403 freshwatermakeup,393_94 hor lime rrearing,3SS_+OO rnducedgasftotation(IGF), 397,399 ion exchangesoftening,400 producedwater recyclE, 394_404 reducingtotal dissolvedsolids (TDS),403_4 wastewatermanagement, 402-3 water recycleat Kern River. 401 Water-wetting,effect on emulsification, 1g Waterwettingof oil sands,l5 Weiss,M., 285.307 Well bore heat loss,52_68 backgroundmaterial, 63 convectiveheat transfer.60 cu-mulative heatflow. 55_56 etfectof insulation,56_6g equivalentradius,5g numeric_al example,63_6g raotantheattransfer,60 rate of heat loss,55 temperaturedistribution. 53_54 with gas-filledannulus,60, 63 with s_team down casing,59, 63 Well packers,59 Well patterns,123-24 Wet-steam splitting,374_75 Whiting. R.i., t5-Willman,et al., laboratory steamfloods,169_7-2 WO emulsions,viscositiesof, 356,390 Wu, C. H., 168-71 Yang,Guihua (peter),34g-53 Yaregaoil mine, 325 Y e e ,C . T . , 2 9 9 Young'smodulus,276
528 Index
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