The Future of Geological Modelling in Hydrocarbon Development - Special Publication no 309

The 3D geological model is still regarded as one of the newest and most innovative tools for reservoir management purposes. The computer modelling of structures, rock properties and fluid flow in hydrocarbon reservoirs has evolved from a specialist activity to part of the standard desktop toolkit. The application of these techniques has allowed all disciplines of the subsurface team to collaborate in a common workspace. In today’s asset teams, the role of the geological model in hydrocarbon development planning is key and will be for some time ahead. The challenges that face the geologists and engineers will be to provide more seamless interaction between static and dynamic models. This interaction requires the development of conventional and unconventional modelling algorithms and methodologies in order to provide more risk-assessed scenarios, thus enabling geologists and engineers to better understand and capture inherent uncertainties at each aspect of the geological model’s life.

The Future of Geological Modelling in Hydrocarbon Development

The Geological Society of London Books Editorial Committee Chief Editor

BOB PANKHURST (UK) Society Books Editors

JOHN GREGORY (UK) JIM GRIFFITHS (UK) JOHN HOWE (UK) PHIL LEAT (UK) NICK ROBINS (UK) JONATHAN TURNER (UK) Society Books Advisors

MIKE BROWN (USA) ERIC BUFFETAUT (FRANCE ) JONATHAN CRAIG (ITALY ) RETO GIERE´ (GERMANY ) TOM MC CANN (GERMANY ) DOUG STEAD (CANADA ) RANDELL STEPHENSON (NETHERLANDS )

Geological Society books refereeing procedures The Society makes every effort to ensure that the scientific and production quality of its books matches that of its journals. Since 1997, all book proposals have been refereed by specialist reviewers as well as by the Society’s Books Editorial Committee. If the referees identify weaknesses in the proposal, these must be addressed before the proposal is accepted. Once the book is accepted, the Society Book Editors ensure that the volume editors follow strict guidelines on refereeing and quality control. We insist that individual papers can only be accepted after satisfactory review by two independent referees. The questions on the review forms are similar to those for Journal of the Geological Society. The referees’ forms and comments must be available to the Society’s Book Editors on request. Although many of the books result from meetings, the editors are expected to commission papers that were not presented at the meeting to ensure that the book provides a balanced coverage of the subject. Being accepted for presentation at the meeting does not guarantee inclusion in the book. More information about submitting a proposal and producing a book for the Society can be found on its web site: www.geolsoc.org.uk.

It is recommended that reference to all or part of this book should be made in one of the following ways: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) 2008. The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309. ˚ . & AUNE , T. 2008. Modelling of dipping clinoform barriers within deltaic outcrop HOWELL , J., VASSEL , A analogues from the Cretaceous Western Interior Basin, USA. In: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 99 –121.

GEOLOGICAL SOCIETY SPECIAL PUBLICATION NO. 309

The Future of Geological Modelling in Hydrocarbon Development

EDITED BY

A. ROBINSON Addax Petroleum Services Ltd., Switzerland

P. GRIFFITHS Midland Valley Exploration, UK

S. PRICE Shell, Norway

J. HEGRE Direction Exploration Production, France

and A. MUGGERIDGE Imperial College, UK

2008 Published by The Geological Society London

THE GEOLOGICAL SOCIETY The Geological Society of London (GSL) was founded in 1807. It is the oldest national geological society in the world and the largest in Europe. It was incorporated under Royal Charter in 1825 and is Registered Charity 210161. The Society is the UK national learned and professional society for geology with a worldwide Fellowship (FGS) of over 9000. The Society has the power to confer Chartered status on suitably qualified Fellows, and about 2000 of the Fellowship carry the title (CGeol). Chartered Geologists may also obtain the equivalent European title, European Geologist (EurGeol). One fifth of the Society’s fellowship resides outside the UK. To find out more about the Society, log on to www.geolsoc.org.uk. The Geological Society Publishing House (Bath, UK) produces the Society’s international journals and books, and acts as European distributor for selected publications of the American Association of Petroleum Geologists (AAPG), the Indonesian Petroleum Association (IPA), the Geological Society of America (GSA), the Society for Sedimentary Geology (SEPM) and the Geologists’ Association (GA). Joint marketing agreements ensure that GSL Fellows may purchase these societies’ publications at a discount. The Society’s online bookshop (accessible from www.geolsoc.org.uk) offers secure book purchasing with your credit or debit card. To find out about joining the Society and benefiting from substantial discounts on publications of GSL and other societies worldwide, consult www.geolsoc.org.uk, or contact the Fellowship Department at: The Geological Society, Burlington House, Piccadilly, London W1J 0BG: Tel. þ44 (0)20 7434 9944; Fax þ44 (0)20 7439 8975; E-mail: [email protected]. For information about the Society’s meetings, consult Events on www.geolsoc.org.uk. To find out more about the Society’s Corporate Affiliates Scheme, write to [email protected] Published by The Geological Society from: The Geological Society Publishing House, Unit 7, Brassmill Enterprise Centre, Brassmill Lane, Bath BA1 3JN, UK (Orders: Tel. þ44 (0)1225 445046, Fax þ44 (0)1225 442836) Online bookshop: www.geolsoc.org.uk/bookshop The publishers make no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility for any errors or omissions that may be made. # The Geological Society of London 2008. All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with the provisions of the Copyright Licensing Agency, 90 Tottenham Court Road, London W1P 9HE. Users registered with the Copyright Clearance Center, 27 Congress Street, Salem, MA 01970, USA: the item-fee code for this publication is 0305-8719/08/$15.00. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. ISBN 978-1-86239-266-3 Typeset by Techset Composition Ltd., Salisbury, UK Printed by MPG Books Ltd., Bodmin, UK Distributors North America For trade and institutional orders: The Geological Society, c/o AIDC, 82 Winter Sport Lane, Williston, VT 05495, USA Orders: Tel. þ1 800-972-9892 Fax þ1 802-864-7626 E-mail [email protected] For individual and corporate orders: AAPG Bookstore, PO Box 979, Tulsa, OK 74101-0979, USA Orders: Tel. þ1 918-584-2555 Fax þ1 918-560-2652 E-mail [email protected] Website http://bookstore.aapg.org India Affiliated East-West Press Private Ltd, Marketing Division, G-1/16 Ansari Road, Darya Ganj, New Delhi 110 002, India Orders: Tel. þ91 11 2327-9113/2326-4180 Fax þ91 11 2326-0538 E-mail [email protected]

Contents ROBINSON . A. The future of geological modelling in hydrocarbon development: introduction

1

FREEMAN , S. R., HARRIS , S. D. & KNIPE , R. J. Fault seal mapping – incorporating geometric and property uncertainty

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PO¨ PPELREITER , M. C., BALZARINI , M. A., HANSEN , B. & NELSON , R. Realizing complex carbonate facies, diagenetic and fracture properties with standard reservoir modelling software

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TVERANGER , J., HOWELL , J., AANONSEN , S. I., KOLBJØRNSEN, O., SEMSHAUG , S. L., SKORSTAD , A. & OTTESEN , S. Assessing structural controls on reservoir performance in different stratigraphic settings

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STREBELLE , S. & LEVY , M. Using multiple-point statistics to build geologically realistic reservoir models: the MPS/FDM workflow

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LABOURDETTE , R., HEGRE , J., IMBERT , P. & INSALACO , E. Reservoir-scale 3D sedimentary modelling: approaches to integrate sedimentology into a reservoir characterization workflow

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JONES , R. R., MC CAFFREY , K. J. W., IMBER , J., WIGHTMAN , R., SMITH , S. A. F., HOLDSWORTH , R. E., CLEGG , P., DE PAOLA , N., HEALY , D. & WILSON , R. W. Calibration and validation of reservoir models: the importance of high resolution, quantitative outcrop analogues

87

˚ . & AUNE , T. Modelling of dipping clinoform barriers within deltaic HOWELL , J., VASSEL , A outcrop analogues from the Cretaceous Western Interior Basin, USA

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RINGROSE , P. S., MARTINIUS , A. W. & ALVESTAD , J. Multiscale geological reservoir modelling in practice

123

ZHANG , P., PICKUP , G. E., MONFARED , H. & CHRISTIE , M. A. Flow upscaling in highly heterogeneous reservoirs

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BENTLEY , M. & SMITH , S. Scenario-based reservoir modelling: the need for more determinism and less anchoring

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CHAKRAVARTY , A., HARDING , A. W. & SCAMMAN , R. Incorporating uncertainty into geological and flow simulation modelling in Chevron: application to Mafumeira, a pre-development field, Offshore Angola

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MARTIN , C. A. L. Addressing uncertainty and remaining potential in a mature field. A case study from the Tertiary of Lake Maracaibo, Venezuela

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KEOGH , K. J., BERG , F. K. & GLITNE PETEK . A method for quantifying geological uncertainties in assessing remaining oil targets: a case study from the Glitne Field, North Sea

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FREEMAN , P., KELLY , S., MACDONALD , C., MILLINGTON , J. & TOTHILL , M. The Schiehallion Field: lessons learned modelling a complex deepwater turbidite

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Index

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The future of geological modelling in hydrocarbon development: introduction ADAM ROBINSON Addax Petroleum, 16 Avenue Euge`ne-Pittard, PO BOX 265, CH-1211, Geneva 12, Switzerland (e-mail: [email protected]) Abstract: The 3D geological model is still regarded as one of the newest and most innovative tools for reservoir management purposes. The computer modelling of structures, rock properties and fluid flow in hydrocarbon reservoirs has evolved from a specialist activity to part of the standard desktop toolkit and the application of these techniques has allowed all disciplines of the subsurface team to collaborate in a common workspace. The papers in this volume result from a two-day conference at the Geological Society that brought together modelling software practitioners from the geoscience community. The papers presented here provide an excellent illustration from across the industry and academia of where we are and give some interesting pointers to where we are heading. The authors and their parent companies and institutes are thanked for sharing this information.

The structural component remains at the core of the geological modelling workflow and the implemention of flow reduction across faults in reservoir models is relatively well-established, particularly in clastic reservoirs. Geological variability at faults leads to errors of several orders of magnitude in predicting absolute flow magnitude. S. Freeman et al. review this geological variability and propose a stochastic modelling workflow to identify high-risk seal or flow zones. Fluid flow associated with faults in carbonate reservoirs generally receives less attention, with the assumption often being such that faults are open to flow and may even behave as conduits. Po¨ppelreiter et al. show an example from the Urdaneta West Field in Venezuela, where faults are characterized according to their tectonic, burial and diagenetic history. Tveranger et al. outline the impact of different tectonic parameters affecting production and simulate these effects against various clastic depositional systems. The reconciliation of soft data (i.e. the conceptual depositional model with detailed facies transitions and complex geometries) and hard data (usually from wells) can be difficult to translate into geologically realistic reservoir models and many models do not, or should not, make it to the reservoir simulator simply because they are not geologically reasonable. Strebelle & Levy propose a pixel-based approach, Multiple-Point Statistics simulation (MPS), which allows the user to input the soft data as a training dataset which can overcome the weaknesses of conventional variogram-based modelling and object-based techniques. Their workflow combines the MPS method with Facies Distribution Modelling (FDM) which utilizes facies probability cubes (derived from multiple datasets)

and provides improved 3D facies control, particularly in areas beyond well control. Labourdette et al. describe an in-house technique for the construction and incorporation of a facies probability cube derived from fine-scale sedimentological information. The facies probability cubes are used to condition pixel-based models as an input probability field or as a soft-conditioner for object-based models in order to evaluate production forecasts under various development scenarios. The need to put more geological reality rather than the ‘virtual reality’ into a geological model is paramount, thus conditioning of geological models with quantified spatial data from rock outcrops is an area currently receiving significant attention. Two articles are illustrative of this practice. Jones et al. describe how state-of-the-art technology (high precision laser scanning and real time GPS) can be used to generate high precision spatial information and input directly into 3D models as analogues, or used to constrain kinematic models of fold or fracture growth. The new technology allows for modelling geological detail at a scale below the grid cells. Howell et al. generated detailed clinoform geometry in deltaic models conditioned by outcrop data from the US Cretaceous Interior Basin. In addition to providing an example of how outcrop data can be directly assimilated into a reservoir model using geospatially reference photographs, the paper highlights the significant impact to estimates of hydrocarbon recovery by not explicitly modelling clinoform geometry in the cellular grid (e.g. where clinoforms were not generated as a facies property in a regular grid led to a significant overestimation of recovery). When modelling at the field scale,

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 1 –3. DOI: 10.1144/SP309.1 0305-8719/08/$15.00 # The Geological Society of London 2008.

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A. ROBINSON

the most effort is usually put in to preserving geological variability at the scale of the facies transition. In their review article, Ringrose et al. highlight the importance of preserving variability at all scales from the pore to the grid cell. Their article focuses on the importance of handling variance at different scales correctly. The approach of explicitly modelling at different scales adds complexity and time to a project although, with several challenges still remaining, the approach is now practical and of proven values; where the multiscale approach has been implemented, the impact on the production forecast is shown to be significant. Zhang et al. consider the impact of upscaling at different stages in a typical project lifecycle. They conclude that during early screening, when many realizations are run, coarse-scale models should be built directly using fine-scale geostatistics, partially alleviating impact of averaging and removal of heterogeneity but at the same time reproducing fine-scale flow results. As a project matures Zhang et al. propose upscaling highly detailed models using well-driven boundary conditions as a method to reducing upscaling error. Is our industry often in denial? Within all the detail of a geological model – and the assumption that the models generated are ‘precise’ – we can easily create a false impression of ‘accuracy’: the sometimes endemic and unfortunate outcome of these factors is that a geological model is sold to management as the ‘solution’. Managing uncertainty in the context of a geological model workflow is therefore not trivial. Bentley & Smith provide us with an overview of the various approaches. They argue against the concept of anchoring to a base case model and favour a scenario-based approach to managing uncertainty. Multiple deterministic realizations are preferred to multiple stochastic simulations as, in the latter case, important parameter interdependencies may be lost and there is a suspicion that the uncertainty space is not fully sampled. Chakravarty et al. give a case study of an offshore West Africa field in predevelopment in which probabilistic forecasts are generated from multiple realizations using a Design of Experiments approach. In this way, the optimal development concept can be selected. A phased development is chosen to help mitigate downside risk. This paper provides an excellent example of how a Design of Experiments approach can be used effectively in hydrocarbon development planning. Martin describes an integrated workflow from the Cenozoic of Lake Maracaibo, Venezuela, in which key reservoir parameters (e.g. sandstone connectivity, fluid contacts) are identified and conditioned

with historical production data. The resulting models are then carried forward as an input to field development planning. A workflow for deriving probabilistic hydrocarbon-in-place volumes is described by Keogh et al. using the Glitne Field of the North Sea as a case study. In another field example, P. Freeman et al. describe the workflow for the construction of the Schiehallion Field model and show how an integrated approach between co-venture partners and across multiple software packages can result in a robust model. Expectation recovery estimates were made for different development options by identifying uncertainty for key parameters and running multiple history-matched models. In summary, it is clear that the role of the geological model in hydrocarbon development planning is key and will be for some time. With the acceptance that digital models are inherently uncertain, any geometry-based analysis, such as well-track planning, reserve estimates or faultsealing investigations, will also carry uncertainty. This means there needs to be an understanding between deterministic geological models to identify those that are partially or entirely probabilistic. A key result of employing techniques to quantify and incorporate geometric uncertainty of these kinds would be that geoscientists, drilling engineers and reservoir engineers would receive more candid 3D prognoses leading to a reduction in drilling and production surprises, and improved drilling prognoses and hydrocarbon recovery. Moving forward, it is anticipated that the next set of challenges that face geologists and engineers will be to provide more seamless interaction between static and dynamic models. This will require the development of conventional and unconventional modelling algorithms and methodologies in order to provide more risk-assessed scenarios, thus enabling geologists and engineers to better understand and capture inherent uncertainties at each aspect of the geological model’s life. This volume arises from a two-day conference hosted at the Geological Society in London on 7–8 March 2005. Speakers from Europe, Canada and the United States gave a total of 27 papers in addition to numerous poster contributions. The conference would not have been possible without the tireless support of the Geological Society, the Petroleum Group, Angharad Hills and that of the technical organizing committee, Ann Muggeridge, Adam Robinson, JoAnn Hegre, Paul Griffiths and Simon Price. On behalf of the committee and the Geological Society, we are also indebted to the following organizations which, in one way or another, gave support: Badley Geoscience Ltd,

INTRODUCTION

BP, ConocoPhillips, Earth Decision Sciences, ExxonMobil, Geomodelling, Midland Valley, Roxar, RPS (formerly Troy-Ikoda), Shell, StreamSim Technologies, Total. The editorial committee would like to thank the following referees, who kindly donated significant time and effort to reviewing the manuscripts and returning them, for the most part, in a timely manner: JoAnn Hegre, Steve Jolley, Paul Griffiths, John Cole, Steve Dee, Mark Bentley, Richard Labourdette, John Williams, John

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Howell, Philip Ringrose, Caroline Hern, Sebastien Strebelle, Simon Price, Jeffrey Yarus, Richard Chambers, Andrew Harding, Charlotte Martin, Mark Sonnenfeld, Alun Griffiths, Paul Freeman, Ingrid Damearschalk, Karen Hoffman, Gillian Pickup, Jamie Pringle, Allard Martinius, Gary Hampson, Kevin Keogh, Quentin Fisher and Jan Rivenaes. Additional thanks are passed to Simon Price and Paul Griffiths for their contributions to this introductory paper.

Fault seal mapping – incorporating geometric and property uncertainty S. R. FREEMAN, S. D. HARRIS & R. J. KNIPE Rock Deformation Research, School of Earth Sciences, University of Leeds, Leeds LS2 9JT, UK (e-mail: [email protected]) Abstract: In this paper, we present workflows, key relationships and results of multiple stochastic fault seal analyses conducted on geocellular geological or (static) reservoir grids. Ranges of uncertainties are computed from new and published datasets for the different input relationships (e.g. throw, VShale to VClay, fault clay prediction, fault rock clay content to permeability); these are used as input into stochastic modelling processes and the impact of each is assessed. The power of stochastic modelling to focus interpretation and risking effort is reviewed. Reducing the uncertainty distributions from the published data ranges has a massive impact on the range of predicted fault seal properties. Halving the uncertainties associated with the computation of the transmissibility multiplier, for instance, reduces this range from 7 to 1–1.5 orders of magnitude of the base-case value (no uncertainty). Importantly, when combined together, the median predictions from each individual parameter do not lead to the median value for the final prediction; average relationships combined together will not therefore produce the average final prediction. This is a powerful result for two reasons: first, current geological modelling packages use global trends to define fault properties and so are likely to predict spurious results; and secondly, reducing the uncertainty on specific relationships by around 50% is an achievable goal. Locally calibrated datasets and relationships (field-specific) based on carefully characterized samples should allow for this improvement in prediction accuracy. This paper presents a review of fault seal techniques, published data and the potential pitfalls associated with the analyses.

Incorporating uncertainty during fault seal analysis via stochastic 3D modelling has the potential to rapidly identify critical high-risk seal or flow zones. The result should be more accurately risked prospects or field geological models. Simple uncertainty incorporation techniques, such as varying throw and clay smear, combined with the computation of the distribution of probable reservoir – reservoir cross-fault juxtaposition windows, are very powerful, but are currently unavailable in most commercial reservoir geological modelling packages. Utilizing these techniques has the potential to improve the accuracy of predictions. In this contribution, we outline workflows to allow uncertainty to be incorporated into fault seal analyses conducted directly on geocellular geological or reservoir models (e.g. pillar-based grids). Stochastic multiple realization techniques are widely implemented in reservoir geological and property modelling processes (Handyside et al. 1992) but are currently under-utilized in fault seal predictions (e.g. James et al. 2004). The strength of stochastic approaches is in the analysis and prediction of results where the key relationships have significant natural variability. Fault morphology and fault rock properties certainly fall within this category (e.g. Antonellini & Aydin 1995; Childs et al. 1997; Knipe et al. 1997, 1998; Fisher & Knipe 1998, 2002; Foxford et al. 1998).

In systems which are known to vary significantly from general trends, the applicability of any single result is questionable. Without understanding the possible range in solutions, it is impossible to appreciate how representative the single solution case is. For that reason, we have developed a stochastic fault seal analysis software package (the ‘Fault Seal Toolbox’) that incorporates and integrates a wide variety of different parameter and uncertainty relationships. Incorporating uncertainty has a range of uses that begin at the initial interpretation and structural modelling stage, and which feed through to flow simulation. In order to conduct stochastic modelling, sets of rules need to be defined that link different relationships, and critically the variability around those relationships also needs to be determined. In this paper, we review previously published studies and new data that inform on these different relationships and uncertainties. The techniques are applied to 3D geocellular models similar in form to those developed in all of the current major reservoir geological modelling and flow simulation packages (e.g. Roxar RMS (www.roxar.com), Eclipse–FloViz and Petrel (www.slb.com)). The workflows presented provide a tried-and-tested implementation of a stochastic fault seal uncertainty analysis. Although our techniques are continually being developed, the core workflows have been used and

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 5 –38. DOI: 10.1144/SP309.2 0305-8719/08/$15.00 # The Geological Society of London 2008.

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applied to both field and prospect assessments in-house for several years and have proved invaluable in defining key risk zones and associated uncertainties. Initially, macro-scale geometric uncertainties are discussed and we review techniques that allow the classification and quantification of the uncertainties. More detailed internal fault zone geometric property relationships are then outlined. An assessment of host and fault rock property parameters and their relationships to observable parameters is documented, together with a characterization of the nature and scale of the uncertainties for each of these parameters. Following the uncertainty definition, the techniques for incorporating these parameters are discussed. Numerous multiple stochastic realizations are presented and reviewed. The applicability of the different techniques and the limitations of single-pass fault seal analysis results are outlined. Our analyses of multiple scenarios and critical result tracking highlight the importance of local data calibration in the drive to reduce uncertainties and allow for meaningful fault rock property predictions to occur.

Sources of uncertainty in fault seal analysis There are three main scales at which to incorporate uncertainty into fault seal analysis. The first relates to the macro-scale structural form of the fault zone. This is the most directly observable (e.g. via seismic) and data pertaining to these uncertainties are potentially quantifiable directly from physical observations. Typically, these uncertainties and errors, primarily relating to seismic imaging and the geological modelling of the data, are not incorporated or classified. Many possible routes to quantify the errors are available and we review several of these later. The second type of uncertainty is associated with the meso- to micro-scale geometric complexities within fault zones. These are relationships which are not directly imageable and hence require relationships to be defined between observable features and target parameters. The same is true for the third set of parameters; these are related to the physical properties of the fault zone (e.g. fault rock permeability). In the following sections, we review the data, uncertainties and relationships at each of these scales.

Continuum and domain classifier data types There are two main data types that can be readily utilized in a fault seal uncertainty analysis. The first consists of parameters that can be directly

mapped to a specific uncertainty value. An example would be a seismic-based parameter which characterizes the signal-to-noise ratio of the horizon interpretation, such as amplitude. This parameter, when correctly normalized, can be used as a direct proxy for uncertainty. During uncertainty analysis, it can be used as a mathematical input to determine the potential range in uncertainty present at any geographic location. In this example, it may well be used to determine the likely uncertainty in fault throw or fault location. The second set of data types consists of domain classifiers. These are ‘processes’ that cannot directly form part of the mathematical computation of uncertainty, but rather they indicate the set or rules governing the choice of parameters contributing to the uncertainty and how those parameters should be used in the calculation of uncertainty. An example of a domain classifier would be fault reactivation. The domain classifier would control, in this case, both the geometric and property relationships and the uncertainty calculations (e.g. Sperrevik et al. 2002).

Geometric properties and uncertainties The macro-scale geometric architecture has many potential uncertainties, each relating to different causes, and each of which can provide a spatially varying quantification of uncertainty. Rather than applying holistic uncertainty values (e.g. throw þ/210 m), a significant improvement in mapping confidence and prediction should result from defining geographically and structurally calibrated uncertainties. Several of the key geometric uncertainties are fault location, fault dip and strike, horizon elevation and horizon projection into the fault zone. Several sources of uncertainty and methods of uncertainty quantification are reviewed below. These relate to surface stability, seismic quality and model interpolations. Additional issues relating to spatially varying depth conversion uncertainty and stratigraphic architecture are not discussed in detail below.

General macro-scale geometric uncertainties The primary source for much of the form of a geocellular model comes from the original seismic interpretation reflector data. Any horizons developed in the geocellular model have to either simplify or inherit the noise present in the original seismic horizon picks. For a fault seal analysis, one of the key aspects is the robustness in which the horizons are projected into the faults (Townsend et al. 1998; Jolley et al. 2007).

FAULT SEAL UNCERTAINTY MAPPING

Assessing the level of noise within the original surface data that has subsequently been used to develop the geocellular model, at a scale that has been used to map and then model the fault architecture, should provide a good understanding of the degree and lateral variation in geometric uncertainty. Few surface-geometric coherency tools are available; for this reason, we have developed our own set. The one that has proven the most useful in defining the geometric uncertainty applied to the seismic surface at the appropriate scale has been termed the ‘surface stability index’, which estimates the elevation of each horizon node by sequentially utilizing ever-wider local neighbourhoods around the central point. The range and distribution in horizon elevation estimates is used to

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quantify the local surface uncertainty. The result is an estimate of how incoherent the surface data are over the scale that is used to develop the geocellular horizons and project that horizon into any fault geometry (see Fig. 1a). The data should, therefore, provide a useful estimate of the degree of uncertainty present in the elevation of the geocellular horizon and the level of confidence in the horizon projection stability and accuracy. In favourable circumstances, the uncertainty in the horizon and fault location can be determined directly using the seismic volume from which the data were initially interpreted. It is tempting to use these data since they form the primary data from which all other data are developed, and so tests and/or parameters derived from the seismic

Fig. 1. Macro-scale geometric uncertainty estimates. (a) Surface stability index. The upper surface shows the surface stability index computed across the horizon. The lower surface shows this data mapped to the cells adjacent to the fault. (b) Fault geohistory classification – in this case, fault reactivation. The grid defines the rules used to compute the macro-scale structural uncertainties. Red ¼ high probability of reactivation; blue ¼ no late reactivation. (c) Angular discordance of the horizon adjacent to the faults. This value measures the angular difference between the surface normals of the horizon on either side of the fault. (d) Fault throw standard deviation (m) utilized for stochastic juxtaposition modelling. The grid has been computed using the normalized angular discordance and normalized surface stability index in conjunction with the fault geohistory classifier. The resulting grid retains lateral variations associated with fault location, type and confidence.

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volume should be relatively objective. It should be noted, however, that seismic-volume-based parameters will also include geophysical imaging artefacts and subjective, user-defined parameters involved in the processing of the seismic data; this is particularly important if more complex attributes are used in the computation of uncertainty. The root mean-square amplitude through a volume in close proximity to the target reflector has proven to provide apparently reliable and consistent results, more so than local seismic reflector amplitudes which tend to be dominated by local geological and structural variations (e.g. Townsend et al. 1998). The volume approach, by comparison, tends to be controlled by the larger-scale signal-tonoise of the area. This should therefore allow the determination of a parameter from which different faults and fault zone locations can be ranked. A set of attributes can be defined that can help quantify potential geometric uncertainties from the geocellular grid geometry. Computing discrepancies between modelled geometries and primary seismic interpretations can provide a useful measure of uncertainty. The primary seismic interpretation data contain geophysical imaging artefacts, the most pertinent of which relate to the Fresnel zone in the near-fault regions (Townsend et al. 1998). The negative impact of this and other features (e.g. poor line balancing and over migration) is usually reduced during the geocellular modelling process. Negative impacts of geocellular modelling usually revolve around data simplification, in which complex (but real) geometries that are difficult to model tend to be simplified to allow the generation of stable solutions. Other issues arise from the simplifications required due to the nature of the geometric grid being imposed; traditional cell-centred grids provide the greatest limitations, whereas unstructured grids provided the greatest flexibility. The nature of the geological structures being modelled imposes limitations on the accuracy with which the geology can be represented within the geocellular grid; simple normal faults can usually be represented with a high degree of accuracy, whereas multiple intersecting faults, including low-angle structures, are more problematic. Computing the misties (spatial discrepancy) between the final grid and the input data is a quick and useful tool to define the potential distribution and magnitude of uncertainty zones. As highlighted, these misties represent both useful and detrimental changes. Although vertical misties are easy to compute, tools for assessing lateral or surface-normal misties, which are more appropriate for assessing the validity of the fault modelling, are less common. Few software environments currently provide tools to assess the distribution and scale

of these modelling discrepancies for faults. It is certainly not yet routine for these data to be taken forward and incorporated into uncertainty and risk analysis of the modelled geometry.

Local fault – horizon intersection geometries Horizon –fault projection distances. Seismic data typically degrade near to fault zones for both geological (e.g. fracturing) and geophysical imaging (Townsend et al. 1998) reasons. The result is that the seismic surface interpretation data are often unstable; even when stable, they are liable to be in error in the near-fault areas. To compensate for these problems, most geocellular modelling packages allow the user to build the model by stepping back from the fault by a set distance, and then taking this more stable 3D horizon form and projecting back into the fault surface using a variety of gridding algorithms. This projection distance is a useful criterion on which to base an uncertainty parameter. Our approach has been to expand on the data traditionally used in the modelling process but to maximize the use of this parameter later in the uncertainty analysis. If these types of data are combined with known structural styles and the geohistories of the faults, then the likely uncertainty in the modelled geometry can be more appropriately characterized. An example would be when faults of a certain orientation and age may favour the development of drag folds (e.g. Hesthammer & Fossen 2000), whereas later, more-lithified stratigraphy may develop more discrete structures. Structural style and geohistory. A fault’s type and its geohistory have a fundamental control on its local geometry and complexity (Childs et al. 1997). Reverse faults typically have a different internal morphology than extensional or strike-slip structures (cf. Childs et al. 1997; Shipton & Cowie 2001; Kim et al. 2003), while simple, early syn-depositional extensional faults have a different form to continuously reactivated, extensional fault zones. Structural style and geohistory are well documented in the structural geology literature as being important in controlling the horizon–fault juxtaposition geometry, but current geological modelling packages treat the horizon–fault intersection problem as a purely geometric challenge based on the data provided. Assigning uncertainty parameters to faulted cells based on structural style and geohistory is straightforward (see Fig. 1b); in our approach we have applied the geohistory styles per fault segment. When this is combined with other parameters, such as the horizon–fault projection distance, the hangingwall– footwall angular discordance and the throw, it

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becomes a powerful parameter in defining likely juxtaposition uncertainties. Fault mislocation and associated interpolation errors – hangingwall –footwall angular discordance. The angular discordance of the footwall and hangingwall stratigraphy provides a guide to the potential juxtaposition uncertainty in the fault zone. The nature of the juxtaposition of stratigraphy that is co-planar will be unaffected by fault mislocation. That is in sharp contrast to non-co-planar stratigraphy, for which the degree of variance in the juxtaposition is a function of the discordance between the hangingwall and footwall stratigraphic orientations (i.e. dips and strikes). Figure 1c shows the angular discordance of the footwall and hangingwall stratigraphy across the faults in a geocellular grid. Combining the horizon –fault projection distance with the angular discordance and structural style provides a wellconstrained set of architectures that should enable better predictions of both geometric style and geometric uncertainty. Figure 1d shows the compounded result of the normalized surface stability index (Fig. 1a) and angular discordance (Fig. 1c) according to the local fault geohistory (Fig. 1b). These data have been used to assign the throw uncertainty along the faults for incorporation into the stochastic modelling. All of the previous parameters, except footwall and hangingwall discordance, provide map-based data. In order for data to be efficiently utilized in the fault seal analysis process, they need to be upscaled and stored as parameters in the geocellular grid. Processing the datasets using median filters has proven the most effective way of preserving uniform data domain margins while stabilizing the results to a scale appropriate for incorporation into geocellular grids. The previous set of parameters and uncertainties are values that can be directly calculated from and for specific fields or prospects. For geometric properties that are below the level of seismic resolution and for nearly all property parameters, much greater interpolations are required and commonly fieldspecific data may not be present. In these situations, parameter rules and relationships need to be utilized that link measurable or observable parameters (e.g. seismic throw or well shale content) to our target parameters (e.g. fault permeability). Various sets of relationships have been defined and used in the literature (cf. Ottesen Ellevset et al. 1998; Manzocchi et al. 1999; Fisher & Knipe 2002; Sperrevik et al. 2002; Yielding 2002). These relationships will be reviewed and the data behind those relationships investigated. For these reasons, the following section presents new data for certain relationships and reviews existing published datasets for others.

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Estimation of strain partitioning All of the previous uncertainties are associated with the development of the most accurate macro-scale structural form of the fault zone. Within that geometry, there is a further level of complication associated with the local fault zone architecture. Complex strain partitioning between multiple slip surfaces and strain accommodated via folding within and adjacent to the main fault damage zone are common processes (e.g. Antonellini & Aydin 1995; Childs et al. 1997; Knipe 1997; Hesthammer & Fossen 2000; Shipton & Cowie 2001). The result is usually that the principal slip surface within the fault damage zone accounts for a portion of the total or cumulative offset of the entire zone, i.e. that modelled or seen via seismic data. Although the tendency is that the principal slip surface will account for a reduced throw, in certain circumstances the main slip surface can dominate the cumulative throw. This is particularly prevalent in complex graben-style fault zones and strike-slip systems where the overall offset across the zone is negligible in comparison to the offset on the main slip surfaces (e.g. Shipton & Cowie 2001; Kim et al. 2003). Determining the true nature of the juxtapositions in the fault zone will have a fundamental control on its sealing nature. Uncertainties in this parameter are critical to incorporate, but currently there are few compiled data. Extensive research has been conducted on statistical populations of fault networks (e.g. Antonellini & Aydin 1994; Knott 1994; Peacock & Sanderson 1994; Knott et al. 1996; Childs et al. 1997; Beach et al. 1999; Hesthammer et al. 2000; Shipton et al. 2002), but few allow the relationship between fault zone architecture as observed via seismic data and the detailed slip plane morphologies to be determined. Figure 2 shows a dataset that partially addresses this issue. Figure 2a shows the offset on the principal slip plane in the fault damage zone relative to the net offset on all faults through the damage zone. The data come from Carboniferous coal bed mine maps from the West Midlands coalfields of the UK, and are a compilation from a series of transects taken across multiple fault zones within a relatively small area (approximately 200 km2). All of the fault zone data come from the same stratigraphic height and they show broadly similar structural form. The data indicate that, in general, the principal slip surfaces accommodate a reduced throw in comparison to the cumulative fault offset across the fault zone. The linear best-fit model through these data indicates that the principal slip surfaces accommodate around 70% of the net fault throw, although there is a substantial scatter around this relationship. Figure 2b shows the estimation error

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Fig. 2. (a) Net fault zone offset versus maximum slip plane offset within that zone. Data from faults historically mined in the Midlands Carboniferous coalfields. The general trend indicates that the principal slip plane accommodates approximately 70% of the net offset. (b) Estimation error percentile distribution profile of the principal slip plane offsets. The estimation is based on the net fault plane offset and the 70% trend line. For all the data: P10 uncertainty ¼ 2%, P50 ¼ 25% and P90 ¼ 160%. For faults with net throws in excess of 4 m: P10 ¼ 2%, P50 ¼ 15% and P90 ¼ 40%. Note that estimation errors in excess of 100% occur when antithetic faults significantly reduce the net fault zone offset.

of the principal slip surface throw based on the net fault throw and the 70% relationship. The sample estimation error is plotted as the difference between the actual percentage sample-to-net throw compared to the 70% global trend. In order to capture the variability in the system, the net fault throws will be modelled as the 70% sampleto-net throw relationship subject to an uncertainty

value. Although this uncertainty parameter is not immediately intuitive, it is computed in a manner to be most applicable to uncertainty modelling. The median uncertainty for the data is approximately 25%. To model uncertainties up to this median value, the net throw would need to be modelled as 70% throw þ/225%, that is a principal slip plane offset of 45% to 95% of the net fault

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offset. The P90 data indicate a large range of around 160% for the global data. Fault zones with in excess of 4 m of net offset show a more stable form, with very few examples showing slip on single faults. This is borne out in Figure 2b by the dramatic reduction in estimation errors (again based on the 70% throw relationship) for those samples. Although the P10 to P50 errors for the total dataset and the samples with more than 4 m net throw are similar, the extreme errors are greatly reduced with a reduction in the P90 error from 160% down to 40%. If only the samples with net throw greater than 4 m are used to define the general trend in Figure 2a, then the principal slip throw to net throw reduces from 70%. If the trend line is forced through zero then the principal slip to net slip reduces to 65%, while for a pure linear trend line this ratio drops even further to approximately 54%. These data provide an initial method of estimating the true throw on the principal slip plane from the mapped throw and the likely uncertainty of that estimate. The data presented in Figure 2 document the principal slip surface to net slip offsets, and these data do not therefore provide a comprehensive estimate of the slip plane throw from the seismically modelled throw. Non-fault-related strain, seismic imaging and geometric modelling uncertainties will not be included within these data. Further work needs to be conducted in this area to provide more comprehensive datasets for this critical juxtaposition uncertainty modelling and the assessment of other datasets to explore the role of strain rate, degree of lithification, reactivation, inversion, etc.

Estimation of fault rock thicknesses To incorporate fault rock properties into reservoir simulation grids, both the permeability of the fault rock and its effective thickness need to be determined. These properties combine to define the transmissivity of the fault (Knai & Knipe 1998). Manzocchi et al. (1999) defined an equation for the fault transmissibility multiplier which links the host and fault rock properties, namely the hangingwall and footwall host rock permeabilities, the simulation grid block size, the fault permeability and the effective thickness of the fault. The fault effective thickness is always unknown in a production situation, so a proxy for the effective thickness is required. A number of authors have published studies on the link between fault offset and fault rock thickness (e.g. Hull 1988; Blenkinsop 1989; Evans 1990; Knott 1994; Antonellini & Aydin 1995; Knott et al. 1996; Childs et al. 1997; Manzocchi et al. 1999). Figure 3a shows fault displacement as a function of fault rock thickness (log-log scale) for a large number of fault zones

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(data from Childs et al. 1997). The dataset is divided into two groups according to the structural character of the fault zone, with open squares showing relatively simple fault zones with single main slip surfaces, and solid diamonds indicating more complex fault zones with multiple main slip surfaces. Linear trend lines (in log-log space) are presented for the total dataset, together with separate well-defined linear relationships for the two different structural architectures (Fig. 3a). Figure 3b shows the sample fault thickness deviation in log space (orders of magnitude) for the different data subsets relative to their own specific trend lines. Note that there is approximately a 40% to 60% reduction in uncertainty between the total dataset and the ‘structural type-specific’ data estimations. Again this reinforces the importance of type-specific data in reducing uncertainties. Figure 4a shows the Childs et al. (1997) data overlain with general ‘rule-of-thumb’ displacement– thickness proportional relationships. Displacement– thickness relationships of 1:30, 1:66 and 1:100 are shown together with the linear trend for simple fault zones. For the seismic-scale structures, any of the 1:30 to 1:100 linear relationships lie within the data cloud. The best-fit line (dashed line) cuts across, but closely approximates, the 1:66 to 1:100 relationships, and any of the relationships can be considered to provide a reasonable estimate. Figure 4b shows that the estimation errors using each of the different trend lines define the same general uncertainty distribution. These data therefore indicate that to appropriately model this type of system it is not the specific displacement–thickness function that is important, but instead it is the uncertainty around that function that needs to be captured. Critically, it is the fault transmissibility (which is proportional to fault permeability and inversely proportional to fault thickness) that controls the resulting cross-fault fluid flow. The inherent property variability needs to be understood over a range of scales, including and below the sub-grid-block scale, to properly understand the flow within the upscaled simulation-scale grid block.

Property parameters and associated uncertainties Fault rock properties are fundamental to the evaluation of fault-related flow. This section reviews the impact of property uncertainties on fault seal analyses, including the potential variation in the stratigraphic sequence, the accuracy of estimating the clay content in host rocks (as these often form the basis of predicting deformed rock properties), the issues of estimating fault rock clay

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Fig. 3. Fault displacement –fault rock thickness relationships. Data from Childs et al. (1997) and references therein. (a) Displacement –thickness data for faults relative to their structural style. Open squares are for simple single slip planes or simple fault zones. Solid diamonds are for complex fault planes with multiple main slip planes. (b) Percentile point deviations away from the linear log-log best fit trend lines shown in (a). For the complex faults, the deviations are: P10 ¼ 0.05, P50 ¼ 0.22 and P90 ¼ 0.5. For the simple fault planes: P10 ¼ 0.05, P50 ¼ 0.34 and P90 ¼ 0.85. For the total dataset: P10 ¼ 0.12, P50 ¼ 0.64 and P90 ¼ 1.26. Values shown are in orders of magnitude. Note that with decreased characterization of the structural style, there is a doubling of the uncertainty.

contents and the transforms to petrophysical properties (permeability and capillary threshold pressures).

Stratigraphic variation We have implemented two contrasting approaches to multiple stratigraphic realizations. In the first approach, we consider varying permeabilities,

facies and host clay contents inside a given structural and stratigraphic framework. This is the most common means of capturing the stratigraphic variation (including both measurement uncertainty and natural variability), but it is sometimes limited in its applicability due to the presence of constant unit thicknesses controlled by the structural model. In the second approach, we consider varying unit thicknesses as well as internal

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Fig. 4. Fault displacement –thickness relationships and linear fault throw to thickness trends. Data from Childs et al. (1997). (a) Data for simple and complex fault zones. Also shown is a best-fit linear log-log trend through the ‘simple fault’ data (dashed line; see text and Fig. 3 for definition). Fault displacement– thickness trends of 1:30, 1:66 and 1:100 are also shown. Note that for the seismic-scale structures, the 1:66 trend provides the closest approximation to the gross linear fit. The data from the more complex fault zones follow the same general trend but are shifted by around 1.5– 2 orders of magnitude. (b) Seismic-scale ‘simple fault’ category fault rock thickness estimation errors using the 1:30, 1:66 and 1:100 displacement– thickness relationships and the linear trend defined by the simple fault dataset. Note that most of the estimation techniques produce similar errors with P50 errors of 0.3– 0.45 order of magnitude and P90 errors of around 0.8–1 order of magnitude.

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properties. In order to co-relate the results from the seal analysis, the simplest approach to analysing the like-for-like results is to match the geocellular cells between the different grids. A large sequence of stratigraphic realizations can be incorporated into the structural model to assess the impact of changing stratigraphies on the seal potential.

Estimation of host rock clay contents The basis for most fault seal predictions is the reservoir model VShale distribution. The VShale data are often taken as a proxy for VClay. A variety of algorithms can then be applied that attempt to predict how that clay content will be modified and distributed across the fault surfaces within the geocellular model (e.g. Fulljames et al. 1997; Yielding et al. 1997; Bretan et al. 2003; Knipe et al. 2004). Critical, therefore, to the whole process and to the value of any fault seal analysis is an accurate assessment of the initial clay distribution. In general, the first step is the sedimentological population of the model, and then the individual facies blocks are subsequently populated out from the well data using the VShale log. Commonly, the VShale data (assumed to be a direct proxy for VClay) are used in the fault seal calculation, and can cause confusion because the relationships commonly quoted for permeability and threshold pressure are related to fault rock clay content and not VShale (e.g. Fisher & Knipe 2002; Sperrevik et al. 2002). The result is that unnecessary uncertainty is introduced into the fault seal analysis. A transformation of the VShale data to VClay should be performed if the permeability –clay or threshold pressure–clay relationships are to be utilized for fault permeability or sealing capacity estimates. Unfortunately, the transformation from VShale to VClay is not as straightforward as one would hope. Figure 5a shows VShale (from gamma ray data) as a function of the clay percentage as determined from XRD data for a North Sea well. A considerable scatter is present within the data. The linear fit to the samples is shown, as are constant clay prediction mistie (drift) lines. The well data used contain a wide variation in VShale values typical of a sand–shale reservoir sequence. Figure 5b shows the percentile clay mistie between the sample clay value and the predicted linear fit. Note that the median mistie is around 8%, with the majority of samples having estimated values 6% to 15% (P33 to P86) away from the predicted value.

Estimation of fault clay content distributions The clay content of fault rocks shows a correlation with the fault rock properties, threshold pressures

and permeability (e.g. Fisher & Knipe 2002). There are several algorithms commonly used for predicting the fault clay distributions. One set aims to define the zones of continuous clays, i.e. clay smearing (e.g. Lindsay et al. 1993; Lehner & Pilaar, 1997; Yielding et al. 1997), and we will describe some of these algorithms below. The second set of algorithms attempts to predict the distribution of clay content along the fault zone. The main algorithm currently implemented is the shale gouge ratio (Yielding et al. 1997; Yielding 2002). This algorithm has been integrated into a number of software platforms and often forms the core code from which simulation grid fault permeabilities are derived (e.g. Roxar RMS (www.roxar.com), Eclipse–FloViz and Petrel (www.slb.com), FAPS/TrapTester and TransGen (www.badleys.co.uk)). Understanding the uncertainties and inherent variability in this prediction is therefore of direct relevance to any field flow simulation being conducted using these software environments. Shale gouge ratio. The shale gouge ratio (SGR) is simply the average clay value of all units that have passed that point on the fault (Yielding et al. 1997). The algorithm assumes a perfect mixing both along the throw vector and across the fault zone. Figure 6a shows an outcrop calibration of the SGR method based on the Moab Fault zone from fieldwork presented in Foxford et al. (1998) (data also from Yielding 2002). The data points show that the observed clay gouge in the fault zone versus that predicted by the SGR algorithm has an error that is centred and is symmetric around zero. The algorithm therefore, in broad terms, provides a sensible estimate of the observed data. Also shown on the graphs are 10%, 20% and 30% clay error lines away from the prediction line. The data points are widely distributed through this zone. Figure 6b shows the percentile error distribution for the sample estimates using the SGR algorithm, and indicates that the median error using the algorithm is approximately 10% clay content. The percentage errors of the estimates (not shown in Fig. 6) are 20 –50% of the measured value, with some approaching 100% (i.e. the SGR value had up to a 100% discrepancy from the original outcrop value). In general, larger percentage errors are observed at lower clay contents due to the larger proportional impact of relatively constant errors on smaller initial values rather than a clayrelated error distribution. When the SGR errors are plotted against the original outcrop clay gouge data, the data points display a random distribution, indicating that the error is not primarily a function of the original stratigraphy but rather a more uniform error across the gouge range.

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Fig. 5. (a) North Sea well VShale– clay content (computed via XRD) data. A linear fit and constant deviation lines from the linear fit are shown. Dashed line represents the VClay ¼ VShale relationship, which would equate to using VShale as a direct proxy for VClay. (b) VClay estimation errors. Solid diamonds represent VClay estimation errors based on a self-determined linear trend estimate, with P10 ¼ 2%, P50 ¼ 8% and P90 ¼ 21%. Open squares represent VClay estimation errors based on VShale ¼ Vclay, with P10 ¼ 1%, P50 ¼ 11% and P90 ¼ 23%. Note that the majority of the misties for the linear trend estimate lie between 7% and 16% clay (P33– P86). Note also that for more than around 40– 50% of the data range the VShale ¼ VClay transform has an additional 5% clay estimation error above the linear transform.

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Fig. 6. SGR uncertainty when compared to Moab outcrop data. Data from Foxford et al. (1998) and Yielding (2002). (a) Observed clay gouge in the Moab Fault zone (Foxford et al. 1998) versus calculated SGR values. Also shown are the SGR error lines. Note that the errors are approximately symmetrical around zero but approach 30% (absolute SGR error and not a percentage of the estimate or original value). (b) Percentile error distribution for the sample estimates using the SGR algorithm.

Uncertainties will be a function of the original heterogeneity of the stratigraphic stacking sequence over the thickness equivalent to the fault throw. The Moab outcrop stratigraphy has a series of contrasting lithologies over a range of scales and so may provide an indication towards the higher end of likely uncertainties. For more homogenous sequences, the SGR algorithm is likely to provide better estimates due to its pure averaging nature. Fault zone processes that lead to non-perfect mixing within the fault zone will, however, negate

the primary assumption of the SGR algorithm and hence lead to inaccurate estimations. Such fault zone processes are fault zone widening, fault refraction, strain localization and the incorporation of lithologies with varying macro-scale viscosities (e.g. Evans 1990; Knott 1994; Knott et al. 1996). These are all processes that are common in fault zones and are likely to be enhanced in sequences with varying rheological properties at a scale similar to the fault throw. The indication therefore is that the SGR should provide a good estimate

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with a relatively small uncertainty in relatively homogenous sections of stratigraphy (on a length scale similar to the fault throw), but that this estimate is likely to degrade and the uncertainty increase in, or close to, zones of major lithological contrast and with increasing throw, where the averaging technique removes the impact of local stratigraphies. Other algorithms. ESGR: limited along-displacement-vector clay mixing. The effective shale gouge ratio (ESGR; Knipe et al. 2004) is a weighted version of the SGR algorithm that assumes nonperfect fault rock mixing along the fault throw vector. A greater contribution to the material in the fault zone is provided by the local host rock hangingwall and footwall rather than stratigraphy which has moved a long way past the point of interest. The result is an algorithm whose estimate fluctuates much more rapidly than the SGR algorithm due to the movement of contrasting stratigraphies past the point of interest. Figure 7 shows data from a fault zone in a sequence of interbedded sands and shales in the Ferron sandstone, Utah, USA (RDR, unpublished internal report). Figure 7a shows the measured clay contents in the fault zone and the markedly different clay content estimates developed for that faulted sequence at the different sample sites. The SGR algorithm predicts values which are similar to the gross host rock clay content. The ESGR algorithm, in contrast, predicts more widely varying values that more closely mimic the measured fault rock values. Figure 7b shows the clay prediction error distribution for the two different algorithms. Both algorithms have low median errors (ESGR ¼ 2% and SGR ¼ 5%) but they have very different gross error distributions. For the SGR estimates, 30% were in error by more than 15% clay content, while the same extreme ESGR error estimates were in error by 3– 6%. In this particular case, with large clay content variations in the stratigraphy, the locally weighted ESGR algorithm has been far more accurate at estimating the local clay distributions in the fault rock. Limited across-fault clay mixing: hangingwalland footwall-specific clay mixing algorithms. In order to include the impact of heterogeneous fault zone mixing (either because of fault rock widening, or variations in the hangingwall or footwall sequences), we have utilized a side-specific (separate hangingwall and footwall) implementation of the above mixing algorithms. The clay mixing prediction is independently based on the stratigraphy on each side of the fault. After computation, the data can be combined via a set of rules (e.g. maximum clay side dominates). In a significant number of cases where these algorithms have been applied to sealing issues, particularly where

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there were large variations in stratigraphy between the hangingwall and footwall, using a side-specific algorithm has provided a simple explanation to the sealing behaviour of a field or trap (as proven via well data) without the need for extreme fault seal values (e.g. very large clay smear factors). The above set of algorithms provide a suite of techniques whose input parameters allow different parts of the host rock sequence to contribute to the prediction of clay distributions in the fault rock. Although previous authors (e.g. Yielding 2002; Knipe et al. 2004) have conducted tests to provide an assessment of possible uncertainties when implementing these algorithms, the amount of data is small and further work is required to identify the key controls on the uncertainties and the scale of those uncertainties. Principally, however, the fault rock clay prediction uncertainty is likely to be controlled by the stratigraphic heterogeneity and the local structural architectural complexity (itself partially controlled by the stratigraphic heterogeneity) over the fault offset range applicable.

Estimation of clay smears Clay smears, as defined by Lindsay et al. (1993), can form in a variety of ways and are controlled by a variety of geological parameters such as lithification state, clay type and effective stress conditions (Lehner & Pilaar 1997). Of interest in fault sealing is the highly impermeable nature of these clay smears when they form continuous clay zones within fault rocks. Permeabilities below 0.0001 mD are common (Fisher & Knipe 2002). The principal control on the continuity of clay smears has been highlighted as a combination of throw and shale unit thickness (e.g. Fulljames et al. 1997). The term clay smear factor, CSF (Yielding et al. (1997); see also clay smear potential (Bouvier et al. 1989; Fulljames et al. 1997)), has been used to define the relative throw–thickness relationship at which the clay smear continuity becomes discontinuous. A wide range in clay smear values has been used and documented (Lindsay et al. 1993). In outcrop, Lehner & Pilaar (1997) document examples with clay smear values of up to around 10, whereas other field outcrop examples show shale-rich layers abruptly terminating against faults (a clay smear factor of 1). Values for the CSF of around 3 (corresponding to the clay bed being offset by twice its own thickness) have proved useful for separating continuous from discontinuous smears. The application of the clay smear algorithm on geocellular grids is relatively straightforward. Once the continuous thickness of stratigraphy above a

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Fig. 7. (a) Measured versus predicted fault rock clay contents from a fault zone in the Ferron sands (interbedded sand–shale sequence), Utah, USA. Data shown are the measured clay contents from outcrop (XRD; solid black circles), and SGR (black diamonds) and ESGR predictions (open squares) of the clay content for those sample point locations. Note that the ESGR algorithm provides a better estimate of the measured values in this outcrop. (b) Percentile clay prediction error profiles. ESGR errors (open squares): P10 ¼ 1%, P50 ¼ 2% and P90 ¼ 4%. SGR errors (solid diamonds): P10 ¼ 1%, P50 ¼ 4% and P90 ¼ 18%.

certain clay threshold value has been determined, the clay smear algorithm is used to determine the distance away from the clay-rich layer that the unit will smear down the fault. Currently, the

range of possible clay smear values that are appropriate for different geological situations is not well constrained. The large range of values currently documented is unlikely to be appropriate

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for all situations and smaller sub-ranges are probably more appropriate for different fault and stratigraphic geohistories. Apart from our current lack of data for defining shale smear factor uncertainties, there are two other problems with the technique. The first is that an arbitrary cut-off value is usually used to define which stratigraphies smear and which do not. This is likely to develop unrealistic results, particularly in sequences that contain significant variations close to the cut-off used (e.g. James et al. 2004). The second problem, and potentially the more significant one, is related to upscaling. The clay smear algorithm uses the thickness of continuous clay-rich material above a set cut-off value to define the continuously smeared area. This vertical continuity is a very scaledependent value. For a shale-rich section with thin interbedded sands, if the highest resolution data were used to define the smear area then the distance between the individual fine sands would apply. If, in contrast, the well data had been up-sampled, then the geocellular grid may contain only a single thick shale with a bulk average clay value. Operating on these two different models developed from the same input data would develop very different results. The first high-resolution model would develop only thin zones of smear which would overlap each other, whereas the upscaled version would develop smears that are potentially orders of magnitude greater in size. The general relationship is that, for a specific clay smear value, the smear thickness predicted by the clay smear algorithm is inversely proportional to the resolution being used – the greater the local heterogeneity then the greater the scale of the problem. The value and range of clay smear values must therefore be applied at a specific resolution scale.

Estimation of fault permeabilities One method commonly implemented to estimate the permeability of a fault is to define a relationship between fault rock clay content and permeability, and to use a fault clay prediction algorithm, such as SGR, to define the fault clay content. This approach is currently in use in a number of software systems. These systems use a set of defined clay– permeability relationships (most now several years old); several industry-standard software packages have the ability to predict fault permeability using other methods. A number of authors have presented such data (e.g. Morrow et al. 1984; Evans et al. 1997; Faulkner & Rutter 1998; Manzocchi et al. 2000; Fisher & Knipe 2002; Sperrevik et al. 2002), and all of these define a large spread in values rather than tight relationships. Unfortunately, this spread in data is usually not highlighted or used in the calculations of fault permeability in the

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current fault seal assessment systems. Figure 8a shows clay content versus log permeability for North Sea Middle/Upper Jurassic reservoirs (data from Sperrevik et al. 2002), and this dataset is particularly powerful because of the area-, lithology- and depth-specific classification of the samples. The data have been subdivided according to the depth of the samples and two trend lines have been placed through the data. These are not meant to represent the ‘real’ function; rather they define one sensible estimation method amongst many. The first is a general trend through the total dataset, while the second is a trend line through the depth-specific samples from 2500–3000 m depth. Figure 8b shows the percentile sample deviation from these two trend lines for the corresponding datasets. The total dataset (Middle/Upper Jurassic reservoirs only) shows a median sample permeability deviation away from the trend line of 1.5 orders of magnitude, with the P90 deviation being in excess of 3 orders of magnitude. The depth-specific samples also show a very significant deviation away from their own trend line, with a median drift of 1 order of magnitude. The data show that there is natural spread in results of around 1 order of magnitude, although this can be as high as 4 orders of magnitude, with significant increases in uncertainty as the level of characterization of the samples decreases. Overall, the depth-specific clay –permeability relationship provides approximately a 30% reduction in variability when compared to the total dataset. This example demonstrates the usefulness of strongly calibrated samples in the drive to optimize estimates and minimize uncertainties. It should also be noted that other fault rock sealing mechanisms may not show a simple fault rock clay content to permeability relationship, particularly for cataclasis and cementation, and this will particularly have an impact for lower clay content and high-permeability host rocks.

Estimation of sealing directly from SGR One method outlined in the literature to predict the sealing or leaking nature of faults is a direct interpretation of the fault rock clay content via SGR. Yielding (2002) presented the SGR and the trap sealing nature (seal or leak) for a series of fields and prospects in the North Sea (see Fig. 9). In this paper, the SGR ranges of sealing and leaking traps were shown for the controlling faults. Unfortunately, general SGR values have been presented rather than those present on the key fault windows. We have assumed a linear distribution of SGR values within the ranges documented by Yielding (2002) to generate the distribution profiles shown in Figure 9a; without

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Fig. 8. (a) Clay content versus fault rock permeability, categorized by the depth of the sample. Data from Sperrevik et al. (2002). Also shown are a linear fit through all the data points and a fit through only the 2500– 3000 m samples. (b) Percentile permeability sample deviation from the trend line estimate for the global trend line and the 2500– 3000 m depth-specific samples. For the depth-specific samples (solid diamonds): P10 ¼ 0.1, P50 ¼ 1.0 and P90 ¼ 2.5. For all samples (open squares): P10 ¼ 0.3, P50 ¼ 1.45 and P90 ¼ 3.1. All values are in orders of magnitude.

further knowledge of these distributions, this assumption was required to provide only an approximate relationship. The graph shows that, rather than there being a unique cut-off value for SGR that can be applied, there is a wide zone of uncertainty. The data from the ‘leaking’ faults overlap significantly with the ‘sealing’ traps. The data indicate that confidence on the sealing nature of the fault can only be defined if the SGR value is either less than around 15% (leaking) or greater

than approximately 40% (sealing). Figure 9b shows the normalized leak probability for a given SGR value. Within the zone from 15% to 40%, there is an approximately linear decrease in probability that the trap will leak. The data indicate that for SGR values less than 32%, the traps have a greater likelihood of leaking than sealing, and the reverse result applies above that value. These relationships, which include a wide range in uncertainty, make geological sense given the

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Fig. 9. Quantification of seal type directly from SGR. Data from Yielding (2002). (a) Normalized frequency distributions of the leaking and sealing traps relative to SGR value (assuming a linear distribution of SGR values from the data provided). Note that below around 15% SGR, all examples are leaking and above 40% all examples are sealing. The 15–40% zone contains a considerable number of examples that are classed as both sealing and leaking. (b) Normalized percentage leaking traps as a function of SGR. Note that between 15% and 40% there is a relatively linear distribution, demonstrating the gradual transition between leak and seal domination through the SGR range.

uncertainties that are likely to be present in the system. The application of a single cut-off value (e.g. 20% is suggested in Yielding 2002) is unlikely to capture the complexity of a system which includes both natural geological variability and modelling inaccuracies. The SGR value is an average of the clay content of the sequence; as such it indicates the sand net:gross of the sequence over the range that

the specific fault throws. If the data are taken at face value, then they would suggest that faults that cut reservoir sequences with host rock sand net:gross values of more than 0.85 would leak and that sequences with sand net:gross values of less than 0.6 would seal. The zone of seal uncertainty shown in Figure 9 would represent reservoirs with local sand net:gross values between 0.6 and 0.85 (over the length scale of the fault throw).

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When these data are combined with the SGR uncertainty (see Fig. 6) (average 10% error þ/2 10%), then it widens the seal uncertainty zone to reservoirs with sand net:gross values between 0.5 and 0.95. Incorporating the VShale to VClay uncertainty widens the zone still further to reservoirs with sand net:gross values between 0.4 and 1. Incorporating the uncertainties for determining the sealing nature of traps directly from the SGR widens the zone out to include the vast majority of natural primary permeability reservoirs. This highlights the fact that applying single cut-off values to single parameters is likely to lead to highly uncertain and possibly unreliable results. This particular example has derived its data from generalized values and is likely to lead to over-estimations of uncertainty. Identifying key fault windows with specific fault rock clay contents (in relation to identified column height supports of a stated hydrocarbon type) is likely to lead to more specific predictions being possible.

Estimation of fault sealing capacity via threshold pressures In order to allow hydrocarbons to cross water-wet faults, the capillary entry pressure of the fault rock must be overcome (e.g. Schowalter 1979; Watts 1987; Fulljames et al. 1997; Fisher et al. 2001; Bretan et al. 2003; Brown 2003). The capillary entry pressure is the maximum pressure differential that can be held across the membrane. In static fluid situations, the sealing capacity is the maximum hydrocarbon column that can be supported across the fault; this relates to the capillary entry pressure, the hydrocarbon–water interfacial tension and the relative densities of the hydrocarbon and water in the system (Fulljames et al. 1997). For dynamic cases, such as in production environments or in areas of hydrodynamic drive, the sealing capacity will be modified away from this static case to account for the additional across-fault pressure differences developed by fluid migration and/or pressure drawdown. The accurate determination of the threshold pressure, and hence the sealing capacity, is critical if sensible estimates of cross-fault hydrocarbon column differences are to be defined. The determination of the threshold pressures has clear relevance to both exploration and production scenarios. Figure 10 shows the relationship between the fault rock clay content and the mercury –air threshold pressure determined via mercury injection porosimetry for Middle/Upper Jurassic reservoir related rocks (data from Sperrevik et al. 2002). Figure 10a shows data from samples taken at all depth ranges (,2500 m to .3600 m, solid

diamonds) and data for samples in the 2500– 3000 m depth interval (open squares). Best-fit linear trends (in log-linear space) have been determined for both the general and depth-specific datasets. The 2500–3000 m samples include disaggregation, cataclasite and phyllosilicate framework fault rocks (see Fisher & Knipe 1998 for definitions). Figure 10b shows the threshold pressure sample estimation errors based on the best-fit trend lines. The depth-specific samples (2500– 3000 m) in general show a 30% decrease in the estimation error across the range of values in comparison to the total data from all sample depths. For the depth-range-specific samples, the median estimation error is around 0.4 orders of magnitude and the P90 error is approximately 0.7 orders of magnitude. These errors appear to be reasonably uniform across the clay range, but the dataset is limited by few high-clay samples. The analysis highlights the need to include the impact of the geohistory (in particular, the temperature and effective stress histories) as a critical means of reducing uncertainty estimates. It should also be noted that the upscaling of laboratory samples to reservoirscale properties and translating laboratory-based measurements to effective fluid and stress conditions introduces additional uncertainties into the above procedures.

Parameter uncertainty summary The previous sections highlight the published relationships between different properties that allow fault rock sealing capacities, fault rock permeabilities and fault transmissibility multipliers to be computed from observable or measurable parameters for fields or prospects. For each of these relationships, we have reviewed the scale and controls on the uncertainties, and Table 1 provides a compilation of these relationships and the scale of the uncertainty. This dataset, when used in conjunction with the directly measurable geometric uncertainties (reviewed earlier), provides a framework from which to integrate and assess the uncertainties during fault seal analysis.

Incorporating uncertainties in geocellular grids Modification of the grid parameters In order to be able to incorporate the different types of uncertainty within a geocellular grid, both the geometric and property parameters within the grid need to be modified in a variety of ways. A combination of both absolute value shifts and percentage shifts is required to honour the different styles of

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Fig. 10. Fault rock clay to threshold pressure data, from Sperrevik et al. (2002). (a) Volume fraction clay content versus log mercury– air threshold pressure for Middle/Upper Jurassic North Sea core samples. Open squares show samples from the 2500– 3000 m depth range, and black diamonds show data from other depths. Linear fits to the depthspecific and all-depth samples are shown. (b) Percentile estimation error distribution profiles for the depth-specific samples and all-depth samples. The linear trend lines shown in (a) have been used for the estimations. Note that the depth-specific samples show around a 30% improvement in estimation across the range.

uncertainty. In certain very specific situations, the application of single shifts and the computation of the resulting properties is useful. An example would be a situation in which it is important to understand the properties of sub-seismic faults.

Fault juxtaposition and clay distributions could then be computed for a percentage of the throw of the main seismic-scale fault. These single computations have their place, but they are ultimately limited by the singular nature of the solution in an

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Table 1. A compilation of the scales and controls on uncertainties for different properties that allow fault rock sealing capacities, fault rock permeabilities and fault transmissibility multipliers to be computed from observable or measurable parameters for fields or prospects General parameters

Estimation methods

Principal uncertainty controls

Improved estimation

Seismic and structural modelling

1. Seismic resolution 2. Structural style

1. Higher seismic resolution 2. Surface geometric processing

Host VClay content (E & P) Fault rock clay content (E & P)

VShale to VClay

Estimation of VClay at the wells Appropriate algorithm

Clay smears (E & P)

Algorithms linking clay stacking sequence and throw

Appropriate algorithm and cut-offs for sequence

Fault rock thickness (P) Fault rock permeability (P) Threshold pressure (E & P) Sealing capacity (E & P)

Algorithms linked to throw

Structural style

XRD calibration of VClay 1. Calibrated algorithm 2. Improved facies population linked with VClay 1. Calibrated algorithm 2. Improved facies population linked with VClay Calibrated relationships

Algorithms linking fault rock clay to permeability Interpretative laboratory measurements Algorithms linked to threshold pressure and fluid properties

Structural style

Calibrated relationships

Sample heterogeneity

Calibrated relationships

Non-static conditions, e.g. hydrodynamic drive

Calibrated relationships

Algorithms linking clay stacking sequence and throw

Locally calibrated uncertainties

1. Minimum resolution (5 –30 m ?) 2. Mapping and modelling uncertainties (20 – 100%) 5 – 25% ? VClay

1. Minimum resolution (c. 10 m) 2. Mapping and modelling uncertainties (40%)

5 – 60% VClay

10% þ/2 10%

2 – 10 ?

þ/21 ?

0.25 – 3 orders of magnitude 1 – 4 orders of magnitude 1 – 2 orders of magnitude 1 – 4 orders of magnitude

0.4 orders of magnitude

10% þ/2 10% ?

1 – 2 orders of magnitude c. 0.5 order of magnitude c. 0.5 order of magnitude

S. R. FREEMAN ET AL.

Throw (Exploration & Production)

Uncertainties

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area of substantial uncertainty. In many cases, it is favourable to be able to capture the uncertainty or range in predicted values for a wide range of inputs. This has historically been difficult both to compute and to visualize for fault seal analysis. Computation speeds have allowed multiplescenario modelling to become routine throughout the industry. This has so far principally been applied in the arenas of stratigraphic and host rock property population (e.g. Handyside et al. 1992). In this paper, we show how these same techniques can be routinely implemented within a fault seal analysis. In the approach adopted here, uncertainties have been incorporated at all stages of the process. Distribution profiles of the uncertainties have been defined for all of the pertinent properties and these have been used as inputs into the modelling; the uncertainties are a function of data quality for the specific dataset.

Application of the uncertainty shifts Two main approaches can be utilized when applying uncertainty shifts. The first is to attempt to preserve the laterally connected nature of the data, while the other is to operate on single faulted grid columns independently. An example would be a situation where a fault throw is to be reduced to 50% of its original value. To compute the resulting impact that this has at one specific fault location is relatively simple. What is not so straightforward is what happens to the adjacent cells. If you attempt to preserve the laterally connected nature of the data, then the throw of the adjacent cells should also be reduced to a similar level prior to its own computation. A complex set of lateral variability rules would need to be generated in order for these data to be calculated. In the simple example of varying fault throw, this could be controlled by a lateral displacement gradient; similarly, a vertical displacement gradient would be required to honour cells above and below the original point of interest. In effect, the entire grid would need to be modified with a complex set of rules for every application of an uncertainty shift at any single point. For a typical grid of 200  200  50 cells, treating each of the 8 cell corner points independently would require operating on 16 million points. If only the faulted cells were monitored then that would reduce the data down to around half a million points. Given the complex nature of the lateral and vertical variability, this would require somewhere in the region of half a billion computations per cell scenario. If several hundred to a thousand realizations were run (required to effectively sample the uncertainty distributions), then for each cell hundreds of billions of calculations

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would be required. This would need to be repeated for each successive cell, although a systematic reduction in the necessary computations would occur for each successive cell as previous data shifts would have captured part of the uncertainty distribution profiles relevant to those cells. Unfortunately, the likely computation time of such an approach is currently prohibitive, and the application of this style of methodology is currently beyond the scope of a ‘rapid’ fault seal evaluation tool, although it may provide a useful avenue in the future. It is also important to note that a significant risk is present with such lateral population implementations due to potentially unforeseen and unrealistic relationships being developed by the imposed rules, and the robustness of the solutions must be confirmed by assessing whether the uncertainty distribution profiles have been fully honoured for each property in every cell. Due to the computational and technical challenges in laterally linked data shifts, our approach has been to operate on each cell individually and perform a significant number of realizations. For each run, the target cell properties and all of the cells that have an impact on the calculation are allowed to vary subject to the specified uncertainty distribution profiles. Typically tens to several thousand realizations are performed per target cell, depending on the complexity of the system and the number of parameter uncertainty distributions included. In order to confirm that sufficient realizations have been performed, the resulting realization samples are back-checked against the primary distribution profiles. One very simple but useful check is to extract the realization case that should most closely approximate the primary input data. Visual and mathematical comparisons of these two models provide a rapid first check to assess whether sufficient realizations have been performed. A second check which can be implemented is to compute, for each parameter, the median spacing between the values used for each of the realizations, and to therefore assess how well the different parameter distributions have been sampled. For example, if the throw was to be varied by 10 m and 100 evenly distributed realizations were to be performed, then the average spacing should be approximately 0.1 m, i.e. realizations would have been performed that sample every 10 cm shift in throw. For the numbers to be meaningful, the sample spacing has to be computed in the appropriate scale (i.e. log or linear space, as appropriate).

Minimizing the bias in uncertainty analysis The approach we present in this paper is aimed at avoiding a common problem with incorporating

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uncertainties, namely having to pre-judge the solution. When run times for scenario modelling are high, attempts are often made to vastly reduce the number of runs by testing a few specific cases in the hope that they will provide a good representation of the possible range of solutions. An example would be to run a model based on the P10, P50 and P90 input parameters. This has the advantage that only three solutions need to be assessed rather than many thousand, but the reliability of those three solutions to inform on the likely variability is questionable. When there is a clear mathematical link between the uncertainties and parameters, the approach is valid, but when this link is less clear (as in the case of fault seal analysis) then this approach can fail to model the data effectively. To avoid this problem, it is better to conduct a large number of realizations. The problem then is how to efficiently manage the results of such analyses.

Visualizing the results One of the main challenges with multiple scenario modelling is the effective visualization and interrogation of the results. Modelling thousands of different scenarios is relatively simple, but if the critical relationships cannot be rapidly identified and isolated then the technique is unhelpful. In this paper, we have utilized three techniques for sorting and visualizing the results of the multiple combined uncertainty analysis. The first technique we have termed ‘critical result traps’, the second ‘auto ranking’ and the third ‘scenario typing’.

Critical result traps ‘Critical result traps’ is the term we have used for our approach to probability mapping. Rather than routinely tracking all of the possible scenarios, very specific criteria are set and only combinations of parameters that lead to a specified result are counted. The result is a probability value for each cell that the specific criteria were successfully met. A simple example is shown in Figure 11. In this case, a faulted geocellular grid of an interbedded sand –shale sequence was analysed (see Fig. 11a). The throws on the faults were allowed to vary from the modelled static case by 10 m standard deviation (this value being representative for this particular dataset) using a Gaussian distribution (with zero mean). The specific criterion set (critical result) was whether a sand–sand window juxtaposition was developed by varying the throw, using the base-case (i.e. mapped) sand–sand window juxtapositions shown in Figure 11b. One thousand realizations were computed for each cell and the

Fig. 11. Juxtaposition analysis and uncertainty incorporation. (a) Host VClay stratigraphy. Yellow ¼ low-clay sand, purple ¼ intermediate-clay impure sands, brown ¼ high-clay shales. The sequence is an interbedded sand–shale sequence with multiple potential reservoir horizons. Top surface is colour coded for depth. (b) Sand–sand window juxtapositions computed from the original geocellular model shown in (a). (c) Sand–sand window juxtaposition probabilities displayed on the original sand–sand cells for the model shown in (a), using 1000 realizations in which the throw was allowed to vary by a 10 m standard deviation and assuming a Gaussian distribution. (d) Low sand–sand juxtaposition case (P90). The probability of a sand–sand window not occurring from the multiple realizations is less than 10%. These cells represent low interpretation risk sand– sand windows. Note that specific sand layers dominate the juxtapositions whereas others are absent (potentially juxtaposition seals). (e) High sand–sand juxtaposition case (P10). The probability of a sand–sand window occurring from the multiple realizations is more than 10%. This represents a very optimistic case for cross-fault juxtaposition analysis. Note that sand layers that initially showed no juxtapositions in the static model (b) now show the potential for window development.

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probability of a sand– sand window occurring was stored in the grid (see Fig. 11c). Once the probability of the solution is mapped back onto the grid, specific parts of the probability distribution can be quickly examined. Figure 11d and e shows the P90 and P10 cells that developed sand –sand windows. For the P90 case (Fig. 11d), the throws on those cells were only changed sufficiently to cause a non-sand juxtaposition in less than 10% of the realizations. We can then classify the existence of those sand –sand windows as ‘high confidence’, or a low interpretation risk. A number of cells had a 100% probability of sand –sand juxtapositions (see Fig. 11c), so that in those cases the range in throw uncertainty was insufficient to offset the sands from one another for any realization. In the P10 case

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(Fig. 11e), a large number of sand –sand windows are shown. Stratigraphic sections originally mapped as unconnected are now shown as possible sand –sand juxtaposition sites. This simple example demonstrates that rapid, time-efficient scenario modelling combined with specific result event tracking can provide powerful insights into the likely variability or risk on the basic geological interpretation model. Figure 12 shows a production-oriented example in which a series of input parameters (fault throw, host clay content, fault clay content to fault permeability, and fault thickness) that contribute to the computation of the Transmissibility Multiplier (TM; Knai & Knipe 1998; Manzocchi et al. 1999) have been allowed to vary. Two critical result tests were run, and the results were monitored

Fig. 12. Critical result trap analyses. (a) Probability of developing a transmissibility multiplier of less than 0.00001 for the reservoir sands. 1000 realizations were performed, allowing the following parameters to vary: fault throw, SGR to fault clay content, fault clay to fault rock permeability, and fault throw to fault rock thickness. Note the red areas which pervade along specific stratigraphic layers and indicate that the low target TM was achieved in nearly all scenarios. (b) Probability of developing a transmissibility multiplier of more than 0.1 for the reservoir sands, using the same parameter uncertainties as in (a). High TM values were only achieved in several specific areas. For a significant proportion of the reservoir stratigraphy, no combination of parameters led to the prediction of large TM values (.0.1). Also shown is the cell location used in Figure 14.

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for sand units in either the footwall or hangingwall. The first was a test for probable production timescale sealing (TM less than 0.00001), and Figure 12a shows the probability of this result occurring (run time around 30 min for 1000 realizations). The grid shows that the right-hand side of the fault, for the majority of sand layers, has a very high probability of a production timescale seal, whereas the left-hand compartment has a low probability. Although large variations in input parameters have been used, a simple and informative outcome is yielded. A second test for production timescale high-flow zones (TM greater than 0.1) was conducted (see Fig. 12b). The analysis shows zero to very low probability of flow across the right-hand fault compartment and flow localized

into specific layers in the left-hand compartment. Conducting uncertainty analyses should help to simplify the geological model rather than complicate the situation. This example demonstrates that, even though 1000 realizations have been conducted, determining critical result probabilities identifies areas of the faults that operate consistently and differently. The same style of analysis can be conducted for prospect risking. Figure 13 shows the probability that the fault can withhold specific oil–water contacts (increasing depths of oil–water contact in Fig. 13a –c). Variations in throw, host clay content, fault rock clay to threshold pressure, and threshold pressure to sealing capacity or column height support have been introduced. The fault

Fig. 13. Prospect analysis probability of column height support for given oil–water contacts. 1000 realizations were performed, allowing the following parameters to vary: fault throw, SGR to fault clay content, and fault clay to fault rock sealing capacity. Target oil– water contacts were: (a) 1775 m, (b) 1810 m and (c) 1850 m. Case (a) shows a high probability of support for all cells across the fault, in comparison to (c) which shows very low (,10%) probabilities of support along the crest of the prospect. Note that for cross-fault flow, both the hangingwall and footwall cells need to be breached.

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has been colour coded for the probability of support. The column height was repeatedly calculated using a Monte Carlo approach based on all of the above parameters and their associated uncertainties. The proportion of successful outcomes (i.e. support for a specified column) was recorded. In Figure 13a, the data predict high confidence that support will occur at all elevations along the fault. The probability decreases through Figure 13b and is low along the upper parts of the fault in Figure 13c. This type of analysis allows for a more independent and objective risking process to be developed for prospect evaluation.

Tracking the key relationships The critical result trap approach provides a powerful means of visually assessing the different sealing nature of the faults in a geocellular grid. Unfortunately, the simple probability value result masks the parameters that led to the critical result occurring, and it is clearly useful to be able to assess which combination of factors led to the final result. This would allow an assessment of critical combinations of the associated parameter ranges and which of these are geologically meaningful rather than statistical aberrations based on a strange combination of uncertainties. In order to track the factors that led to the solutions, cells can

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be targeted and all of the input parameters recorded. Figure 14 is a value diagram showing the 1000 realizations for the individual cell highlighted in Figure 12b. In this instance, the critical result test was set to capture all results that led to a transmissibility multiplier in excess of 0.1 for the reservoir sand units (production timescale cross-fault flow, as discussed for Fig. 12b), and the scenarios leading to this result have been highlighted. All of the other scenarios that failed to produce the high TM value are represented by black lines. Of interest is the control of throw on the critical TM value. Figure 14 shows that three very specific scenarios led to the high TM result. These involved throws which allowed the sand to be self-juxtaposed, or juxtaposed against its next two immediate sand neighbours. This type of data can subsequently be used to back-check against the original data (e.g. seismic) to determine whether this requirement is geologically plausible.

Auto-ranked models Although the critical result trap approach is useful in defining probabilities of final outcomes, it does not yield specific results that can be taken forward for flow simulation modelling. One method to allow vast numbers of realizations to be conducted and data to be carried forward is auto ranking of the

Fig. 14. Individual parameter inputs for 1000 realizations for one cell, whose location is shown in Figure 12b. The lines represent individual realization input values. The test was for a TM value of greater than 0.1, and the successful realizations are highlighted in purple. This value diagram highlights that very specific throw values control the final result, whereas variations in SGR, fault rock thickness and permeability were less influential.

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final result. Key data, such as the transmissibility multiplier, can be stored (together with all the property values required to develop the result); following modelling, the data can be automatically ranked and the particular percentile result extracted. In this way, the percentile distributions of the final result data can be used for forward flow modelling.

Figure 15 shows an example in which a series of property values have been allowed to vary and the associated TM value on sand–sand windows has been recorded. Although this is a rapid technique and in most situations should provide useful estimates, this approach does, however, have a number of limitations. The first is that, in

Fig. 15. Auto-ranked transmissibility multiplier values for sand–sand window juxtapositions from a 1000 realization simulation. Host clay content, fault clay content to fault rock permeability, and fault throw to fault rock thickness were all allowed to vary. The technique automatically ranked the results for each cell and extracted grids at: (a) P10, (b) P50 and (c) P90, using the same colour scale. The technique highlights the potential range in solutions across the grid. The auto-ranked data can be extracted and taken forward for flow simulation.

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order for the data to be carried forward for flow simulation, the property on the fault has to map directly back to the physical geometry of the geocellular grid. Geometric properties such as the throw or stratigraphic thickness cannot therefore be varied in the calculation and then applied back to the original grid geometry; this is principally because the cross-fault grid connections will change, and these are the critical windows which will control the results of any flow simulation (e.g. Manzocchi et al. 1999). However, a wide suite of property uncertainties can still be modelled and incorporated. These include host and fault rock clay contents, fault rock permeabilities determined via fault rock clay contents, and fault rock thicknesses derived from fault throw data. The second limitation is that the same final percentile result value (e.g. P50 TM) may have developed by combinations of widely differing parameters for neighbouring cells. To develop the result on one cell may, for example, require the clay value to be significantly under-estimated, whereas it may need to be over-estimated on the next. It is thus possible that geologically unreasonable lateral changes would be required to produce the same final result for neighbouring cells. This is a fundamental limitation of conducting multiple scenario modelling on isolated faulted columns (i.e. cell properties are allowed to vary independently from its lateral neighbour) rather than modifying the grid properties for every cell for every realization. Given sufficient numbers of realizations, this problem should be minimized. The scale of the problem can be identified via parameter cell tracking (e.g. see Fig. 14).

Scenario typing – parameter clustering The auto-ranking procedure in conjunction with the unbiased uncertainty incorporation provides a powerful way to determine the range in final solutions possible for a model based on certain input parameters and their uncertainties. One of its limitations is the difficulty in determining the geological combinations that led to the specific solution occurring for all cells across the grid. The individual cell realization tracking technique provides an in-depth means of assessing specific geological controls, but it is prohibitive to apply globally. One method to bridge the gap between these two end-member analysis techniques is parameter clustering. Critical ranges of parameter values can lead to specific results, as highlighted by Figure 14 when high TM values correlate to specific throw ranges. The throw parameter for the result in Figure 14 therefore displays a high degree of increased clustering relative to its total range of variation. This observation can be used to rank the relative controlling

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influences of the different parameters. If the median parameter space values and ratios are computed and incorporated into the grid, then the parameters that show the greatest clustering, and hence influence, can be defined for each fault around the field. These data can then be used to assess the likely uncertainties and the geological sense of such results.

Assessing the impact of the uncertainties of individual parameters As well as defining the general uncertainty within the system, it is useful to assess how different uncertainty parameters affect the final result. This can initially be used to understand the data better, but more powerfully as a tool to identify the largest component of risk and allow data to be gathered in the most effective manner for improving the accuracy of the prediction. Uncertainties defined by Figures 4, 5, 6 and 8 were used to introduce variations in fault throw to fault rock thickness, VShale to clay content, fault rock clay content predictive function (e.g. SGR, ESGR, clay smears), and fault clay to fault permeability, respectively. In this particular example, the host permeability was kept at its original value, but this could also be made uncertain to account for stratigraphic variability. Figure 16 shows the realization results for predicting the TM within one specific cell from a field-scale grid. The central 80% of results derived from the global uncertainties create 5 orders of magnitude variation in the TM prediction for the same input values. Intriguingly, the case with no included uncertainties relates to approximately the 70th percentile result. This indicates that, if the variation observed in the previous relationships is meaningful, then the true TM value should be around 1 order of magnitude lower than that predicted from the global trends. This observation is in accordance with published results of predicted TM values versus flow simulation history matches (e.g. Sperrevik et al. 2002). As well as the base-case model (all uncertainties allowed), the simulations were repeated with the uncertainty in each parameter sequentially removed. The results presented in Figure 16 all show the same general range in uncertainties (approximately 4 –5 orders of magnitude over the central 80%) with a drift from the combined uncertainty case (base-case model) of typically less than half an order of magnitude. This indicates that no single parameter dominates the range in results. Removing errors in either the fault rock clay to permeability content or the SGR to fault rock clay content would indicate a slightly higher flow situation. However, removing the throw to fault

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Fig. 16. Percentile transmissibility multiplier predictions for one cell through 50 different realizations using the global trends and uncertainty ranges documented previously. The graph shows the base-case model (all uncertainties included) together with realizations when uncertainties on one of each of the parameters are removed. Removing the uncertainty from any single parameter has relatively little impact on the overall uncertainty (around 0.5 versus 6 orders of magnitude for the central 90% of the data).

rock thickness uncertainty had no discernible impact, and removing the VShale to clay content uncertainty developed an overly sealing result in comparison to the combined uncertainty basecase model. The data indicate that the scales of uncertainties observed in the published literature have a similar level of impact on the final result, and therefore a better characterization of each of these relationships is important in providing an improvement in the prediction.

Global uncertainties versus locally calibrated examples Incorporating all of the uncertainties defined by the global datasets, derived from the merging of all of the datasets available, produces a vast range in the predicted nature of cross-fault flow, as demonstrated by the example presented in Figure 16. The global uncertainties can therefore produce relatively meaningless results. A significant reduction in specific parameter uncertainties is possible if the samples are better characterized and locally calibrated according to the host and fault geohistory. In order to assess how the level of uncertainty correlates with an improvement in prediction, all of the uncertainties have been reduced by the

same percentage and the realizations corresponding to the combined uncertainty base-case situation of Figure 16 repeated. The results shown in Figure 17 illustrate that there is a dramatic improvement in prediction accuracy as the percentage uncertainty is reduced. When the uncertainty falls to 50% of the original global errors, the TM prediction is within 1–1.5 orders of magnitude of the zero-uncertainty result. This is encouraging since reducing the uncertainties of the different global relationships to apply for specific reservoirs in specific areas by 50% is an achievable goal. The data reinforce the need for locally calibrated datasets for useful cross-fault flow predictions.

Using uncertainty analysis to define the risks of specific issues Rather than conduct a full uncertainty analysis, the ability to vary rapidly and determine the probabilities of different scenarios occurring provides a powerful means of understanding the risks due to different geological factors. Fault throw is a significant uncertainty and, depending on the nature of the stacking sequence and the throw variability, it will have different levels of impact across any particular prospect or field. Figure 18a and c shows the static

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Fig. 17. Transmissibility multiplier ranges taken from a single cell of a field-scale grid. The graph shows the results of 50 realizations with 100%, 70%, 50%, 35%, 10% and 0% of the full global uncertainty values. Note that when the uncertainty falls below 50% of the global uncertainty, the central 80% of the data lie within approximately 1 –1.5 orders of magnitude of the base-case (no uncertainty) result. Also note that the zero-uncertainty case does not cross the other curves at the P50 level. Thus the P50 ‘average’ result, which includes a degree of uncertainty, is not a good approximation of the real ‘zero-uncertainty’ value.

sand –sand window juxtapositions and Fig. 18b and d shows the probability of sand –sand windows occurring based on uncertainty in the throw estimate. The technique identifies areas in which varying the throw will have an impact and what the likely risk is for any particular window subject to that throw variation. This information can be used directly as a risking tool. More powerfully, it allows key areas to be identified for further analysis, and so allows for a better quantification of the geological structure and hence risk. The uncertainty tool should therefore allow initial risk zones to be identified, quantified, and then subsequently better evaluated. A second useful uncertainty analysis procedure is to define the sand –sand windows which are not smeared under the clay smear factor algorithm. By combining throw variations with clay smear calculations (clay smear factors varying according to a Gaussian distribution over a range of 2), the impact of incorporating clay smearing into the juxtaposition analysis can be defined (compare Fig. 19a and c with the static model in Fig. 18a and c). Figure 18b and d shows the sand–sand window distribution colour coded according to its probability of occurring when no clay smear calculation is included, and Figure 19b and d shows the same model but with the above clay smear uncertainties incorporated. A comparison of Figures 18 and 19

shows how the number and size of unsmeared sand –sand windows dramatically changes around the field when the clay smear uncertainty is incorporated.

Discussion and conclusions Currently, the published literature on fault statistics and fault rock properties contains some examples of the critical property relationships required to predict cross-fault flow behaviour. However, the datasets are relatively small considering the global importance of accurate field flow simulation and prospect risking. These datasets all contain significant spread in the data, regardless of how specifically the data are characterized (although greater characterization significantly reduces the spread). In some cases this variability may be measurement related, but in most cases the spread appears to represent natural geological variability. Conducting a fault seal assessment based on single fixed relationships is therefore, by definition, unlikely to capture this natural variability of the system. In certain situations, the median relationship case (as defined by the best-fit trend lines) may be useful (e.g. dominant permeability for flow simulation), but in other situations it may be the extremes that control the result (e.g. lowest

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Fig. 18. (a) 3D view of the fault sand– sand windows, with red and blue distinguishing different sides of the fault as the algorithm sweeps through the grid in the two axis directions. (b) 3D view of the sand–sand window probabilities incorporating throw uncertainty (see Fig. 1b). The colour denotes sand– sand juxtaposition probability. (c, d) show map views of the models (a, b), respectively. Note that if no uncertainty is used then the sand– sand window mapping technique highlights key areas. Incorporating throw uncertainty widens those zones, and in this case potential sand–sand windows occur along the majority of the fault network. Small geometric variations in this model have the potential to develop large impacts on cross-fault fluid flow.

sealing capacity that controls the size of the accumulated prospect column). Geometric property relationships, which are arguably more important (e.g. James et al. 2004) for fault seal analysis, are still less well documented. Data have been presented here that indicate the relative size of the principal slip plane offset to the overall fault zone; this is critical since it partially controls the nature of the local fault juxtapositions. This style of data needs to be enhanced and should incorporate the ductile component of the strain, seismic imaging and reservoir-scale geological modelling factors. Over the last decade in the arena of field flow simulation there has been a general drive to move away from treating faults as either completely

open or closed, to cross-fault fluid flow, and to incorporating more realistic fault rock properties (e.g. Manzocchi et al. 1999; Sperrevik et al. 2002). A significant number of the geological and flow simulation modelling packages allow the fault permeability to be incorporated via transmissibility multipliers (e.g. Roxar RMS, Eclipse–FloViz and Petrel, FAPS/TrapTester and TransGen), but this computation is usually conducted based on global published relationships. The series of structural style and structural geometry parameters that have been utilized in our analyses and which inform on likely juxtaposition uncertainties are currently unavailable in most industry-standard software packages.

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Fig. 19. (a, c) 3D and map views, respectively, of unsmeared sand– sand windows along the faults in the original geocellular model. (b, d) 3D and map views, respectively, of unsmeared sand– sand windows computed with a throw uncertainty of 10 m standard deviation and a clay smear factor uncertainty range of 2 (both Gaussian distributions). The colour denotes sand–sand window probability for the 400 realizations performed.

Applying stochastic modelling techniques to 3D fault seal analyses has proved very powerful, rapid to conduct and relatively easy to implement. This approach has helped to improve mapping, focus interpretation effort, better define geographic risk areas along faults, understand the scale of the risks and uncertainties more accurately, determine the variance in the results due to specific uncertainties and allow the quantification of the quality of the fault seal prediction. The approach has applications both to juxtaposition and fault membrane seal analysis. There are four main tasks involved in undertaking such fault seal uncertainty analyses: (i) characterizing the relationships between observable data and fault seal input; (ii) defining the natural geological uncertainty around that relationship;

(iii) conducting multiple realizations in a manner that honours the data and minimizes statistical aberrations; and (iv) rapidly visualizing and interrogating the results. In this paper, we have identified a number of different approaches that achieve these goals. Conducting multiple stochastic realizations on various fault sealing properties using trends and data ranges defined in the published literature develops results that show massive variances. For example, up to 5 –7 orders of magnitude range in the transmissibility multiplier are predicted from parameter uncertainties based on welldefined, naturally occurring global trends, subject to a constant geometric configuration. This demonstrates that applying global trend relationships

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is likely to lead to very anomalous results. The impact of single-parameter uncertainties has been assessed and indicates that no single-parameter relationship dominates; a reduction in the uncertainty of one single parameter develops a relatively minimal improvement in prediction accuracy. Reducing all of the overall uncertainty ranges by half does, however, create a considerable impact on the prediction accuracy. This level of uncertainty improvement can be achieved if locally calibrated datasets are used in conjunction with globally defined trends. Interestingly, the zero-uncertainty, ‘best-fit’ trend line case, which is the approach used by the majority of geological and flow simulation modelling packages, generates a TM prediction that is typically 1–2 orders of magnitude higher than expected in comparison to the models with the uncertainties incorporated (cross-fault flow rates are predicted to be too high by several orders of magnitude). This observation fits well with the observation by a number of authors that the TM-based flow simulation results were significantly in error (e.g. Sperrevik et al. 2002). Thankfully, reducing the uncertainty range from that of global datasets dramatically improves this prediction. If the uncertainty is reduced to around 35% of the global uncertainty, then the prediction accuracy improves to approximately 1 order of magnitude. Both published and unpublished data indicate that this level of improvement is feasible, but only with very well-characterized field-specific datasets. Utilizing fault-specific geohistory classifiers (see Fig. 1b) in conjunction with geohistoryspecific relationships (e.g. Fig. 3) should allow for the effective implementation of locally calibrated relationships, which consequently greatly reduce uncertainty and hence produce more accurate predictions. In the above analysis, we have highlighted that utilizing the most well-calibrated data is crucial for minimizing the range of solutions. The next stage in the workflow would be to calibrate the predictions against physical observations of hydrocarbon accumulations and/or dynamic data. In areas with less locally calibrated data, a stronger emphasis needs to be placed against such observations of hydrocarbon accumulations and production data. In addition to the sources of uncertainty discussed and modelled in this paper, additional uncertainties arise from the effects of multiphase flow (Manzocchi et al. 2002; Fisher & Jolley 2007), multiple fault strands within the fault damage zone (Harris et al. 2007), and the internal juxtapositions of high/low permeability zones within the fault zone (Fredman et al. 2007). The overall results of this analysis therefore identify that there is a need to develop property

and geometric relational databases that allow field- or prospect-specific property relationships to be defined and calibrated. These data, rather than globally defined trends, need to be utilized if meaningful predictions of cross-fault flow parameters are to be achieved. We would like to thank all the members of RDR Ltd for their input into the development of the software and workflows presented here. We would also like to thank the reviewers, Stephen Dee and John Cole, for their insightful comments; their reviews have helped provide focus for this paper.

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S HIPTON , Z. K. & C OWIE , P. A. 2001. Damage zone and slip-surface evolution over mm to km scales in high-porosity Navajo sandstone Utah. Journal of Structural Geology, 23, 1825– 1844. S HIPTON , Z. K., E VANS , J. P., R OBESON , K. R., F ORSTER , C. B. & S NELGROVE , S. 2002. Structural heterogeneity and permeability in faulted eolian sandstone: implications for subsurface modelling of faults. American Association of Petroleum Geologists Bulletin, 86, 863–883. S PERREVIK , S., G ILLESPIE , P. A., F ISHER , Q. J., H ALVORSEN , T. & K NIPE , R. J. 2002. Empirical estimation of fault rock properties. In: K OESTLER , A. G. & H UNSDALE , R. (eds) Hydrocarbon Seals Quantification. Norwegian Petroleum Society (NPF), Special Publication, 11, 109– 125. T OWNSEND , C., F IRTH , I. R., W ESTERMAN , R., K IRKEVOLLEN , L., H A˚ RDE , M. & A NDERSEN , T. 1998. Small seismic-scale fault identification and mapping. In: J ONES , G., K NIPE , R. J. & F ISHER , Q. J. (eds) Faulting, Fault Sealing and Fluid Flow in Hydrocarbon Reservoirs. Geological Society, London, Special Publication, 147, 1 –25. W ATTS , N. L. 1987. Theoretical aspects of cap-rock and fault seals for single and two phase hydrocarbon columns. Marine and Petroleum Geology, 4, 274– 307. Y IELDING , G. 2002. Shale gouge ratio-calibration by geohistory. In: K OESTLER , A. G. & H UNSDALE , R. (eds) Hydrocarbon Seals Quantification. Norwegian Petroleum Society (NPF), Special Publication, 11, Elsevier, Amsterdam, 1– 15. Y IELDING , G., F REEMAN , B. & N EEDHAM , D. T. 1997. Quantitative fault seal prediction. American Association of Petroleum Geology Bulletin, 81, 897–917.

Realizing complex carbonate facies, diagenetic and fracture properties with standard reservoir modelling software ¨ PPELREITER1, MARIA A. BALZARINI2, BIRGER HANSEN3 & MICHAEL C. PO RONALD NELSON4 1

Qatar Shell Research and Technology Centre, PO 3747, Doha, Qatar (e-mail: [email protected])

2

Shell International E&P, 200N Dairy Ashford, Houston, Texas, 77049, USA 3

Eriksfiord AS, Chausee de Fleurus 6040, Jumet, Belgium

4

Broken N Consulting Inc., 445 Wrangler Road, Simonton, Texas, 77476-1017 USA Abstract: Geocellular modelling of diagenetically altered carbonates is challenging as geometries and pore systems often appear irregular. It has long been recognised, however, that tectonic evolution forms a framework that can influence patterns of carbonate facies, diagenesis and fracturing, the combination of which determines reservoir geometries and properties. Unravelling these processes can reveal trends that were not evident from well data alone. Such trends are useful in building geocellular models that extrapolate reservoir properties along them and can be used for economic screening of undrilled areas. This paper shows how standard reservoir modelling software can be used to model complex geology. In particular, it is shown how a carbonate reservoir model was constructed based on concepts of facies, burial diagenesis, hydrocarbon charge and fracturing. Workflows are discussed that were employed to distribute reservoir properties related to these processes.

The Maracaibo Basin in north-west Venezuela (Fig. 1) is one of the oldest petroleum provinces in the world. One of the key producing intervals is the Cogollo Group (Fig. 1), a deeply buried (5000–6000 m) limestone reservoir. This study concerns the Urdaneta West field, which, in contrast to other Cogollo fields in the Maracaibo Basin, is not a fracture-only play. It produces primarily from grain-dominated beds with secondary (leached) porosity as well as fractures. These pore types created a complex reservoir architecture (Fig. 2) that constitutes the main uncertainty for field development. Wells in the Urdaneta West field only produce at economic rates when they encounter sufficient porosity-height, i.e. leached grainy layers. Thus, the prediction of sufficient matrix porosity is of key economic importance. Average porosities and permeabilities are low, ,3% and ,0.01 mD, respectively (Fig. 3). However, locally, porosities between 10% and 20% and permeabilities in the tens of a millidarcy are common (Fig. 3). These rock properties are significantly higher than would be expected at present burial depths (Scholle & Halley 1985; oral communication P. Wagner 2002; Ehrenberg & Nadeau 2005). This is attributed to the fact that a significant proportion of the pore volume is secondary (vuggy) in nature, probably due to burial diagenesis.

Additionally early hydrocarbon charge of structurally elevated parts of the field might have reduced post-leaching cementation in certain areas and subsequent fracturing might link up ‘matrix sweet spots’.

Geological setting The Cogollo Group, of Aptian to Albian age (Renz 1981), was deposited in the Maracaibo Basin. This basin extended some 50 000 km2 across portions of north-west Venezuela, Peru, Ecuador and Colombia (Castillo & Mann 2006). It was part of the Lower Cretaceous passive continental margin (Vahrenkamp et al. 1993) (Fig. 3). The Cogollo Group in the study area is some 370 m (1200 ft) thick and composed of thin shoal packstones and grainstones (potentially containing matrix porosity) intercalated with thick lagoonal wackestones and mudstones (tight, potentially fractured) (Bartok et al. 1981). Global sea-level rise and greenhouse conditions triggered platform growth over a thin veneer of continental clastics or in some areas directly upon basement rocks. Oscillations of relative sea level led to migrations of the carbonate ramp and development of six large-scale depositional sequences (Azpiritxaga 1991).

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 39–49. DOI: 10.1144/SP309.3 0305-8719/08/$15.00 # The Geological Society of London 2008.

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Fig. 1. (a) Location of the Urdaneta West field in NW Venezuela. (b) Location of the Urdaneta West field at the western margin of Lake Maracaibo. (c) Stratigraphy of the Urdaneta field. Indicated are the main stages of basin development in NW Venezuela and the components of the Cogollo Play.

Database The dataset used in this study includes all available cores and cuttings from the Urdaneta West field. Seismic was re-evaluated, from a reprocessed 3D seismic volume (Fig. 3), with emphasis put on structural features. A detailed and consistent re-evaluation of openhole logs from 56 wells was performed. Furthermore, 17 borehole image logs were re-interpreted focusing on fractures, stress indicators and secondary porosity. This analysis was accompanied by a quick-look study of 14 dipmeter logs as well as rock strength and acoustic measurements from core plugs. Additionally,

detailed basin modelling results were integrated and supported by an extensive literature review. Integrated sedimentologic-stratigraphic, petrophysic and dynamic analyses provided the ingredients for the conceptual reservoir model discussed below (Fig. 4).

Facies and thickness Observations Gross reservoir thickness at Urdaneta West is well constrained by more than 50 well penetrations.

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Fig. 2. The interplay of facies, fault/fracture, fault- and charge-related diagenesis are major factors influencing the complex reservoir architecture and pore structure in carbonate reservoirs diagenetically altered during burial.

Facies distribution is well known from cores, cuttings, openhole logs and borehole image logs at the field crest but poorly constrained at the flanks. Petrographic analysis showed that economically significant porosity is present only in grainy facies, i.e. skeletal packstones and grainstones (Fig. 4) that occur in a cyclic fashion. Stacking pattern controls the vertical occurrence of grainy facies. Thick packages with the highest percentage of grainy layers occur mostly at the transgressive base and the regressive top of medium-scale stratigraphic cycles. Six large-scale stratigraphic cycles were correlated regionally across the carbonate platform for some 300 km using core-calibrated wells. The crosssections revealed an aggradational facies architecture with thin grainstone sheets extending for tens of kilometres (Fig. 5). Cross-sections support observations of earlier workers that packstones and grainstones preferentially occur on palaeohorst blocks (Bartok et al. 1981), suggesting antecedent topography influenced facies distribution (Lomando 1999). Gross reservoir thickness on such palaeohorst blocks is lower compared to palaeograben areas; net reservoir thickness however can be higher. Thickness maps of large-scale stratigraphic units were constructed (Fig. 5). These maps were superimposed on gravity, magnetic and seismic fault

traces. It appears that smaller thickness, particularly in the lower part of the reservoir Apon Formation, corresponds to low gravity and low magnetic susceptibility and seems aligned with NE–SW striking horst blocks (Bartok et al. 1981; Lugo 1991). Cores, cutting logs and outcrop data show a subtle trend of more muddy textures with increasing gross thickness away from horst blocks. Decreasing thickness of large-scale stratigraphic units corresponds to horst blocks with slower subsidence and a higher percentage of grainy shoal beds.

Modelling A layering scheme, based on sequence stratigraphic units, was established that separated layers with specific textures and pore types. The lateral variability within each layer is limited on field scale. A facies model was then built with the two major rock types: grainy, skeletal packstone and grainstone and muddy, tight mudstone and wackestone (Fig. 5). These were distributed stochastically using trend maps. Trends were applied in poorly constrained areas away from current well control. The perceived control of facies by antecedent topography was used as circumstantial evidence to model facies with thickness trends. Thus, the

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Fig. 3. (a) Type section of the Cogollo Group at Urdaneta West. The 370 m thick Cogollo Group is deposited above Lower Cretaceous Rio Negro sandstones. The reservoir is covered by Upper Cretaceous La Luna argillaceous limestones (source rock). The Cogollo limestones are generally tight with three layers with matrix porosity and permeability. (b) Porosity profiles of the uppermost porous layer plotted on a top Cogollo structure depth map (red colours indicate high areas whereas dark blue colors show the structurally deepest areas). Note the large amount of seismically visible faults. Different colours of the fault indicate a different origin of these faults.

Fig. 4. Conceptual model showing the distribution of vuggy pores and fractures in the Cogollo reservoir. The tectonic evolution plays a major role in the development of porosity.

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Fig. 5. Workflow to derive a facies model by integrating local and regional information. (a) Seismic stratigraphy is used to identify and map thicknesses of large-scale stratigraphic units. (b) Gravity and magnetic maps are checked to understand regional orientation and boundaries of major structural units. (c) Well-log correlation of intra-reservoir (Cogollo Group) cycles linked with facies analysis can show syn-depositional thickness and facies trends. (d) Thickness map of intra-reservoir cycle compared to other property maps might reveal common pattern which can be used as circumstantial evidence for field-scale models. (e) The summary of the observations can help to construct more accurate facies trends at field scale.

percentage of grainy textures was gradually decreased with increasing gross thickness (Fig. 5).

Fault-related diagenesis Observations Most porosity was secondary in nature, either biomouldic or vuggy (solution enlarged) that occurred almost exclusively in skeletal packstones and grainstones. Interestingly, vuggy pores were associated with ‘exotic cement phases’ such as baroque dolomite, authigenic kaolinite, and chalcedony (Vahrenkamp et al. 1993). These show a geochemical signature, i.e. salinity, temperature, isotopes, incompatible with the original depositional system. Diagenetic phases, mentioned above, are similar in secondary pores and fractures. This suggests a late burial origin of these pores (Esteban & Taberner 2003). Moreover, elevated secondary porosity in existing wells seems to occur mostly in the vicinity of seismic-scale basement-rooted faults. Secondary porosity along basement-rooted faults (Knipe 1993) is well known from various

reservoirs (Hurley & Budros 1990; Wilde & Muhling 2000; Boreen & Colquhoun 2003; Tinker et al. 2004; Davies & Smith 2006). The geometries of fault-related leaching zones are also documented from outcrop analogue studies (Wilson 1990; Lopez-Horgue et al. 2005). The examples mentioned are possible analogues for the diagenetic alterations at Urdaneta West. Accordingly, corrosive fluids migrated through a sandstone aquifer at the base of the Cogollo Group, the Rio Negro Formation (Fig. 2). The most effective vertical pathways for corrosive fluids are expected to be critically stressed strike-slip faults, fault tips and relay zones (Hickman et al. 2003; see also Fig. 5d). The pre-existing texturecontrolled porosity and permeability network influenced the lateral distance fluids migrated into the formation. Porosity and permeability of diagenetic zones varies laterally from leached/fractured rocks along fault zones with permeabilities of over 100 mD, to lightly leached matrix rocks with maximum permeabilities of a few millidarcies located a few kilometres onto the platform. Width of leached zones can vary from only a few metres

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¨ PPELREITER ET AL. M. C. PO

in tight rocks up to several kilometres in more permeable rocks. Timing of leaching with respect to compaction is critical in creating sufficient secondary porosity. Vertically, the strongest leaching is observed beneath low permeability shales and argillaceous carbonates, which might have hindered ascent of corrosive fluids and forced them laterally into slightly better permeable layers.

Modelling The structural history from the Cretaceous to present day was re-evaluated from a reprocessed 3D seismic volume to characterize faults as possible pathways for diagenetic fluids. Basement-rooted faults were separated from shallow overburden

faults. All Miocene and shallow overburden faults were ignored in terms of the leaching process. Basement-rooted faults were subdivided into Upper Carboniferous (ENE striking), Jurassic (NNE striking) and Eocene (NNW striking) faults, based on seismic stratigraphy and attribute analysis (Galarraga et al. 2005). Leaching corridors were only modelled along basement-rooted faults, which were present during the Eocene, the inferred time of leaching (Fig. 6). The lateral extent of leached rock, i.e. areas of elevated porosity, was modelled as a function of texture, fault length, rugosity, structural history and stress state at the inferred time of leaching. The stress state of all basement-rooted fault zones (Fig. 6) was approximated with a geomechanical workflow following

Fig. 6. Workflow to identify likely leached fault compartments that are suspected to have aureoles with elevated porosities along them. (a) All seismic scale faults interpreted at Urdaneta West. (b) Only basement-rooted faults, which are differentiated according to their origin into Pre-Jurassic (Upper Carboniferous) (pink), Jurassic (black) and Eocene (light blue) faults. (c) Faults are differentiated by stress values (an output parameter of the geomechanical algorithm), which is scaled to relatively high or low likelihood of leaching. (d) Fault intersections, interaction areas and fault top lines, along the basement-rooted faults (compare Fig. 6b) are additional locations of possible leaching.

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Fig. 7. The sequence of figures shows input parameters/results of the geomechanical model used to assess the leaching potential of fault segments. (a) Mechanical stratigraphy built to mimic variable fracture intensity. (b) Rose diagrams (plotted on top Cogollo depth map) showing fracture orientations in the Cogollo from borehole image logs and oriented cores. Dark blue lines show the interpreted orientation of maximum horizontal stress (SHmax). (c) Faults are represented by grid cells in the 3D model. The fault property shown here is fault strike, one parameter for the calculation of stress. (d) Normal stress values calculated at every fault cell. (e) Stress values are scaled to permeability range observed in the existing wells.

Hansen (2002) that resembles the methodology outlined by Akbar et al. (2003) and Wynn et al. (2005). The algorithms were set up directly in the geocellular modelling package, i.e. Petrel (Fig. 7), details of which are discussed in Po¨ppelreiter et al. (2005). The model requires the 3D representation of elastic rock properties, external stress field, and a relationship between stress and fracture permeability. These parameters are derived from regional tectonic knowledge, borehole image logs, density and sonic logs, pore pressure distribution, leak-off tests, laboratory tests, pressure tests and fault orientation (Zoback 2007). The vertical distribution of rock elastic properties was achieved by extending the sequence stratigraphic layering scheme with aspects of a mechanical stratigraphy. Tight layers were separated according to shaliness and thus their likelihood to be fractured (Fig. 7). Shaly units, earlier lumped with tight limestones, were separated out as they might have limited ascent of corrosive fluids, having neither matrix nor fracture permeability. The output of the geomechanical model included normal and shear stress for every fault cell. The ratio of these stresses was used as semi-

quantitative measure for the tendency of a fault to slip (Jaeger & Cook 1979). It was converted into fracture permeability (Bai & Elsworth 1994; Bai et al. 1999), thus representing the likelihood of corrosive fluids to circulate across (Fig. 7). The stress ratio was converted to width of leached zones (Fig. 8) by scaling it to the measured distance of elevated porosities near faults in existing wells. Thus, the width of leaching corridors was varied from 800 m to 2500 m in grainy facies, and a maximum of 200 m in muddy facies. Fault intersections, fault tip areas and relay zones (Fig. 6), particularly prone to migration of diagenetic fluids (Hickman et al. 2002, 2003) were screened using the Poly3D software (Stanford University) to predict likely areas with tensile and shear failure (Bourne et al. 2000, 2001). Selected fault intersections, fault tip areas and relay zones were separately modelled as ‘leaching hot spots’ about 5000 m in diameter. These were added to the leaching corridors described above. Subsequently, matrix porosity models for leaching corridors were created using porosity logs of wells with elevated porosities only. Different stochastic realizations were created.

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Charge-related diagenesis Observations Petrographic analysis showed that some of the secondary porosity (biomouldic, vuggy) in previously leached grainy facies was lost due to cementation, not because of facies change or lack of vuggy porosity. Cementation is commonly observed at structurally low areas of the field while structurally higher parts of the field commonly preserved some pore space in the thickest grainy beds along faults (Bartok et al. 1981). Those shallower areas might be less cemented because of early hydrocarbon charge as discussed for other areas by Marchand et al. (2002) and Wilkinson et al. (2006).

Modelling

Fig. 8. Leaching corridors, i.e. areas with elevated porosities, are modelled along critically stressed, basement-rooted faults in grainy facies.

Charge history and structural evolution at the greater Urdaneta West area were analysed to investigated the possibility of hydrocarbon fill having reduced cementation (Fig. 9). A basin model was used to reconstruct charge history. Results

Fig. 9. Workflow used to model the effect of hydrocarbon charge on porosity distribution pattern. (a) Areas with lower porosities are commonly associated with cemented vugs as observed in cores and cuttings. (b) All possible continuous seismic events are mapped to investigate the structural evolution of top Cogollo. (c) Examples of the reconstructed top Cogollo structural configuration at Middle Eocene and Upper Miocene times (red ¼ structurally shallow, blue ¼ deep); (d) Two arbitrary oil columns (thick and thin) added to the top Cogollo map. Structurally high areas might have experienced less cementation due to early charge. Black dots indicate well locations. (e) Porosity modelling in palaeohigh area as function of height above palaeo-oil –water contact.

REALIZING COMPLEX PROPERTIES WITH RESERVOIR MODELLING SOFTWARE

suggested first hydrocarbon charge occurred during Middle Eocene times (oral communication M. Nosiara 2003). Structural history was reconstructed using nine seismic depth maps of continuous, conformable seismic events. These horizons, ranging in age from Lower Cretaceous to Pliocene, were mapped across the field. The overburden layers were decompacted and the geometry of top Cogollo restored by flattening the individual seismic events. This study showed that an embryonic anticlinal structure started to develop at Urdaneta West from Middle Eocene times onward (Fig. 9). Subsequently, the nine individual depth maps were stacked. An area that remained structurally high through time emerged. An arbitrary oil column was added to the reconstructed top reservoir maps to estimate the extent of early charged structural highs (Fig. 9). Two scenarios, a thin and a thick oil column, were tested to estimate its impact on the extent of hydrocarbon-filled areas. The region with the highest chance of accumulating hydrocarbons, and thus escaping cementation, was located in the southern part of the field. There is a good fit between this persistent structurally high area and the location of wells with better porosity. The outline of this structural high was superimposed on the 3D porosity model of fault-related leaching corridors to separate leached open from leached cemented regions. Subsequently, porosity was modelled with a depth trend superimposed on the fault-leached porosity volume as described above. Porosity was modelled, in the palaeo-high areas, as a function of height above palaeo-oil– water contact (Fig. 9) to represent increasing cementation with decreasing oil saturation.

Fracturing Observations Production at Urdaneta West is dominated by matrix flow but well rates and pressure behaviour suggest the influence of fractures. Cores and image logs indicate fractures occur as unidirectional northwest–south-east striking joints and polydirectional fracture corridors next to faults. The degree of fracturing within individual layers seems to vary with mechanical properties, particularly shaliness (Li & Schmitt 1998).

Modelling Layer-bound unidirectional joints are implemented as directional multipliers. Maps with specific factors for specific layers were used to increase matrix permeability to a level approximating

47

productivity index and well behaviour. Faultrelated fracture corridors (Trice 1999) are represented by specific grid cells. The width of fracture corridors was estimated from seismic semblance maps and image logs. These suggested widths of Jurassic fault zones of about 200 m, while Upper Carboniferous and Eocene faults are approximately 100 m wide. Fault zones were modelled in the geocellular model as discrete corridors represented by grid cells. Fault strike was assigned as a property to those cells (Fig. 7). The ratio of normal and shear stress, calculated from the geomechanical model was used to scale permeability to values similar to those derived from well analysis (Barton et al. 1995).

Results The combination of several factors appears important for creating sufficiently porous zones at the Urdaneta West field. These included: † early texture-controlled porosity-permeability network; † conductive fracture network as conduits for corrosive fluids; † regional aquifers and favourable fluid flow direction for corrosive fluids; † hydrocarbon charge and trap formation; and † layer-bound and fault-related fracture networks. The integrated approach to analysis and modelling of reservoir property provided a tool to represent various property volumes that concur with the conceptual geological model and conform to the observed property patterns in existing wells. Thus, various geological scenarios were tested to estimate the impact on reservoir property distribution. Reservoir models were simulated and history-match was achieved adding confidence in the model results. The models highlighted the southern part of the field as a region with potentially better reservoir properties. These results were used for well planning in this geologically complex carbonate reservoir.

Conclusions 1. Geometries and pore systems of diagenetic zones are often complex and constitute a major uncertainty for field development. 2. Tectonic evolution might provide a template that controlled facies, diagenesis and reservoir property distribution. Its reconstruction may help to better understand and model complex diagenetic zones. 3. Burial diagenesis may be an important factor for porosity creation at the Urdaneta West field.

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4. The extent of porous leaching zones was possibly controlled by the interplay of an early texture control porosity-permeability network, conductive structural conduits, and regional fluid flow via aquifers that transported corrosive fluids as well as hydrocarbon charge and trap evolution. 5. The use of trend maps and simple algorithms permitted the representation of a complex conceptual reservoir model using largely standard geocellular modelling tools. The workflow might assist in field development or exploration activities of diagenetically altered carbonate reservoirs in general. We would like to acknowledge the contributions from our colleagues: A. Dombrowski, S. Engel, M. de Keijzer, X. Marquez, G. Sagasti, P. De Sousa and P. Wagner. The careful review by C. Cleneay improved the initial manuscript and is gratefully acknowledged. Specific comments by reviewers Mark Bentley and Richard Labourdette are very much appreciated, and helped to clarify aspects of the text. We wish to thank Shell Venezuela for their permission to publish this paper.

References A KBAR , A. H., B ROWN , T., D ELGADO , R. ET AL . 2003. Watching rocks change–mechanical earth modelling. Oilfield Review, 2, 22–39. A ZPIRITXAGA , I. 1991. Carbonate depositional style controlled by siliciclastic influx and relative sea level changes, Lower Cretaceous Central Maracaibo Lake, Venezuela. University of Austin, Master Thesis, 151pp. B AI , M. & E LSWORTH , D. 1994. Modelling of subsidence and stress-dependent hydraulic conductivity for intact and fractured porous media. Rock Mechanics and Rock Engineering, 27, 209 –234. B AI , M., F ENG , F., E LSWORTH , D. & R OEGIERS , J.-C. 1999. Analysis of stress-dependent permeability in nonorthogonal flow and deformation fields. Rock Mechanics and Rock Engineering, 32, 195– 219. B ARTOK , P., R EIJERS , T. J. A. & J UHASZ , I. 1981. Lower Cretaceous Cogollo Group, Maracaibo basin, Venezuela-sedimentology, diagenesis, and petrophysics. AAPG Bulletin, 65, 1110–1134. B ARTON , C. A., Z OBACK , M. D. & M OOS , D. 1995. Fluid flow along potentially active faults in crystalline rock, Geology, 23, 683–686. B OREEN , T. D. & C OLQUHOUN , K. 2003. The Ladyfern gas field–Canada is still hiding mammoths. Abstracts AAPG Annual Meeting, 12, A17. B OURNE , S. J., I TA , J. J., K AMPMAN -R EINHARTZ , B. E., R IJKELS , L., S TEPHENSON , B. J. & W ILLEMSE , E. J. M. 2000. Integrated fractured reservoir modelling using geomechanics and flow simulation. AAPG Bulletin, 1395–1518. B OURNE , S. J., R IJKELS , L., S TEPHENSON , B.J. & W ILLEMSE , E. J. M. 2001. Predictive modelling of naturally fractured reservoirs using geomechanics and flow simulation. GeoArabia, 6, 27– 42.

C ASTILLO , M. V. & M ANN , P. 2006. Cretaceous to Holocene structural and stratigraphic development in south Lake Maracaibo, Venezuela, inferred from well and three-dimensional seismic data. AAPG Bulletin, 90, 529–565. D AVIES , G. R. & S MITH , L. B., J R . 2006. Structurally controlled hydrothermal dolomite reservoir facies: An overview. AAPG Bulletin, 90, 1641–1690. E HRENBERG , S. N. & N ADEAU , P. H. 2005. Sandstone vs. carbonate petroleum reservoirs: A global perspective on porosity-depth and porosity-permeability relationships. AAPG Bulletin, 89, 435–445. E STEBAN , M. & T ABERNER , C. 2003. Secondary porosity development during late burial in carbonate reservoirs as a result of mixing and/or cooling of brines. Journal of Geochemical Exploration, 79, 355– 359. G ALARRAGA , M., E NGEL , S. & H ANSEN , B. 2005. Detailed 3D seismic interpretation using HFI seismic data, fault throw and stress analysis for fault reactivation in the Cogollo group, Lower Cretaceous, Urdaneta West Field, Maracaibo Basin. SPE n8 95060. H ANSEN , B. 2002. Geomechanics in 3D. Abstract of talk, Roxar user group meeting, Paris, Abstract volume. H ICKMAN , R. G., K ENT , W. N., O DEGARD , M. E. & M ARTIN , J. R. 2002. Where are the Trenton-Black River hydrothermal dolomite-hosted fields of the Illinois Basin? Abstract of talk, AAPG 31st Annual Eastern Section Meeting, Conference Volume, Champaign, Illinois. H ICKMAN , R. G., K ENT , N. W., O DEGARD , M., H ENSHAW , N. & M ARTIN , J. 2003. Hydrothermal Dolomite Reservoirs. A Play Whose Time Has Come. Abstract of talk, AAPG Annual Convention, Salt Lake City, Abstract Volume. H URLEY , N. F. & B UDROS , R. 1990. Albion-Scipio and Stoney Point fields– U.S.A. In: B EAUMONT , E. A. & F OSTER , N. H. (eds) Stratigraphic Traps I: AAPG Treatise of Petroleum Geology Atlas of Oil and Gas Fields, 1 –37. J AEGER , J. C. & C OOK , N. G. W. 1979. Fundamentals of Rock Mechanics. (3rd edn) New York, Chapman & Hall, 28– 30. K NIPE , R. J. 1993. The influence of fault zone processes on diagenesis and fluid flow. In: H ORBURY , A. D. & R OBINSON , A.G. (eds) Diagenesis and Basin Development. AAPG Studies in Geology, 36, 135– 151. L I , Y. & S CHMITT , D. R. 1998. Drilling-induced core fractures and in situ stress. Journal of Geophysical Research, 103, 5225–5239. L OCKNER , D. A. & B EELER , N. M. 2002. Rock failure and earthquakes. In: L EE , W. K., K ANAMORI , H., J ENNINGS , P. & K ISSLINGER , C. (eds) International Handbook of Earthquake and Engineering Seismology. San Diego, CA, Academic Press, 81A, 505–537. L OMANDO , A. J. 1999. Structural influence on facies trends of carbonate inner ramp systems, examples from the Kuwait– Saudi Arabian Coast of the Arabian Gulf and Northern Yucatan, Mexico. GeoArabia, 4, 339– 360. L OPEZ -H ORGUE , M. A., F ERNANDEZ M ENDIOLA , P. A., I RIARTE , E., S UDRIE , M., C ALINE , B., G OMEZ , J.-P. & C ORNEYLLIE , H. 2005. Fault-related hydrothermal dolomite bodies in Early Cretaceous Platform

REALIZING COMPLEX PROPERTIES WITH RESERVOIR MODELLING SOFTWARE Carbonates. Poster, 10th French Sedimentological Congress. L UGO , J. M. 1991. Cretaceous to Neogene tectonic control on sedimentation: Maracaibo basin, Venezuela. PhD Thesis, University of Texas, Austin. M ARCHAND , M. E., S MALLEY , P. C., H ASZELDINE , R. S. & F ALLICK , A. E. 2002. Note on the importance of hydrocarbon fill for reservoir quality prediction in sandstones. AAPG Bulletin, 86, 1561–1571. P O¨ PPELREITER , M., B ALZARINI , M. A., D E S OUSA , P. ET AL . 2005. Structural control on sweet spot distribution in a carbonate reservoir: Concepts and 3D Models (Cogollo Group, Lower Cretaceous, Venezuela). AAPG Bulletin, 89, 1651– 1676. R ENZ , O. 1981. Venezuela. In: R EYMENT , R. A. & B ENGSTON , P. (eds) Aspects of Mid-Cretaceous Regional Geology. Academic Press, New York, 197–220. S CHOLLE , P. E. & H ALLEY , R. B. 1985. Burial diagenesis: out of sight, out of mind! In: B EAUMONT , E. & F OSTER , N. H. (eds) Reservoirs III. Treatise of Petroleum Geology Reprint Series, 5, 294–319. T INKER , S. W., C ALDWELL , D. H., C OX , D. M., Z AHM , L. C. & B RINTON , L. 2004. Integrated reservoir characterization of a carbonate ramp reservoir, South Dagger Draw Field, New Mexico: seismic data are only part of the story. In: E BERLI , G., M ASSAFERRO , J. L. & S ARG , J. F. (eds) Seismic Imaging of Carbonate Reservoirs and Systems. AAPG Memoir, 81, 91– 105. T RICE , R. 1999. Application of borehole image logs in constructing 3D static models of productive fractures in the Apulian Platform, Southern Apennines. In: L OVELL , M., W ILLIAMSON , G. & H ARVEY , P. (eds) Borehole Imaging; Applications and Case

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Histories. Geological Society, London, Special Publications, 159, 155–176. V AHRENKAMP , V. C., F RANSSEN , R. C. W. M., G RO¨ TSCH , J. & M UNOZ , P. J. 1993, Maracaibo Platform (Aptian-Albian), northwestern Venezuela. In: S IMO , J. A. T., S COTT , R. W. & M ASSE , J. P. (eds) Cretaceous Carbonate Platforms. AAPG Memoir, 25, 25–33. W ILDE , A. R. & M UHLING , P. 2000. Comparison between the Lennard Shelf MVT Province of Western Australia and the Carlin Trend of Nevada: Implications for genesis and exploration. In: C LUER , J. K., P RICE , J. G., S TRUHSACKER , E. M., H ARDYMAN , R. F. & M ORRIS , C. L. (eds) Geology and Ore Deposits 2000: The Great Basin and Beyond. Geological Society of Nevada Symposium Proceedings, 769– 781. W ILKINSON , M., H ASZELDINE , S. R. & F ALLICK , A. E. 2006. Hydrocarbon filling and leakage history of a deep geopressured sandstone, Fulmar Formation, United Kingdom North Sea. AAPG Bulletin, 90, 1945–1961. W ILSON , E. N. 1990. Dolomitisation front geometry, fluid flow patterns, and the origin of massive dolomites: The Triassic Latemar buildup, northern Italy. American Journal of Science, 290, 741– 796. W YNN , T., B ENTLEY , M., S MITH , S., S OUTHWOOD , D. & S PENCE , A. 2005. In situ stress properties in reservoir models. In: The Future of Geological Modelling in Hydrocarbon Development. Meeting abstract volume, 154. Z OBACK , M. D. 2007. Reservoir geomechanics: earth stress and rock mechanics applied to exploration, production and wellbore stability. Cambridge University Press.

Assessing structural controls on reservoir performance in different stratigraphic settings J. TVERANGER1, J. HOWELL1, S. I. AANONSEN1, O. KOLBJØRNSEN2, S. L. SEMSHAUG1, A. SKORSTAD2 & S. OTTESEN3 1

Centre for Integrated Petroleum Research, University of Bergen, Alle`gaten 41, N-5007 Bergen, Norway (e-mail: [email protected]) 2

Norwegian Computing Centre, PO 114 Blindern, N-0314 Oslo, Norway 3

Statoil, Forus, N-4035 Stavanger, Norway

Abstract: The present study attempts to qualify the impact of tectonic parameters on hydrocarbon production in reservoir models representing four clastic depositional environments. Eleven sectors from existing 3D reservoir models, representing fluvial, tidal, shallow marine and deep marine depositional settings, were re-sampled into a fixed-volume, unfaulted model grid. Each sample was permutated into 73 different faulted model configurations by using predefined combinations of fault patterns, maximum fault-throw, shale gouge ratio and shale smear factor. The resulting 803 models were run in a fluid flow simulator and results statistically analysed to identify changes in fluid flow response caused by changing model input parameters. Finally, outcomes for each of the four depositional environments were compared. Although an inadequate database and technical limitations with the input models restrict our ability to draw quantitative conclusions, a number of qualitative interpretations can be made. The four investigated stratigraphies respond differently to identical fault parameter settings. Thus, there is a clear link between the depositional model input and the impact that faults have on production parameters. This suggests that sedimentological factors have a significant influence on which and to what extent fault parameters affect petroleum production. Varying degrees of impact can be identified for each fault parameter in each of the four depositional model types. Within the limitation of this study, a qualitative assessment of these is formulated.

Fault properties play a key role in controlling entrapment and movement of hydrocarbons in the subsurface, during both migration and production (Bouvier et al. 1989; Harding & Tuminas 1989; Knipe et al. 1997; Gauthier & Lake 1993). Characterization of structural heterogeneities, in terms of their spatial distribution and properties (hereinafter referred to as fault parameters), should therefore be an integral part of any detailed reservoir simulations of a faulted reservoir (Knipe et al. 1997). Fault property modelling, and thereby also simulated production performance of faulted reservoirs, is commonly performed using a combination of established modelling parameters. Previous work on reservoir response to changes in fault parameters has shown the following to be important: (1) sedimentary facies; (2) density of faults; (3) choice of fault seal algorithm; and (4) the relationship between the clay content of the fault and its permeability (Ottesen et al. 2003). However, at present, there is a lack of comparative studies of production performance in different depositional architectures subjected to identical tectonic deformation, although research into the subject is on the increase (Lescoffit & Townsend 2005; Ottesen

et al. 2005). The present study contributes to that effort by investigating the combined effects of fault parameters and depositional architecture using a new workflow. A series of predefined, deterministic fault parameter settings were implemented in reservoir models of identical size, representing four different depositional environments – deep marine, shallow marine, fluvial and tidal – sampled from existing reservoir models of producing oilfields and outcrop analogues. Fluid flow simulation of all model permutations was carried out and results analysed statistically to identify how changing fault parameters influence production response in each of the four depositional settings. The number of parameters and model permutations involved in a study of this kind impose certain limitations on model size and grid resolution if CPU-cost is to be kept within limits. The reservoir and outcrop models which were sampled displayed wide variety in terms of resolution and details included. Only some of the reservoir and outcrop models used as input included high resolution data. For our study, all samples were rescaled to an identical resolution of 50 m  50 m  0.3 m, which allows capture of general architectural

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 51–66. DOI: 10.1144/SP309.4 0305-8719/08/$15.00 # The Geological Society of London 2008.

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stacking patterns, but is insufficient to include detailed sedimentary structures. Thus, although the chosen resolution is representative for producing fields, effects caused by finer-resolution sedimentary structures are not the subject of this study. Our simulations are limited to testing scenarios of water flooding of an oil-filled reservoir.

Methods and tools Three software modelling tools were utilized: IRAP-RMSTM 7.2 for geomodelling and sampling procedures; HAVANATM (Hollund et al. 2002) for modelling fault configurations and properties, and ECLIPSE 100TM for fluid flow simulation. The statistical analysis was performed using SplusTM 6.0. The chosen work procedure involved four steps which can be summarized as follows: (1) Sampling of facies and petrophysical data from unfaulted sectors of 11 existing 3D reservoir model realizations (representing fluvial, tidal, shallow marine and deep marine depositional settings) into an unfaulted grid with fixed size; (2) Generating a series of structural model cases with varying complexity by combining deterministic parameter values for fault density/fault patterns, maximum throw, shale gouge ratio (SGR) curves (Yielding et al. 1997) and shale smear factor (SSF) values (Lindsay et al. 1993) and combine these with the sampled lithologies; (3) Simulating the resulting models in a reservoir fluid flow simulator while keeping well positions and sampled lithological parameters (see below) fixed for all model runs. Eight production parameters (listed below under fluid flow simulation) were monitored; and (4) Performing a statistical analysis of parameter input and simulation results to isolate the impact of fault pattern complexity, throw, SGR and SSF on each of the eight monitored production parameters for each of the 11 sampled model realizations.

Sampling procedure A number of existing RMSTM models, including both actual subsurface reservoirs and onshore analogues and representing fluvial, tidal, shallow marine and deep marine depositional environments, were made available for sampling (Table 1). The models exhibit a range of model-building techniques and grid resolutions, ranging from simple, low-resolution models with few facies and constant petrophysical values (like sample DeMa1, Table 1), to highly sophisticated, high-resolution models with complex petrophysical model setups (like sample Tid2). The two onshore analogue models (ShMa1 and Tid1) did not initially include petrophysical data. Synthetic petrophysical models had to be generated for these two models. The petrophysical model for ShMa1 was set up using an existing general database for petrophysical properties of shallow marine facies. Tid1, on the other hand, utilizes the same petrophysical model setup as Tid2. Two of the samples (Flu2 and Flu3) are derived from the same model setup but picked from two different model realizations. Clearly, the sample population forms a highly varied platform for this study; the effects of this will be discussed later. To transfer facies and petrophysical parameters from the chosen 11 model realizations to a common format, a fixed volume (1500 m  1000 m  30 m) from each realization was sampled into a similarsized, unfaulted, unrotated grid here termed the ‘BASE-grid’. The top surface of the BASE-grid slopes gently from 1997 m TVD msl in the north to 2168 m TVD msl in the south. The bottom of the grid is parallel to the top but positioned 30 m deeper. Resolution of the BASE-grid was fixed at 50 m  50 m  0.33 m (i.e. 30  20  90 cells for the full model), yielding a total of 54000 cells. RMSTM 7.2 required the rescaling procedure to be separated into a ‘horizontal’ and a ‘vertical’ step. Thus, allowing the operator to perform quality

Table 1. List of geological model realizations used as input Depositional setting

Sample

Comment

Deep marine

DeMa1 DeMa2 ShMa1 ShMa2 ShMa3 Tid1 Tid2 Tid3 Flu1 Flu2 Flu3

Offshore field model. Constant petrophysical values for each facies Same model as DeMa 1. Stochastic petrophysical realization Onshore analogue, synthetic petrophysical data Offshore field model Offshore field model Onshore analogue, petrophysical data from Tid2 model Offshore field model Offshore field model Offshore field model Offshore field model Same model as Flu2 but different model realization

Shallow marine Tidal Fluvial

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control and check for inconsistencies during each step of the rescaling. Resampling was therefore performed in three steps: (1) Identify a volume in the model realization (1500 m  1000 m  30 m) containing depositional architectural elements typical for the sedimentary environment represented by the model; (2) Generate an unrotated grid with 50 m  50 m horizontal resolution conforming to, and having the same vertical resolution as, the input model in the chosen position, and perform a ‘horizontal rescaling’ from the input model into this grid; and (3) Generate a new unrotated grid with 50 m  50 m  0.33 m resolution in the same position and perform a ‘vertical rescaling’ from the previous grid into the new grid before transferring the sample to the actual BASE-grid using ijk-indexing. Both facies and petrophysical parameters for all models were sampled using this procedure. All continuous parameters were rescaled using arithmetic averages.

Depositional model parameters The following 3D model parameters were needed to perform the intended study using the software tools listed above: porosity (PORO), permeability in x, y and z (PERMX, PERMY, PERMZ), shale volume fraction (VSHALE), and a simplified facies parameter (FACIES) differentiating between ‘sand’ (0) and ‘shale’ (1). Parameters for porosity (PORO) and horizontal permeability (PERMX) were available for most models. The ‘missing’ parameters had to be estimated using the available petrophysical parameters and the parameter for sedimentary facies. In some models, a Vshale parameter had been generated based on a Vshale log; however, this is not a standard procedure when building a reservoir model, and of the RMSTM models used in the present project, only three realizations included this parameter. To generate a Vshale parameter in a consistent way, Vshale mean values and standard deviations were specified for each sedimentary facies in the sampled realizations (Table 2). These values were used as input to the transformation functions in the petrophysical modelling module of RMSTM, to produce a stochastic realization for the VSHALE parameter. Upper and lower cut-off values for Vshale were specified as 0.7 and 0.1 respectively. These petrophysical jobs were run on the resampled BASE models and not on the original input models. Final mean values for porosity, permeability, Vshale, Havana FACIES and Net/Gross for the 11 samples are listed in Table 3; comparative

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cross plots of the BASE models are shown in Figure 1.

Fault modelling The fault modelling tool HAVANATM (Hollund et al. 2002; Holden et al. 2003) was used to superimpose 72 different combinations of the deterministic fault parameter values described below onto the 11 BASE-models (Fig. 2). Four model parameters were chosen and assigned two or three sets of predetermined values: (1) fault density/fault patterns – three different deterministic cases (see details below); (2) maximum throw – two cases: 20 m and 35 m; (3) Shale Smear Factor (SSF) – four cases: 0, 3, 5 and 7; and (4) shale gouge ratio to fault permeability transform – three cases/curves: ‘High’, ‘Low’ and 0. This yields a total of 72 different combinations of structural parameter values/structural cases in addition to the unfaulted BASE case. The values for each fault modelling input parameter are detailed below. All deformation structures used here are normal faults.

Fault density and maximum throw Three deterministic, synthetic fault patterns representing different degrees of fault density and increasing complexity were defined (Figs 2 and 3). These, in principle, represent fault data derived from seismic interpretations with increasing levels of resolution. The first contains six ‘large’ Parametric Fault Model (PFM) faults, the second includes the same six large faults plus a further 11 ‘medium’ PFM faults. The third case includes the 17 medium and large faults plus 50 ‘sub-seismic faults’. ‘Large fault’ is in the present context used to specify faults with a displacement greater than 15 m (i.e. half of BASE model thickness). The ‘subseismic’ faults have an average displacement of about 2 m. They have no geometrical expression in the grid, but their impact on fluid flow is captured by using transmissibility multipliers as described in Manzocchi et al. (1999). Dips of all faults vary around 60 degrees, except for the three N –S trending ‘large faults’ which are close to vertical. The ‘maximum throw’ parameter for the faults was set at either 20 or 35 m; the latter implies nonjuxtaposition of the model interval across the fault at its position of maximum throw. The three fault patterns and the two alternatives for maximum throw were combined to generate six different structural combinations which in the present context are termed ‘faultsets’ and treated as one fault parameter in the statistical analysis.

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Table 2. List of facies in the input models, and their estimated and calculated mean Vshale values and standard deviations (std). The Vshale numbers for facies marked with * were calculated from actual Vshale logs when these were present in the model. Values for the other facies are estimated. The column to the right marked ‘HavanaTM FACIES’ indicates if a facies is classified as ‘sand’ (0) or ‘shale’ (1). This parameter is used as input to the fault modelling in Havana. Not all listed facies for one depositional environment occur in the same model RMSTM facies

Vshale

std

HavanaTM FACIES

Hemipelagic Overbank Sheet sandstone Channel Background Cemented Coal Upper shoreface Lower shoreface Offshore transition zone Tidal and floodplain fines Upper to lower shoreface Marginal marine Meander Trough X-bedded Mudfilled Mixed Sandy Subtidal Soil Shellbed Bayfill Cemented Tidal channel sand* Heterolithic channel sand* Mudfill* Mixed tidal flats* Subtidal flats* Bayfill* Sandy* Cemented Tidal mud flats* Tidal sand bar* Tidal mouth bar* Tidal channel sand* Channels* Crevasse* Floodplain* Bay mudstone Background_1 Background_2 Background_3 Cemented

0.7 0.4 0.25 0.1 0.3 0.1 0.1 0.1 0.3 0.5 0.6 0.25 0.1 0.2 0.1 0.5 0.4 0.3 0.3 0.5 0.1 0.6 0.1 0.15 0.2 0.5 0.4 0.3 0.6 0.3 0.1 0.7 0.3 0.3 0.2 0.2 0.44 0.6 0.7 0.3 0.5 0.5 0.1

0.05 0.1 0.1 0.05 0.25 – – 0.05 0.2 0.1 0.05 0.2 0.05 0.05 0.05 0.1 0.1 0.1 0.05 0.1 – 0.1 – 0.05 0.1 0.1 0.1 0.05 0.1 0.1 – 0.1 0.1 0.1 0.1 0.16 0.2 0.1 0.1 0.2 0.2 0.15 –

1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0

Depositional model Deep marine

Shallow marine

Tidal

Fluvial

Fault sealing parameters HAVANATM calculates fault permeability based on lithology and fault displacement using the concepts of Shale Smear Factor (SSF) and Shale Gouge Ration (SGR). SSF is defined as the ratio of fault displacement to shale layer apparent thickness (i.e. measured along the fault trace) and is used to

define where on the fault plane the shale smear is estimated to be continuous. In the present project, SSF cut-off values of 0, 3, 5 and 7 were used, which implies that a given shale layer generates a continuous smear along the fault plane equalling 0, 3, 5 or 7 times the apparent thickness of the shale layer. SGR is an estimate of the shale or clay content in a fault zone. Measurements of cored fault properties

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Table 3. Mean values for porosity, permeability (in three dimensions), Vshale, net:gross, and Havana Facies in the 11 samples from different depositional environments. Permeability values are in millidarcies; all other numbers are given as fractions. Where PERMZ was not present in the input model, this was estimated by using a copy of PERMX multiplied by a factor of 0.1. Cut-off value for net:gross was set at 25 mD. See also Figure 1 Model

Porosity

PERMX

PERMY

PERMZ

Vshale

N/G

Havana Facies

DeMa1 DeMa2 ShMa1 ShMa2 ShMa3 Flu1 Flu2 Flu3 Tid1 Tid2 Tid3

0.281 0.155 0.140 0.260 0.288 0.260 0.092 0.070 0.259 0.280 0.239

337.829 216.508 183.901 1672.700 572.602 740.601 39.680 28.665 332.072 755.163 61.544

337.829 216.508 183.901 1672.700 572.602 740.601 39.680 28.665 332.072 755.163 61.544

33.78 21.65 13.362 867.262 389.439 228.323 3.968 2.866 33.207 72.431 9.025

0.335 0.328 0.289 0.276 0.225 0.540 0.425 0.475 0.306 0.289 0.446

0.90 0.64 0.64 0.61 0.90 0.62 0.23 0.17 0.94 0.95 0.57

0.581 0.851 0.488 0.444 0.719 0.997 0.594 0.693 0.320 0.335 0.486

show a relationship between fault permeability and clay content (Fisher & Knipe 2001). Different fault permeability/SGR curves are used as input to fault transmissibility calculations. The fault permeability/SGR curves used here are the same as those employed in the sampled original reservoir models; for the two onshore analogues, curves were chosen from models with similar depositional environments. Two cases/curves were employed in

the test: ‘High’ and ‘Low’, differing by two orders of magnitude. All SGR values are listed in Table 4.

Fault property modelling The sampled petrophysical data were exported from the BASE grid to separate files (.PERM .PORO .FACIES .VSHALE). The BASE grid (.GRDECL) was also exported from IRAP-RMSTM into the

Fig. 1. Cross plots of parameter bulk values for the 11 samples. There is a clear overlap of properties between samples from the different depositional settings. PERMX values are given in millidarcies; Vshale and Porosity as fractions.

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Fig. 2. Flow chart showing the combinations of fault parameters for the different structural cases. The final cases are labelled according to configuration: [fault pattern; 1, 2 or 3]-[max. throw; 20 or 35]SGR[0, 2 or 1]SSF[0, 3, 5 or 7].

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Fig. 3. Fixed PDO used in the fluid-flow simulations. Producers and injectors are vertical. All three fault patterns are indicated (cf. Fig. 2).

HAVANATM modelling directory. Using the HAVANATM RunSum Action module, which allows running the different fault-seal parameter combination together in one single run, HAVANATM provided a series of 72 structural cases, each including a faulted grid and fault transmissibility multipliers, for each of the 11 samples. These files were exported to ECLIPSETM and used as input to the fluid-flow simulations. No upscaling was performed; the simulations were run using the same resolution as the BASE grid. All structural cases and their combinations of fault parameter settings are shown in Figure 2.

Fluid flow simulation The simulations were run using a fixed Plan for Development and Operation (PDO) consisting of two vertical water injectors and three vertical oil producers (Fig. 3), all perforated throughout the

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full reservoir thickness. Model volume was set as initially oil-filled with a reference pressure of 200 bar at 2000 m TVD msl. One set of relative permeability curves and one capillary pressure curve was used for all models. Viscosity of oil was varied following a linear function from 2.313 cp at 202.7 bar reservoir pressure to 2.940 cp at 377.7 bar reservoir pressure. Viscosity of water was kept constant at 0.38 cp. Production and injection were balanced to maintain a BHP in the producers of 150 bar. Simulations were terminated after 7200 days or when water-cut reached 90%. The following eight production parameters were monitored: † Time to end (i.e. 90% water cut). † Time to water breakthrough (WBT). † Time to 1 Movable Pore Volume (MPV) injected. † Recovery at end of production (90% water cut). † Recovery at WBT. † Recovery at 1 MPV injected. † Cumulative production at 10 days. † 10% discounted production. Simulation outcomes for all runs are shown in Figure 4.

Statistical analysis The objective of the statistical analysis was to identify how the different fault factors contribute to the total variability in the monitored production variables. Total variability of the data is split into the variance components that are caused by the fault factors and their interactions. The variance components were estimated using the Restricted Maximum Likelihood method (REML) (Corbeil & Searle 1976); uncertainty bounds were assessed using parametric bootstrap with Gaussian variance components; see Appendix A.

Table 4. Fault permeability for different values of SGR as used in this study.Values in millidarcies. The SGR curves are those originally used in the sampled reservoir models. Values for the two onshore analogues Tid1 and ShMa1 are taken from Tid2/Tid3 and ShMa3 respectively. Numbers in brackets refer to indices used when labelling the structural cases (cf. Figure 2) SGR

0 10 14 20 30 40 100

DeMa1, DeMa2, ShMa2

Flu1, ShMa1, ShMa3

Tid1, Tid2, Tid3, Flu1, Flu2

High (2)

Low (1)

High (2)

Low (1)

High (2)

Low (1)

1000 500 100 1 0.01 0.000011 0.000010

10 5 1 0.001 0.000011 0.000011 0.000010

100 50 10 0.1 0.001 0.000011 0.000010

1 0.5 0.01 0.0001 0.000012 0.000011 0.000010

1 0.5 0.3 0.1 0.001 0.000011 0.000010

0.01 0.005 0.0003 0.0001 0.000012 0.000011 0.000010

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Fig. 4. Simulation results for all cases listed in Figure 2. The plots show results listed from unfaulted (BASE) to the left to most complex (3-35SGR1SSF7) to the right. Simulation results for any given parameter were used to estimate variance components. The set of estimated variance components defines the statistical model that is the best guess for the model which generated the data. Note: The extreme responses in sample Flu1 are probably caused by non-representative sampling into the BASE grid resulting in a very high proportion of shale (see also Fig. 1).

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Fig. 4. (Continued).

Variance components In the statistical analysis, it is natural to use variance components, since these are additive. This approach estimates how much the fault factors and their interactions contribute to the

total variability. Let Y denote a production variable and A, B and C denote fault factors. A production variable is a function of all these three factors defined through the flow equations, i.e. Y ¼ K0 þ K(A, B, C), with K0 being the average level and the complex function K(A,B,C) representing the

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total variability around this level. When the total variability is split into variance components, this corresponds to splitting the total response into orthogonal functions, that is: K(A,B,C) ¼ KA (A) þ KB (B) þ KC (C) þ KAB (A,B) þ KAC (A,C) þ KBC (B,C) þ KABC (A,B,C) with KA(A), KB(B), and KC(C) denoting main effects of the fault factors; KAB(A, B), KAC(A, C), and KBC(B, C), second order interactions between fault factors; and KABC(A, B, C) third order interactions. In this context, the variance component is the squared magnitude of the corresponding function. The main effect of A is thus kKAk2; correspondingly, the interaction effect between A and B is denoted as kKABk2 etc. In the current context, the term KABC(A, B, C) is denoted a residual term because it includes the variability that remains after all lower order interactions are taken into account. In a traditional statistical setting, the residual term also include effects of unobservable factors, i.e. observation noise. In the current experimental design, all factors are controlled in the computer experiment and hence only the third order interactions remain in the residual term. The total variance is the sum of the variance components, i.e. for a three factor case: kK k2 ¼ kKA k2 þ k KB k2 þ kKC k2 þ kKAB k2 þ kKAC k2 þ kKBC k2 þ kKABC k2 The total variance of a production variable is obtained when all factors are allowed to vary freely. The variance component caused by one factor equals the decrease in variance when this factor is kept fixed. If two factors are fixed, the decrease in variance is generally larger than the sum of the two due to the second order interaction. Variance component due to a higher order interaction is defined as the additional reduction when the lower order interactions are subtracted. If one factor is allowed to vary and all other factors are kept fixed, the observed variance equals the effect of this factor plus the effect of all higher-order interactions that include this factor. When levels are compared and reported, it is natural to use the standard deviation since this is at the same scale as the production variable. The relative standard deviations are reported, i.e. kKAk/kKk etc.

Results and interpretation Simulation results are shown in both parts of Figure 4. Simulation parameters show a wide spread of outcomes when identical fault parameter combinations are applied, even for samples from the same group of depositional environments. This spread is larger than the observed variations caused by changing the fault parameters for the individual models, and shows that simulation responses in this study are mainly controlled by the choice of sedimentological/petrophysical input parameters with structural parameters playing a secondary role. This suggest that the potential shortcomings related to the procedure used when sampling facies and petrophysical data from existing models should be kept in mind. (1) Non-uniformity of input model formats for sampling. The models, even within the same category of depositional environments, had generally been built by different people and for differing purposes, using a plethora of grid orientations/resolutions, various facies subdivisions and different level of detail and complexity as to petrophysical model setup. All these factors had to be adapted and accommodated when resampling into the BASE grid to obtain a common format, but an unwanted, unquantifiable, case-specific bias probably still remains; (2) Size of the BASE (sampling) grid: ‘Typical’ elements of a given depositional architecture in the input models in some cases exceeded the size of the BASE grid, thus making it difficult to find an optimal place to pick a representative sample; and (3) Size of the input model population: In hindsight, too few samples were used for each depositional environment. This, combined with the sometimes large spread in simulation responses for models within one category of depositional environments, makes any firm quantification of differences between the four depositional environments statistically untenable. The stated shortcomings, which all impact on how representative a given sample may or may not be for a given depositional environment represented at the chosen scale of modelling, influenced our decision to approach the interpretation of the final results qualitatively rather than quantitatively. This was done in order to avoid presenting misleading absolute measures of ‘difference’ based on a too low and too heterogeneous number of cases. Plots of variance components and averaged variance components were generated for each combination of monitored simulation parameter and fault model input parameter (Figs 5 and 6). In simple terms, these plots show the estimated effect that a given fault parameter has on a specific

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Fig. 5. Variance component plot after completing step four of the bootstrap; here exemplified by fault parameter variance components to ‘recovery at end’ for all models. Coloured areas indicate the 80% confidence interval for a given fault factor and combinations along the x-axis; black bars indicate the 50 percentile. In simple terms, high values for relative standard deviation indicate that a fault factor or fault combination have a high impact on simulation outcomes.

simulation parameter outcome in each of the four depositional environments. High values on the Y-axis reflect high impact; zero or low values reflect low or no impact. In the plots, estimated effect is shown as black lines. The coloured error

bars show the P10-P90 interval reflecting the estimate uncertainty. Considering the large spread of responses within the different depositional environment groups, an aggregate measure of the variance components

Fig. 6. Variance components averaged for each depositional environment; exemplified by the simulation parameter ‘Recovery at end’.

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should provide a very robust method for highlighting any differences between them. However, it should be kept in mind that the number of samples for each environment is low and that extreme responses in one of these samples may bias the results (Fig. 5). For a qualitative assessment, Y-axis cut-offs for estimated values of the averaged variance components were set at 0.1 and 0.3, implying that if a fault parameter for a given depositional environment has an estimate between 0.1 and 0.3, it is considered to have an ‘impact’ on the monitored simulation parameter outcome; if above 0.3, it is considered to have a ‘significant impact’, and if lower than 0.1, ‘no impact’ (Table 5). These cut-off values were chosen subjectively based on an overall consideration of the estimates, which for most cases were very low due to a small sample population and large spread in outcomes for each depositional environment modelled. A straightforward way of synthesizing the results from Table 5, in order to qualify the

degree of impact a certain fault parameter has on simulation outcomes in general, is to generate an ‘impact index’. The impact index is simply the number of monitored simulation parameters that are affected by a specific fault parameter. From Table 5, ‘impact’ is counted as 1, ‘significant impact’ is counted as 2 and ‘no impact’ is counted as 0. This gives a maximum score of (8  2 ¼ 16) for a specific fault parameter if it influences all simulation parameters ‘significantly’. This index can be easily plotted for each fault parameter and depositional environment as shown in Figure 7. The qualitative impact index allows us to rank the fault parameters according to their effect on overall production performance in the four depositional environments. Another simple qualitative way of summarizing Table 5 is to count the number of fault parameter/ fault parameter combinations affecting any of the eight simulation parameters. This ‘Sensitivity index’ count is performed in a way similar to the

Table 5. Qualitative assessment of fault parameter impact on simulation parameter outcomes. Fault parameters influence is split into ‘impact’ (marked by ‘x’ in the table) and ‘significant impact’ (marked by ‘XX’) See text for definitions. Note that the fluvial models produced beyond the time limit of 7200 days, implying that the results for ‘Time to End’ were not obtained for the fluvial models

Shallow marine Faultset SGR SGR þ Faultset SSF SGR þ SSF SSF þ Faultset Deep marine Faultset SGR SGR þ Faultset SSF SGR þ SSF SSF þ Faultset Tidal Faultset SGR SGR þ Faultset SSF SGR þ SSF SSF þ Faultset Fluvial Faultset SGR SGR þ Faultset SSF SGR þ SSF SSF þ Faultset

Time to end

Time to WBT

Time to 1 MPV inj.

x x x

x x

x x x

XX x

x XX

x x

XX

Recovery at abandonment

XX

Recovery at 1 MPV inj.

Prod. at 10 days

Production; 10% discounted

x x

x XX x

x XX

x x

x

x

x

x x

x

XX

Recovery at WBT

XX

XX x

XX

XX

x

XX

x

XX x XX

XX

x x

x

x

x x

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Fig. 7. Comparison of impact indices between the four depositional environments. The impact index gives a relative measure of how the different fault parameters influence simulation outcomes in the four different depositional environments in general. The impact index is a simple, weighted count based on Table 5 of how many of the eight simulation parameters are affected by a specific fault parameter or parameter combination.

impact index described above by counting ‘impact’ as 1 and ‘significant impact’ as 2 and ‘no impact’ as 0. The resulting plots for each depositional environment are shown in Figure 8. The impact and sensitivity index (Figs 7 and 8) highlights contrasting responses between the four depositional environments in qualitative terms: Shallow marine systems: Faultset and choice of SGR permeability transform are the most important fault parameters influencing production behaviour. Impact of structural factors on production response is limited to time-dependent variables and recovery at WBT.

Deep marine systems: All fault parameters influence one or more simulation parameters, with faultset and choice of SGR permeability transform being the most important. Changing the faultset parameter causes a significant response on ‘Time to WBT’ and a less-pronounced response for ‘Recovery at end of production at 10 days’. Changes in SGR strongly affect ‘Recovery at end of production’ and ‘Recovery at WBT’. Lesspronounced effects of SGR were recorded for ‘Time to end’, ‘Time to 1 MPV injected’, ‘Recovery at 1 MPV injected’ and ‘10% discounted production’.

Fig. 8. Comparison of sensitivity indices between the four depositional environments. The sensitivity index is a weighted count, based on Table 5, of how many of the six fault parameter/parameter combinations affect a specific simulation parameter. ‘Impact’ in Table 5 is counted as 1; ‘Significant impact’ is counted as 2.

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Tidal systems: Choice of SGR permeability transform is by far the most important fault parameter. Changing SGR has a significant effect on all the monitored production parameters. Impact of varying SSF is limited to ‘Time to 1 MPV injected’. Changing the faultset only affects production behaviour marginally. Fluvial systems: The fluvial models produced beyond the maximum simulation time of 7200 days, without reaching 90% water-cut, imply that the responses of the time-dependent production parameters, except ‘Cumulative production at 10 days’, cannot be evaluated. Responses of the other monitored production parameters are dominated by a combination of SGR and SSF, which show a high impact on ‘Recovery at end of production’ and ‘Recovery at 1 MPV injected’. Changing faultset had only minor impact on simulation responses. It should be emphasized that due to the limitations of the present study as described above, the general validity of these results should be treated with caution pending further testing.

This appears to support Lescoffit & Townsend (2005) who, based on an oil-filled model setup closely resembling the one used in this study, conclude that fault pattern influences time-dependent variables but not recovery. The contrasts in fault parameter impact magnitude observed for nearly all production parameters both within one depositional environment and between them (Fig. 4), is interesting and slightly at odds with Lescoffit & Townsend (2005) who define a number of ‘primary factors’, including sedimentary model, fault seal model and fault pattern, which they conclude should have significant impact on almost all production variables, and ‘secondary factors’ (fault permeability, fault throw and fault zone thickness) whose impact varies and is closely linked to the sedimentological model used as input. However, in the present study the fault pattern does not seem to significantly affect any production parameters in the tidal or fluvial models (Table 5, Fig. 7). Surprisingly, this may indicate that fault pattern should be classed as ‘secondary factor’ as defined by Lescoffit & Townsend (2005).

Discussion Compared to recent results from similar sensitivity studies of production response to fault parameter settings (e.g. Ottesen et al. 2005; Lescoffit & Townsend 2005), both similarities and discrepancies can be identified. Ottesen et al. (2005) perform their sensitivity test on a full-field model of a gas field and use a single model realization of a near-complete Brent stratigraphy as sedimentological input. Comparing their results with ours is difficult as their paper describes a gas field, as opposed to the oil-filled scenarios used in our study; furthermore, it is devoid of information about model dimensions, grid resolution, actual model size, simulation setup and detailed sedimentological information which all may potentially influence results. A further obstacle to comparison is that their simulations were performed on a stratigraphic succession containing multiple depositional environments. This makes it difficult to isolate potential effects arising from the presence of contrasting sedimentologies in the same model. The pronounced influence of fault density on recovery factor in shallow marine parts of the Brent model tested by Ottesen et al. (2005) was not observed for two of the three shallow marine cases in our study (Figs 4, 5). Although in general fault density/faultset qualitatively appears to be the most important parameter affecting production performance in the shallow marine cases (Fig. 7), impact is limited to the time-dependent variables (e.g. ‘Time to WBT’, ‘Time to end’ and ‘Time to 1 MPV injected’) and ‘Recovery at WBT’.

Conclusions Our results suggest that two models from the same depositional environment may respond very differently to the presence of faults, which is consistent with the conclusions of Lescoffit & Townsend (2005). Although patterns of response could tentatively be identified for the four depositional environments, the present study suffers from an inadequate input database. Furthermore, the size of the BASE grid is too small; distinguishing depositional architectures of the four depositional environment types selected for this study are in some cases larger than the BASE grid used in the simulations. Based on a qualitative approach, we may nevertheless draw the following tentative conclusions: (1) Shallow marine, deep marine, tidal and fluvial reservoir models respond differently to similar fault model parameter settings; (2) Differences are most likely caused by contrasting depositional architectures as the samples exhibit a high degree of overlap of sample bulk values for mean porosity and permeability; (3) Simulation response in faulted shallow marine reservoirs is dominated by fault density and SGR, but effects are generally minor; (4) In deep marine systems, all modelled fault parameters showed significant impact on production parameters, with SGR being the most important factor; (5) Response in faulted tidal reservoirs is strongly dominated by the choice of SGR values.

STRUCTURAL CONTROLS ON RESERVOIR PERFORMANCE

Fault pattern complexity does not appear to play a significant role for tidal reservoirs; and (6) SSF and to a lesser extent SGR and fault pattern were the most important aspects in the fluvial reservoirs. As for tidal reservoirs, fault pattern complexity plays a minor role in fluvial reservoirs. Our results show that in order to arrive at reliable conclusions with regard to fault impact in different depositional environments, a systematic approach, involving the use of a large number of synthetic depositional models, is needed. This would provide a full parametric description of the depositional input models, thereby allowing a more sophisticated and reliable analysis of the link between simulation results and input parameters. Until the interplay between sedimentological and structural factors is better understood, any generalizations concerning the impact of faults on reservoir performance should be treated with caution. The authors acknowledge Statoil for funding this project and granting its publication. We would like to thank Alvar Braathen and our reviewers Quentin J. Fisher and Jan Christen Rivenæs for their constructive comments which significantly improved the manuscript.

Appendix A Bootstrap The bootstrap method (Efron & Tibshirani 1993) was used to estimate the uncertainty in the variance components; this is achieved in the following four steps: (1) Estimate the variance components. The set of estimated variance components defines the contribution of each individual factor. These estimates are then used to generate statistical models that have the same variance components as the estimated ones (Fig. 4); (2) Use the estimated model to generate a large number of independent datasets that have the same size as the original data. In our case, we generate 400 datasets of size 72, and assume the variables have a multi-Gaussian distribution with the estimated variance components; (3) In each of the 400 datasets generated in step 2, we performed the same estimation procedure as for the original dataset in step 1. This yields 400 estimates for each of the variance components of interest. These estimates represent the uncertainty for the variance components; and (4) Based on the selection of 400 estimates, we selected the 10th and 90th percentile to represent the uncertainty. The interval that is defined by the two values represents an 80% confidence interval for the estimate. Individual values can also be interpreted as the limit of a one-sided 90% confidence interval from above or below respectively (Fig. 5). As shown in the examples in Figures 5 and 6, the components are reported as standard deviations; the corresponding bounds are the percentiles from the empirical distributions obtained in step 4.

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References B OUVIER , J. D., S IJPESTEIJN , K., K LUESNER , D. F., O NYEJEKWE , C. C. & VAN DER P AL , R. C. 1989. Three-dimensional seismic interpretation and fault sealing investigations. American Association of Petroleum Geologists Bulletin, 73, 1397–1414. C ORBEIL , R. R. & S EARLE , S. R. 1976. Restricted maximum likelihood (REML) estimation of variance components in the mixed model. Technometrics, 18, 31–38. E FRON , B. & T IBSHIRANI , R. J. 1993. An introduction to bootstrap. Monographs on Statistics and Applied Probability, 57. Chapman & Hall. F ISHER , Q. J. & K NIPE , R. J. 2001. The permeability of faults within siliciclastic petroleum reservoirs of the North Sea and Norwegian continental shelf. Marine and Petroleum Geology, 18, 1063– 1081. G AUTHIER , B. D. M. & L AKE , S. D. 1993. Probabilistic modelling of faults below the limit of seismic resolution in Pelican Field, North Sea, offshore United Kingdom. American Association of Petroleum Geologists Bulletin, 77, 761–777. H ARDING , T. P. & T UMINAS , A. C. 1989. Structural interpretation of hydrocarbon traps sealed by basement normal blocks and at stable flank of foredeep basins and at rift basins. American Association of Petroleum Geologists Bulletin, 73, 812–840. H OLDEN , L., M OSTAD , P., N IELSEN , B. F., G JERDE , J., T OWNSEND , C. & O TTESEN , S. 2003. Stochastic structural modelling. Mathematical Geology, 35, 899– 914. H OLLUND , K., M OSTAD , P., N IELSEN , B. F. ET AL . 2002. Havana – a fault-modelling tool. In: K OESTLER , A. G. & H UNSDALE , R. (eds) Hydrocarbon Seal Quantification. Norwegian Petroleum Society (NPF), Special Publication, 11, 157– 171. K NIPE , R. J., F ISHER , Q. J., J ONES , G. ET AL . 1997. Fault Seal Prediction Methodologies, Applications and Successes. In: M ØLLER -P EDERSEN , P. & K OESTLER , A. G. (eds) Hydrocarbon Seals – Importance for Exploration and Production. NPF Special Publication, 7, 15–38. L ESCOFFIT , G. & T OWNSEND , C. 2005. Quantifying impact of fault modelling parameters on production forecasting for clastic reservoirs. In: B OULT , P. & K ALDI , J. (eds) Evaluating Fault and Cap Rock Seals. AAPG Hedberg Series, No. 2, 137– 149. L INDSAY , N. G., M URPHY , F. C., W ALSH , J. J. & W ATTERSON , J. 1993. Outcrop studies of shale smear on fault surfaces. In: F LINT , S. & B RYANT , A. D. (eds) The Geological Modelling of Hydrocarbon Reservoirs and Outcrop Analogues. International Association of Sedimentology, 15, 113– 123. M ANZOCCHI , T., W ALSH , J. J., N ELL , P. & Y IELDING , G. 1999. Fault transmissibility multipliers for fluid flow simulation models. Petroleum Geoscience, 5, 53–63. O TTESEN , S., O SLAND , R., H EGSTAD , B. K. ET AL . 2003. Why understanding reservoir uncertainty is essential to increase recovery and identify remaining hydrocarbons in existing fields. In: S TRAND , T. (ed.) The Norwegian Continental Shelf: An Advanced ‘Laboratory’ for Production Geoscience 2003. NGF Abstracts and Proceedings, 3, 29.

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O TTESEN , S., T OWNSEND , C. & Ø VERLAND , K. M. 2005. Investigating the effect of varying fault geometry and transmissibility on recovery: Using a new workflow for structural uncertainty modelling for clastic reservoirs. In: B OULT , P. & K ALDI , J. (eds)

Evaluating Fault and Cap Rock Seals. AAPG Hedberg Series, No. 2, 125–136. Y IELDING , G., F REEMAN , B. & N EEDHAM , D. T. 1997. Quantitative fault seal prediction. American Association of Petroleum Geologists Bulletin, 81, 897–917.

Using multiple-point statistics to build geologically realistic reservoir models: the MPS/FDM workflow SEBASTIEN STREBELLE & MARJORIE LEVY Chevron Energy Technology Company, 6001 Bollinger Canyon Road, Building D, San Ramon, CA 94583-2324, USA (e-mail: [email protected]) Abstract: Building geologically realistic reservoir models that honour well data and seismic-derived information remains a major challenge. Conventional variogram-based modelling techniques typically fail to capture complex geological structures while object-based techniques are limited by the amount of conditioning data. This paper presents new reservoir facies modelling tools that improve both model quality and efficiency relative to traditional geostatistical techniques. Geostatistical simulation using Multiple-Point Statistics (MPS) is an innovative depositional facies modelling technique that uses conceptual geological models as training images to integrate geological information into reservoir models. Replacing the two-point statistic variogram with multiple-point statistics extracted from a training image enables to model nonlinear facies geobody shapes such as sinuous channels, and to capture complex spatial relationships between multiple facies. In addition, because the MPS algorithm is pixel-based, it can handle a large amount of conditioning data, including many wells, seismic data, facies proportion maps and curves, variable azimuth maps, and interpreted geobodies, thus reducing the uncertainty in facies spatial distribution. Facies Distribution Modelling (FDM) is a new technique to generate facies probability cubes from user-digitized depositional maps and cross-sections, well data, and vertical facies proportion curves. Facies probability cubes generated by FDM are used as soft constraints in MPS geostatistical modelling. They are critical, especially with sparse well data, to ensure that the spatial distribution of the simulated facies is consistent with the depositional facies interpretation of the field. A workflow combining MPS and FDM has been successfully used in Chevron to model important oilfield assets in both shallow- and deep-water depositional environments. Sedimentary environments can be characterized by a succession of deposition of elements, or rock bodies, through time. These elements are traditionally grouped into classes, commonly named ‘depositional facies’, based on their lithology, petrophysical properties, and biological structures. For example, the typical depositional facies encountered in fluvial environments are high permeability sand channels, with leve´es and crevasse splays, having a more variable range of permeability and net-to-gross ratio, within a background of low permeability shaley facies.

Reservoir heterogeneity, and hence flow performance, is primarily controlled by the spatial distribution of depositional facies. Reservoir characterization best practice typically recommends first modelling the depositional facies, and then populating each simulated facies with its corresponding specific porosity and permeability distributions. However, this best practice is often ignored, mainly because traditional facies modelling techniques suffer from some important limitations: † Variogram-based facies simulation techniques, such as sequential indicator simulation, SIS (Deutsch & Journel 1998), allow construction of facies models conditioned to well, seismic, and production data. However, in most SIS models, the simulated depositional elements do not look geologically realistic. This is essentially because the two-point statistic correlation function (the variogram) is not sufficient to model curvilinear or long-range continuous

facies bodies such as sand channels (Strebelle 2000). † Object-based simulation methods (Lia et al. 1996; Holden et al. 1998; Viseur 1999), which do allow the simulation of quite realistic facies architecture, may not be able to integrate dense well datasets or soft constraints, such as 3D seismic data. An innovative alternative approach using multiple-point statistics, first proposed by Guardiano & Srivastava (1993), and further developed by Strebelle (2002), combines the ability to reproduce ‘shapes’, the strength of object-based methods, with the speed and ease of dataconditioning provided by the variogram-based techniques. The main idea behind Multiple-Point Statistics simulation, or MPS, is to go beyond the two-point statistic variogram by inferring higher order, multiple-point statistics from a training image – a three-dimensional conceptual geological

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 67–74. DOI: 10.1144/SP309.5 0305-8719/08/$15.00 # The Geological Society of London 2008.

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model of the facies believed to be present in the reservoir. A detailed mathematical description of the MPS program is provided in the Section on MPS simulation and in Strebelle (2000). In simple words, MPS extracts patterns, characterized by multiple-point statistics moments, from the training image, and anchors these patterns to the reservoir well data. In sparse well environments, however, additional geological information may be required to control the spatial distribution of the simulated facies between the wells. That information can be typically derived from the geologist’s interpretation of the core data and the local depositional setting. Facies Distribution Modelling, or FDM, allows the modeller to quantify such geological information into a facies probability cube to better constrain the MPS model. This paper describes the MPS/FDM workflow implemented by Chevron in the reservoir modelling software Gocad, and presents an application of this workflow to a tidal-dominated reservoir using data from a real field case study.

Training image The training image is an important concept and requirement for the application of MPS in reservoir modelling; and can be defined as a 3D numerical rendering of the interpreted reservoir geology. The training image should capture the range of possible dimensions and shapes of the facies bodies believed to be present in the subsurface, as well as the spatial associations between facies. The training image is, however, a purely conceptual geological model; it contains only relative spatial information, and in particular, it is not conditioned to any hard data. Photographs of outcrops, or sketches hand drawn by a geologist, and then digitized, were first proposed as potential training images; however, they provide only 2D (map view or

cross-sectional) information. Combining such 2D training images to generate 3D training images relies on weak hypotheses that may not correctly reproduce the facies patterns (Strebelle 2000; Okabe 2004). Generating unconditional simulated facies realizations, using object-based or processbased methods, appears to be the most straightforward way to obtain 3D training images. In the workflow developed at Chevron, the object-based method used to build 3D training images proceeds in two steps: 1 First, the user provides a description of each depositional facies, except for the background facies, which is generally shale. More specifically, the user needs to define the map view and crosssection shapes of the facies bodies, the distribution of possible dimensions (length, width, thickness) and orientation of these bodies, and, if relevant, their sinuosity (amplitude and wavelength). Facies body dimensions can be estimated from well log data and good quality seismic, but they may also be obtained from outcrop data and reservoir databases. 2 Then the different facies are combined to make a 3D training image according to userspecified erosion rules and relative lateral and vertical positioning constraints, derived from core data analysis and geologists’ knowledge of the local depositional environment. The 3D training image is typically made using an unconditioned object-based or process-based modelling method. For the tidal-dominated reservoir case study used to illustrate the MPS/FDM workflow in this paper, five depositional facies with significant variations of porosity and permeability range were interpreted: shale, tidal sand bars, tidal sand flats, estuarine sands, and transgressive lags. The geometrical characteristics of each facies, except for the shale background, were defined from well logs and analogue outcrop data. Table 1 provides the mean geometrical parameter values

Table 1. Geometrical and stratigraphic description of each facies, except shale background, for the tidal-dominated reservoir under study Facies type

Conceptual description

Tidal sand bars

Ellipses w/upper sigmoidal cross-section Sheets (rectangles) Sheets (rectangles) Sheets (rectangles)

Tidal sand flats Estuarine sands Transgr. lags

Stratigraphic constraints

Eroded by sand bars On top of estuarine sands

Length (m)

Width (m)

Thickness (ft)

Orientation (degrees)

3000

500

5

35

2000

1000

6

35

4000

2000

8

35

3000

1000

4

35

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Fig. 1. Map-view section of the training image built for the tidal-dominated reservoir under study.

used for the base-case model. Uncertainty assessment in the MPS/FDM workflow through the generation of alternative training images and facies probability cubes is addressed by Chakravarty et al. (2007). The training image thus captures the information identified by the geologists. For example, the tidal sand bars, which represent the main reservoir facies, hence the main target for new well drilling, are preferentially oriented N35E (which is the general interpreted deposition direction of the system), and they erode the sand flats when both facies overlap (Fig. 1). The dimensions of the training image should be at least twice as large as the dimensions of the largest facies elements; the training image may be smaller than the simulation grid.

Simulation constraints One important assumption underlying the inference of multiple-point statistics from the training image and their reproduction in the MPS model is the stationarity of the field under study. Facies relative proportions, geometries, and spatial associations, must be statistically stationary to validate the assumptions in generating the multiple-point statistics (Strebelle & Zhang 2004). Yet, in reality, most reservoirs are not statistically stationary. Local topographic constraints such as the presence of a salt dome, sea-level cycles, or changes of sedimentation sources, lead to significant spatial variations of facies proportions (horizontal and vertical trends), and body geometry (orientation and size). These non-stationary variations (e.g. in facies proportion statistics) can be extracted from well and/or seismic data using statistical analysis tools (Strebelle et al. 2002). For example: † Facies proportion maps and curves can be obtained from well data by computing facies proportions layer-wise or column-wise.

† Variable azimuth maps can be estimated from seismic data by computing at each grid cell local variograms in all possible directions, and retaining the direction of major continuity (greatest variogram range) as the local azimuth. † Seismic data can be calibrated to well data using simple linear regression, or using more advanced techniques such as principal component analysis, to generate a facies probability cube. However, in reservoirs with sparse well data where no seismic or poor quality seismic data are available, most information derives from the geologist’s interpretation of the core data and the local reservoir setting. More conceptual modelling tools are then required to transform such qualitative information into numerical data that can be used in the MPS reservoir modelling program. For example, interpreted depositional directions can be digitized, and then interpolated, to obtain a 2D azimuth map. Regarding the spatial distribution of the facies, an innovative technique, named Facies Distribution Modelling or FDM, was developed at Chevron to generate a 3D facies probability cube from the geologist’s interpretation of the local depositional environment. FDM uses the following three-step process: 1. First, the modeller digitizes cross-sections reflecting his/her interpretation of the correlation between wells, along with vertical proportion sections representing conceptual models of vertical facies trends. These cross-sections and vertical proportion sections are assigned relative weights, and combined with the well data into a single vertical proportion curve. 2. Then the user digitizes depositional (horizontal) facies trends, or more exactly, regions where each depositional facies is expected to occur. Filters are applied to these depocentre regions to gradually decrease the probability of occurrence of the facies outside the region

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Fig. 2. Stratigraphic grid built for the tidal-dominated reservoir under study, and location of the seven wells penetrating the reservoir.

boundary. Truncation regions can be define the outermost limits that can extend to. 3. The facies proportion curves depocentre regions are finally combined facies probability cube.

added to a facies and the into a 3D

The tidal-dominated reservoir under study is vertically delimited by two successive maximum flooding surfaces. These maximum flooding surfaces, interpreted from the seven wells drilled in the field, were used as top and bottom surfaces

to build a northeast oriented stratigraphic grid of 254  119  15 cells, with an average cell size of 40 m  40 m  1m (Fig. 2). A vertical proportion curve was digitized based on the reservoir well data, and according to common trends observed in other tidal-dominated reservoirs (Fig. 3): † The bottom of the reservoir is characterized by shale deposition, corresponding to a typical highstand system.

Fig. 3. Facies proportion curve and corresponding sequence stratigraphic interpretation for the tidal-dominated reservoir under study.

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Fig. 4. Facies depocentre maps digitized for the tidal-dominated reservoir under study.

† The tidal bars are predominantly present above the sequence boundary, that is, in the upper half of the reservoir. † Both the tidal sand flats and the transgressive lags increase upward, but do not constitute a large proportion of facies. † The estuarine sand is predominant at the top of the reservoir, above the sequence boundary, corresponding to a late lowstand or transgressive system. Depocentre maps were then digitized, based on the geologist’s interpretation of the well log data and the local depositional setting (Fig. 4): † The tidal bars tend to be predominant in the southeast part of the field and decrease to the northwest.

† The tidal sand flats are present only in the SE and NW. † The estuarine sands are present in the middle of the field and tend to be less common both to the southeast and the northwest. † The transgressive lags appear only to be present in the SE. Shale represents the background facies, and can occur everywhere. Because of the uncertainty on the boundaries of the depocentre regions and the interpretation of gradual rather than sharp facies transition zones, large filters, between 2000 and 4000 m wide, were applied to gradually decrease the probability of occurrence of the facies away from the depocentre region boundaries. The resulting facies probability

Fig. 5. Map view sections of the FDM facies probability cube generated for the tidal-dominated reservoir under study.

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cube obtained by combining the facies proportion curve with the depocentre maps is fully consistent with the depositional interpretation of the reservoir (Fig. 5): † The highest probability of shale occurrence is in the lower part of the reservoir, below the sequence boundary (highstand system). † The probability of tidal sand bar occurrence is particularly high above the sequence boundary, in the southeast part of the field. † The probability of estuarine sand occurrence is low everywhere, except at the top of the reservoir, preferentially in the middle of the field (lowstand/transgressive system). Note that, in each grid cell, the facies probabilities are standardized to sum to 1.

MPS simulation The MPS simulation program used at Chevron is based on the public algorithm SNESIM (Single Normal Equation SIMulation) developed at Stanford University (Strebelle 2000). SNESIM is a pixel-based direct sequential simulation algorithm, which means that all simulation grid cells are visited only once along a random path and simulated cell values become conditioning data for cells visited later in the sequence. Any unsampled grid cell u visited along the random path is simulated as follows: 1. Look for the n conditioning data (original well data or previously simulated cell values) closest to u. These conditioning data form a data event dn that is characterized by a particular geometrical configuration (the data locations relative to u), and a particular set of data values (the facies at the data locations). 2. Scan the training image to find all training replicates of dn (same geometric configuration and same data values as dn). For each replicate, record the facies value at the central location of the training replicate. By central location, we mean the grid cell corresponding to the relative location of u in the data event dn. 3. The estimated conditional probability of each facies at u is computed as the proportion of central locations of dn training replicates where that facies occur. 4. Draw a simulated facies value from the resulting local probability distribution using MonteCarlo sampling, and assign that value to the grid cell u. Note that if no exact replicate of dn can be found in step 2, conditioning data are neglected one by one, starting from the furthest data away from u,

until at least one replicate of the resulting reduced data event can be found. MPS Simulation is very similar to Sequential Indicator Simulation (SIS), the main difference being that the conventional variogram is replaced by a multiple-point correlation function derived from a training image. Therefore, the main advantages of SIS are preserved in MPS: † MPS is still a stochastic algorithm. Alternative realizations can be generated by changing the seed of the random path or the Monte-Carlo drawing process. † MPS is not specific to any geological environment, as long as a training image can be provided. † The well data are snapped (or ‘blocked’) to the grid prior to the simulation, which ensures that the final model honours all data exactly. However, replacing the variogram with a training image not only allows the user to generate more geologically realistic facies models, but also makes MPS much easier to understand and to apply than SIS. Finally, simulation time is quite similar to SIS if, instead of repeatedly scanning the whole training image at each unsampled node to search for training replicates of the local conditioning data event, all conditional facies probabilities that can be inferred from the training image are stored, prior to the simulation, in a dynamic data structure called a search tree (Strebelle 2000). In addition to the well data, different simulation constraints can be imposed on the MPS model to account for spatial variations of facies proportions (horizontal and vertical trends), and body geometry (orientation and size): † A variable azimuth field and/or a variable object size field can be integrated into the MPS model by applying local affinity (rotation and rescaling) transformations to the training image (Strebelle & Zhang 2004). † Target facies proportions, either global, regional, vertical or areal, can be imposed on the model using an internal process named ‘servo-system’ that monitors the current proportions of simulated facies, and, incrementally adjusts the facies probabilities inferred from the training image as a function of the difference between the current proportions and the target simulation proportions (Strebelle 2000). † Facies probability cubes obtained through seismic data calibration or geological interpretation using FDM are accounted for in MPS models using the conditional independence formula proposed by Journel (2002). That formula allows the combination, at each simulation grid cell, of the conditional facies

THE MPS/FDM WORKFLOW

probabilities inferred from the training image with the local seismic data or geological interpretation derived facies probabilities into a single facies probability distribution from which a simulated facies is drawn. An MPS model was generated for the tidaldominated reservoir studied, using the training image and the FDM cube previously generated. The model was conditioned to the seven wells displayed in Figure 1. The average facies probabilities calculated from the FDM cube were used as the target marginal facies proportions for the simulation: † † † † †

shale, 66% tidal sand bars, 17% tidal sand flats, 4% estuarine sands, 10% transgressive lags, 3%.

The information provided by the training image and the FDM cube allows the MPS model to be perfectly consistent with the information highlighted by the geologists (Fig. 6). Notice, in particular, the following for the sand bars, which represent the main reservoir facies:

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† The sand bars have an elongated ellipsoidal geometry, are preferentially oriented N35E, and erode the sand flats when both facies overlap, as indicated by the training image. † The sand bars prevail in the southeast part of the reservoir, mostly above the sequence boundary, as indicated by the FDM facies probability cube. For the sake of comparison, an alternative model was generated using the conventional variogrambased technique SIS. Spherical variogram models with ranges equal to the facies body dimensions in the MPS training image were used. In the SIS model, the sand bars do not have the elongated ellipsoidal shape that they have in the MPS/FDM model, and that they are expected to have in the actual reservoir (Fig. 6). This difference appears to have a major impact on the connectivity and the flow simulation performance of the model. In addition, the proportion of estuarine sands, which represents the second main reservoir facies, is fairly high in the northwest part of the SIS model, especially in the bottom layers, which is not consistent with the sequence stratigraphic interpretation of the reservoir.

Fig. 6. Map-view sections of the MPS/FDM and SIS models generated for the tidal-dominated reservoir under study.

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Conclusions This paper presents an innovative workflow to build reservoir facies models that captures key depositional facies elements characterized by unique and predictable properties and shapes, while honouring not only well and seismic data, but also geological concepts. This new facies modelling workflow proceeds in three steps. First, unconditional object-based simulation tools are used to build a 3D training image, which provides a conceptual description of the facies bodies expected to have been deposited in the reservoir. Then FDM allows the modeller to digitize a facies proportion curve and some facies depositional maps, based on his/ her interpretation of the well data, and his/her knowledge of the local geological setting. The curve and the maps are combined into a numerical 3D cube that provides the probability of occurrence of each facies in any reservoir simulation grid cell. Finally, the facies model is generated using a new geostatistical approach named MPS. MPS reproduces the facies correlation patterns displayed by the training image, while honoring the well data and being consistent with the spatial facies distribution induced by the FDM probability cube. The MPS/FDM workflow has been used for the last three years at Chevron in very different geological settings: deep-water as well as shallow-water reservoirs, both in clastic and carbonate environments. The method could, however, be employed by anyone using public domain and commercially available software. The authors wish to thank the management of Chevron Energy Technology Company for permission to publish this paper. Special thanks go to Julian Thorne and Deyi Xie for their work in developing FDM, as well as to Andrew Harding, Sebastian Leigh, Rachel Preece, and many other Chevron reservoir modellers for their feedback and suggestions to improve the MPS/FDM workflow.

References C HAKRAVARTY , A., H ARDING , A. W. & S CAMMAN , R. 2007. Incorporating uncertainty into geological and

flow simulation modelling in Chevron: application to Mafumeira, a pre-development field, Offshore Angola. In: R OBINSON , A., G RIFFITHS , P., P RICE , S., H EGRE , J. & M UGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 161– 179. D EUTSCH , C. V. & J OURNEL , A. G. 1998. GSLIB: Geostatistical Software Library and User’s Guide. 2nd edn, Oxford University Press. G UARDIANO , F. & S RIVASTAVA , R. M. 1993. Multivariate Geostatistics: Beyond Bivariate Moments. In: S OARES , A. (ed.) Geostatistics-Troia. Kluwer Academic Publications, 1, 133–144. H OLDEN , L., H AUGE , R., S KARE , Ø. & S KORSTAD , A. 1998. Modelling of fluvial reservoirs with object models. Mathematical Geology, 30/5. J OURNEL , A. 2002. Combining knowledge from diverse sources: an alternative to traditional data independence hypotheses. Mathematical Geology, 34/5. L IA , O., T JELMELAND , H. & K JELLESVIK , L. E. 1996. Modelling of facies architecture by marked point models. In: B AAII , E. Y. & S CHOFIELD , N. A. (eds) Fifth International Geostatistics Congress. Kluwer Academic Publishers, Dordrecht, The Netherlands. O KABE , H. 2004. Pore-Scale Modelling of Carbonates. Unpublished PhD Thesis, Imperial College, London. S TREBELLE , S. 2000. Sequential Simulation Drawing Structures from Training Images. Unpublished PhD Thesis, Department of Geological and Environmental Sciences, Stanford University. S TREBELLE , S. 2002. Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics. Mathematical Geology, 34/1. S TREBELLE , S., P AYRAZYAN , K. & C AERS , J. 2002. Modelling of a Deepwater Turbidite Reservoir Conditional to Seismic Data Using Multiple-Point Geostatistics. SPE n8 77425 presented at the 2002 SPE Annual Technical Conference and Exhibition, San Antonio. S TREBELLE , S. & Z HANG , T. 2004. Non-Stationary Multiple-Point Geostatistical Models. In: L EUANGTHONG , O. & D EUTSCH , C. V. (eds) Geostatistics Banff 2004. Vol. 1, 235–244. V ISEUR , S. 1999. Stochastic Boolean Simulation of Fluvial Deposits: a New Approach Combining Accuracy and Efficiency. SPE n8 56688 presented at the 1999 SPE Annual Technical Conference and Exhibition, Houston.

Reservoir-scale 3D sedimentary modelling: approaches to integrate sedimentology into a reservoir characterization workflow RICHARD LABOURDETTE1, JOANN HEGRE2, PATRICE IMBERT1 & ENZO INSALACO1 1

Total, Geoscience Technologies, Dept ISS, CSTJF, Avenue Larribau, 64018 Pau Cedex, France 2

Total E&P UKplc, Geoscience Research Centre, Crawpeel Road, Altens Industrial Estate, Aberdeen AB12 3FG, UK, present address: Gaz de France, Direction Exploration Production, Avenue du Pre´sident Wilson, 93 211 St Denis La Plaine Cedex, France (e-mail: [email protected]) Abstract: Reservoir production is highly dependent on reservoir models. A key problem faced in the development of a hydrocarbon reservoir is that of constructing a reservoir model that can generate reliable production forecasts under various development scenarios. Therefore, geological models have to be built in three dimensions (3D). Unfortunately, manual construction of 3D geological models (deterministically) is almost impossible, which explains why geologists often limit their interpretation to two dimensional (2D) correlation panels, fence-diagrams or maps. Consequently, geological conceptual models are rarely included or considerably simplified in reservoir models used for flow simulations and replaced by stochastic or geostatistic approaches. In spite of this admission of failure, sedimentological cross-sections and maps contain most of the knowledge and concepts of sedimentologists. They represent the outcome of sedimentological studies, including available well data, seismic interpretation and especially sedimentological and environmental concepts, incorporating all facies transitions and successions in a high-resolution stratigraphic framework. They allow fine temporal- and spatial-scale sedimentological heterogeneities to be identified. The integration of these fine-scale sedimentological heterogeneities is an essential step in improving the precision and accuracy of static reservoir models and volumetric calculations. This paper demonstrates the quantitative influence of introducing sedimentological information into the reservoir characterization workflow using a simple deterministic workflow. The described incorporation of sedimentological knowledge through facies 3D proportions cubes allows a direct assessment to facies distribution multi-realization scheme and associated uncertainties by applying stochastic simulations.

Stochastic simulations can distribute spatially within reservoir models, facies and other properties observed at wells, using calculated or approximated variograms, spatial observed relationship or imposed object shapes. The choice between which stochastic approaches to use is therefore dependent on the geologically realistic distribution of heterogeneities obtained by conditional simulations. Stochastic modelling approaches are described on the assumption of stationarity of the random function, leading most of the time to unrealistic reservoir models. Due to the low density of hard data in the oil industry (well spacing) and geological spatial variability, stationarity is an hypothesis which should not be tested. Recent developments of stochastic simulation were conducted in between two opposing concerns: the quest of objectivity favouring hard data (Journel & Deutsch 1993; Journel 1996) and the quest of trying to integrate additional information on spatial distribution. So when non-stationarity is suspected at the scale of the domain to be modelled, external drifts can

be integrated into the modelling workflow to constrain stochastic simulations. Then lateral geological variability has to be extracted using other quantitative means. Several approaches have been developed during recent years to quantify this lateral variability, using analogue geological situations (e.g. Ravenne & Beucher 1988; Bryant & Flint 1993; Dreyer et al. 1993; Grammer et al. 2004), seismic surveys (e.g. Beucher et al. 1999; Marion et al. 2000; Raghavan et al. 2001; Strebelle et al. 2003; Andersen et al. 2006), hand-drawn sections (e.g. Cox et al. 1994) or more elaborated approaches in relation to sedimentological concepts (Massonnat 1999; Massonnat & Pernarcic 2002). Another advantage of stochastic simulation techniques is their flexibility in incorporating soft information coded under the format of local prior probabilities (Rudkiewicz et al. 1990; Goovaerts 1997; Deutsch 2002; Mallet 2002). This local prior probability can be represented as proportion cube (or facies probability cube) in reservoir models.

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 75–85. DOI: 10.1144/SP309.6 0305-8719/08/$15.00 # The Geological Society of London 2008.

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3D facies proportion cube definition A 3D facies proportion cube is the description of reservoir models in terms of vectorial properties (each cell of the model contains the probability of occurrence of each facies represented in the model). This cube represents the distribution of facies and contains a 3D estimation of associated uncertainty. A deterministic gridded model can be described in terms of proportions by a relatively simple method (Figs 1 and 2). For each horizontal layer of the grid, the occurrence of facies probability can be extracted and transferred as 2D vectorial property (Fig. 1a). When these 2D vectorial properties are stacked vertically, a proportion curve (one dimension) representing the vertical evolution of facies proportions is obtained (i.e. facies evolution through depth; Fig. 1b). This deterministic gridded model can also be described vertically. Each single column of the model can be defined by the proportion of each facies it contains (Fig. 2a). The map of all vertical proportions is a new vectorial proportion, called ‘proportion map’, representing the horizontal evolution of vertical proportions; it is a representation of facies evolution in a 2D map (Fig. 2b). The combination of the proportion curve and map will give the 3D facies proportion cube.

This description of a simple deterministic model is the basis of our workflow. From the available sedimentological dataset, a vertical proportion curve and a proportion map are built.

Introducing sedimentological concepts in cross-sections Based on sequence stratigraphy concepts and knowledge of the studied area, the sedimentologist describes the lateral and vertical evolution of facies tracts from one well location to another. Facies not encountered at well locations, but conceptually identified to be part of the studied facies tract (Fig. 3), can be introduced. This example shows three alternative sedimentological interpretations of facies extensions between two wells. The lateral facies extent is based on the geologist’s knowledge of the studied system tract, therefore this knowledge can be integrated into the designed sedimentological cross-section. In the Figure 3a example, the facies 7 (dark blue) is recognized to have narrow extensions, whereas in the Figure 3b interpretation, its extension is known to be wide. These differences will induce contrasting probabilities in the final 3D proportion cube. In scenario A, facies 7 associated proportions will be

Fig. 1. From (3D) grid to (1D) curve. (a) For each horizontal layer of the grid, the occurrence of facies probability can be extracted and transferred as 2D vectorial property. (b) When these 2D vectorial properties are stacked vertically, a proportion curve (one dimension) representing the vertical evolution of facies proportions is obtained.

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Fig. 2. From (3D) grid to (2D) map. (a) Each single column of the model can be defined by the proportion of each facies it contains. (b) The map of all vertical proportions is a new vectorial proportion, called ‘proportion map’, representing the horizontal evolution of vertical proportions; it is a representation of facies evolution in a 2D map.

constrained near well B location, whereas in scenario B, these proportions will be extended away from well B. Subsequent stochastic simulations, driven by the created proportions, will follow the defined sedimentological trends. In Figure 3c, the sedimentologist integrates a facies (Facies 4, pale yellow) to be part of the studied facies tract. The introduction of this facies within the cross-section will imply a modification of the derived proportions and therefore of stochastic facies distributions in the final model. The introduction of sedimentological facies extensions does not change the global certainty zones usually defined as high certainty at well location and low certainty away from well bores, but introduces the sedimentological concept as an external drift for subsequent stochastic simulations. The sedimentological cross-sections represent the spatial distribution of facies and the only uncertainty carried by sedimentological cross-sections is located at facies transition zones. As imaged in the following simple example (Fig. 4), the cross-section shows facies where they are known to occur (interpreted with high degree of certainty).

Conversely, intermediate areas between facies A and B are symbolised by interfingering A and B facies, representing lower degree of certainty. Furthermore, the drawing design of the facies transition zone contains the related uncertainty (Fig. 4). This allows, in cases where facies interfingering does not physically occur (e.g. erosional limit of channel in floodplain shale), to introduce an uncertainty on the facies limit position.

Extracting proportion curves and maps from sedimentological cross-sections As the sedimentological cross-sections contain all the information necessary for the construction of a 3D proportion cube and if we assume that they are representative of the entire 3D modelled volume, then from each sedimentological crosssection a vertical and a horizontal proportion curve can be extracted (Fig. 5). This extraction procedure is divided into two phases. The first allows the construction of a vertical proportion curve, by

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Fig. 3. Introducing sedimentological concepts into cross-sections. Example showing three alternative sedimentological interpretations of facies extensions between two wells. (a) The facies 7 (dark blue) is recognized to have a narrow extension; facies 7 associated proportions will be constrained near well B location. (b) The facies 7 (dark blue) is interpreted to have wide extension; facies 7 associated proportions will be extended away from well B. (c) The sedimentologist integrates a facies (facies 4, pale yellow) as to be part of the studied facies tract. The introduction of this facies within the cross-section will imply a modification of the derived proportions and therefore of stochastic facies distributions in the final model.

Fig. 4. Facies transition zone uncertainty. Cross-section showing facies where they are known to occur (interpreted with high degree of certainty). Intermediate areas between facies A and B are symbolized by interfingering A and B facies, representing lower degree of certainty. The drawing design of the facies transition zone contains the related uncertainty. (a) The interpretation shows a narrow transition zone between facies A and B; the result is a narrow uncertainty area on facies transition position. (b) The interpretation shows a wide transition zone between facies A and B; the result is a wide uncertainty area on facies transition position.

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Fig. 5. How to build proportion curves. (a) Construction of a vertical proportion curve, by calculating the facies proportions along horizontal layers defined on each cross-section. (b) Creation of a horizontal proportion curve, by calculating the facies proportions along vertical columns defined on each cross-section.

calculating the facies proportions along horizontal layers defined on each cross-section (Fig. 5a). The second creates a horizontal proportion curve, by calculating the facies proportions along vertical columns defined on each cross-section (Fig. 5b). In the described workflow, vertical proportion curves are considered first. All vertical proportion curves can be merged (with a different weighting factor if necessary, depending on sedimentological certainty on correlations) to build a single proportion curve for the stratigraphic interval modelled. Once vertical proportion curves are constructed, horizontal proportion curves positioned along the selected cross-sections (one curve per sedimentological cross-section) are used to build a proportion map through a phase of interpolation. The interpolation between previously defined horizontal proportion curves need not be linear between cross-sections, and is typically guided by ‘trend lines’ defined by any available source of information, typically seismic interpretation (e.g. amplitude map) or conceptual sedimentary model (e.g. expected geometry, curvature of channels or palaeogeography maps), (Fig. 6). The final step is to implement the 3D Discrete Smoothed Interpolation (3D DSI) technique after Mallet (1989). 3D DSI interpolates facies between wells using vertical proportion curves and proportion maps as key constraints (Fig. 7). The final result is a distribution of probability values for each facies where the sum of facies probabilities at any given node of the grid is equal to one.

The 3D DSI process allows the integration of additional constraints acting as external drift for the interpolation. These external constraints can be introduced within the modelling workflow as 3D a priori facies probabilities derived from seismic attributes (Ruijtenberg et al. 1990; Haas & Dubrule 1994; Fontaine et al. 1998; Beucher et al. 1999; Grijalba-Cuenca et al. 2000; Marion et al. 2000; Strebelle et al. 2003; Andersen et al. 2006; Escobar et al. 2006), or stratigraphic simulation results derived from tools e.g. DIONISOS (Granjeon 1997; Granjeon & Joseph 1999; Burgess et al. 2006), SEDSIM (Griffiths et al. 2001) or FLUVSIM (Duan et al. 1998). These different key constraints can have various relative weightings according to their importance or to the certainty associated with each of them (Fig. 8).

The influence of the stratigraphic framework An understanding of the depositional model and thus of facies occurrences is necessary to compute facies proportions correctly. Most of the time, the easiest way to understand the depositional model is to link the interpretation to sequence stratigraphy analysis. Furthermore, the reliability of our modelling workflow needs to be connected to stratigraphic framework. Most of the time, stratigraphic cycles display coherent facies tract trends along wells

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Fig. 6. How to build a proportion map. (a) Facies boundaries are extracted from sedimentological map. (b) Trend lines are created by addition of contours. (c) Vertical proportions are interpolated along trend lines, resulting in the creation of a proportion map.

Fig. 7. How to build the 3D proportion cube. Vertical proportion curves and proportion maps are combined using the 3D Discrete Smoothed Interpolation (Mallet 1989). The final result is a distribution of probability values for each facies in three dimensions where the sum of facies probabilities at any given node of the grid is equal to one.

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Fig. 8. Key constraints for the 3D Discrete Smooth Interpolation (DSI). In addition to well interpretation, sedimentological cross-sections and proportion maps and curves, the 3D DSI process allows the integration of additional constraints acting as external drift for the interpolation. These external constraints can be introduced within the modelling workflow as 3D a priori facies probabilities derived from seismic attributes or stratigraphic simulations results derived from DIONISOS, SEDSIM or FLUVSIM. These different key constraints can have various relative weightings according to their importance or to the certainty associated with each of them.

Fig. 9. Influence of stratigraphic framework in proportion construction. Example showing a simple geological model with two distinct sedimentological facies distribution trends. (a) If this model is considered as a single cycle in the workflow, the resulting 3D proportion cube is incoherent. (b) If the initial model is divided into two distinct cycles and our workflow is applied separately on each sequence, then the result is coherent and produces a good facies distribution outcome.

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and cross-sections, which are necessary to ensure their 3D representation. This can be illustrated with a simple geological model with two distinct sedimentological facies distribution trends (Fig. 9). If this model is considered as a single cycle in the workflow, the resulting 3D proportion cube is incoherent (Fig. 9a). As this model has two distinct trends, treating them as a single stratigraphic entity provides a single proportion map which is fairly homogeneous; the two sedimentary trends cancel each other, resulting in a poor rendering of the sedimentary concepts and architecture. If the initial model is divided into two distinct cycles and our workflow is applied separately on each sequence, then the result is coherent and is a good facies distribution outcome (Fig. 9b).

Workflow results Basis for multi-realizations of facies distribution/uncertainty assessment This deterministic 3D proportion cube is a background trend for subsequent geostatistical facies simulations, such as Truncated Gaussian Simulation

(TGS) and Sequential Indicator Simulation (SIS). According to the stochastic approach chosen, facies distributions will vary. By using SIS, facies are modelled separately and independently; in this way, possible constraints of their relative position are not taken into account (Journel & Alabert 1990; Journel & Deutsch 1993). TGS is based on direct algorithms, without any iterative process. Ravenne & Beucher (1988) and Rudkiewicz et al. (1990) proposed this direct approach to take into account the facies spatial relationship. This approach allows the simulation of concomitant facies, such as those in shoreface deposits and those in most carbonate depositional settings. All the facies have the same variogram reflecting the same spatial continuity and implying the same anisotropy and correlation length. Figure 10 shows an example of Truncated Gaussian Simulation applied on a proportion cube for an oolitic ramp from the Middle East Gulf region. The result of our modelling workflow is several ‘equiprobable’ 3D facies distributions of realistic appearance. They contain an external drift generated by the geologist and have an element of uncertainty reflected by the multi-realization scheme, all this with classical geostatistical

Fig. 10. Use of the proportion cube as basis for geostatistical facies distributions. Example of Truncated Gaussian Simulations applied on a proportion cube created from a Middle East Gulf region oolitic ramp. The result of our modelling workflow is several ‘equiprobable’ 3D facies distributions of realistic appearance.

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Fig. 11. Use of the proportion cube as conditioning constraint for object simulations. Example of a proportion cube applied to distribute mouth bar architectural elements in the Tunu Field (Mahakam, Indonesia). Channel distributaries are introduced deterministically in the model, whereas mouth bar architectural elements are simulated according to their width, thickness, length or width-to-thickness ratio; using a 3D proportion cube derived from sedimentological cross-sections and maps.

constraints to well data. The stratigraphic grid populated with facies or major facies associations can then be used as an input to petrophysical modelling or seismic inversion.

Basis for object-based models The 3D proportion cube can also be used as a softconditioning constraint for object simulations, which are widely used methods for facies simulations (Dubrule 1989; Haldorsen & Damsleth 1990; Caers 2005). The object distribution is guided by the 3D proportion cube. Figure 11 shows an example of mouth bar distribution achieved using the object-based methodology in Tunu Field (Mahakam, Indonesia). Channel distributaries are introduced deterministically in the model, whereas mouth bar architectural elements are simulated according to their width, thickness, length or width-to-thickness ratio, using a 3D proportion cube derived from sedimentological cross-sections and maps. As previously discussed, the final model provides several ‘equiprobable’ 3D object distributions and can then be used as an input to petrophysical modelling or seismic inversion.

Conclusions The workflow is based on simple modelling techniques; it allows sedimentologists to deterministically integrate their interpretations and concepts into the reservoir characterization workflow, with all available attributes to guide them. This workflow

also integrates sedimentological uncertainty on heterogeneity distribution, leading to the construction of a 3D proportion cube used in uncertainty studies. Also the resulting 3D proportion cube is a unique output (vectorial property), which acts as an input for various facies distribution methods (e.g. TGS, SIS or Object-based) without any distortion of initial inputs. These results are then populated with petrophysical properties using classical geostatistical methods. Deterministic modelling coupled with stochastic or geostatistic models provide interesting solutions to the main challenges of reservoir modelling, the construction of 3D geologically realistic representation of heterogeneity and the quantification of uncertainty through the generation of, not one, but a variety of possible models or ‘realizations’. The authors would like to thanks Yannick Boisseau, Dominique Marion, Bruno Michel, Olivier Robbe and Philippe Samson for their involvement in the workflow construction, and John K. Williams and Adam Robinson for their constructive comments and suggestions on the manuscript.

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Calibration and validation of reservoir models: the importance of high resolution, quantitative outcrop analogues RICHARD R. JONES1,2, KENNETH J. W. MCCAFFREY3, JONATHAN IMBER3, RUTH WIGHTMAN3, STEVEN A. F. SMITH3, ROBERT E. HOLDSWORTH3, PHILLIP CLEGG3,4, NICOLA DE PAOLA3, DAVID HEALY3,5 & ROBERT W. WILSON3,6 1

Geospatial Research Ltd., Dept. of Earth Sciences, University of Durham, DH1 3LE, UK (e-mail: [email protected]) 2

e-Science Research Institute, University of Durham, DH1 3LE, UK

3

Reactivation Research Group, Dept. of Earth Sciences, University of Durham, DH1 3LE, UK

4

Current address: GeoPressure Technology Ltd., Mountjoy Research Centre, Stockton Road, Durham, DH1 3UZ, UK 5

Current address: Institute of Geoscience Research, Curtin University of Technology, GPO Box U1987, Perth WA6845, Australia

6

Current address: BP, Chertsey Road, Sunbury-on-Thames, Middlesex, TW16 7BP, UK Abstract: Rapidly developing methods of digital acquisition, visualization and analysis allow highly detailed outcrop models to be constructed, and used as analogues to provide quantitative information about sedimentological and structural architectures from reservoir to subseismic scales of observation. Terrestrial laser-scanning (lidar) and high precision Real-Time Kinematic GPS are key survey technologies for data acquisition. 3D visualization facilities are used when analysing the outcrop data. Analysis of laser-scan data involves picking of the point-cloud to derive interpolated stratigraphic and structural surfaces. The resultant data can be used as input for object-based models, or can be cellularized and upscaled for use in grid-based reservoir modelling. Outcrop data can also be used to calibrate numerical models of geological processes such as the development and growth of folds, and the initiation and propagation of fractures.

Petroleum geologists have utilized a wide variety of different kinds of geological modelling over many years. These have helped to increase our understanding of basin dynamics, hydrocarbon systems and petroleum-related processes. Collectively, the various different approaches to modelling have spanned many orders of magnitude, from characterizations of overall lithospheric-scale properties, down to modelling of grain-scale processes (Fig. 1a). Types of modelling include analogue and numerical methods. Analogue models (e.g. sand-box models, flume experiments etc.) have a long track record of providing useful insights into structural and sedimentological processes. Numerical-based approaches to modelling are ubiquitous in hydrocarbon exploration and production, aided by ever-increasing improvements in the priceperformance ratio of computers. Common to all modelling strategies is the need to calibrate the model with realistic values of geological properties, and to test the validity of the model in

relation to real-world petroleum systems. Input for models often relies most heavily on indirect geophysical data (Fig. 1b), particularly regional gravity and magnetic survey, 3D seismic and well-log data, together with direct analysis of well core, when available. Further input can be gained from studying suitable reservoir analogues (Fig. 1c). Direct geological observations made on well-exposed outcrops can help to reduce some of the uncertainty normally associated with remotely imaged geophysical data. Another significant advantage is that outcrop analogues that show reservoir scale geometries also capture scales of observation that extend down to subseismic levels. Thus, outcrop studies help to fill the gap in the scale range (below c. 2.5  101 m) not normally captured using geophysical methods, and provide greater dimensionality than well logs and core, which are essentially 1D in nature. Although reservoir analogues have been used by petroleum geologists for many years, they have traditionally been based on predominantly qualitative

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 87–98. DOI: 10.1144/SP309.7 0305-8719/08/$15.00 # The Geological Society of London 2008.

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Fig. 1. Schematic diagram showing the approximate range of scales typically covered by a variety of types of numerical and analogue modelling. (a) Representative examples of modelling methods. (b) Examples of indirect geophysical observations typically used to calibrate models of petroleum systems. (c) Types of direct observations that are essential in validating the results of modelling. Outcrop analogues are particularly important in covering the lack of indirect geophysical data for scales of observation below seismic resolution. From McCaffrey et al. (2005b).

outcrop studies. Within an overall study area, any quantitative study is typically restricted to only small regions of outcrop. Furthermore, most studies use 1D analysis methods, such as logging sedimentary sections, or measuring fractures along a line transect. Such limitations can be overcome by using a number of modern digital survey technologies (Fig. 2), including methods based on highprecision GPS, laser-based distance measurement, and calibrated digital photography. This paper discusses ways in which survey methodologies based on digital technologies such as these can be

combined to capture detailed geospatial outcrop data, and how the data can be interpreted to produce quantitative reservoir analogues that are 3D (or semi-3D) in character, which can help to calibrate and validate geological models used by reservoir geologists.

Quantitative reservoir analogues Where possible, when developing new procedures to capture and process quantitative outcrop data,

Fig. 2. Examples of methods of digital data acquisition. (a) Real-Time Kinematic (RTK) dGPS, stationary base-station. In the field, differential GPS locates the base station with an accuracy of c. 0.5 m; this is improved by post-processing to c. 10 mm. (b) Two RTK dGPS rover units. A positional fix relative to the base-station can be made instantaneously, typically with a precision of c. 10 mm. (c) MDL LaserAce 300 laser-ranging device, with hand-held PDA data-logger. The laser-ranger is used to measure the precise location of individual observations and structural measurements relative to the instrument. RTK GPS is then used to measure the accurate location of the instrument, and thus the absolute position of all its relative measurements. (d) Terrestrial laser-scanning using MDL Quarryman. The data captured includes x,y,z position and intensity information for each point scanned, and the resultant laser-scan point-cloud can be imported into most 3D visualization tools. (e) False-colour laser-scan point-cloud from MDL scanner, imported into Gocad. (f) Riegl LMS-Z360i laser-scanner, with top-mounted high resolution digital camera

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Fig. 2. (Continued) (to give true-colour point-cloud data) and RTK dGPS unit to record precise scanner location. (g) True-colour point-cloud data from Riegl LMS-Z360i scanner. Locations: (a) analysis of fault-related folding, Howick, NE England (see Pearce et al. 2006a); (b) segmented faults, Lamberton, SE Scotland; (c) study of onshore analogues for Devonian clastics of West Orkney Basin, Kirtomy, N Scotland; (d– e) faulting in Carboniferous sandstone/shale sequence, NE England; (f–g) study of fractured carbonates, Flamborough, E. England.

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we have based our approach on basic principles adopted from standard hydrocarbon exploration strategies. In this way, our workflows utilize elements of digital data acquisition, data processing, 3D computer graphics, and geological interpretation. Our workflows group together a range of complementary methods, collectively termed ‘GAVA’ (Geospatial Acquisition, Visualization & Analysis).

Acquisition Our primary survey methods (Fig. 2) are based on a combination of terrestrial laser-scanning (e.g. Ahlgren & Holmlund 2002; Jennette & Bellian 2003; Jones et al. 2004; Løseth et al. 2004a, b; Bellian et al. 2005; Clegg et al. 2005), laser-ranging (Xu et al. 2001; Løseth et al. 2003; Jones et al. 2004), high-precision GPS (e.g. Xu et al. 2000; Maerten et al. 2001; McCaffrey et al. 2005a; Pearce et al. 2006a, b), and digital photogrammetry (Pringle et al. 2001, 2004; Hodgetts et al. 2004). The most suitable technology to capture a given outcrop depends on a number of factors: † the purpose of the study; † the nature of the outcrop, including amount of exposure and accessibility; † the level of detail required; † the spatial precision needed; and † the time and cost constraints. In most situations, optimum results are obtained by combining more than one method. Terrestrial laser-scanning is our preferred core technology for acquisition of highly detailed, photo-realistic outcrop models. This is usually supported by highprecision ‘Real Time Kinematic’ (RTK) GPS to provide geospatial control, as well as laser-ranging to allow additional geological observations and measurements to be referenced to the laser-scan data with centimetre precision. The resultant outcrop models are sufficiently detailed to be used for virtual field trips, and provide enhanced ability to study parts of the exposure that are not easily (or safely) accessible on the real-world outcrop. Virtual outcrop models can be further analysed to provide quantitative information about structural and sedimentological architectures (see below). Where possible, valuable additional 3D constraint on outcrop models can be gained by acquiring data from the shallow subsurface, using methods that include ground-penetrating radar (GPR), ultrashallow seismics, and boreholes sited behind the outcrop face (e.g. Pringle et al. 2003, 2006; Young et al. 2003; Stepler et al. 2004). To construct a complete reservoir-scale model at the resolution of a highly detailed virtual outcrop analogue would place unrealistic demands on available hardware performance. An effective strategy to

overcome this issue is to build multiscale models, in which local areas of detailed outcrop are placed within a wider geological and topographical context by including nested levels of coverage (Jones et al. 2008a). Multiscale models can provide reasonably seamless coverage from outcrop to basin scales, with larger areas showing progressively less detail. Whilst data capture at the outcrop scale typically uses survey-grade equipment (laser-scanners and RTK dGPS), coverage for larger areas uses digital geological mapping (McCaffrey et al. 2005a; Clegg et al. 2006; Wilson 2006) and regional-scale remotely imaged data (e.g. satellite and aerial images, geophysical datasets).

Visualization Visualization is closely linked to analysis and interpretation of the acquired digital outcrop data, and is of central importance in maximizing the usefulness of the virtual outcrop model as a reservoir analogue. In our work, we routinely use a range of visualization equipment that varies in terms of processor power, memory (RAM), and graphics capability, as well as cost. Most modern desktop PCs have impressive 3D visualization capability, and are powerful enough for routine visualization and analysis. For example, we typically use high-end PCs running Windows or Linux to visualize and analyse laser-scan datasets comprising coloured point-clouds containing up to 20 million points (typically covering an outcrop area of 1–3 km2), or to visualize a multiscale model consisting of 1000 km2 of regional satellite data, as well as 100 km2 of high resolution imagery and digital geological map data, plus local areas of detailed virtual outcrop data embedded into the model. For more demanding visualization tasks involving larger datasets, we use a dedicated Silicon Graphics workstation. 3D visualization is enhanced by using autostereoscopic displays (Fig. 3a), which provide a stereoscopic image without the need for stereoglasses (Holliman 2006), and which significantly improve the users’ ability to work with 3D data. For fully immersive real-time interactive graphics sessions, we use a purpose-built HIVE (High Impact Visualization Environment) equipped with stereoscopic back-projection and 3D wireless tracking system (Fig. 3b). The HIVE can be driven from Windows, Linux and Silicon Graphics environments. Because desktop PCs have a lower overhead in terms of maintenance and technical support, we generally use low-end machines for much of the preliminary processing, basic visualization tasks, and construction of first versions of a virtual model, reserving the high-performance, immersive graphics environment for detailed

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Fig. 3. Data analysis in 3D visualization environments. (a) Dual-head graphics display with both auto-stereoscopic (left) and normal screens (right), on Windows PC using Schlumberger’s Petrel software. The auto-stereoscopic screen is similar in appearance to a standard LCD display, but generates a 3D image without the need for stereo glasses. (b) Collaborative 3D interpretation session in fully immersive, interactive HIVE, using custom point-cloud visualization software on a high-end PC running Linux.

re-interpretation and collaborative sessions involving multiple users (Fig. 3b). The various different formats of geospatial data used in virtual outcrop models are compatible with many of the visualization software tools in common use in exploration and production environments. For smooth visualization of laser-scan data, the choice of software can be critical, since not all visualization tools are optimized to display very large point-cloud datasets. Trial and error, and a degree of experience, is often needed to optimize the performance of a particular combination of hardware and software. One advantage of some of the software tools that are specifically designed to render point-cloud data is that it is possible to use different visualization modes for display of the outcrop model (Fig. 4). Showing all the data as individual

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Fig. 4. Different visualization modes for laser-scan point-cloud data. (a) Rendering data as individual points can be efficient for the graphics hardware, and is particularly useful when picking precise geological surfaces in the raw data. (b) Meshing the point-cloud and draping a detailed image over the meshed surface needs to be optimized carefully to avoid placing much higher demands on hardware, but when done well can give photo-realistic results even close-up to the model (height of arch: c. 2 m).

points (‘glyphs’) is very efficient in terms of computing power (so very large datasets can be manipulated in real-time), though there is a lack of detail when close to the outcrop. By converting the pointcloud into a meshed surface, and draping a digital image onto the mesh, it is possible to show very high levels of detail in the model. However, this carries a much higher overhead in terms of graphics performance, so that it is best suited for showing close-up areas of detail, or for viewing larger models that have been decimated to reduce the number of panels in the mesh (at the expense of detail in the surface topography).

Analysis – interpretation of geospatial data to produce 3D models Virtual outcrop models are no substitute for real field study on the outcrop, and geological

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observations in the field are always the most important element in maximizing the analysis of digital data to full effect. However, using a virtual model in addition to field study can certainly enhance interpretation significantly. Visualizing the model allows the geologist to view parts of the outcrop that are not normally accessible (e.g. areas or outcrop above head height, cliff sections flanked by water), and the ability to zoom rapidly in and out from the outcrop provides perspective at different scales of observation. Elevated vantage points can often give a clearer view of stratigraphy, and it is useful to be able to navigate quickly to the exact viewpoint that shows how structures or other geological features are aligned in 3D. Often it is useful to try viewing positions inside an outcrop looking out, as it can sometimes be easier to recognize geological surfaces from a vantage point inside the rock. The virtual model can also be rendered using false colour to emphasize different aspects of the outcrop. Most importantly, the digital data provide the basis for geospatial analysis of the outcrop to derive quantitative interpretation of structural geometries (e.g. Maerten et al. 2001; Ahlgren et al. 2002; Jones et al. 2004; Trinks et al. 2005; Pearce et al. 2006a, b; Kokkalas et al. 2007) and sedimentological architectures (e.g. Pringle et al. 2001, 2004, 2006; Løseth et al. 2003, 2004a, b; Jennette & Bellian 2003; Hodgetts et al. 2004; Bellian et al. 2005; Labourdette & Jones 2007). Examples of quantitative information derived from virtual outcrop models and used in reservoir modelling include:

Fig. 5. (a) Fault picking in laser-scanner point-cloud data. (b) Interpolated plane through the picked points. (Study of fractured carbonates, Flamborough, E. England. See also Waggott et al. 2005.)

best constrained when good 3D exposures are used, and/or when additional data are available from the shallow subsurface close to the outcrop.

† † † † †

Calibration of geological modelling using digital outcrop data

In most cases, the virtual outcrop data are interpreted by ‘picking’ stratigraphic and structural surfaces within the point cloud (Fig. 5), in a process comparable with horizon picking in 3D seismic (Jones et al. 2004; Clegg et al. 2005; Trinks et al. 2005). The picks are combined with other data measured directly in the field (e.g. surface traces of structures surveyed with RTK dGPS equipment), and the point sets are interpolated to produce continuous surfaces that can be extrapolated into (and out of) the subsurface. Clearly, interpolation is

Once the virtual outcrop data have been fully picked, the resultant stratigraphic–structural interpretation can be used to calibrate reservoir models. Interpolated surfaces are imported into object-based modelling software for further analysis (e.g. Gocad, Petrel, 3DMove, TrapTester etc.), or the model can be cellularized and upscaled for use in cell-based modelling and fluid-flow simulation. A seminal study by Løseth and co-workers (Løseth 2004; Løseth et al. 2004), using virtual outcrop models as a framework for simulating hydrocarbon production, has emphasized the critical influence of fine-scale heterogeneity, both on STOIIP (Stock Tank Oil Initially in Place) and sweep rates. Using a fine-scale model incorporating channel geometries derived from digital outcrop data, the study showed that standard upscaling and modelling methods in this case significantly overestimated reserves by as much as twice the actual

overall facies distribution; lateral variations in stratigraphy; morphology of fluvial and submarine channels; turbidite architectures; fold geometries, including non-cylindrical anticlinal closures and whale-back fold culminations; † 3D fracture distributions, giving a characterization of bulk structural heterogeneity; † fracture orientation, density and connectivity, and their relation to fold closures; and † effects of subseismic-scale damage zones adjacent to basin-scale faults.

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magnitude. Studies such as these highlight the importance of calibrating reservoir models with real-world outcrop data recorded by direct observation from reservoir scale down to subseismic resolution (cf. Fig. 1c). In addition to the calibration of reservoir models, digital outcrop data can also be used as a quantitative basis for calibration of other kinds of modelling, including detailed studies that examine structural geometries in relation to a wide range of other variables such as petrophysical properties and geological processes. Numerical modelling methods have the advantage that individual variables can be isolated and their effects studied, so that large amounts of a model’s parameter-space can be fully examined. The disadvantage is that since all modelling requires simplifying assumptions to be made, care is needed to ensure that complex numerical models retain a reasonable approximation to geological reality. In contrast, digital outcrop data provide an excellent quantitative measure of real-world geology, but there are still far too few available outcrop studies to be able to

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populate multi-parameter models adequately. By combining both approaches, however, we can use the sparse but validated outcrop data as key reference points with which to calibrate the results of multiparameter numerical modelling (Fig. 6). The following case studies illustrate the way in which detailed digital outcrop data can be used as a basis for improved reservoir characterization and increased understanding of structural processes. The case studies are part of ongoing work to analyse seismic- to subseismic-scale faulting, and to quantify relationships between fracturing and folding. The study areas lie in the northernmost onshore outcrops of the Carboniferous Northumberland Basin, and are related to a phase of Late Carboniferous oblique extension (De Paola et al. 2005a).

Case study: displacement patterns in relay faults The long-term aims of this study are to analyse 3D geometry and displacement patterns of small-scale

Fig. 6. Symbolic depiction of the use of quantitative outcrop data to calibrate multiparameter numerical models. The results of numerical modelling can populate the entire parameter-space (here limited to three variables for clarity), but need to be validated with real-world data: the outcrop data (represented by individual spheres) are sparse, but represent points of geological reality within the numerical model.

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Fig. 7. Segmented faulting in sandstone/shale sequence at Lamberton, SE Scotland: (a) outcrop photo; (b) structural interpretation showing exposed fault planes and fault tips; (c) lidar laser scan data from the outcrop, with fault panels picked from three sandstone horizons (note: the sandstone pedestal on the right of the photo in (a) was removed by erosion prior to acquisition of the lidar data); (d) meshed fault panels imported into Badley’s TrapTester for further analysis; (e) example of fault attribute data derived from the outcrop model: plot of throw population showing exponential distribution (Imber et al. 2007); (f) numerical analysis of relay fault development using elastic dislocation modelling.

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segmented fault and fracture systems seen in outcrop, to compare these quantitatively with larger-scale structures imaged in 3D seismic, and to use the 3D outcrop models to test the effect of the fracture network on fluid flow. Figures 7a and 7b show a set of segmented normal faults in a sandstone/shale sequence from coastal exposures at Lamberton, SE Scotland (Wightman et al. 2007; Imber et al. 2007). The faults exposed at Lamberton have small displacements, typically of the order of 1021 m, and therefore in order to ensure that the precision of the digital equipment was adequate for such a small-scale study, measurements of fault tips and hangingwall and footwall cut-offs were repeated using three different methods. Fault geometry and displacement were directly measured in the field using both RTK dGPS equipment (see Fig. 2b), and also by manual measurements of fault plane dip and offset using compass-clinometer, steel rule and measuring tape. In addition, the outcrop was scanned in detail using lidar equipment, and the position of the footwall and hangingwall cut-offs (and hence fault displacements) were derived from the virtual laser scan point cloud (Fig. 7c). Data were then exported to TrapTester,

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Gocad and ArcGIS software for further analysis (Fig. 7d). Many different spatial and geometrical attributes can be rapidly derived directly from the 3D network model; the cumulative fault throw plot shown in Figure 7e is just one of many examples (Imber et al. 2007). The virtual outcrop dataset and derived 3D fracture network model are now being used by the project sponsors (BG Group and Shell) to extract additional quantitative fracture characteristics as part of their ongoing exploration activities. We are also using the Lamberton data to condition numerical models of relay fault development based on elastic dislocation methods (Fig. 7f; Healy et al. 2004), and to compare the real-world data with the predictions of distinct element modelling (cf. Imber et al. 2004).

Case study: 3D fold geometry and models of fold development Mesoscale folds in the Northumberland basin are intimately associated with domains of wrenchfaulting during regional transtension (De Paola et al. 2005a, b). Folds are typically highly noncylindrical, with fold amplitude often decreasing

Fig. 8. Non-cylindrical fold development at Howick (a, c), and Scremerston (b, d), NE England: (a) RTK survey of a single folded bedding surface; (b) laser scanning of a tight fold pair. A, B, & C are reference points to help comparison between upper and lower images; (c) meshed RTK data (fold surface contoured according to curvature); (d) lidar data with picked fracture traces across the fold hinge.

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rapidly along strike from local culminations and antiformal closures. In many localities, the strong mechanical anisotropy of the limestone/sandstone/shale sequence is also likely to have had an important influence on fold development. Folded bedding surfaces in coastal exposures in NE England were surveyed using RTK dGPS equipment at Howick (Fig. 8a, c; Pearce et al. 2006a), and RTK and laser scanning at Scremerston (Fig. 8b, d; Pearce et al. 2006b). The raw field data from the folded surfaces were meshed using Matlab and Gocad software to form a detailed model of the fold geometry (Fig. 8c). This was the basis for comparison with models of faultpropagation folding (McCaffrey et al. 2005b), based on the trishear models of Cristallini & Allmendinger (2001). The data have also been used to compare spatial variations in fracture density with position on the fold and curvature of the fold surface, to test the supposition that the highest concentration of fracturing will coincide with greatest curvature (Pearce et al. 2006b).

Conclusions There is currently renewed interest in outcrop geology within the hydrocarbon sector, driven by a need to improve reservoir characterization during exploration, as well as ongoing efforts to tackle production-related issues. New methods of digital field survey, in particular terrestrial laser-scanning supported by high-precision Real Time Kinematic dGPS equipment, allow quantitative outcrop geology to be captured with unprecedented levels of detail and geospatial accuracy. Digital data can be analysed using standard 3D visualization facilities, and interpreted and collated into virtual outcrop models, which encapsulate the geospatial distribution of sedimentological and structural architectures. Multiscale virtual models combine data from several orders of magnitude, and help to place detailed outcrop data in the wider context of reservoir or regional-scale geology. Data from outcrop models can be exported in standard industry formats for further analysis in many modelling software packages. These include object-based tools (e.g. TrapTester, 3DMove, Petrel, Gocad), and cell-based reservoir modelling software (e.g. Eclipse, IRAP RMS etc.). Digital outcrop data can also be used to validate the predictions made by other kinds of modelling, including numerical models of geological processes such as the formation of folds and the development of 3D fracture arrays. Thus, outcrop data can provide a quantitative 3D framework for the calibration and validation of deterministic and stochastic geological models

used in hydrocarbon exploration and production. Virtual outcrop models fill an important gap in the range of scales of observable geological data (Fig. 1). Quantitative outcrop data have demonstrated the critical importance of small-scale anisotropy imaged at a finer resolution than typical grid sizes used in reservoir modelling, and future improvements in the ability of modelling software to match geological reality will significantly enhance reservoir characterization. Editorial assistance from Paul Griffiths and constructive reviews from Jamie Pringle and an anonymous referee have helped to improve this paper. Parts of this work were developed with assistance of the following sponsors: Ocean Margins Link project (NER/T/S/2000/01018), funded by Statoil UK Ltd, BP Group and NERC; FR3DA consortium members Shell, BG and DTI; as well as NERC Follow-on Funding (NE/C506964/1). RRG gratefully thank Schlumberger and Badleys for noncommercial software licences and ongoing assistance. Mark Pearce gave valuable assistance with data collection and interpretation. Nick Holliman and Immo Trinks at the e-Science Research Institute at Durham, and Dave Stevenson, Gary Wilkinson and members of RRG have given essential assistance.

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Modelling of dipping clinoform barriers within deltaic outcrop analogues from the Cretaceous Western Interior Basin, USA ˚ SMUND VASSEL & TANJA AUNE JOHN HOWELL, A Centre for Integrated Petroleum Research, University of Bergen, N5007 Norway (e-mail: [email protected]) Abstract: Deltaic reservoirs typically contain seaward-dipping surfaces termed clinoforms. Shale and carbonate cements covering clinoforms can frequently form a barrier or baffle to horizontal flow within reservoirs, However, clinoforms are not typically included in static or flow simulation models because they are often not identified in well data and little is known about their 3D geometry. High quality outcrops such as Cretaceous deposits of the US Western Interior Seaway provide an ideal opportunity to study clinoform geometry and shape, and to model their effects on flow. Within this study, two deltaic systems have been studied. The first is the Ferron Delta which crops out in the Wasatch Plateau, central Utah and is a highstand complex comprised of a number of small, overlapping lobes. Clinoforms are common and their 3D geometry is controlled by the position of the lobes. Large growth fault structures within the lobes add to the potential reservoir complexity. The forced regressive Panther Tongue Delta crops out in the Book Cliffs of Utah and is comprised of downstepping lobes with internal clinoforms. Data for modelling included traditional sedimentary logs, photomontages and calibrated photo logs. Models were built in IRAP RMS using a variety of modelling techniques from simple Truncated Gaussian Simulations on a regular grid to object modelling of shale barriers within a dipping grid designed to follow the clinoforms. The models were flow simulated as a means of comparing the different techniques for representing the heterogeneity results show that not modelling clinoforms explicitly in a dipping grid can lead to significant overestimates in the forecasted production; water injection in a down depositional dip position is optimum, and that there are only limited production differences between highstand and lowstand deltas.

Shallow marine, deltaic deposits comprise significant reservoirs in many parts of the World. When studied in core and well log data, such reservoirs typically comprise upward-coarsening packages of sediment with the best reservoir properties towards the top of the individual progradational packages (parasequences; Van Wagoner et al. 1990). Thin shale beds occur throughout the packages (Fig. 1), clustered towards the lower part of the units. In outcrops, these shale beds can be seen to have a dipping geometry that follows the palaeo-position of the delta-front (Fig. 1). These dipping surfaces are termed clinoforms and their dipping nature is typically not recognized or is ignored in subsurface datasets despite the fact that they may produce barriers and baffles to both vertical and horizontal flow (Fig. 1; Ainsworth et al. 1999). 3D clinoform geometry in fluvio-deltaic systems is poorly understood and little is currently documented on either the controls on clinoform shape or their influence on reservoir performance. The aim of this paper is to capture the geometry of clinoforms from two high quality outcrop sections in Utah – the Ferron Member of the Mancos Shale Formation and the Panther Tongue Member of the Starpoint Formation (Figs 2 and 3). These represent a highstand (Ryer 1981;

Gardner 1995) and a falling stage/lowstand (Newman & Chan 1991; Posamentier & Morris 2000) delta complex respectively. The outcrop data have been represented in a subsurface modelling system (Roxar’s RMS software) and have been flow-simulated with the aim of assessing the effects of shale-draped and cemented clinoforms on reservoir fluid flow, the effects of different modelling strategies and to investigate accommodation controls on clinoform geometry and simulated reservoir performance. To enable the outcrops to be recreated in the reservoir modelling system, data were collected using a combination of standard and novel field techniques. This paper also outlines the techniques for the rapid and inexpensive collection of field data for the building of outcrop reservoir models and procedures for the construction and interrogation of these models in a subsurface reservoir modelling package.

Previous studies Both the Ferron Sandstone and the Panther Tongue have been studied previously within their context as part of the Cretaceous fill of the Western Interior Basin (Young 1955; Armstrong 1968), as sequence

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 99–121. DOI: 10.1144/SP309.8 0305-8719/08/$15.00 # The Geological Society of London 2008.

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Fig. 1. Delta front clinoforms in core and outcrop. (a) Thin siltstone bed within delta front sandstones. This siltstone is interpreted as a shale drape on a sandy clinoform and may potentially provide a dipping barrier within the reservoir. Core from the Muddy Creek #2 well which penetrates the modelled outcrops 3 km outside the study area. (b) Outcrop view of the Ferron 1 unit in Ivie Creek. Note the upward-coarsening and thickening of the sandstone beds and the dipping nature of the delta front sandstones and shales. These clinoforms represent the palaeoposition of the delta front. (c) Schematic representation of a prograding delta front. Fluctuations in the fluvial output result in the deposition of interbedded sandstone and mudstone on the dipping delta front. These dipping beds define the clinoforms. (d). Schematic diagram to illustrate how clinoforms affect fluid flow within a reservoir. The dipping nature of the continuous shale barriers results in fluids being unable to move in either a horizontal or vertical direction (black arrows), while holes in the shale barriers permit a tortuous flow path (white arrows).

stratigraphic case studies (Van Wagoner et al. 1990; Van Wagoner & Bertram 1995 and references therein; Howell & Flint 2004; Hampson & Howell 2005) and as reservoir analogues (Bhattacharya & Giosan 2003; Bhattacharya & Tye 2004; Ryer 2004; Anderson et al. 2004; Forster et al. 2004; van den Bergh & Garrison 2004). These previous studies form the basis for this work and are refereed to where relevant below. The application of outcrops as reservoir analogues has a long history (Miall 1988; Reynolds 1999; Bryant & Flint 1993; Dreyer & Falt 1993; Alexander 1993; Willis & White 2000; Bryant et al. 2000 and numerous others). The application of reservoir modelling software to represent outcrops and simulate flow within

them is a relatively new approach. Previous studies include the pioneering work of the SAFARI project on fluvial strata (Dreyer & Falt 1993) and more recently in turbidites (Stephen et al. 2001; Pringle et al. 2004; Hodgetts et al. 2005), in shallow marine systems (Stephen & Dalrymple 2002; Howell & Flint 2002; Forster et al. 2004; van den Bergh & Garrison 2004) and in a variety of carbonate settings (Grammer et al. 2004 and references therein). The distribution of clinoforms in delta front deposits and their possible effects on reservoir performance in the Ferron Member have been discussed by van den Bergh & Garrison (2004), Anderson (2004) and Forster et al. (2004).

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Fig. 2. Stratigraphic cross-section of the Mesaverde Group within the Western Interior Basin with the study intervals highlighted (modified from Armstrong 1968).

Fig. 3. Location of the study areas within Utah. Insets show detail of the two study areas with the location of the outcrop logs (red dots) and calibrated photo logs (blue dots) shown.

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Clinoform geometries and their effects on fluid flow in shoreface systems were discussed and modelled from the lower part of the Brent Group in the North Sea by Wehr & Brasher (1996) who illustrated that overoptimistic assumptions of recovery from oilfields would occur if the clinoforms were ignored. Hampson (2000) described clinoform geometries from outcrops while their theoretical effects on flow were modelled by Jackson & Muggeridge (2000). The latter authors concluded that shales only had a significant effect on flow if they were steeply inclined and laterally very extensive. This conclusion is highly pertinent to the present study. Ainsworth et al. (1999) discussed the effects of clinoforms in lacustrine deltaic reservoirs.

Geological setting and study areas The Western Interior Basin of the USA developed during the Cretaceous as a response to flexural loading of the American plate associated with the development of the Sevier Orogenic belt on the western margin of the continent (Kauffman 1977; Roberts & Kirschbaum 1995). During the Late Cretaceous (Turonian), the basin underwent a marine transgression and by the Campanian formed an epicontinental seaway up to 1500 km wide that stretched from Alaska to the Gulf of Mexico (Armstrong 1968). The two intervals which form the basis for this study were deposited on the western margin of this seaway as part of the Mesaverde Group clastic wedge that filled the basin (Young 1955). Overall, the clastic wedge prograded from the west towards the east, although many of the shoreline systems, including those in this study, are oriented obliquely or even orthogonal to this predominant progradation direction. The Mesaverde Group clastic wedge is comprised of fluvial, coastal plain and shallow marine deposits. The shallow marine deposits include wave-dominated shoreface systems (Young 1955; Howell & Flint 2004 and others) such as the Blackhawk Formation (Young 1955) and fluvial-dominated deltas such as the Panther Tongue Member and lower parts of the Ferron Sandstone Member which are the focus of this study. Sediment supplied to the shoreline systems was eroded from the uplifted lower Palaeozoic deposits to the west. The Middle to Late Cretaceous climate of the region was warm, wet and subtropical (Roberts & Kirschbaum 1995). Peat swamps, including large raised mires (Doelling 1979; Bohacs & Suter 1997; Davies et al. 2006) covered much of the coastal plain region behind the shorelines. The Turonian-aged Ferron sandstone (Ryer 1981, 1983) represents a large shoreline complex that outcrops on the western edge of the San

Rafael Swell (Fig. 3). The focus of this study is lowermost parasequence in the Ferron (F1 of Ryer 1981; Gardner et al. 2004) which outcrops in the area around Ivie Creek (Fig. 2). The specific study area comprises a 35 m thick interval in a 2  7.3 km area with the long axis orientated parallel to the depositional dip direction. The sedimentology of the Ferron delta complex has been previously described by Ryer (1981) and its sequence stratigraphy by Gardner (1995) and Gardner et al. (2004). The Ferron 1 is a 30 m thick deltaic sandbody that prograded towards the NW (Cotter 1976). In the Ivie Creek area (Fig. 3), this unit is comprised of 20 separate delta lobes, has a positive (i.e. progradational and aggradational) shoreline trajectory and forms part of a highstand systems tract (Garrison & van den Bergh 2004). The outcrops show welldefined clinoforms, distributary channels and a number of large growth faults, developed as the delta was prograding (Bhattacharya & Giosan 2003). The Ferron was the subject of an extensive study by the Utah Geological Survey (Chidsey et al. 2004) which included reservoir modelling of a part of the Ivie Creek area (Fig. 3). The Panther Tongue sandstone outcrops in the northern Book Cliffs and along the NW margin of the San Rafael Swell (Young 1955; Newman & Chan 1991). The focus of this study is a 7.1  4.3 km outcrop area within the excellent exposure around the town of Helper and in nearby Spring Canyon (Fig. 3). The Panther Tongue is a 25 m thick sandbody, deposited as a river-dominated delta (Newman & Chan 1991; Posamentier & Morris 2000; Howell & Flint 2004) with very well-developed clinoforms and a large distributary channel complex (Newman & Chan 1991). The Panther Tongue lacks associated coast plain deposits and is interpreted to have been deposited as a falling stage or forced regressive deposit while relative sea-level was falling (Posamentier & Morris 2000). Progradation was towards the S and SW. The top of the Panther Tongue is a planar horizontal surface locally represented by a well-developed transgressive lag deposit (Newman & Chan 1991; Hwang & Heller 2002). Within the study area (Fig. 3), the Panther Tongue is comprised of a series of deltaic lobes which are defined by changes in clinoform dip direction and are more difficult to distinguish than those in the Ferron 1 unit. Growth faults were not observed in any of the studied intervals.

Methodology Field data collection techniques Data required to capture the geometry of the clinoforms were collected in the field using a

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combination of traditional field techniques (sedimentary logging and mapping) and newly developed methods, designed to efficiently capture the high volumes of spatial information required to accurately recreate the clinoform surfaces (Fig. 4). Traditional logging in which the grainsize, textural parameters, biogenic and sedimentary structures, nature of bed contacts and palaeocurrent information were recorded at a scale of 1:50 were undertaken on 14 sections in the Ferron 1 unit and 10 sections in the Panther Tongue (Fig. 3). In addition to the logging, all of the outcrops were photomontaged. In this montaging, photos were taken from a known position (mapped using a handheld GPS, accuracy þ/2 5 m). A scale was included in every photo within the montage, comprised of a fluorescent ball suspended vertically down the cliff on a tape measure by an assistant. The ball was positioned in such a way as to be visible in the photos and the assistant would record the length of tape from the top of the cliff to the ball and a GPS location. From these photomontages, it was then possible to trace surfaces and produce Calibrated Photo Logs (CPL). Calibrated photo logs were constructed by calculating a vertical scale from the recorded length of the tape for the centre of each photo. This scale was then tested against the known height of the assistant, and photos with more than 10 cm (c. 5%) error were rejected. The photos were then used to produce basic facies logs and point sets. Facies logs were compared and quality controlled by comparison to the traditional sedimentary logs. The point sets comprise XYZ coordinates for the intersection of the CPL and key surfaces, recognized and traced at outcrop and in the montages. The XY position for each point is taken from the GPS reading at the top of the cliff and the Z is taken as a distance or ‘depth’ below the top of the studied unit, which was treated as a planar and horizontal datum surface. Using the top of the deltaic bodies as a horizontal datum is a pragmatic approach to the problems associated with poor Z accuracy from the GPS, the presence of tectonic dip and other possible structural features such as post-depositional faulting. It is recognized that this may introduce subtle errors, but given that the purpose of the study is to look at clinoform geometries that are far more steeply dipping than the tectonic dip and that regional mapping indicates the top of both units is very close to flat, these errors are not considered significant. Other errors in the approach such as the accuracy in the XY position associated with using a handheld GPS (þ/2 5 m) are also not considered significant as they are significantly lower than the grid dimensions (typically 50 m – see below) in the modelling system, i.e. moving any of the XY locations by up to 10 m

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would not alter the geometry of the final model significantly as the CPLs would still sit within the same column of grid cells. These methods were found to be an efficient, cheap and sufficiently accurate method of producing the large volumes of spatial data required to build the reservoir-style models that were used to capture the geometries of the clinoforms.

Data processing Once the logs, CPLs and photomontages were collected, they were interpreted and prepared for modelling (Fig. 4). Key surfaces representing bedset (delta lobe) boundaries were interpreted from changes in facies stacking and changes in clinoform dip and orientation (see below). These lobe boundaries were mapped in the field and on the montages, and converted into point sets. Facies that were documented in the field (see below) were interpreted in the CPLs. The dataset for the Panther Tongue model includes 13 surfaces with a total of 720 points, 410 CPLs and 10 traditional logs. The dataset for the Ferron includes 21 surfaces with a total of c. 960 points, 168 CPLs and 14 traditional logs. Models were built and flow simulated within Roxar’s RMS software, a commercially available reservoir modelling package (Fig. 4). As the system is designed to deal with subsurface data, a number of new workflows and procedures were required which are outlined and discussed below. The CPLs and traditional logs were converted into text files that could be read as ‘well logs’ and ‘point sets’ by the reservoir modelling system (Fig. 4). The well logs are an ascii text file with the XYZ location of the point at which the well passes into a new facies or zone, X and Y are taken from the GPS reading and are constant for the whole log (i.e. the tape measure and the ‘well’ are assumed to be vertical). The Z reading is calculated from the vertical distance (depth) below the datum surface. Point sets are ascii text files that record XYZ positions at which a specific surface intersects a series of CPLs. The procedure for building the models from the outcrop data is discussed below.

Facies and sedimentology Both the Ferron 1 and the Panther Tongue are interpreted as river-dominated delta systems (Fig. 5; Bhattacharya & Walker 1992). A detailed discussion of the sedimentology of both of these delta systems is beyond the scope of this paper and has been presented elsewhere (Newman & Chan 1991; Gardner 1995; Bhattacharya & Giosan 2003;

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Fig. 4. Data collection methodology. (a) Outcrop of the Ferron with a traditional sedimentary log taken on the righthand side and a calibrated photo log in the centre. The assistant with the scale (tape and ball) is circled. (b) Outcrop data are used to create a text file which can be read into the modelling system as a well. (c) The wells are then used to produce point sets and (d) recreate the key bedset bounding surfaces. Surface shown is top of bedset 12. (e) Same surface viewed from the SE intersecting the DEM. Note that the dip of the delta front is very difficult to determine with no vertical exaggeration of the model volume.

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Fig. 5. Facies associations identified within the study. Typical log and example photos from the Ferron 1 are shown. Facies model is modified after Bhattacharya & Davies (2001).

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Chidsey et al. 2004 and references therein). The following summary describes, interprets and discusses the systems within a framework of ‘modelling facies’ (Fig. 5). These are sedimentary facies that have similar and consistent petrophysical properties and that can be mapped in 3D at a scale that can be captured with the grid resolution used in the models.

Offshore claystones and siltstone Both of the studied delta systems are underlain and overlain by blue-grey siltstones and claystones. These mudrocks are typically heavily weathered and are not always well exposed. Where seen, they commonly lack internal sedimentary structures and/or are extensively bioturbated with a diverse ichnofauna. Where present, sedimentary structures include planar horizontal lamination and wave ripples. Bedding is poorly developed and, where observed, beds are between 0.1 and 0.8 m. Sideritic nodules locally follow bedding planes. These deposits are interpreted to have been laid down in an offshore environment, close to, or beneath wave base. The dominant depositional mechanism was the settling of fine-grained material from suspension, probably from buoyant hyperpycnal plumes at the river mouth. The low proportion of sedimentary structures and poorly defined bedding are attributed to extensive bioturbation. The presence of sparse wave ripples and the diverse ichnofaunas indicate a relatively welloxygenated and shallow water shelf environment (Bhattacharya & Walker 1992). Standard core analyses of comparable facies from subsurface datasets indicate that these facies are non-reservoir. Properties assigned to facies for the flow simulations are summarized in Table 1.

Delta front sandstones The main portion of the deltaic bodies is comprised of interbedded sandstones and siltstones. The sandstones are very well sorted, fine to lower medium Table 1. Deterministic petrophysical values used to condition the facies-based models. The values used were taken from Manzocchi et al. (2008) and are considered to be typical mid-range that occur in a typical North Sea reservoir Facies Offshore Prodelta Lower Delta Front Upper Delta Front Channel

Porosity

Kh (mD)

Kv (mD)

0.03 0.12 0.15 0.25 0.25

0.06 20 90 854 1000

0.001 0.001 1.65 165 200

grained and occur in beds that are typically 0.1 to 4 m thick and dip at between 1 and 78. Overall, there is an upward increase in bed thickness and a decrease in the proportion of interbedded siltstones. Internally, beds are either massive or dominated by current-generated sedimentary structures including basal sole marks, planar lamination and ripple cross-stratification. Individual beds commonly show evidence for waning flows passing upward from massive to planar-laminated to rippled. Thicker beds contain amalgamation surfaces indicating episodic deposition. Soft sediment deformation associated with dewatering is locally abundant. Wave ripples are also locally present at the tops of beds. Trace fossils are rare and the degree of bioturbation is typically low. Where present, traces include Ophiomorpha, Skolithos, Arenicolites and escape structures. Within the Ferron 1, draped cross-bedding and hummocky cross-stratification are present but rare. These sandstones were deposited by periodic hyperpycnal density currents in the lower part of the delta front (Bhattacharya & Walker 1992). Individual flows deposited event beds which represent the passage of a sand-laden density current down the delta front. Evidence for waning flow, localized reworking by wave ripples, escape structures and siltstone interbeds, indicates that these events were episodic, potentially initiated by increased run off within the fluvial systems that fed the delta (Bhattacharya & Walker 1992) associated with storms in the hinterland. The association of these current-generated structures with shallow water ichnofaunas, wave ripples and the dip of the beds indicates deposition in a delta front setting (Bhattacharya & Walker 1992). Core analysis data from subsurface analogues and in the case of the Ferron from outcrop studies (Forster et al. 2004) indicate that these deposits are potentially key reservoir facies. For the purpose of modelling, they have been subdivided into two subfacies– upper delta front and lower delta front. The upper delta front is defined as having a mean bed thickness greater than 2.5 m and less than 10% siltstone interbeds. The lower delta front comprises thinner sandstone beds and a higher percentage of interbedded siltstones. This distinction is largely arbitrary as the transition between the units is gradational. They were separated in order to allow the extent of the shaledraped clinoform beds (see below) to be varied systematically within the models.

Delta front siltstones Interbedded with the sandstones described above are a series of thin, laterally continuous siltstone beds 1–30 cm thick. Beds may be comprised of

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silt with variable amounts of very fine-grained sandstones. The facies also includes some very fine-grained silty sandstones that have a similar distribution and occurrence to the siltstones. The mean thickness and proportion of siltstone beds increase downward within the deltaic bodies. Siltstone beds typically dip at 1–78 and are laterally continuous in a strike-and-dip direction for 100–4000 m in a depositional dip direction and 100–4000 m in a depositional strike direction. These siltstones are typically dark in colour and are either bioturbated or contain wave and more rarely current ripples. Ripples are locally draped with dark clay and/or organic material. Rare double drapes interpreted as tidal in origin are present in both the Panther Tongue and the Ferron. These siltstones are interpreted to have been deposited either as the final phase of the density flows that deposited the sandstones described above or in between flow events as drapes across the delta front. The upward-thinning and reduction in siltstone bed frequency is attributed to erosion by subsequent sandstone-depositing events being more prevalent toward the top of the delta front. Minor reworking by wave and potentially tidal currents took place between density flow events. The siltstone beds are considered to have non reservoir properties and have been modelled discretely because such bodies will produce either barriers or at least baffles to flow. A key aspect of the modelling is the effects that these dipping barriers have upon simulated production.

Distributary channel facies Both the Panther Tongue and the Ferron contain intervals that are interpreted as being deposited within distributary channels; however, they differ somewhat between the two units. Within the Panther Tongue, a 25 m thick stack of massive trough cross-stratified to rarely planar bedded sandstone with a broad channel geometry (.1200 m wide) occurs in Spring Canyon (Fig. 3). Closer inspection reveals that the broad channel geometry is somewhat misleading and that the massive sandstones that fill the channel actually interfinger with the adjacent delta front facies. This relationship was documented by Olariu et al. (2005); their paper gives a full and detailed description of the facies geometries. Channel-shaped sandbodies in the Ferron within the study area are typically smaller (5 m  25 m) and show a clearly erosional contact with the underlying and adjacent delta front deposits. The Ferron channels are more variable than their Panther Tongue counterparts and include massive sandstones, heteroliths with lateral accretion surfaces, horizontally bedded heteroliths and mudstones.

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The channel-shaped bodies are interpreted as the products of deposition within the channels that fed sediment to the delta front. The Ferron channels cut through the delta lobes that they overlie and were probably genetically related (i.e. feeding sediment) to younger lobes that lay in a more basinward direction. Deposition occurred as the channel was active (in the case of the lateral accretion surfaces) and later once the channel was abandoned. The Panther Tongue channel complex is somewhat more complex. The overall thickness and lack of a single cut margin indicate that the channel was active at the same time that the lobe was being deposited. Deposition of massive sandstones occurred in channel and proximal mouthbar settings that aggraded as the delta was building seaward (Bhattacharya & Walker 1992; Olariu et al. 2005). Growth faults. The Ferron Sandstone contains a series of structures interpreted as the product of active growth faulting during the progradation of the delta (Gardner 1995; Bhattacharya & Davies 2001; Bhattacharya & Gisosan 2003). These are absent from the Panther Tongue. Growth fault structures include large sandbodies (up to 15 m thick) bounded at their base by fault slip planes marked by slickensides. The faults exhibit a listric geometry and detach either into siltstone beds within the delta front or, in the case of the larger structures, into the underlying offshore siltstones. The faults are oriented broadly E–W and downthrown to the north (offshore); however, in plan view they have a markedly scoop-shaped geometry. Beds within the hangingwall block are comprised of current-rippled and planar-laminated sandstones that have been rotated until they dip at up to 808. The original depositional structures are well preserved and soft sediment deformation is surprisingly rare. Very small (cm scale) faults and deformation bands are common. The preservation of current-deposited structures within highly rotated beds and the low abundance of soft sediment deformation and slumping indicate that the growth faults grew by a process of creep. It is proposed that once initiated, subsequent sediment loading may have driven movement on the faults, such that they never had a surface expression on the sea-floor. Preservation of original structures and the presence of deformation bands indicate at least partial lithification of the sediment at the base of the rotated fault blocks. Petrophysically, the sandstones within the hangingwall blocks of the fault were considered to be the same as the delta front sandstones. This is confirmed by the outcrop studies of the Utah Geological Survey (Forster et al. 2004).

Delta lobes and parasequences Both of the modelled intervals are considered here to represent a single parasequence, following the

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original definition of Van Wagoner et al. (1990) of a parasequence as an upward-coarsening succession of strata bounded by a marine flooding surface or its correlative conformity. The top surfaces of both units are planar, horizontal (at least at the scale of the study areas) and represented by a sharp juxtaposition of offshore deposits over upper delta front, distributary channel and locally, in the case of the Ferron, delta-top coals. The top of the Panther Tongue is locally marked by a coarse-grained, highly bioturbated transgressive lag that is up to 0.3 m in thickness (Hwang & Heller 2002). This upward transition to offshore deposits indicates a landward dislocation of the shoreline of several to tens of kilometres (Van Wagoner et al. 1990). The Ferron 1 unit has previously been interpreted as a parasequence set

(Garrison & van den Bergh 2004) although no evidence for rises in relative sea-level that dislocated the shoreline was observed within the unit in this study. Within both study intervals, there is also a smaller-scale packaging of the sediments into bedsets. A bedset is represented by a genetically related set of beds at a smaller scale to a parasequence and with a more limited lateral extent (Campbell 1967; Van Wagoner et al. 1990). The bedsets differ somewhat between the two units although the interpretation of their genesis is similar (see below). Within the Ferron, the overall upward-coarsening package can be subdivided into a series of smaller upward-coarsening bedsets which are typically 2–6 m thick (the parasequences of Garrison & van

Fig. 6. Selected bedset surfaces documenting the evolution of the Ferron 1 delta. (a) Top bedset 1; (b) top bedset 4; (c) top bedset 6; (d) top bedset 9; (e) top bedset 14; (f) top bedset 19. In all cases, the vertical exaggeration is  10 and North is towards the top of the view.

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den Bergh 2004). Mapping of these units indicates that they have a lobate plan view shape (Fig. 6). Twenty different packages have been mapped within the study area and they show a compensational stacking pattern (Fig. 6). Bedsets in the Panther Tongue are typically defined on the basis of changes in clinoform angle and they show a less well-defined upward-coarsening nature. Mapping of these bedsets also indicates a compensational stacking pattern although there is a higher degree of progradation within the depositional system (Fig. 7).

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As no evidence was observed for a marked landward migration of the shoreline in association with the formation of any of the coarseningupward units, they are interpreted as bedsets rather than parasequences. These bedsets are the result of delta lobe switching related to autocyclic avulsion of the distributary channel system. Lobes within the Ferron were deposited while the shoreline had a gradually climbing trajectory. This resulted in frequent and shallow distributary channels that were able to readily avulse. Channel switching introduced sediment into sheltered interdistributary bays

Fig. 7. Selected bedset surfaces documenting the evolution of the Panther Tongue delta. (a) Top bedset 3; (b) top bedset 4; (c) top bedset 6; (d) top bedset 9; (e) top bedset 11; (f) top bedset 13. In all cases, the vertical exaggeration is 10 and North is towards the top of the view.

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(Elliott 1974) between older lobes and resulted in deposition of the observed upward-coarsening units. Within the Panther Tongue, a falling shoreline trajectory resulted in a distributary channel that was less able to avulse and a stronger basinward progradation of the delta (Posamentier & Morris 2000). While there was still a degree of lateral migration, falling sea-level resulted in less lateral shifting and less well-defined upward-coarsening within the individual lobes. The geometry of the lobes is a major factor that could potentially affect the simulated fluid flow through the two units. The model building and flow simulation is discussed in the following section.

Model construction Modelling of the two delta systems was undertaken in Roxar’s IRAP RMS software which was designed, and is typically used for, modelling subsurface reservoirs. The procedure followed was similar to that used for subsurface systems although there are some significant differences which stem largely from the different data types. The data used to build a subsurface model typically include two, or sometimes more, seismically mapped surfaces and a limited amount of well data. Once depth converted, the seismic surfaces are used to create surfaces within the model. The surfaces form the basis for the structural modelling, they guide the position of further (calculated) surfaces and they define the boundaries to the modelling zones. The modelling grid is comprised of cells which may be stacked proportionally (i.e. there are a constant number of layers of cells within a zone) or which may have constant thickness arranged parallel to a surface, typically either the top or base of the reservoir zone. The size of the individual cells within the grid should ideally reflect the scale of the heterogeneity that should be captured in the model. In reality, grid resolution is also heavily influenced by the limitations of the modelling software and the field size, especially for the numerically expensive, dynamic model used for simulation. Typical resolution for a static geomodel is currently between 1–5 million cells and a dynamic model around 100 000 cells. For a typical North Sea field, this results in grid cells that are 50 –100 m in the X and Y dimensions and 0.5 to 5 m in the Z dimension. Grids are populated with petrophysical properties that are either extrapolated directly from measured properties at the wells or that are linked to the facies. Facies within the model are distributed using a combination of user-based rules on facies distribution, object size, expected lateral and vertical juxtapositions and the well observations. Facies-specific

petrophysical properties are then introduced stochastically using variograms derived from measured observations of the core analysis data. The models are then upscaled and flow simulated. Models built from outcrops are based upon somewhat different datasets. There is generally a far greater number of vertical sections (wells), a far better conceptual understanding of the distribution of intrareservoir surfaces and facies and much better constraint on the scale, geometry and distribution of heterogeneities. Surfaces that are identified in the outcrop can be traced and correlated between wells with a higher degree of resolution and confidence than in the subsurface. The procedure developed for modelling the outcrop data is outlined below. Initially, a datum surface was defined. This formed the basis for all of the Z values within the model. In both of the case studies presented here, the datum surface was the top of the respective delta system. This surface is created as a horizontal surface placed at 1000 m depth. The depth is important for the subsequent flow simulation. Once the datum is defined, the point sets and CPLs can be hung from it and the data for each are imported. The point sets are used to define the position in the model of the various bedset (deltalobe bounding) surfaces (Figs 6 and 7). A typical point set for a surface contains between 25 –100 points. The point sets are imported and extrapolated by gridding. The gridding of the surfaces is an iterative process based upon the point set, the observed data and the authors’ conceptual interpretation of the distribution and geometry of the surface between the outcrops (Fig. 5). The surface geometry is also heavily influenced by the choice of gridding algorithm. In virtually all cases, the conceptual understanding and desired geometry was best achieved by a local b-spline algorithm which is highly suited to datasets with moderate to large volumes of point data. Once satisfactory surfaces were created, they were kept constant for the subsequent modelling steps. As such, these surfaces provide a deterministic framework in which different grid building and populating stages could be investigated. Once the model zones were defined within the framework of the surfaces, the well data from the outcrop logs and CPLs with facies were imported. Up to 300 of these were used for each model. Modelling grids were then built (Fig. 8). Given that the two study areas were similar in size to a typical North Sea field, it follows that the grids would be of similar sizes. Ideally, the grid should be parallel to the main geological heterogeneity; two gridding strategies were used in the final models. The first grid design used a regular thickness grid that followed the top surface of the model (i.e. horizontal).

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Fig. 8. Regular and dipping grids. (a) Outcrop of the Panther Tongue showing the continuous, dipping nature of the clinoforms. (b) A regular grid that follows the upper surface of the zone captures the dipping nature of the geology where the top of the zone is dipping, but not where the top of the zone is flat. This results in (c) facies models that are unable to capture the continuous dipping nature of the barriers. (d) A dipping grid which follows a guide surface designed to follow the clinoforms. (e) The facies realization in the dipping grid is able to capture a more realistic clinoform geometry including shales along the clinoform.

This is a typical approach commonly used in subsurface settings. The second technique involves creating a dipping grid that follows a guide surface, designed to capture the heterogeneity created by the clinoforms. A separate grid was created for each zone. Testing the use of a dipping grid is important as it is difficult to capture dipping barriers such as the shales associated with the clinoforms within regular and even proportional grids where the X and Y dimensions are much greater than Z. A key aspect of this study is to compare traditional gridding techniques with dipping grids designed specifically to follow the clinoform dip (Fig. 8). The various models were then populated with facies on a zone by zone (bedset) basis. The facies modelling followed the following procedure (Fig. 9):

1. The broad-scale facies distributions were modelled using a facies belts approach. In this, a Truncated Gaussian Simulation is used to capture belts of parallel facies (MacDonald & Aasen 1994). The mean position of the facies belts boundaries and parameters such as the aggradation angle, belt width and degree of interfingering between the belts are defined by the user and conditioned from the outcrop observations (Fig. 9c). As the facies belts approach relies on the creation of a regular ‘simbox’ for the simulation, it is very difficult to achieve the required distributions within a zone that has a dipping grid. Consequently, the facies belt modelling was carried out within a regular grid (Fig. 9c) and then resampled into the dipping grid using a nearest neighbour resampling algorithm (Fig. 9d). Visual inspection of cross-sections,

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Fig. 9. Model building workflow. Once the deterministic surfaces have been created, two grids are built, one dipping (a) and one regular (b). A facies belt realization is generated in the regular grid (c). This is resampled to the dipping grid (d) and then merged (e) with an object based realization which captures the clinoform shales (f). Petrophysical properties are then added and the model is flow simulated (g).

cut through the model parallel to the main outcrop faces, indicates that the models adequately captured the geometries in the original geology. 2. A number of different methods were attempted to create the dipping shales associated with the clinoforms, including placing a very high degree of stochastic noise on the boundaries in the

facies belt simulation. Ultimately, an object-based approach in which the delta front siltstone facies was modelled as objects in a background within the dipping grid was used (Fig. 9e). This provided the best visual match to the outcrop observations. The shape and position of these objects were conditioned from the well data and the observations

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from the outcrop. These shale objects were then selectively resampled and merged with the facies belt model such that the shales occur only in the delta front sandstones and not in the offshore or channel deposits (Fig. 9f). This produced the required delta front facies with a high proportion of dipping shales (Fig. 9f). A key parameter was the continuity of the shale draped on the clinoform surfaces. In both the Panther Tongue and the Ferron, two different shale clinoform lengths were modelled: short clinoforms c. 200 m and longer clinoforms (.1 km) to capture discontinuous but pervasive barriers and virtually continuous barriers. In all cases, the proportion of the shale objects was conditioned from the outcrop observations and kept constant at 20%. 3. The small, sandstone-dominated channels in the Ferron were included with the upper delta front as they were too small to represent accurately within the model and the majority were sand-filled and petrophysically very similar to the delta front sandstones (Moiola et al. 2004; Forster et al. 2004). The large distributary channel in the Panther Tongue was modelled as a separate zone, which was populated with 90% channel sand in a background of delta front sandstone. This effectively captured the interfingering of the channel complex with the underlying delta front deposits. 4. Modelling growth faults: initially significant effort was expended in mapping the growth faults and accurately representing the fault surfaces within the reservoir model. However, given their lateral scale (less than 100 m), it was found that the geometry and nature of the fault planes could not be captured in the model. Consequently, the faults were modelled by detailed surface editing of a submodel that was used to create a sandbody that represented the hangingwall fill of the fault. This body of sandstone that represents the infill of the hangingwall depocentre was then resampled into the model, replacing the facies that were previously present. 5. Once each lobe was modelled, the facies for each zone were visually inspected for geological integrity and compared to the montages to ensure that the geometries were correctly captured. Once a satisfactory realization was achieved, it was resampled into a multigrid for petrophysical modelling and flow simulation. The facies-based models were then populated with petrophysical properties (Fig. 9g). As the models were built to investigate the comparative effects of geometries on fluid flow, the same deterministic properties were assigned on a facies-by-facies basis to all of the models. Stochastic procedures were not used here as these would have introduced additional noise into the results. The values used were taken

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from analogous North Sea fields and are summarized in Table 1. Following the petrophysical modelling, the geomodels were upscaled and resampled to allow flow simulation. Grid size in the dynamic model was set to 100 m  100 m  0.4 m in order to maintain as much of the vertical resolution as possible. The facies that were modelled in the higher resolution geomodels were also resampled in to the dynamic models in order to visually link the facies and petrophysical properties. Flow simulation was undertaken in the RMS finite difference, black oil simulator. The dynamic properties used to condition the models are summarized in Appendix 1. As the aim was to investigate geometric effects on flow, typical mid-range properties were used and kept constant between model runs. The field development plan for the flow simulations was based upon a line-drive water injection between two rows of three vertical wells. For each model, water injection was carried out both up-depositional dip and down-depositional dip to determine if clinoform direction was relevant to production (cf. Wehr & Brasher 1996). Flow rates of 500 standard cubic metres (Sm3/day) were used for both injectors and producers with a bottomhole pressure of 300 bar in the injectors. The simulations were run for 30 years or until the field produced a 30% water cut. Producers were temporarily shut down if water cut exceeded 30%. It is important to note that the purpose of the exercise is to use flow simulation as a dynamic test of reservoir heterogeneity and to produce values that could be compared between different models. More advanced reservoir engineering and optimization of the production was beyond the scope of this study.

Experimental set-up Several hundred different models were built and simulated, of which 16 are considered here (Table 2). The simulation results were used to test the following hypotheses: 1. That there is a difference in simulated performance if clinoforms are explicitly modelled. For this, we compare results from the highest resolution and most deterministic models with a series of models built from a simple facies belts realization conditioned to data from 10 wells. 2. Clinoforms modelled in a dipping grid produce significantly different flow simulation results to clinoforms modelled in a regular grid. 3. Modelled clinoform length and continuity is an important parameter. 4. Lowstand and highstand deltas have significantly different simulated reservoir behaviours

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Table 2. Models built and flow simulated in this study Model code

Grid type

Facies tools

Clinoform lengths

Waterflood direction

Ferron 1 Ferron 1 Ferron 1 Ferron 1 Ferron 1 Ferron 1 Ferron 1 Ferron 1 Panther Tongue Panther Tongue Panther Tongue Panther Tongue Panther Tongue Panther Tongue Panther Tongue Panther Tongue

Regular Regular Regular Regular Dipping Dipping Dipping Dipping Regular Regular Regular Regular Dipping Dipping Dipping Dipping

Facies belts Facies belts Facies belts and facies composite Facies belts and facies composite Facies belts and facies composite Facies belts and facies composite Facies belts and facies composite Facies belts and facies composite Facies belts Facies belts Facies belts and facies composite Facies belts and facies composite Facies belts and facies composite Facies belts and facies composite Facies belts and facies composite Facies belts and facies composite

None None Short Short Short Short Long Long None None Short Short Short Short Long Long

Up depositional dip Down depositional dip Up depositional dip Down depositional dip Up depositional dip Down depositional dip Up depositional dip Down depositional dip Up depositional dip Down depositional dip Up depositional dip Down depositional dip Up depositional dip Down depositional dip Up depositional dip Down depositional dip

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Fe-Reg-Belts-Up Fe-Reg-Belts-Dw Fe-Reg-BeltsþOb-Up Fe-Reg-BeltsþOb-Dw Fe-Dip-Short-up Fe-Dip-Short-Dw Fe-Dip-Long-up Fe-Dip-Long-Dw Pn-Reg-Belts-Up Pn-Reg-Belts-Dw Pn-Reg-BeltsþOb-Up Pn-Reg-BeltsþOb-Dw Pn-Dip-Short-up Pn-Dip-Short-Dw Pn-Dip-Long-up Pn-Dip-Long-Dw

Delta

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indicating that accommodation controls clinoform geometry and subsequent reservoir performance. 5. The effects of water flood direction versus delta progradation direction. The simulation results were investigated for total recovery after 30 years of production and recovery factor. Recovery factor (RF) is a ratio of the recovered oil to the total oil in place. It is expressed as a percentage. Looking at RF allows comparison of the results from the two delta systems. The results are presented graphically (Figs 10 and 11) and in table form (Table 3).

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Discussion The results from the various models illustrate that there is a very large spread of production data. Total production varies from 0.40 to 1.55 million Sm3 which represents a range in RF between 14 and 54%. Given that all of the models are built from the same two outcrop datasets, have similar net : gross values and the same petrophysical, it must be concluded that these differences are due to the way in which the facies geometries are represented in the models.

Fig. 10. Flow simulations from the Panther Tongue showing the effects of the different modelling approaches; colours show fluid saturations (warm colours ¼ water, cold colours ¼ oil). All simulations are for water injection in a down-dip direction (towards left of view) after 20 years of simulated production. (a) Simple model built on a regular grid with facies belts but no clinoforms. (b) Regular grid with facies belts and clinoforms. (c) Model with dipping grid and short clinoforms. (d) Model with dipping grid and long clinoforms. (e) Outcrop view of the Panther Tongue; this view is located close to the central part of the cross-sections shown above.

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Fig. 11. Flow simulation results. (a) Cumulative production through time. (b) Cumulative recovery factor through time. Key to various model runs is given in Table 2.

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Table 3. Summary of flow simulation results Model Fe-Reg-Belts-Up Fe-Reg-Belts-Dw Fe-Reg-BeltsþOb-Up Fe-Reg-BeltsþOb-Dw Fe-Dip-Short-up Fe-Dip-Short-Dw Fe-Dip-Long-up Fe-Dip-Long-Dw Pn-Reg-Belts-Dw Pn-Reg-Belts-Up Pn-Reg-BeltsþOb-Dw Pn-Reg-BeltsþOb-Up Pn-Dip-Short-Dw Pn-Dip-Short-Up Pn-Dip-Long-Dw Pn-Dip-Long-Up

Total production (106 m3)

Recovery Factor (%)

Discounted production (mil USD)

13.1 13.4 13.3 15.5 4.4 4.0 8.3 11.2 10.6 10.4 9.6 9.6 7.1 7.4 4.9 3.6

44.54 45.82 46.74 54.40 15.47 13.90 29.78 40.34 45.13 44.32 45.28 45.28 33.07 34.28 23.11 16.98

240.3 240.2 247.6 252.6 76.6 72.0 177.0 197.0 208.56 187.32 207.7 189.42 164.11 139.59 95.23 75.39

Regular vs. dipping grids The models that were built with a regular grid (Fig. 10a, b) produce the most oil and have the highest recovery factors (RF between 40.3 and 54.4%, mean 46.4%; Fig. 11a, b). These models have a fairly low spread of RF values and all eight models sit within a 14% range. The models built with the dipping grids (Fig. 10c, d) show a far greater spread of RF values (13.9 – 40.3%) with a much lower mean (25.9%; Fig. 11a). As the dipping grid follows the geological heterogeneity and includes the dipping barriers, it is considered to be a better representation of the geology than the regular grid. Given that the majority of reservoir models from subsurface systems do not attempt to capture the clinoforms, it is concluded that they will typically overestimate both production and recovery.

Modelling clinoforms Jackson & Muggeridge (2000) concluded that the presence of dipping, discontinuous shales would reduce sweep efficiency if the barriers cover large areas and were dipping steeply. Representing clinoforms as shale objects within the regular grids did not capture the reduction in flow associated with the clinoforms. In both delta systems, the presence of barriers in the regular grid marginally improved recovery (Fig. 11a). To capture the clinoforms effectively, shale objects were introduced to dipping grids (Fig. 10c, d). These are associated with a significant drop in reservoir performance (Fig. 11a, b) and it is concluded that this strategy is better at capturing the true character of the reservoir. This is an important conclusion since dipping

clinoforms are rarely modelled explicitly and the results of this study suggest that even modelling them as objects within a regular grid will not capture their continuity and geometry and subsequently their effects on flow.

Shale length associated with clinoforms The shale bodies associated with the clinoforms were modelled with two different lengths: short bodies (c. 200 m; Fig. 10c) and long bodies (.1 km; Fig. 10d). In all cases, the net : gross was conditioned to the outcrop and kept constant at 20%. Shale length has a significant effect on recovery with a wide spread of recorded values (Fig. 11a, b). In the Ferron models, the short shale lengths had a far more detrimental effect on recovery than the longer ones (Fig. 11b). The opposite was true in the Panther where the model with the shorter shales produced better. In both systems, the longer clinoforms were most sensitive to waterflood direction with waterflood down depositional dip being much less favourable than sweeping the oil updip (Fig. 11a, b). Visual inspection of the fluid saturations illustrates that displacing the oil in a downdip direction results in pockets of oil being trapped beneath the shales, against the water leg. The difference between the systems is interesting. In the Ferron, the long clinoforms do not form extensive barriers and the increase in tortuosity associated with a higher number of short barriers is the dominant factor reducing production. Given that any particular shale clinoform object is confined to a single lobe, the lack of extensive barriers may be because the individual delta lobes stack vertically, and laterally, providing communication

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between sandbodies in adjacent lobes, and oil is trapped behind the shales in a number of small pockets. In the Panther Tongue, the lobes are narrower and stack in a forward steeping manner. This means that the longer shale lengths more effectively compartmentalize the system. The models are extremely sensitive to the total number of bodies and the values assigned to clinoform lengths (Fig. 11a, b). This is significant because such data are not available from the subsurface and must be drawn from analogues. The choice of a suitable analogue is consequently very important.

Water flood direction Within any given model, two production strategies were tested with water injection in an up-depositional dip direction and in a down-depositional dip direction (Fig. 11a, b). The results show that the variety in model performance associated with the water injection direction is typically much less than that associated with the model building strategy. The most significant differences in production occur when the long clinoforms are modelled as discussed above (6–10% reduction in RF). In virtually all cases, the production is better when the oil is swept up depositional-dip. These results indicate that the clinoforms may channel the sweeping water up from the OWC, towards the top of the model and into the producers. This is contrary to the results of Wehr & Brasher (1996) who found that sweeping oil in a down-dip direction was preferable. There are two key differences between Wehr & Brasher’s models and those presented here. They modelled shoreface rather than the deltaic systems (with far less clinoforms) and the strata in their models were dipping (c. 68). The structural dip results in a greater influence of gravity. Either of these factors could explain the different conclusions reached.

Highstand vs lowstand deltas A key purpose of this study was to compare the simulated production from two systems deposited in different accommodation regimes (Fig. 11a, b). The average recovery factors are very similar and significantly less than the differences introduced by using the different modelling strategies. The mean discounted production for all of the Ferron models is higher than for the Panther Tongue models, indicating that production from the highstand delta is more efficient that its lowstand counterpart (Fig. 11a, b). The key difference between the systems is that in the Ferron the long clinoform shales have less effect than the short ones while the opposite is true in the Panther Tongue. The highstand Ferron is also more sensitive to waterflood direction than the Panther Tongue. The stacking

of individual lobes in the Ferron models leads to greater vertical compartmentalization, although this is not reflected in the results which are governed by the lateral sweep of the oil.

Conclusions Within this paper, we have documented a methodology for the relatively inexpensive collection of large quantities of field data suitable for the building of reservoir style models from outcrops. Data were collected using a combination of traditional field logging techniques and the collection of geospatial, referenced, scaled photo logs (CPL). These data were then used to build reservoir style models. The model building workflow is based upon the 3D reconstruction of a series of surfaces that represent the individual bedsets boundaries within the delta. These deterministic surfaces provide an insight into the evolution of the delta and also provide a framework for experimentation with different grid build strategies and different grid population methods. Dynamic testing of the models was then used to determine the key controls on variability in the simulated production from the systems. From the simulated production results, the following conclusions are drawn. 1. The greatest variability in reservoir performance in the current study came from model building strategy. This is far greater than the difference between the two delta systems or differences associated with the waterflood direction. 2. Within each delta system, the suite of models that were built used exactly the same surface geometries, conditioning log data, net : gross values and petrophysical properties. All differences in the results are due to the way in which the models are built and how the heterogeneities are represented. 3. Models with regular grids that ignore the presence of dipping shales associated with clinoforms will greatly overestimate recovery from deltaic systems (by up to three times). 4. Models with dipping grids designed to follow delta front clinoforms capture the dynamic behaviour of the reservoir systems better than the regular grids typically used in modelling, although this may be impractical when trying to model a subsurface field. 5. Clinoforms appear in core or well log data as thin shales and are commonly ignored; although it may not be possible to model them explicitly, their effects should be accounted for. 6. A key aspect to the modelling is the length scales used for the shale objects that drape the clinoforms. As clinoforms cannot typically be mapped in the subsurface, these length scales should be drawn from outcrop analogue studies. 7. The model runs were sensitive to the shale length parameters used. In the highstand Ferron

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delta system, shorter shale lengths associated with a greater number of bodies greatly reduced recovery, whilst in the lowstand Panther Tongue delta system, long shale lengths were more effective at partitioning the body. This was the only significant difference between the studied highstand and lowstand delta systems. 8. In addition to the implications for subsurface studies, we have also demonstrated strategies for model construction from outcrop datasets and the utility of reservoir modelling software to synthesize and view outcrop data in 3D. Funding for this project was received from the Statoil funded e-learning project at the University of Bergen. Chris Edwards suggested working on the Ferron and directed us to Ivie Creek. The work has benefited from discussion with Gary Hampson and Matt Jackson, Imperial College London on the challenges of modelling deltaic systems. Roxar are acknowledged for software and the Utah Geological Survey are thanked for their continued enthusiasm and access to core and log data. The manuscript benefited from comments by Gary Hampson, an anonymous reviewer and the editors.

Appendix 1. Flow simulation set-up parameters Max. length of run Other run cut offs

30 years Wells shut at 30% water Report step 1 year Rock compressibility 0.000 043 5 1/bar Rock reference pressure 275.79 bar Spec. gravity oil 0.8 Gas/Oil ratio 142.486 Sm3 Corey exp Water Oil–water Saturation end points Sorw Swcr Rel. Perm. end points kromax krw Top of model 1000 m Oil– Water contact 1015 m OWC capillary pressure 0 Reference Depth 1023 m Reference Pressure 103 bar Wells Injectors Producers Flow rate Injectors Producers Bottom hole pressure Injectors Initial oil in place Panther Ferron

4.0 3.0 0.2 0.2 1.0 0.4

3 3 500 Sm3/day 500 Sm3/day 300 bar 2.85 þ e07 2.12 þ e07

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dominated deltaic shorelines; Upper Cretaceous Blackhawk Formation, Book Cliffs, Utah, USA. In: G IOSAN , L. & B HATTACHARYA , J. P. (eds) River Deltas – Concepts, Models and Examples. Society for Economic Paleontologists and Mineralogists Special Publication, 83, 133– 154. H ODGETTS , D., D RINKWATER , N., H ODGSON , D. M., K AVANAGH , J., F LINT , S. S., K EOGH , K. & H OWELL , J. A. 2005. Three-dimensional geological models from outcrop data using digital data collection techniques: an example from the Tanqua Karoo depocentre, South Africa. In: C URTIS , A. & W OODS , R. (eds) Geological Prior Information: Informing Science and Engineering. Geological Society Special Publication, 239, 57–75. H OWELL , J. A. & F LINT , S. S. 2002. Application of Sequence Stratigraphy in Production Geology and 3-D Reservoir Modelling. Gulf Coast Society for Economic Petrologists and Mineralogists, 22, 141–146. H OWELL , J. A. & F LINT , S. S. 2004. Sequence stratigraphical evolution of the Book Cliffs Succession. In: C OE , A. (ed.) The Sedimentary Record of Sea-Level Change. Cambridge University Press/The Open University. H WANG , I. G. & H ELLER , P. 2002. Anatomy of transgressive lag; Panther Tongue Sandstone, Star Point Formation, central Utah. Sedimentology, 49, 977–999. J ACKSON , M. D. & M UGGERIDGE , A. 2000. Effect of Discontinuous Shales on Reservoir Performance during Horizontal Waterflooding. Journal of Society of Petroleum Engineers, 5, 446–455. K AUFFMAN , E. G. 1977. Geological and Biological Overview: Western Interior Cretaceous Basin. The Mountain Geologist, 14, 75– 99. M AC D ONALD , A. C. & A ASEN , J. O. 1994. A prototype procedure for stochastic modeling of facies tract distribution in shoreface reservoirs. In: Y ARUS , J. M. & C HAMBERS , R. L. (eds) Stochastic Modeling and Geostatistics; Principles, Methods, and Case Studies. American Association of Petroleum Geologists Computer Applications in Geology, 3, 91–108. M ANZOCCHI , T., C ARTER , J. N., S KORSTAD , A., F JELLVOLL , N., S TEPHEN , K. D., H OWELL , J. A. ET AL . 2008. Sensitivity of the impact of geological uncertainty on production from faulted and unfaulted shallow marine oil reservoirs – objectives and methods. Petroleum Geoscience, 14, 3 –15. M IALL , A. D. 1988. Reservoir Heterogeneities in Fluvial Sandstones: Lessons from Outcrop Studies. American Association of Petroleum Geologists Bulletin, 72, 682–697. M OIOLA , R. J., W ELTON , J. E., W AGNER , J. B., F EARN , L. B., F ARELL , M. E., E NRICO , R. J. & E CHOLS , R. J. 2004. Integrated Analysis of the Upper Ferron Deltaic Complex, Southern Castle Valley, Utah. In: C HIDSEY , T. C., J R ., A DAMS , R. D. & M ORRIS , T. H. (eds) Regional to Wellbore Analog for Fluvial-Deltaic Reservoir Modeling: The Ferron Sandstone of Utah. AAPG Studies in Geology, 50, 79–91. N EWMAN , K. F. & C HAN , M. A. 1991. Depositional facies and sequences in the Upper Cretaceous Panther Tongue Member of the Star Point Formation,

MODELLING OF DIPPING CLINOFORM BARRIERS Wasatch Plateau, Utah. Geology of east-central Utah. Utah Geological Association Special Publication, 65– 75. O LARIU , C., B HATTACHARYA , J. P., X U , X., A IKEN , C., Z ENG , X. & M C M ECHAN , G. 2005. Integrated study of ancient delta front deposits, using outcrop, ground penetrating radar and three dimensional photorealistic data. Cretaceous Panther Tongue sandstone, Utah. In: B HATTACHARYA , J. P. & G IOSAN , L. (eds) River deltas: concepts, models and examples. SEPM Special Publication, 83. Tulsa, OK. P OSAMENTIER , H. W. & M ORRIS , W. R. 2000. Aspects of the stratal architecture of forced regressive deposits. In: H UNT , D. & T UCKER , M. E. Sedimentary Responses to Forced Regressions. Geological Society of London Special Publication, 172, 19–46. P RINGLE , J. K., W ESTERMAN , A. R., C LARK , J. D., D RINKWATER , N. J. & G ARDINER , A. R. 2004. 3D high-resolution digital models of outcrop analogue study sites to constrain reservoir model uncertainty: an example from Alport Castles, Derbyshire UK. Petroleum Geoscience, 10, 343–352. R EADING , H. G. & C OLLINSON , J. D. 1996. Clastic Coasts. In: R EADING , H. G. (ed.) Sedimentary Environments; Processes, Facies and Stratigraphy, 154– 231. R EYNOLDS , A. D. 1999. Dimensions of Paralic Sandstone Bodies. American Association of Petroleum Geologists Bulletin, 83, 211– 229. R OBERTS , L. N. R. & K IRSCHBAUM , M. A. 1995. Paleogeography and the Late Cretaceous of the Western Interior of middle North America; coal distribution and sediment accumulation. U.S. Geological Survey professional paper, 115. R YER , T. A. 1981. Deltaic coals of Ferron Sandstone Member of Mancos Shale; predictive model for Cretaceous coal-bearing strata of Western Interior. American Association of Petroleum Geologists Bulletin, 65, 2323–2340. R YER , T. A. 1983. Transgressive-regressive cycles and the occurrence of coal in some Upper Cretaceous strata of Utah. Geology, 11, 207–210. R YER , T. A. 2004. Previous Studies of the Ferron Sandstone. In: C HIDSEY , T. C., J R ., A DAMS , R. D. & M ORRIS , T. H. (eds) Regional to Wellbore Analog for FluvialDeltaic Reservoir Modeling: The Ferron Sandstone of Utah. AAPG Studies in Geology, 50, 3–38.

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Multiscale geological reservoir modelling in practice PHILIP S. RINGROSE, ALLARD W. MARTINIUS & JOSTEIN ALVESTAD Statoil Research Centre, N-7005 Trondheim, Norway (e-mail: [email protected]) Abstract: Geological systems exhibit variability and structure at a wide range of scales. Geological modelling of subsurface petroleum reservoirs has generally focused on the larger scales, driven by the types of measurement available and by computation limitations. Implementation of explicitly multiscale models of petroleum reservoirs is now realistically achievable and has proven value. This paper reviews the main approaches involved and discusses current limitations and challenges for routine implementation of multiscale modelling of petroleum-bearing rock systems. The main questions addressed are: (a) how many scales to model and upscale; (b) which scales to focus on; (c) how to best construct model grids; and (d) which heterogeneities matter most? The main future challenges identified are the need for improved handling of variance and more automated construction of geological and simulation grids.

This paper reviews implementation of multiscale geological modelling for oil and gas field reservoir studies. Multiscale reservoir modelling is defined here as any method which attempts to explicitly represent the rock properties at several scales within a petroleum reservoir. In geologically based multiscale modelling, the scales modelled are based on geological concepts and processes, and the models are designed for use in flow simulation, production forecasts and field development planning. The more general issue of scaling up flow properties is not considered in detail; that is, numerical or analytical methods for estimating effective or equivalent flow properties at a larger scale, given some set of finer-scale rock properties. Upscaling methods for single and multiphase flow are reviewed elsewhere (e.g. Renard & de Marsily 1997; Barker & Thibeau 1997; Ekran & Aaasen 2000; Pickup et al. 2005).

Multiscale geological modelling concepts The importance of multiple scales of heterogeneity for petroleum reservoir engineering has been recognized for some time. Haldorsen & Lake (1984) and Haldorsen (1986) proposed four conceptual scales associated with averaging properties in porous rock media: microscopic (pore-scale), macroscopic (representative elementary volume above the pore scale), megascopic (the scale of geological heterogeneity and or reservoir grid blocks) and gigascopic (the regional or total reservoir scale). Weber (1986) showed how common sedimentary structures including lamination, clay drapes and crossbedding affect reservoir flow properties, and Weber & van Geuns (1990) proposed a framework for constructing geologically based reservoir models for different depositional environments. Corbett et al. (1992) and Ringrose et al. (1993)

argued that multiscale modelling of water– oil flows in sandstones should be based on a hierarchy of sedimentary architectures, with smaller-scale heterogeneities being especially important for capillary-dominated flow processes (Huang et al. 1995). The hierarchy of sedimentary architectures may be difficult to infer. Campbell (1967) established a basic hierarchy of sedimentary features related to fairly universal processes of deposition, namely lamina, laminasets, beds and bedsets. Miall (1985, 1988) showed how the range of sedimentary bedforms can be defined by a series of bounding surfaces from a first order surface bounding the laminaset to fourth (and higher) order surfaces bounding, for example, composite point-bars in fluvial systems. Figure 1 illustrates the geological hierarchy for an example heterolithic sandstone reservoir. Lamina-scale, lithofacies-scale and sedimentary sequence-scale are the most important elements, although further scales and components can undoubtedly be argued. In addition to the importance of correctly describing the sedimentary length scales, structural (Fig. 1d) and diagenetic processes act to modify the primary depositional fabric. Numerical modelling at the pore-scale has been widely used to better understand permeability, relative permeability and capillary pressure behaviour for representative pore systems (e.g. Bryant & Blunt 1992; Bryant et al. 1993; McDougall & Sorbie 1995; Bakke & Øren 1997; Øren & Bakke 2003). Pore-scale modelling allows flow properties to be related to fundamental rock properties such as grain size, grain sorting and mineralogy. The application of pore-scale models routinely in larger-scale models requires a framework for assigning several pore-scale models within assumed lamina or lithofacies-scale models. Kløv et al. (2003) and

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 123– 134. DOI: 10.1144/SP309.9 0305-8719/08/$15.00 # The Geological Society of London 2008.

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Fig. 1. Field outcrop sketches illustrating multiscale reservoir architecture. (a) Sand and silt laminasets from a weakly bioturbated heterolithic sandstone. (b) Sandy and muddy bedsets in a tidal deltaic lithofacies. (c) Prograding sedimentary sequences from a channelized tidal delta. (d) Fault deformation fabric around a normal fault through an interbedded sand and silty clay sequence.

Theting et al. (2005) give recent examples where pore to field upscaling has been implemented. Statistical methods for representing the spatial architecture of geological systems generally fall into two classes. Sequential Gaussian or indicator simulation provides a robust framework for integrating sparse data from well or seismic observations and creating equiprobable maps of interwell architecture (e.g. Journel & Alabert 1990). Object modelling (e.g. Holden et al. 1998) involves the generation of discrete geological objects using a marked point process. Commonly, the two approaches are combined, with object-based models giving the geological framework and continuous Gaussian simulation providing a field of property variation within and between objects. Process-based approaches also employ conventional geostatistical methods but add further constraints to create more realistic models of 3D sedimentary architecture (e.g. Rubin 1987; Wen et al. 1998; Ringrose et al. 2003). Multipoint geostatistical and pattern recognition methods (Strebelle 2002;

Caers 2003) allow further potential for incorporating the detailed textures of 3D geological heterogeneities into reservoir simulation models. These developments have resulted in a wide range of methods available for geological reservoir modelling. Here, the implementation of multiscale modelling using these approaches is discussed. In particular, the following questions are considered: (1) How many scales to model and upscale? (2) Which scales to focus on? (3) How to best construct model grids? (4) Which heterogeneities matter most?

How many scales to model and upscale? Despite the inherent complexities of sedimentary systems, dominant scales and scale transitions can be identified (Fig. 2). These dominant scales are based both on the nature of rock heterogeneity and the principles of establishing macroscopic

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Fig. 2. Example of geologically based reservoir simulation models at four scales: (a) Model of pore space used as the basis for multiphase pore network models from Øren & Bakke 2003 (50 mm cube); (b) Model of laminasets within a tidal bedding facies from Nordahl et al. 2005 (dimensions 0.05 m  0.3 m  0.3 m); (c) Facies architecture model from a sector of the Heidrun Field showing patterns of tidal channel and bars (dimensions 80 m  1 km  3 km); (d) Reservoir simulation grid for part of the Heidrun Field illustrating grid cells displaced by faults in true structural position (dimensions 200 m  3 km  5 km).

flow properties. The four principal scales result in three scale transitions: (1) Pore to lithofacies. This is where a set of pore-scale models is applied to specific models of lithofacies architecture to infer representative or typical flow behaviour for that lithofacies. The lithofacies is a basic concept in the description of sedimentary rocks and presumes an entity that can be recognized routinely. The lamina is the smallest sedimentary unit at which fairly constant grain deposition processes can be associated with a macroscopic porous medium, and the lithofacies comprises some recognizable association of lamina and laminasets. In certain cases where variation between laminae is small, pore-scale models could be applied to the laminaset or bedset scales. (2) Lithofacies to geomodel. This is where a larger-scale geological model, comprising a sequence stratigraphic model and structural model, postulates the spatial arrangement of lithofacies or rock units. Here, the geomodel is taken to mean a geologically based model of the reservoir, typically resolved at the sequence or zone scale. Other terms used are shared earth model, geological architecture model or static rock model. Uncertainties are inherent in the geomodel; however, some degree of expectation of spatial trends is essential.

(3) Geomodel to reservoir flow simulator. This stage may often be mainly required due to computational limitations, but is nevertheless important to ensure good transformation of a geological model into three-dimensional grid optimized for flow simulation (e.g. within the constraints of finitedifference multiphase flow simulation). Features related to structural deformation (faults, fractures and folds) occur at a wide range of scales (Walsh et al. 1991; Yielding et al. 1992) and may not naturally fall into a stepwise upscaling scheme. Structural features are typically incorporated at the geomodel scale; however, effects of smaller-scale faults may also be incorporated as effective properties using upscaling approaches. Typically, structural features are included as a two-fold hierarchy: explicitly modelled faults and fractures (larger scale) and implicitly modelled faults and fractures (smaller scale). The incorporation of fault transmissibility into reservoir simulators is considered elsewhere (e.g. Manzocchi et al. 2002). Conductive fractures may also affect sandstone reservoirs, and are often the dominant factor in carbonate reservoirs. Approaches for multiscale modelling of fractured reservoirs have also been developed (e.g. Bourbiaux et al. 2002).

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Historical focus over the last few decades has been on including increasingly more detail into the geomodel, with only one upscaling step being explicitly performed. Full-field geomodels are typically in the size range of 1–10 million cells with horizontal cell sizes of 25–100 m and vertical cell sizes of order 0.5– 10 m. Multiscale modelling allows for better flow unit characterization and improved performance predictions (e.g. Pickup et al. 2000; Scheiling et al. 2002). There are also examples where million-cell models are applied at the sector or near-well model scale, reducing cell sizes to the dm-scale. Detailed modelling of the near-well region generally also requires methods to correctly model radial flow geometry (e.g. Durlofsky et al. 2000). Recent focus on explicit small-scale lithofacies modelling includes the use of million cell models with mm to cm size cells (e.g. Ringrose et al. 2005; Nordahl et al. 2005). Numerical pore-scale modelling employs 0.1–1 million network nodes (e.g. Øren & Bakke 2003). Model resolution is always limited by computational power, and although continued efficiencies and memory gains are expected in the future, the use of available numerical discretization at several scales within a hierarchy is clearly needed, instead of continually driving for higher resolution at one of the scales (typically the geomodel). Upscaling methods impose further limitations on the value and usability of models within a multiscale setting. In conventional upscaling from a geological model to a reservoir simulation grid, the various approaches used cover a range of degrees of simplification (we use a Cartesian coordinate convention with x and y as the horizontal axes and z as the vertical axis; Dx, Dy and Dz refer to grid cell dimensions): (1) Averaging of well data directly into the flow simulation grid. This approach essentially ignores upscaling and neglects all aspects of smaller-scale structure and flows. The approach is fast and simple and may be useful for quick assessment of expected reservoir flows and mass balance. It may also be adequate for very homogeneous and high permeability rock sequences. (2) Single-phase upscaling only in Dz. This commonly applied approach assumes a simulation grid designed with the same Dx and Dy as the geological grid. The approach is often used where complex structural architecture provides very tight constraints to design of the flow modelling grid. Upscaling essentially comprises use of averaging methods but ensures a degree of representation of thin layering or barriers. Also, where seismic data give a good basis for the geological model in the horizontal dimensions, vertical upscaling of fine-scale layering to the reservoir simulator scale is typically required.

(3) Single-phase upscaling in Dx Dy and Dz. With this approach, multiscale effective flow properties are explicitly estimated and the upscaling tools are widely available (diagonal tensor or full tensor pressure solution methods). Multiphase flow effects are however neglected. (4) Multiphase upscaling in Dx Dy and Dz. This approach represents an attempt to calculate effective multiphase flow properties in larger-scale models. The approach has been used rather too seldom due to demands of time and resources. However, the development of steady-state solutions to multiphase flow upscaling problems (Smith 1991; Ekrann & Aasen 2000; Pickup & Stephen 2000) has led to wider use in field studies (Pickup et al. 2000; Kløv et al. 2003). These four degrees of upscaling complexity help define the number and dimensions of models required. The number of scales modelled is typically related to the complexity and precision of the answer sought. Improved oil recovery (IOR) strategies and reservoir drainage optimization studies are usually the reason for starting a multiscale approach. A minimum requirement for any reservoir model is that the assumptions used for smaller-scale processes (pore-scale, lithofaciesscale) are explicitly stated. For example, a typical set of assumptions historically used might have been: ‘We assume that two special core analysis measurements represent all pore-scale physical flow processes and that all effects of geological architecture are adequately summarized by the arithmetic average of the well data.’ However, assumptions such as these were rarely stated, although implicitly assumed. More ideally, some explicit modelling at each scale should be performed using 3D multiphase upscaling methods.

Which scales to focus on? The Representative Elementary Volume (REV) concept (Bear 1972) provides the framework for understanding geological and measurement scales. This concept is widely referred to but infrequently implemented in a multiscale context. The original concept refers to the scale at which pore-scale fluctuations in flow properties approach a constant value both as a function of changing scale and position in the porous medium, such that a statistically valid macroscopic flow property can be defined. However, rock media present several such scales where smaller-scale variations approach a more constant value (Fig. 3). It is not generally clear how many such length scales exist in a particular rock medium, or indeed if an REV can be established at the scale necessary for reservoir flow simulation. However, a degree of representativity and

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Fig. 3. Sketch illustrating multiple scales of REV for permeability compared with a multiscale geological modelling framework and typical scales of measurement (adapted from Bear 1972; Nordahl 2004).

stability of estimated flow properties is required for flow modelling within a multiscale framework. Jackson et al. (2003) and Nordahl & Ringrose (2008) have shown that a lithofacies-scale REV can be achieved at the c. 0.3 m length scale for models of tidal heterolithic bedding. Whatever the true nature of rock variability, it is a common mistake to assume that the averaging inherent in any measurement method (e.g. electrical logs or seismic wave inversion) relates directly to the averaging scales in the rock medium. For example, core samples are often at an inappropriate scale for determining representativity (Corbett & Jensen 1992; Nordahl et al. 2005). Typical practice in petroleum reservoir studies is to assume that an average measured property for any rock unit is valid and that small-scale variability can be ignored. Valid statistical treatment of sample data is a large topic treated thoroughly elsewhere (e.g. Isaaks & Srivastava 1989; Jensen et al. 2000). An illustration of the challenge of correctly inferring permeability values from well data is illustrated here using an example well dataset (Fig. 4 and Table 1). This 30 m cored well interval comprises a tidal deltaic reservoir unit with heterolithic lithofacies and moderate to highly variable petrophysical properties. The permeability variations within this unit are large and determining an appropriate upscaled (or average) permeability is a challenge. The same well dataset is discussed in detail by Nordahl et al. (2005). Table 1 compares the permeability statistics for different types of data from this well: (a) high resolution probe permeameter data; (b) core plug data; (c) a continuous wireline

log based estimator of permeability for the whole interval; and (d) a blocked permeability log as might be typically used in reservoir modelling (blocking refers to averages of discrete intervals). Statistics for the natural log of permeability, ln(k), are shown (as the population distributions are approximately log normally distributed). It is well known that the sample variance should reduce as sample scale is increased. Therefore, the reduction in variance between datasets (c) and (d) is expected. It is, however, a common mistake in multiscale modelling for an inappropriate variance to be applied in a larger-scale model, e.g. if core plug variance were used to model the upscaled geomodel variance. Comparison of datasets (a) and (b) reveals another form of variance that is commonly ignored. The probe permeameter grid (2 mm spaced data over a 10 cm  10 cm core area) shows a variance, s2, of 0.38 [ln(k)]. The core plug dataset for the corresponding lithofacies interval (Estuarine bar), has s2 ln(k) ¼ 0.99, which represents variance at the lithofacies scale. However, blocking of the probe permeameter data at the core plug scale shows a variance reduction factor of 0.79 up to the core plug scale (column 2 in Table 1). Thus, in this dataset (where high resolution measurements are available), a significant degree of variance is missing from the datasets conventionally used in reservoir modelling. Improved treatment of variance in reservoir modelling is clearly needed and presents a challenge for future work. The statistical basis for treating population variance as a function of sample support volume is well established with

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Fig. 4. Example dataset from a tidal deltaic flow unit illustrating treatment of permeability data used in reservoir modelling.

the concept of Dispersion Variance (e.g. Isaacs & Srivastava 1989), where: s2 ða, cÞ ¼ s2 ða, bÞ þ s2 ðb, cÞ total variance variance variance within blocks between blocks where a, b and c represent different sample supports (for example, a ¼ point values, b ¼ block values and c ¼ total model domain). The variance adjustment factor, f, is defined as the ratio of block variance to point variance and can be used to

estimate the correct variance to be applied to a blocked dataset. With additive properties, such as porosity, treatment of variance in multiscale datasets is relatively straightforward, using the concept of Dispersion Variance. However, it is much more of a challenge with permeability data as flow boundary conditions are an essential aspect of estimating an upscaled permeability value. (The Dispersion Variance equation strictly applies only to additive, uncorrelated properties.) Multiscale geological modelling is an attempt to represent smaller-scale structure and variability as an upscaled block value. In this process, the principles of flow upscaling are

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Table 1. Variance analysis of example permeability dataset Estuarine bar lithofacies

Whole interval (flow unit)

(a) Probe k data

Probe data at plug scale

Core plug data

(b) Core plug data

(c) Wireline k-estimate

(d) Blocked well data

Scale of data

10  10 cm; 2 mm spaced data

c. 15–30 cm spaced core plugs

c. 15– 30 cm spaced plugs

15 cm digital log

2 m blocking

N ¼ Mean ln(k) s2 ln(k) Variance adjustment factor, f

2584 7.14 0.38 –

2  2 cm squares of 2 mm-spaced data 25 7.14 0.30 0.79

11 6.39 0.99 –

85 1.73 8.44 –

204 2.32 5.94 –

16 2.17 4.80 0.81

essential; however, improved treatment of variance is also critical. There is, for example, little point in rigorously upscaling a core plug sample dataset if it is known that the dataset is a poor representation of the true population variance. Within a multiscale geological framework, the recommended approach is to first identify the length scales where variance approaches a minimum, and then design the modelling and upscaling scheme to explicitly capture the effects of rock architecture at the scales where spatial variance cannot be ignored (Fig. 3).

How to construct geomodel and simulator grids? The construction of three-dimensional geological models from seismic and well data remains a relatively time-consuming task requiring considerable manual work both in construction of the structural framework and, not least, in construction of the grid for property modelling. Problems especially arise due to complex fault block geometries including reverse faults and Y-faults (i.e. Y-shaped intersecting faults in the vertical plane). Difficulties relate partly to the mapping of horizons into the fault planes for construction of consistent fault throws across faults. Problems also occur with lowangle stratigraphic intersections, where a decision has to be made to ignore cells thinner than a certain resolution. Currently, most commercial gridding software is not capable of automatically producing adequate 3D grids for realistic fault architectures, and significant manual work is necessary. Grid lines along fault surfaces are constructed and manual editing is mainly used to ensure that stratigraphic horizons correctly meet the fault planes. Upscaling procedures for regular Cartesian grids are well established, but the same

operation in realistically complex grids is much more challenging. The construction of 3D grids suitable for reservoir simulation is therefore also non-trivial and requires significant manual editing. The reasons for this are several: † The grid resolutions in the geological model and the simulation models are different, leading to missing cells or misfitting cells in the simulation model. The consequences are overestimation of pore volumes, possibly wrong communication across faults, and difficult numerical calculations due to a number small or ‘artificial’ grid cells. † The handling of Y-shaped faults using corner point grid geometries now widely used in black oil simulators is difficult. Similarly, the use of vertically staircased faults improves the grid quality and flexibility, but does not solve the whole problem. When using grids with staircased faults, special attention must be paid to estimation of fault seal and fault transmissibility. There is generally insufficient information in the grid itself for these calculations, and the calculation of fault transmissibility must be calculated based on information from the geological model. † The handling of dipping reverse faults using staircased geometry in a corner-point grid requires a higher total number of layers than for an unfaulted model. This is presently not available in simulation gridding software. † Regions with fault spacing smaller than the simulation grid spacing give problems for appropriate calculation of fault throw and zone to zone communication. Gridding implies that smaller-scale faults are merged and a cumulated fault throw is used in the simulation model. This is not possible with currently available gridding tools, and an effective fault transmissibility,

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including non-neighbour connections, must be calculated based on information from the geomodel, i.e. using the actual geometry containing all the merged faults. † Flow simulation accuracy depends on the grid quality, and the commonly used numerical discretization schemes in commercial simulators have acceptable accuracy only for ‘near’ orthogonal grids. Orthogonal grids do not comply easily with complex fault structures, and most often compromises must be made between honouring geology and keeping ‘near orthogonal’ grids. Figure 5 illustrates how some of these problems have been addressed in recent field studies. Solutions include: (a) detailed manual grid construction including staircase faults to handle Y-faults; (b) addition of smaller faults not explicitly modelled in the geomodel directly into the flow simulation grid; (c) decisions to ignore some faults when their effect on flow is expected to be minor. However, some gridding problems cannot be fully resolved using the constraints of corner point simulation grids, and optimal, consistent and

automated grid generation based on realistic geomodels is a challenge. The use of unstructured grids (e.g. triangular tessellation) reduces the gridding problems; however, robust, reliable and costefficient numerical flow solution methods for these unstructured grids are not widely available or efficient. Improved and consistent solutions for construction of structured grids and associated transmissibilities have been proposed (e.g. Manzocchi et al. 2002; Tchelepi et al. 2005); however, calculations for staircased faulted grids need improved formulation. Despite these challenges and the high degree of manual editing involved, the best approach for gridding geological and flow simulation models is to separate out structural features into their modelling categories: (a) Faults explicitly modelled in the structural framework of the geomodel. (b) Faults explicitly modelled in the flow grid – a subset of (a). (c) Small-scale faults represented in the flow grid as effective permeability factors. (d) Neglected faults (not included in (a) or (c)).

Fig. 5. Illustration of the transfer of a structural geological model to a reservoir simulation grid.

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Table 2. Summary of selected studies comparing multiscale factors on petroleum reservoir performance

Sequence model Sand fraction Sandbody geometry Vertical permeability Small-scale heterogeneity Fault pattern Fault seal

Shallow marine1

Faulted shallow marine2

V S

V S

S

S

n/a n/a

S S

Fluvial3

Tidal deltaic4

Fault modelling5

V S

S S V S n/a n/a

V n/a n/a n/a n/a S S

S n/a n/a

V ¼ Very significant factor; S ¼ Significant factor; n/a ¼ not assessed. 1 Kjønsvik et al. 1994 2 England & Townsend 1998 3 Jones et al. 1993 4 Brandsæter et al. 2001a, 2004 5 Lescoffit & Townsend 2005

Workflows will require some iteration and sensitivity analysis to confirm an appropriate choice of classes. Recent unpublished studies for large structurally complex petroleum reservoirs have c. 300 faults in class (a) and c. 100 faults in class (b). A similar scheme can be applied to fractures or stratigraphic barriers, where these are important.

Which heterogeneities matter? There are a number of published studies where the importance of different geological factors on reservoir performance have been assessed (e.g. the SAIGUP project, Manzocchi et al. 2008). Table 2 summarizes the findings of a selection of such studies in which a formalized experimental design with statistical analysis of significance has been employed. The table shows only the main factors identified in these studies (for full details, refer to sources). What is clear from this work is that several scales of heterogeneity are important for each reservoir type. While one can conclude that stratigraphic sequence position is the most important factor in a shallow marine depositional setting or that vertical permeability is the most important factors in a tidal deltaic setting, each case study shows that larger- and smaller-scale factors are always significant. This is a clear argument in favour of explicit multiscale reservoir modelling. Furthermore, in the studies where the effects of structural heterogeneity were assessed, both structural and sedimentary features were found to be significant. That is to say, structural features and uncertainties cannot be neglected and are fully coupled with stratigraphic factors.

Several projects have demonstrated the economic value of multiscale modelling in the context of oilfield developments. An ambitious study of the structurally complex Gullfaks Field (Jacobsen et al. 2000) demonstrated that 25 millioncell geological grid (incorporating structural and stratigraphic architecture) could be upscaled for flow simulation and resulted in a significantly improved history match. Both stratigraphic barriers and faults were key factors in achieving improved pressure matches to historic wells data. This model has further been used for assessment of IOR using CO2 flooding. Multiscale upscaling has also been used to assess complex reservoir displacement processes, including gas injection in thin-bedded reservoirs (Fig. 6) (Pickup et al. 2000; Brandsæter et al. 2001b, 2005), wateralternating-gas (WAG) injection on the Veslefrikk Field (Kløv et al. 2003), and depressurization on the Statfjord Field (Theting et al. 2005). These studies typically show of the order of 10–20% difference in oilfield recovery rates when advanced multiscale effects are compared with conventional single-scale reservoir simulation studies. The economic impact of multiscale modelling was estimated by Elfenbein et al. (2005) as giving at least 16 million barrels of additional oil for a typical large oilfield, and for marginal or challenging oilfields the value of detailed multiscaled modelling can represent the difference between success and failure.

Summary of potential and pitfalls Multiscale reservoir modelling has clearly moved from a conceptual phase, with method development on idealized problems, into a practical phase, with

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Fig. 6. Gas injection patterns in a thin-bedded tidal reservoir modelled using a multiscale method and incorporating the effects of faults in the reservoir simulation model (from a study by Brandsæter et al. 2001b). Reservoir cross-section is c. 25 m thick and c. 5 km long.

more routine implementation on real reservoir cases. The modelling methods have achieved sufficient speed and reliability for routine implementation (generally using steady-state methods on near-orthogonal corner-point grid systems). However, a number of challenges remain which require further developments of methods and modelling tools. In particular: † Multiscale modelling within a realistic structural geological grid is still a major challenge. † Correct handling of variance from multiplescale datasets is frequently neglected. † The tool-set for upscaling is still incomplete and far from integrated (e.g. multiphase flow, gridding and fault seal are generally treated in separate software packages and require much data conversion). We thank our colleagues for useful discussions and contributions to illustration and examples, especially Inge Brandsæter, Erlend Eldholm, Oddvar Lia, Andrew McCann, Tor Anders Knai, Kjetil Nordahl, Per Arne Slotte, Thomas Theting and Pa˚l Eric Øren. StatoilHydro ASA is thanked for permission to publish this material.

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Flow upscaling in highly heterogeneous reservoirs P. ZHANG1,2, G. E. PICKUP1, H. MONFARED1,3 & M. A. CHRISTIE1 1

Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK (e-mail: [email protected])

2

BP Exploration Operating Co. Ltd, Burnside Road, Farburn Industrial Estate, Dyce, Aberdeen, AB21 7PB, Scotland, UK

3

National Iranian Oil Company (NIOC), Hafez Crossing, Taleghani Avenue, Tehran, Iran Abstract: In the early stages of field development, there are many uncertainties and the current trend is to generate coarse-scale models so that many simulations can be run rapidly in order to determine the main sensitivities in a model. However, at a later stage, more data are available and there is less uncertainty in the model, so a more detailed modelling approach is desirable. In this paper, we discuss two modelling procedures which are suitable for different stages of the life of a field, and address the problem of upscaling at each stage. First, we consider a novel approach for generating coarse-scale models for evaluating uncertainty. When there is a large amount of uncertainty, the generation of fine-scale models is too time-consuming, and upscaling them by large factors may produce large errors. We demonstrate an alternative approach for modelling at a coarse scale, while preserving the heterogeneity of the fine-scale distribution, in such a way as to reproduce the fine-scale flow results. Secondly, we focus on more detailed geological models, generated at a later stage of field development. These models may comprise millions of grid cells, and may be highly heterogeneous. Such models require upscaling, but traditional methods may be very inaccurate. We have developed a method for upscaling using well-drive boundary conditions. Tests of this method show that it can reliably reproduce the fine-scale recovery in a range of models.

The conventional approach for estimating hydrocarbon recovery is to generate complex geological models with multimillion grid cells. Such models are time-consuming to construct, so that relatively few versions are generated, despite the fact that there is much uncertainty in reservoir structure. Large models generally require upscaling to reduce the number of cells for flow simulation, and much fine-scale detail may be lost during this stage. In addition, engineers may significantly alter the model permeabilities during historymatching, so the final model may be quite different from the original one. To overcome these problems, ‘top-down’ and ‘scenario-based’ approaches are now being developed (e.g. Williams et al. 2004; Bentley & Woodhead 1998). In cases where there is much uncertainty, for example at the start of field development, large numbers of coarse-scale models are generated so that the effects of uncertainty can be fully investigated. Later in the life of a field, the data may be more certain, and more detailed models may be required to assess issues such as infill drilling and EOR strategies. At this stage, more careful simulation and upscaling may be necessary. The aim of this paper is to consider upscaling and its applicability during early and late stages of field development. We start with a brief discussion on

conventional upscaling methods, and then introduce the SPE 10 model which was used in this study. Then we investigate the nature of coarse-scale permeabilities, using history-matched values which reproduce the fine-scale results. This helps us to explain how errors in conventional upscaling arise, and leads to a suggestion for an alternative modelling approach for the early stages of field development. We then consider cases where more detailed modelling is required (later stages of field development), and put forward an improved method for upscaling, suitable for highly heterogeneous models with complex geological structures.

Upscaling In this paper, we are focusing on upscaling as a means of reducing the number of cells in the geological model, so that it can be used for full field simulation. At this level, usually only single-phase upscaling is performed, because two-phase upscaling is timeconsuming and difficult to apply (e.g. Barker & Thibeau 1997). A number of reviews of single-phase upscaling methods have been written (e.g. Renard & Marsily 1997), so we do not provide a full review here. Instead, we concentrate on pressure solution methods. Figure 1 shows a schematic diagram of this

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 135– 144. DOI: 10.1144/SP309.10 0305-8719/08/$15.00 # The Geological Society of London 2008.

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Fig. 1. Schematic diagram of the pressure solution method of upscaling. The steps are: (1) select a coarse cell and apply boundary conditions; (2) solve the pressure equations to obtain the fine-scale pressure distribution; (3) calculate the interblock flows, and sum to give the total flow, Q; (4) use Darcy’s law to calculate the effective permeability.

approach. In this figure, we show a particular form of boundary conditions (step 1) – i.e. fixed pressure at the edges and no flow through the sides. Although other boundary conditions may be applied, these are most commonly used, and have been employed in this study. (In the SPE 10 study (Christie & Blunt 2001), these boundary conditions gave the most accurate results.) Also, in this version of the method, the boundary conditions are applied to each coarse cell, and this is referred to as the local upscaling method.

The SPE 10 model In this study, we have used the geological model (model 2) from the 10th SPE Comparative

Solution Project on Upscaling (Christie & Blunt 2001), and we present an overview of the main features of the model, before describing the tests. This model represents part of a Brent sequence, and consists of 60  220  85 cells, each of 20  10  2 ft. The top 35 layers represent the Tarbert formation (a prograding nearshore environment) and the bottom 50 layers represent the Upper Ness formation (fluvial); see Figure 2. The kv/kh ratio in the model was 0.3 in the channels and 1023 in the background. There are five wells: a water injector and four oil producers, arranged in a five-spot pattern. The relative permeabilities are similar for oil and water: a power-law with an exponent of 2. The viscosity of water is 0.3 and that for oil is 3.0, making the flood unstable.

Fig. 2. Porosity distribution of the SPE 10 model. The model size is 1200  2200  170 ft, and the porosity ranges from 0.0 (darkest shade) to 0.5 (lightest shade).

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Calculation of coarse-scale permeabilities using history-matching A comparison of methods for upscaling the SPE 10 model is presented in Christie & Blunt (2001) and additional upscaling tests are presented in Pickup et al. (2004). Usually, upscaling tests involve comparing fine- and coarse-scale results. However, in this paper, we turn the problem round, and calculate the coarse-scale permeabilities using history-matching. This means that we adjust the coarse-scale permeabilities until we obtain the same recovery rates as in the fine-scale simulation. In this way, we investigate the type of permeability distribution which gives the ‘correct answer’. (Note that, in this example, it was sufficient just to use the oil rate for history-matching. In more complex examples, you might need to use additional quantities, such as pressure, watercut or GOR.)

Methodology We employed the pilot-point approach for adjusting the permeability distribution during historymatching (e.g. Cuypers et al. 1998). Experience from benchmarking and analogue case studies could be used to determine the locations of the pilot points. A set of points (pilot points) is selected, and during the history-matching process, the absolute permeability is altered at these points. The permeabilities in the rest of the model are calculated using Sequential Gaussian Simulation (Deutsch & Journel 1998). The Neighbourhood Approximation (NA) algorithm (e.g. Christie et al. 2002) was used for history-matching. This is a stochastic algorithm which identifies regions of parameter space that give good history matches, and then preferentially samples in these regions to obtain better matches. We used a coarse-scale grid of 5  11  6 (upscaling factor of 3400), with 11 pilot points distributed randomly throughout the model. The procedure is shown schematically in Figure 3, and is described in more detail below. The spatial structure of the fine-scale model was characterized using semivariograms. The average semivariogram in each of the six coarse layers was calculated and fitted to a spherical or exponential model. These semivariograms were used in Sequential Gaussian Simulation (Deutsch & Journel 1998), along with the fine grid permeability pdf (probability density function) to produce coarse-scale permeabilities. The starting point for the history match was a coarse-scale model which had been obtained by upscaling using the local pressure solve method described above. During the history-matching procedure, permeability multipliers were applied to the pilot points to adjust the horizontal

Fig. 3. Schematic diagram of history-matching procedure.

permeability (kx and ky). The permeability in the z-direction was fixed, as were the permeabilities at the wells. The same permeability multiplier was applied to each of the six layers.

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Fig. 4. Comparison of the cumulative oil production.

The NA algorithm was run on the resulting coarse models. A waterflood was simulated in each model, and the oil rates for each well were compared with the fine-scale values, using the following misfit function: 

M¼

2

n X m WOPR fji  WOPRcji 1X , 2 j¼1 i¼1 sj2

where WOPR is the well oil production rate; f ¼ fine, c ¼ coarse; i ¼ 1 . . . n is the number of time steps; and j ¼ 1 . . . m is the number of production wells (four in this case). The results from history-matching are never unique, and the NA algorithm is frequently used to generate a range of matched models. However, in this case, we present a single model with the smallest misfit.

Results A comparison of the cumulative oil recovery for the fine-scale model, the upscaled model and the best history-matched model is shown in Figure 4. It can be seen that the history-matched model reproduces the fine-scale model very well, but the upscaled model overestimates the recovery. Figure 5 shows a comparison of the probability density function (pdf) for the fine, the upscaled and the history-matched models. The graph is plotted in terms of the natural logarithm of the permeability. The fine-scale distribution is bimodal. However, this has been lost in the upscaling

process, and the upscaled pdf is much narrower than the fine-scale one. The pdf from the historymatched model is similar to that of the fine-scale.

Discussion The graph of the probability density functions (Fig. 5) can be used to explain why the upscaled model gives a poor result for the cumulative recovery (Fig. 4). Upscaling reduces the variability in the permeability distribution, and this reduces the amount of physical dispersion of the flood front (e.g. Zhang & Tchelepi 1999). Therefore, in the upscaled model, water breaks through later than in the fine-scale model, and the recovery is higher. In the case of the history-matched model, the permeabilities are adjusted to reproduce the fine-scale recovery. This means that the amount of physical dispersion is preserved, and the pdf is similar to that of the fine-scale model. Instead of upscaling, it might have been more accurate to obtain the coarse-scale permeability values by sampling from the fine-scale values. Figure 6 shows a comparison of random sampling of the fine-scale grid compared with upscaling. Although there is considerable error in the average recovery from 1000 realizations of the random sampling method, the results are slightly more accurate than local upscaling. (Note that these results apparently contradict Durlofsky (1992), who concluded that, unless the scale-up factor was small compared to the correlation length, it was better to upscale rather than to

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Fig. 5. Comparison of the probability density functions.

sample. However, Durlofsky (1992) was considering single-phase steady-state flow. In the current study, we are using two-phase flow, and the dispersion in the flood front has to be maintained at the coarse scale.) This study shows that upscaling by a large factor (3400 in this case) can give rise to large errors in the predicted recovery. Therefore, if many models are to be simulated to take account of uncertainty, it is unwise to generate lots of fine-scale models and

upscale them. (Also, the time taken to generate many fine-scale geological models is prohibitive.) In order to produce unbiased results in coarse-scale models, we need to generate an appropriate amount of variability in the model. This suggests that it is better to create coarse-scale models by sampling the fine-scale structure or using fine-scale geostatistics, than to generate fine-scale models and upscale them. This procedure is suitable for reservoirs where there is much uncertainty, such as in the

Fig. 6. Comparison of upscaling with random sampling. (The results for the random sampling are the average of 1000 realizations.)

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early stages of field development, when a range of models must be evaluated rapidly. As a field is developed, more information, such as logs or cores from additional wells and more production history, becomes available so more detailed models may be created. For example, a second generation of models may be constructed which have several 10s of 1000s of cells. If fewer realizations are constructed (due to less uncertainty), such models can easily be simulated without the need for upscaling. Later in the life of a field though, multimillion cell models may be required for investigating EOR strategies or placement of additional wells. In this case, upscaling will be necessary, and it is important to use an accurate method, otherwise the detail in the model will be lost.

multimillion cell models. (The problem with large models is simulating multiphase flow, because the pressure equations may need to be solved thousands of times.)

A new approach A global upscaling approach has been selected here. We refer to the method as the Well Drive Upscaling (WDU) method, because we set the pressures at the wells, in the single-phase flow simulation (Fig. 7). From the results of the global single-phase simulation, we calculate upscaled transmissibilities, where transmissibility, Tx, in the x-direction is defined as: Tx ¼

A more accurate upscaling method In the study described above, we used the pressure solution method with locally applied no-flow boundary conditions. This method is frequently used in industry because it is simple, but more accurate results may be obtained with a little more effort. For example, frequently non-uniform coarse grids are constructed to maintain the permeability heterogeneity whilst reducing the number of grid cells. (See, for example, Garcia et al. 1992; and Durlofsky et al. 1996) With this approach, the amount of physical dispersion in the coarse-scale model is closer to that of the fine-scale model, and so the watercut and recovery are more accurately reproduced. However, the use of singlephase upscaling with non-uniform coarsening is likely to break down if the upscaling factor is so large that high and low permeability channels are merged. In that case, the relative permeabilities must also be upscaled to give the correct flux (Wallstrom et al. 2002). Another source of error in upscaling is the effect of boundary conditions. In the study above, we applied local, no-flow, boundary conditions, i.e. we fixed the pressures at each edge of a coarse cell and applied sealed boundaries to the edges. These boundary conditions are unlikely to reproduce the actual pressures and flows within the fine grid. The effect of boundary conditions may be reduced by using a ‘flow-jacket’ or ‘skin’ around each coarse cell. The boundary conditions are then applied to this larger region. This method is sometimes referred to as the extended local method (Chen et al. 2003). A more accurate approach is to perform a single-phase flow simulation on the whole fine-scale model. This is referred to as a global approach (Holden & Nielsen 2000). Performing a single pressure solve over a fine grid is feasible, even for very large

kx A Dx

where kx is the x-direction permeability, Dx is the distance between the centres of adjacent grid cells and A is the area perpendicular to flow (¼DyDz). The transmissibilities in the y- and z-directions are defined in a similar manner. The upscaled transmissibilities are calculated as follows (Fig. 8): (1) Sum the fine-scale flows; (2) Average the pressure, using pore volume weighting; and (3) Apply Darcy’s law. By calculating the coarse-scale transmissibilities directly, we save time in the coarse-scale simulation, and avoid errors arising from calculating the coarse-scale transmissibilities from the effective permeabilities. Zhang et al. (2005) and Zhang (2006) give full details of the method, along with the results of tests on a variety of heterogeneous models, such as sand/shale models and channel models. A technique for estimating the optimum coarse grid size is described in Zhang et al. (2007).

Fig. 7. An example of well drive boundary conditions. P1 and P2 are pressures, with P1 . P2.

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involved in performing the two-phase flow calculations, the PVW method is not feasible for multimillion cell models. On the other hand, the WDU method involves only a single pressure solve so it is a viable approach.

Examples of the WDU method We have tested the WDU method on a number of heterogeneous models (Zhang et al. 2005). Here, we show two sets of results using the SPE 10 model. Fig. 8. Schematic diagram of method for upscaling transmissibilities.

The WDU method, as described above, can be applied to problems where a single relative permeability curve is used for the whole geological model. However, when there are multiple relative permeability curves (e.g. one for each rock type), a decision has to be made as to which curve to use in a coarse cell (which may contain a number of different rock types). Often, coarse-scale curves are chosen according to the ‘majority vote’ (the relative permeability curve belonging to the majority of the fine cells). However, this can give rise to errors. We have extended the WDU method to include an analytical calculation of the coarse-scale relative permeabilities: we average the fine-scale relative permeabilities using transmissibility weighting. This approach does not require a two-phase flow simulation, and is therefore quick and feasible for large models. Again, more details may be found in Zhang et al. (2005).

Comparison between the WDU method and dynamic two-phase upscaling The new WDU method is essentially a single-phase upscaling approach. A number of two-phase dynamic upscaling methods have been developed, but they are not robust (Barker & Thibeau 1997), and they are time-consuming because they require two-phase flow simulations. However, we mention one procedure here, the Pore Volume Weighted (PVW) method (Schlumberger 2004) because we have compared it with the WDU method. Both methods use pore volume weighting to average the pressure in a coarse block. In the PVW method, this calculation is performed for each phase in order to calculate the upscaled relative permeability, while in the WDU method it is only applied to single-phase flow to calculate upscaled transmissibility. (In the PVW method, as described in the Eclipse PSEUDO manual, the upscaled absolute transmissibility is estimated by averaging the fine-scale permeabilities.) Because of the time

Case 1. In the first example, we use a single layer (layer 59) of the SPE 10 model (Fig. 9). This layer is very heterogeneous, with a complex channel structure, so provides a rigorous test for the method. Note that the permeability range covers eight orders of magnitude. Also, since this is only a 2D model, we were able to perform a full two-phase flow simulation. The size of the fine grid is 60  220 cells, and this was upscaled to 10  22 cells (an upscaling factor of 60). For this test, we modified the well locations and the relative permeabilities. Rather than arbitrarily placing the injector well in the middle of the model and the producers in the corners, we shifted the wells to high permeability channels. Since the permeability distribution is bimodal (channel and background facies), we used two relative permeability curves (Fig. 10a). After performing the single-phase upscaling, we calculated the average relative permeability curves for each coarse cell, using the method described above. The results are shown in Figure 10b. The number of relative permeability curves could be reduced by grouping similar curves together, but in this study we used all the curves. The results for the WDU method were compared with the results of the fine-scale model, the local upscaling method with ‘majority vote’ relative permeabilities, and the PVW upscaling method (Schlumberger 2004). (In the case of the PVW

Fig. 9. Layer 59 of the SPE 10 model.

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Fig. 10. (a) Input relative permeability; (b) upscaled relative permeabilities.

method, we used a full fine-scale two-phase flow simulation, which would not be feasible in a real field model.) The oil saturation distributions after the injection of one pore volume of water are shown in Figure 11. It can be seen that the local upscaling method gave a poor reproduction of the saturation distribution, but the WDU and PVW methods produced good results. Figure 12 shows the cumulative oil production. Again, the WDU and PVW methods reproduced the fine-scale results much better than the local upscaling method. Since the PVW method involved twophase simulation of the whole fine-scale grid, this method should reproduce the fine-scale results with reasonable accuracy. The WDU method only used a single-phase flow simulation but, by using appropriate boundary conditions, the main flow paths through the model were maintained. The results are as good as the PVW method, but with much less time and effort. Case 2. In this test of the WDU method, we upscaled the full SPE 10 model, using the original specifications for well locations and relative

permeabilities (Christie & Blunt 2001). The 60  220  85 cell model was upscaled to 10  22  17 (scale-up factor of 300). A comparison of the oil production rate for well P1 is shown in Figure 13. The fine-scale results used here are those supplied in the SPE 10 study (Christie & Blunt 2001). Note that we could not run the PWV method in this case because there were too many cells in the full 3D SPE model. It can be seen that the WDU method gives much better results that the local upscaling method.

Discussion The WDU method is more time-consuming than the local upscaling method, but it is still feasible to use this method for multimillion cell models. We have shown that, in highly heterogeneous models with complex structures, it is more accurate than the local pressure solution upscaling method which is commonly used. However, in models with a low level of heterogeneity, the local method is often adequate, so there is no advantage in applying the WDU method. We suggest that this method is appropriate for highly heterogeneous models, where careful simulation is required, e.g. in mature fields for planning infill drilling or IOR schemes. At this stage, there is likely to be less uncertainty, and it is worthwhile spending more time on modelling and flow simulation.

Summary

Fig. 11. Comparison of the saturation distributions in layer 59, after the injection of one pore volume.

In this paper, we suggest two alternative procedures for modelling and simulating flow in hydrocarbon reservoirs. In cases where there is much uncertainty, such as during the early stages of field life, building detailed reservoir models with millions of grid cells is not worthwhile. Instead, effort should be concentrated on evaluating many (thousands or tens of thousands) coarse-scale models, in order to evaluate the

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Fig. 12. Comparison of cumulative oil production in layer 59.

uncertainty. However, flow simulation in coarse-scale models may produce erroneous results. In particular, we show that if the level of heterogeneity is underestimated, the recovery may be overestimated. We propose that, at this stage of reservoir modelling, it may be more accurate to generate coarse-scale models using fine-scale geostatistics, rather than generating fine models and upscaling. Our tests show that, although this method is not very accurate, it is on average slightly more accurate than upscaling.

On the other hand, there are times when more precise simulation is required, such as later in field development, or for simulating parts of a reservoir in more detail. In this case, we suggest that a global single-phase simulation is carried out to reduce the errors in upscaling. This provides more accurate single-phase upscaling, which increases the accuracy of coarse-scale two-phase flow simulation. Although this method is more time-consuming than conventional approaches (such as local upscaling methods), it is feasible

Fig. 13. Oil production rate for well P1 of the SPE 10 model.

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for multimillion cells models, and is worth the extra effort to achieve more accuracy, especially in highly complex models. This work was part of the Uncertainty and Upscaling Project at Heriot-Watt. We acknowledge the support of the following companies: Anadarko, BG, BP, JOGMEC, Petronas and the UK DTI. Hashem Monfared was sponsored by NIOC. We should also like to thank Schlumberger for the use of the Eclipse reservoir simulation package.

References B ARKER , J. W. & T HIBEAU , S. 1997. A critical review of the use of pseudo relative permeabilities for upscaling. SPE RE, 12, 138 –143. B ENTLEY , M. R. & W OODHEAD , T. J. 1998. Uncertainty handling through scenario-based reservoir modelling. SPE n8 39717, presented at the SPE Asia Pacific Conference on Integrated Modelling for Asset Management, Kuala Lumpur, Malaysia, 23– 24 March. C HEN , Y., D URLOFSKY , L. J., G ERRITSEN , & W EN , X. H. 2003. A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations. Advances in Water Resources, 26, 1041–1060. C HRISTIE , M. A. & B LUNT , M. J. 2001. Tenth SPE comparative solution project: A comparison of upscaling techniques. SPE REE, 4, 308–317. C HRISTIE , M. A., S UBBEY , S. & S AMBRIDGE , M. 2002. Prediction under uncertainty in reservoir modeling. 8th European Conference on the Mathematics of Oil Recovery, Freiberg, Germany, 3– 6 Sept. C UYPERS , M., D UBRULE , O., L AMY , P. & B ISSELL , R. 1998. Optimal choice of inversion parameters for history-matching with the pilot point method. 6th European Conference on the Mathematics of Oil Recovery, Peebles, Scotland, 8– 11 Sept. D EUTSCH , C. V. & J OURNEL , A. G. 1998. GSLIB: Geostatistical Software Library and User’s Guide. 2nd edn, Oxford University Press. D URLOFSKY , L. J. 1992. Representation of grid block permeability in coarse scale models of randomly heterogeneous porous media. Water Resources Research, 28, 1791–1800.

D URLOFSKY , L. J., B EHRENS , R. A., J ONES , R. C. & B ERNATH , A. 1996. Scale up of heterogeneous three dimensional reservoir descriptions. SPE Journal, 1, 313–326. G ARCIA , M., J OURNEL , A. G. & A ZIZ , K. 1992. Automatic grid generation for modeling reservoir Heterogenetics. SPE RE, 7, 278– 284. H OLDEN , L. & N IELSEN , B. F. 2000. Global upscaling of permeability in heterogeneous reservoirs; the output least squares (OLS) method. Transport in Porous Media, 40, 115–143. P ICKUP , G. E., M ONFARED , H., Z HANG , P. & C HRISTIE , M. A. 2004. A new way of looking at upscaling. 9th European Conference on the Mathematics of Oil Recovery, Cannes, France, 3–6 Sept. R ENARD , P. & M ARSILY , G. DE 1997. Calculating equivalent permeability: A review. Advances in Water Resources, 20, 253–278. SCHLUMBERGER 2004. Eclipse Pseudo Software Package Manual. W ALLSTROM , T. C., H OU , S., C HRISTIE , M. A., D URLOFSKY , L. J., S HARP , D. H. & Z OU , Q. 2002. Application of effective flux boundary conditions to two-phase upscaling in porous media. Transport in Porous Media, 46, 155– 178. W ILLIAMS , G. J. J., M ANSFIELD , M., M AC D ONALD , D. G. & B USH , M. D. 2004. Top-Down Reservoir Modelling. SPE n8 89974, presented at the SPE Annual Technical Conference, Houston, Texas, 26–29 Sept. Z HANG , D. & T CHELEPI , H. 1999. Stochastic analysis of immiscible two-phase flow in heterogeneous media. SPE Journal, 4, 380–388. Z HANG , P., P ICKUP , G. E. & C HRISTIE , M. A. 2005. A new upscaling approach for highly heterogeneous reservoirs. SPE n8 93339, presented at the SPE Reservoir Simulation Symposium, Houston, Texas, 31 January–2 February. Z HANG , P. 2006. Upscaling in highly heterogeneous reservoir models. PhD Thesis, Heriot-Watt University, January. Z HANG , P., P ICKUP , G. E. & C HRISTIE , M. A. 2007. A New Technique for Evaluating Coarse Grids Based on Flow Thresholding. Petroleum Geoscience, 13, 17–24.

Scenario-based reservoir modelling: the need for more determinism and less anchoring MARK BENTLEY & SIMON SMITH TRACS International Consultancy Ltd., Falcon House, Union Grove Lane, Aberdeen, Scotland, AB10 6XU, UK (e-mail: [email protected]; [email protected]) Abstract: The scenario-based reservoir modelling method places a strong emphasis on the deterministic control of the model design, contrasting with strongly probabilistic approaches in which effort is focused on the ‘richness’ of a geostatistical algorithm to derive multiple stochastic realizations. Scenario-based approaches also differ from traditional ‘rationalist’ modelling, which often involves the construction of only a single, best-guess or base-case model. The advantage of scenario modelling is that there is no requirement to anchor on a preferred, base-case model, and it is argued here that selection of a base case is detrimental to achieving appropriately wide uncertainty ranges. Multiple-deterministic scenario modelling also carries the advantage of maintaining explicit dependency between model parameters and the ultimate model outcome, such as a development plan. The approach has been applied widely to new fields, where multiple deterministic reservoir simulations of a suite of static models can be easily handled. The approach has also been extended to mature fields, in which practical approaches to multiple-history matching are required. Mature field scenario modelling, in particular, illustrates the weaknesses of base-case modelling, and delivers a strong statement on the non-uniqueness of modelling in general. Current issues are the need to develop better methodologies for multiple-history matching, and for linking discrete, deterministic, scenario-based outcomes to probabilistic reporting. Experimental design methods offer a solution to the latter issue, and a simple, practical workflow for its application is described.

Scenario-based modelling has become a popular means of managing subsurface uncertainty, although opinions differ on the nature of the ‘scenarios’, particularly with reference to the relative roles of determinism and probability. The idea of alternative, discrete subsurface scenarios (analogous to the concept of ‘multiple working hypotheses’) followed on logically from the emergence of integrated reservoir modelling tools (Cosentino 2001; Taylor 1996). These emphasized the use of 3D ‘static’ reservoir modelling, ideally fed from 3D seismic data and leading to 3D ‘dynamic’ reservoir simulation, generally on a full-field scale (Fig. 1). When appreciating the numerous uncertainties involved in constructing such field models, the desire for multiple models naturally arises. Although not universal (see discussion in Dubrule & Damsleth 2001), the application of multiple modelling techniques is now widespread, with the alternative models described variously as ‘runs’, ‘cases’, ‘realizations’ or ‘scenarios’. The multiple terminologies are more than semantic. The notion of multiple modelling has been explored differently by different workers, the essential variable being the balance between deterministic and stochastic inputs. This is reflected in differing applications of geostatistical algorithms, and differing ideas on, and expectations of,

the role of the probabilistic component of the modelling. The contrasting approaches broadly fall into three groups (Fig. 2): 1. Rationalist approaches, in which a preferred model is chosen as a base case. The model is either run as a technical best guess, or with a range of uncertainty added to that guess. This may be either a þ/2 percentage in terms of the model output, often volumes in-place (Fig. 3a), or separate low case and high cases flanking the base case (Fig. 3b). This is the modelling approach which most closely maintains the pre-3D modelling approach to reservoir characterization – ‘traditional’ determinism. 2. Multiple stochastic approaches, in which a large number of realizations or outcomes are probabilistically generated by geostatistical simulation (Fig. 4). The deterministic input lies in the setting of the boundary conditions for the simulation based on a conceptual geological model. 3. Multiple deterministic approaches, which avoid making a single best-guess, or choosing a preferred base-case model (Fig. 5). A smaller number of models are built, each one reflecting a different, manually defined reservoir concept. Geostatistical simulations may be applied in the building of the 3D model but the selection of the model realizations

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 145– 159. DOI: 10.1144/SP309.11 0305-8719/08/$15.00 # The Geological Society of London 2008.

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the underlying philosophy of uncertainty assessment will briefly be recalled and a definition of ‘scenario modelling’ will be offered. Based on a review of three applications of multiple-deterministic scenario modelling, strengths and weaknesses will be summarized, and a recommendation as to how to address two current weak points will be made.

Approaches to model-based uncertainty-handling The limits of rationalism

Fig. 1. The 3D reservoir modelling process for a single model realization. The key element which is captured is the point-to-point dependency between static and dynamic model elements.

is made manually rather than by statistical simulation (van de Leemput et al. 1995). Any of the above have been referred to as ‘scenario modelling’ by different workers. It is proposed here that although all three approaches have application in subsurface modelling, multipledeterministic scenario-building is the preferred route in most circumstances. In order to make this case,

The traditional rationalist approach described above is effectively simple forecasting – making a ‘best guess’ – and puts faith in the ability of an individual or team to make a reasonably precise judgement. If presented as the best judgement of a group of experts, then this appears reasonable. The weak point is that the best guess is only reliable when the system being described is well ordered and well understood, to the point of being highly predictable (Mintzberg 1990). It must be assumed that enough data is available from past activities to predict a future outcome with confidence, and this applies equally to production forecasting, exploration risking, volumetrics or well prognoses. In practice, this is rarely the case in the subsurface, except perhaps fields with large ( . 100) well stocks. There is, nevertheless, a strong tendency for individuals, particularly managers, to desire

Fig. 2. Ternary diagram summarizing three end-member approaches to uncertainty-handling: multiple deterministic, multiple stochastic and the single ‘best guess’. Many modelling studies blend these techniques; all can be mapped within this spectrum.

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Fig. 3. Diagramatic representation of base-case, or strongly ‘rationalist’, approaches: (a) the extreme end-member case is the single best guess; (b) even with the addition of a þ/2 spread, the approach is still anchored on the initial best guess, and therefore lies to the base-case end of the spectrum of possible approaches.

a best guess, and to subsequently place too much confidence in that guess (Baddeley et al. 2004). It is often stated that for mature fields, a simple, rationalist approach may suffice because uncertainty has reduced through the field lifecycle. It is suggested here that this is a fallacy. The magnitude of the initial development uncertainties tends to

decrease with time but as the lifecycle progresses new, more subtle uncertainties arise. For example, the subtleties of a heterogeneous but broadly connected sand-rich reservoir may not be a major issue during the early lifecycle, but will be highly significant as the final infill wells are placed later in field life. The impact of uncertainties in terms of their

Fig. 4. Diagramatic representation of the multiple stochastic approach. The spread of outcomes is generated by statistcally sampled multiple realizations of an initial base case.

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Fig. 5. Diagramatic representation of the multiple deterministic, ‘scenario-based’ approach. The spread of outcomes is generated by multiple, deterministically defined starting concepts, some of which may require differing modelling techniques to evaluate. There is no selection of an initial base case; the technique is not anchored.

ability to erode value may therefore be as great near the end of the field life as at the beginning. Despite the above, rationalist, base-case modelling remains common across the industry. In a review of 90 modelling studies conducted by the authors and colleagues across many companies, field modelling was based on a single, best-guess model in 36% of the cases (Smith et al. 2005). This is despite a bias in the sampling from the authors’ own studies, which tend to be scenariobased. Excluding the cases where the model design was influenced by the authors, the proportion of base case-only models rose to 60%.

Anchoring and the limits of geostatistics The process of selecting a best guess in spite of wide uncertainty is referred to as anchoring, and is a well-understood cognitive behaviour (Baddeley et al. 2004). Once anchored, the tendency to fully explore the uncertainty range reduces as the outcomes become overly influenced by the anchor point. This often occurs in statistical

approaches to uncertainty-handling, as these tend to be anchored in the available data and may therefore make the same rational starting assumption as the simple forecast, although adding ranges around a ‘most probable’ prediction. Geostatistical simulation allows definition of ranges for variables, followed by rigorous sampling and (ideally) combination of parameters to yield a range of results, which can be interpreted probabilistically. If the input data can be specified accurately, and if the combination process maintains a realistic relationship between all variables, the outcome may be reasonable. In practice, however, input data are imperfectly defined and the ‘reasonableness’ of the automated combination of variables is hard to verify. Statistical rigour is applied to datasets which are not necessarily statistically significant and an apparently exhaustive analysis may have been conducted on insufficient data sources. The validity of the outcome may also be weakened by centre-weighting of the input data to

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variable-by-variable best guesses. Although this can be avoided by careful definition of potentially irregular probability density functions to describe complex data distributions, this is not necessarily undertaken. Centre-weighting of the input data creates an inevitability that the ‘most likely’ probabilistic outcome will be close to the initial best guess – the geostatistical simulation itself is ‘anchored’. It is therefore argued that the application of geostatistical simulation does not in itself compensate for a natural tendency towards a rationalist best guess – it often tends to simply reflect it. The crucial step is to select a workflow which removes the opportunity for anchoring on a best guess; this requires deterministic intervention and is what scenario modelling, as defined here, attempts to address.

Scenarios defined The definition of ‘scenario’ adopted here follows that described by van der Heijden (1996), who discussed the use of scenarios in the context of corporate strategic planning. Scenarios are: ‘a set of reasonably plausible, but structurally different futures’. Alternative scenarios are not incrementally different models based on slight changes in continuous input data (as with multiple probabilistic realizations), but models which are structurally distinct, based on some design criteria. Translated to oil and gas field development, a ‘scenario’ is a plausible development outcome, and the ‘scenario approach’ to modelling is defined as the building of multiple, deterministically driven models of development outcomes. Each scenario is a complete and internally consistent static/dynamic subsurface model with an associated plan tailored to optimize its development. In an individual subsurface scenario, there is clear linkage between technical detail in a reservoir model, and an ultimate commercial outcome; a change in any element of the model detail prompts a quantitative change in the outcome and the dependency between all parameters in the chain between the changed element and the outcome is unbroken. This contrasts with many probabilistic simulations, in which model design parameters are statistically sampled and combined, and in which dependencies between variables may be lost, or collapsed into simple correlation coefficients. The scenario approach therefore places a strong emphasis on deterministic representation of a subsurface concept: geological, geophysical, petrophysical and dynamic. Without a clearly defined concept of the subsurface – clear in the sense that a geoscientist could represent it as a simple sketch – the modelling cannot progress

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meaningfully. Geostatistical simulation may be intrinsic to the modelling workflow but the design of the scenarios is determined directly by the modeller. Multiple models are based on multiple, deterministic designs. This distinguishes the workflows for scenario modelling, as defined here, from multiple stochastic modelling which is based on statistical sampling from a single initial design. The two approaches are not mutually exclusive. A thorough workflow may involve the deterministic definition of multiple scenarios, followed by multiple probabilistic realizations (changing the seed number only) within a given scenario. This can be done to check for sensitivities in the model building, for example whether volumetrics are sensitive to the chance positioning of sand bodies above or below a hydrocarbon–water contact. In the experience of the authors, however, the spread of results from multiple stochastic sensitivities tends to be less than that between the deterministic scenarios – hence the argument here that the key to addressing a full uncertainty range lies in an awareness of the large-scale deterministic controls on the reservoir models. Scenario-based approaches therefore place emphasis on a listing and ranking of uncertainties, from which a suite of scenarios will be deterministically designed, with no attempt being made to select a best guess case up-front.

Basis of design The key to success in scenario modelling lies in deriving a ‘correct’ list of key uncertainties, a matter of experience and judgement. However, there is often a tendency to conceptualize key uncertainties for at least the static reservoir models in terms of the parameters of the STOIIP equation (Stock Tank Oil Initially In Place). For example, when asked to define the key uncertainties in the field, modellers will often quote parameters such as ‘porosity’ or ‘net sand count’ as key. If the model building progresses with these as the key variables to alter, this will most likely be represented as a range for a continuous variable, anchored around a best guess. A better approach is to question why porosity is a significant uncertainty. It will either emerge that the uncertainty is not that significant or, if it is, then it relates to some underlying factor, such as heterogeneous diagenesis, or some local facies control which has not been extracted from the data analysis. For example, in Figure 6 a probability density function (PDF) of net-to-gross is shown. A simplistic approach would involve taking that PDF, inputting it to a geostatistical algorithm and allowing sampling of the range to account for the

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Fig. 6. Determining underlying causative uncertainties to populate the uncertainty list. In this case, net-to-gross is presented as an uncertainty (upper diagram). However, the underlying driving issue is the uncertainty over the depositional architecture, and alternative scenarios should be generated for this underlying factor. Within each scenario, the net-to-gross spread may be a second order issue rather than a principal uncertainty (lower diagram).

uncertainty. As the data in the figure illustrate, this would be misleading, because the range is reflecting mixed facies types. The need is to understand the facies distribution and isolate the facies-based factors – in this case the proportion of different channel types – and then establish whether this ratio is known within reasonable bounds. If not known, the uncertainty can be represented by building contrasting, but realistic, facies models (the basis for two alternative scenarios) in which these elements specifically contrast. The uncertainty in the net-to-gross parameter within each scenario is probably a second-order issue. In defining key uncertainties, the need is therefore to chase the source of the uncertainty to the underlying causative factor and model the conceptual range of uncertainty of that factor with discrete cases, rather than simply input a data

distribution for a higher-level parameter such as net-to-gross.

Application – greenfield The application of scenario modelling has been most successfully reported in the case of new or ‘greenfield’ cases. Van der Leemput et al. (1995) described an application of scenario-based modelling in the context of an LNG field development plan (FDP). Once sufficient proven volumes were established to support the scheme, the commercial structure of the project focused attention of the issue of the associated capital expenditure. CAPEX therefore became the prime quantitative outcome of the modelling exercise, driven largely by well numbers and the requirement for and timing of gas compression.

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The model scenarios were driven by a selection of principal uncertainties summarized in Figure 7. Five static and six dynamic uncertainties (three related to well productivity) were identified, based on the judgement of the project team and input from peers. Maintaining the uncertainty list became a continuing process, iterating with new well data from appraisal drilling, and the changing views of the group. For the FDP itself, the uncertainty list generated 22 discrete scenarios, each of which was matched to the small amount of production data, then individually tailored to optimize the development outcome over the life of the LNG scheme. The outcomes, in term of impact on CAPEX, are shown in Figure 7. A key learning from this exercise was that a list of 11 uncertainties was unnecessarily long to generate the ultimate outcome, although convenient for satisfying concerns of stakeholders. The effect of statistical dominance meant that the range was not driven by all 11 uncertainties, but by 2–3 key uncertainties to which the scheme was particularly sensitive (to well productivity in particular) (Fig. 7).

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Contrary to common expectations, gross rock volume on the structures was not a key development issue, even though the fields were large and each had only 2–3 well penetrations at the time of the FDP submission. The key issue was the potential enhancements of well deliverability offered by massive hydraulic fracturing – not a factor typically at the heart of modelling studies. The majority of the issues normally addressed by modelling: sand body geometries, relative permeabilities, aquifer size etc., were certainly poorly understood, but could be shown to have no significant impact on the scheme. In hindsight, the dominant issues were foreseeable without modelling. In the light of the above, continued post-FDP modelling became more focused, with a smaller number of scenarios fleshing out the dominant issues only. Tertiary issues were effectively treated as constants. The above was conducted without selecting a ‘base-case’ model. A development scheme was ultimately selected by the surface engineering team, but this was based on a range of outcomes defined by the subsurface team. Scenario modelling for greenfields has been conducted many times since the publication of this example. In the experience of the authors, the

Fig. 7. Summary of the Barik greenfield case study. The uncertainty list (represented by the column of icons) generated a suite of multiple-deterministic scenarios, the impact on project cost (the issue of interest) is shown on the spider plot. In hindsight, the issue was overanalysed. The outcome was predictably insensitive to a number of uncertainties, and dominated by the well performance uncertainty. The study delivered an outcome range, with no base case selected up-front.

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early learnings described above have held true, notably: † large numbers of scenarios are not required to capture the range of uncertainty; † the main uncertainties can generally be identified through cross-discipline discussion prior to modelling – if not, these can be established by running quick sensitivities; † the dominant uncertainties on a development project do not always include the issue of gross rock volume, even at the pre-development phase; and † it is not necessary to select a base-case model.

Application – brownfield Two published examples are summarized here which illustrate the extension of scenario modelling to mature (‘brown’) fields. The first concerns the case of the Sirikit Field in Thailand (Bentley & Woodhead 1998). The requirement was to review the field mid-life and evaluate the potential benefit of introducing water

injection to the field. At that point, the field had been on production for 15 years, with 80 wells producing from a stacked interval of partially connected sands. The required outcome was a quantification of the economic benefit of water injection, to which a scenario-based approach was to be applied. The uncertainty list is summarized in Figure 8. The static uncertainties were used to generate the suite of static reservoir models for input to simulation. In contrast to the greenfield cases, where production data are limited, the dynamic uncertainties were used as the history-matching tools – the permissible parameter ranges for those uncertainties being established before the matching began. A longer account of the study is given in Bentley & Woodhead (1998), notably the workflow for multiple–history matching and scaling of results. A compiled production forecast for the ‘no further drilling case’ is shown in Figure 8. The difference between that spread of outcomes and the spread from a parallel set of outcomes which included water injection, were used to quantify

Fig. 8. Summary of the Sirikit brownfield case study. The static uncertainty list was used to generate the scenarios and the dynamic uncertainties used as variables in history matching. With all models matched, the incremental production forecasts varied by several factors. With all models plausible, there was no requirement to select a base case.

SCENARIO-BASED RESERVOIR MODELLING

the value of the injection decision. Of interest here is the nature of that spread. Although all models gave reasonable matches to history, the incremental difference between the forecasts was larger than that expected by the team. It was hoped that some of the static uncertainties would simply be ruled out by the matching process. Ultimately, none were, despite 80 wells and 15 years of production history. The outlier cases were reasonable model representations of the subsurface, none of the scenarios was strongly preferred over any other, and all were plausible. A base case was not chosen. The outcome makes a strong statement about the non-uniqueness of simulation model matches. If a base-case model had been rationalized based on preferred guesses, any of the seven scenarios could feasibly have been chosen – only by chance would the eventual median model have been selected. Sirikit also confirmed that multiple deterministic modelling was achievable in reasonable study times, and gave a surprisingly wide range of model forecasts. A second example of scenario-based logic to mature fields, using a modified workflow, is a case from the Gannet B Field in the Central North Sea (Bentley & Hartung 2001; Kloosterman et al. 2003). The issue to model in Gannet B was the risk and timing of potential water breakthrough in one of the field’s two gas producers, and placing value on alternative contingent activities postbreakthrough. As with the cases above, the study started with a listing and qualitative ranking of principal uncertainties in a cross-discipline forum. Unlike the previous cases, it proved not to be possible to match all static reservoir models with history. The lowest volume realization would not match. The model outcome – a range of water-cut breakthrough times, is illustrated in Figure 9. The Gannet B study offered some additional insights into mature field scenario modelling: † although the truism is offered that multiple models can match production data (there is no uniqueness to history matches), the converse is not necessarily true; – not everything can be matched; † the above may be more likely to be true in smaller fields, where physical field limitations play a role earlier in a field history; and † in the specific case of Gannet B, the principal matching tool was 4D seismic data, not production data; it was the matching of simulated acoustic impedance changes versus the observed seismic amplitude changes which was the matching target for the multiple model scenarios.

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Fig. 9. Summary of the Gannet B brownfield case study. The static uncertainty list was used to generate the scenarios, which were history matched using the single principal dynamic uncertainty. With all models matched, the time to water breakthrough was forecast for the two wells in the field. The study outcome was the time range shown and there was no preferred base case; selection of a base case would have significantly distorted the result.

Scenario modelling – benefits The scenario-based approach as defined here offers specific advantages over base-case modelling and multiple probabilistic modelling: 1. Determinism: the dominance of the underlying conceptual reservoir model, which is deterministically applied via the model design. Although the models use any required level of geostatistical

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simulation to recreate the desired reservoir concept, the geostatistical simulation results are not used to select the cases to be run, nor to quantify the uncertainty range in the model outcome. 2. Lack of anchoring: the approach is not built on the selection of a base case or best guess. Qualitatively, the natural tendency to underestimate uncertainties is less prone to occur if a best guess is not required – the focus lies instead on an exploration of the uncertainty range. 3. Dependence: direct dependence between parameters is maintained through the model process; a contrast between two model realizations is fed through directly to two quantitative, generally commercial outcomes, which allow the significance of the uncertainty to be evaluated. 4. Transparency: although the models may be internally complex, the workflow is simple, and feeds directly off the uncertainty list, which may be no more complex than a short list of the key issues which drive the uncertainty range. If the key issues which could cause a project to fail are identified on that list, the modelling process will evaluate the outcome in the result range. The focus is therefore not on the intricacies of the model build (which can be reviewed by an expert, if required), but on the uncertainty list, which is transparent to all interested parties.

Scenario modelling – issues to resolve Two potential weak points of the scenario approach need to be addressed: 1. It is generally assumed that more effort will be required to manage multiple models than a single

model, particularly when brownfield sites require multiple history matching; and 2. As each scenario is qualitatively defined, the link to statistical descriptions of the model outcome (e.g. P90, P50, P10 definitions) is similarly qualitative. As some common model outputs, notably volumetrics, are reported in the form of cumulative probability distributions, the issue of mapping deterministic cases onto a probabilistic distribution arises. Possible ways forward on these issues are discussed below.

Multiple model handling Multiple model handling in greenfield sites is not necessarily a time-consuming process. Figure 10 illustrates results from a recent unpublished study involving 120 discrete development scenarios. These were manually constructed from permutations of six underlying static models and dynamic uncertainties in fluid distribution and composition. The static models were deemed feasible, and the permutations were defined based on combining uncertainties which could be deemed independent (e.g. sand architecture and fluid compositions). This was an exhaustive approach in which all combinations of key uncertainties were assessed. The final result could have been achieved with a smaller number of scenarios, but the full set was run simply because it was not particularly timeconsuming (the whole study ran over roughly five person-weeks, including static and dynamic modelling). The case illustrates the efficacy of multiple

Fig. 10. An exhaustive route to the definition of a probabilistic S-curve; over 100 deterministically created static/dynamic simulations, considered equally plausible.

SCENARIO-BASED RESERVOIR MODELLING

static/dynamic modelling in greeenfields, even when the compilation of runs is manual. This issue is more pressing for brownfield sites, although the cases described above from Sirikit and Gannet illustrate that workflows for multiple model handling in mature fields can be made practical. This is being improved further by the emergence of a new breed of automatic history-matching tools which achieve model results according to input guidelines that can be deterministically controlled. It is suggested that the running of multiple models is not a barrier to scenario modelling, even in fields with long production histories. Once the conceptual scenarios have been clearly defined, it often emerges that complex models are not required, and this comes with a significant timesaving. Cross-company reviews by the authors indicate that model-building exercises which are particularly lengthy are typically those where a very large, detailed, base-case model is under construction. History matching is often pursued to a level of precision disproportionate to the accuracy of the static reservoir model it is based on. By contrast, multiple modelling exercises tend to be more focused and, perhaps paradoxically, may be quicker to execute than the very large, very detailed basecase model-builds.

Linking deterministic models with probabilistic reporting: experimental design A recent development has been the merging of deterministically defined scenario models with probabilistic reporting using a collection of approaches broadly described as ‘experimental design’. This methodology offers a way of generating probabilistic distributions of hydrocarbons in place or reserves from a limited number of deterministic scenarios, and of relating individual scenarios to specific positions on a cumulative probability, or ‘S’ curve. In turn, this provides a rationale for selecting specific models (e.g. P90, P50 and P10) for screening development options. Experimental design is a well-established technique in the physical and engineering sciences where it has been used for several decades (e.g. Box et al. 1978). It has recently become popular in reservoir modelling and simulation (e.g. Egeland et al. 1992; Yeten et al. 2005; Li & Friedman 2005). It offers a methodology for planning experiments so as to extract the maximum amount of information about a system using the minimum number of experimental runs. In the subsurface, this can be achieved by making a series of reservoir models which combine uncertainties in

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ways that are specified by a theoretical template or ‘design’. The type of design depends on the purpose of the study and on the degree of interaction between the different variables. One of the simplest approaches is the Plackett – Burman formulation (Plackett & Burman 1946). This design assumes there are no interactions between the uncertain variables and that a relatively small number of experiments are sufficient to approximate the behaviour of the system. More elaborate designs, for example D-optimal or BoxBehnken (Alession et al. 2005; Peng & Gupta 2005) attempt to analyse different orders of interaction between the uncertainties and require a significantly greater number of experiments. A key aspect of experimental design is that the uncertainties are generally expressed as endmembers. The emphasis on making a base case, best guess for any variable is reduced, and can be removed. The combination of Plackett-Burman experimental design with the scenario-based approach is shown by the case below from a mature field redevelopment plan involving multipledeterministic scenario-based reservoir modelling and simulation. The purpose of the modelling was to build a series of history-matched models that could be used as screening tools for a field development. As with all scenario-based approaches, the workflow started with a listing of the uncertainties, thought in this case to be: † Top reservoir structure: caused by poor quality seismic and ambiguous depth conversion. This was modelled using alternate structural cases capturing plausible end-members. † Thin-beds: the contribution of intervals of thinbedded heterolithics was uncertain as these intervals had not been produced or tested in isolation. This uncertainty was modelled by generating alternative net-to-gross logs. † Reservoir architecture: uncertainty in the interpretation of the depositional model was expressed using three conceptual models: tidal estuarine, proximal tidal-influenced delta and distal tidal-influenced delta models (Fig. 11). Each model was built as a complete geocellular model realization involving both deterministic and probabilistic components (deterministic for structure, stratigraphy and facies associations; probabilistic infill for facies and faciesdependent reservoir properties). † Sand quality: this is an uncertainty simply because of the limited number of wells and was handled by defining alternative cases for facies proportions, the range based on the best and worst sand quality seen in wells to date.

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Fig. 11. Compound summary of the application of experimental design to link deterministic, scenario-based models with probabilistic output. Top image: discrete deterministic cases for reservoir architecture; left: weightings used for each uncertainty in the Monte Carlo sampling of the response variable function; right centre: output of the Monte Carlo run expressed as a probabilistic S-curve, showing the P50 compared with an initial ‘best guess’; bottom right: tornado plot showing sensitivity of the outcome to the input variables (the principal uncertainties).

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† Reservoir orientation: modelled using alternative orientations of the palaeodip. † Fluid contacts: modelled using plausible endmembers for fluid contacts. These six uncertainties were combined using a 12-run Plackett-Burman design. The way in which the uncertainties were combined is shown in the Table 1 where the high-case scenario is represented by þ1, the low-case scenario by 21 and a mid-case by 0. Two additional runs have been added, one using all the mid-points and one using all the lows. Neither is theoretically necessary but they serve as useful reference points in the analysis of the results. The 14 reservoir models were built and the hydrocarbon volumes determined for each reservoir unit. In this case, the hydrocarbon volume is the output parameter of interest: the ‘response data’. A linear least squares ‘response function’ for that data was derived, expressing the volumetric outcome as a function of the six identified uncertainties. The quality of the fit could be quantified using statistical measures or simply as a plot of modelled versus predicted volumes. Once the functional relationship between the model outcome (volumes in this case) and the underlying uncertainties had been established, a spread of volumes could be generated by Monte Carlo analysis to generate a probabilistic distribution. To generate the spread, the distribution shape for each uncertainty between the end-member possibilities (represented by the deterministic selection of the 21 and þ1 realizations) was defined in the Monte Carlo simulator. If the nature of the given uncertainty was such that all cases between the end-members were possible and equally likely, then a uniform

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distribution was selected; if the uncertainty was a choice between discrete alternatives, such as between alternative facies association models, then a discontinuous distribution was chosen, and so on. The choices made for this case are shown in Figure 11. The Monte Carlo simulation was then run on the function, sampling these distributions, which are effectively acting as weights in the regression. As the weighting on the uncertainties changes from run to run, the volumetric outcome changes, and the result is a spread of outcomes which can be represented as a probabilistic, or S-curve, distribution. The analysis was conducted using standard commercially available software. Three advantages of this workflow are highlighted. First, it makes a link between probabilistic reporting and discrete multiple-deterministic models. This can be used to provide a rationale for selecting models for simulation. For example, P90, P50 and P10 models can be identified from this analysis and it may emerge that models reasonably close to these probability thresholds were built as part of the initial experimental design. Alternatively, it may show that new models need to be built. This is easy to do now that the impact of the different uncertainties has been quantified, and is an improvement on an arbitrary assumption that a high-case model, for example, represents the P10 case. Secondly, the workflow focuses on the endmembers and on capturing the range of input variables, avoiding the need to make an erroneous best guess. Finally, the approach provides a way of quantifying the impact of the different uncertainties via tornado diagrams or simple spider plots, which can in turn be used to steer further data-gathering in a field. Moreover, having

Table 1. Plackett-Burman design for a suite of deterministic reservoir models involving six uncertainties. For this case, the response data values represent in-place gas volumes in Billion Standard Cubic Feet Run order 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Structure

Quality

Contacts

Architecture

Thin beds

Orientation

Response

21 21 21 1 21 1 1 1 21 21 1 1 0 1

1 21 21 21 21 21 1 21 1 1 1 1 0 1

1 1 21 1 21 1 21 21 21 1 21 1 0 1

1 1 21 1 1 21 1 21 21 21 1 21 0 1

21 1 21 21 1 21 1 1 21 1 21 1 0 1

1 21 21 1 1 21 21 1 1 21 21 1 0 1

1178 380 109 1105 402 1078 1176 1090 870 932 1201 1245 956 1656

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conducted an experimental design, it may emerge that the P50 outcome is significantly different from any initial best guess, as illustrated in Figure 11.

therefore avoids the pitfall of model anchoring, the avoidance of which is believed to be the key to maintaining a wide, but plausible, range of uncertainty in the modelling workflow.

Conclusion

The authors would like to thank Richard Chambers and Kevin Keogh for supportive reviews of this discussion.

1. Scenario-based approaches are a better approach to base-case modelling, as results from the latter are anchored around best-guess assumptions. The latter are invariably misleading because knowledge of the subsurface is insufficiently predictive. 2. ‘Scenarios’ are defined here as ‘multiple, deterministically driven models of development outcomes’, and are preferred to multiple stochastic modelling exercises for uncertainty-handling, the application of which is limited by the same data-insufficiency issue which limits base-case modelling. Each ‘scenario’ is a plausible development future based on a specific concept of the subsurface, the development planning response to which can be optimized. 3. The application of geostatistical techniques, and conditional simulation algorithms in particular, is wholly supported as a means of building a realistic subsurface model – usually infilling a strongly deterministic model framework. Multiple probabilistic models also have a role in the QC of the modelbuilding process, notably to check for sensitivity of the outcome to random selections made during a conditional simulation. However, geostatistical modelling techniques are not seen as the principal tool for uncertainty-handling. Deterministic techniques are preferred for reasons of transparency, relative simplicity, and because each scenario can be individually validated as a plausible subsurface outcome. 4. Scenario-based modelling is readily applicable to greenfield sites but, as the examples shown here confirm, it is also practical at mature brownfield sites, where multiple-history matching may be required at the simulation stage. 5. One current area of improvement which benefits from continuing attention in scenario-based workflows is the approach to multiple-history matching. This is aided by increased computing power but benefits more from rethinking modelling workflows. 6. A second area of current research is the marrying of deterministically selected scenarios with probabilistic reporting. The preferred option presented here is a simple, pragmatic application of experimental design formulation. The technique can be applied to a small number of deterministic scenarios, and makes no requirement to pre-select a base-case or ‘best-guess’ model. The approach

References A LESSION , L., C OCA , S. & B OURDON , L. 2005. Experimental design as a framework for multiple history matching: F6 further development studies. SPE Asia Pacific Oil and Gas Conference and Exhibition, Paper SPE n8 93164. B ADDELEY , M. C., C URTIS , A. & W OOD , R. 2004. An introduction to prior information derived from probabilistic judgements: elicitation of knowledge, cognitive bias and herding. In: C URTIS , A. & W OOD , R. (eds) Geological Prior Information: Informing Science and Engineering. Geological Society, London, Special Publications, 239, 15–27. B ENTLEY , M. R. & H ARTUNG , M. 2001. A 4D surprise at Gannet B – a way forward through seismicallgconstrained scenario-based reservoir modelling. EAGE Annual Technical Conference. Amsterdam. Abstract. B ENTLEY , M. R. & W OODHEAD , T. J. 1998. Uncertainty Handling Through Scenario-Based Reservoir Modelling. SPE Asia Pacific Conference on Integrated Modeling for Asset Management. Kuala Lumpur, Malaysia, SPE n8 39717. B OX , G., H UNTER , W. & H UNTER , J. 1978. Statistics for Experimenters. An Introduction to Design, Data Analysis and Model Building. Wiley, New York. C OSENTINO , L. 2001. Integrated Reservoir Studies. Editions Technip, Paris. D UBRULE , O. & D AMSLETH , E. 2001. Achievements and challenges in petroleum geostatistics. Petroleum Geoscience, 7, 1– 7. E GELAND , T., H ATLEBAKK , E., H OLDEN , L. & L ARSEN , E. A. 1992. Designing Better Decisions. SPE European Petroleum Computer Conference, Stavanger, Norway. SPE n8 24275. K LOOSTERMAN , H. J., K ELLY , R. S., S TAMMEIJER , J., H ARTUNG , M., VAN W AARDE , J. & C HAJECKI , C. 2003. Successful application of time-lapse seismic data in Shell Expro’s Gannet Fields, Central North Sea, UKCS. Petroleum Geoscience, 9, 25–34. L I , B. & F RIEDMAN , F. 2005. Novel Multiple Resolutions Design of Experiment/Response Surface Methodology for Uncertainty Analysis of Reservoir Simulation Forecasts. SPE Reservoir Simulation Symposium. The Woodlands, Texas 2005, SPE n8 92853. V AN DER H EIJDEN , K. 1996. Scenarios: the Art of Strategic Conversation. John Wiley & Sons, Chichester. V AN DE L EEMPUT , L. E. C, B ERTRAM , D., B ENTLEY , M. R. & G ELLING , R. 1995. Full field reservoir modelling of Central Oman gas/condensate fields.

SCENARIO-BASED RESERVOIR MODELLING SPE Annual Technical Conference and Exhibition, Dallas, USA, SPE n8 30757. M INTZBERG , H. 1990. The design school: reconsidering the basic premises of strategic management. Strategic Management Journal, 11, 171– 195. P ENG , C. Y. & G UPTA , R. 2005. Experimental design and analysis methods in multiple deterministic modelling for quantifying hydrocarbon in-place probability distribution curve. SPE Asia Pacific Conference on Integrated Modelling for Asset Management. Kuala Lumpur, Malaysia, SPE n8 87002. P LACKETT , R. & B URMAN , J. 1946. The Design of Optimum Multifactorial Experiments. Biometrika, 33, 305–325.

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S MITH , S., B ENTLEY , M. R., S OUTHWOOD , D. A., W YNN , T. J. & S PENCE , A. (2005). Why reservoir models so often disappoint – some lessons learned. Petroleum Studies Group meeting, Geological Society, London. Abstract. T AYLOR , S. R. 1996. 3D Modeling to Optimize Production at the Successive Stages of Field Life. SPE Formation Evaluation, 11, 205– 210. Y ETEN , B., C ASTELLINI , A., G UYAGULER , B. & C HEN , W. H. 2005. A Comparison Study on Experimental Design and Response Surface Methodologies. SPE Reservoir Simulation Symposium. The Woodlands, Texas, SPE n8 93347.

Incorporating uncertainty into geological and flow simulation modelling in Chevron: application to Mafumeira, a pre-development field, Offshore Angola A. CHAKRAVARTY1, A. W. HARDING2 & R. SCAMMAN3 1

Chevron Energy Technology Co., Seafield House, Hill of Rubislaw, Aberdeen, AB15 6XL, UK (e-mail: [email protected]) 2

Chevron Energy Technology Co., 6001 Bollinger Canyon Rd., San Ramon CA 94583, USA (e-mail: [email protected]) 3

Chevron Africa & Latin America Exploration & Production Co., 1500 Louisiana St, Houston TX 77002, USA (e-mail: [email protected]) Abstract: In this paper, we describe a reservoir-modelling case history of Mafumeira, a Chevronoperated field located in Offshore Angola. The field has only six well penetrations and lies within the closure of nearly 60 square kilometres; the purpose of the study was to capture a range of subsurface uncertainties for evaluation of the development options. We used a Depositional Facies Modelling scheme utilizing recent developments in Multiple Point Geostatistical Simulation and reservoir property uncertainty analysis to generate five static reservoir models. After scaleup, flow simulations were conducted on each model for different field development options using a Design of Experiments (DoE) methodology and a preferred development option was selected. The geology of Mafumeira field is complex. The multiple point geostatistical simulation used a training image consisting of seven depositional facies. The training image is a 3D conceptual model of the facies present and the facies associations; it captures complex spatial relationships between multiple facies, and non-linear shapes such as sinuous channels. The facies simulation was conditioned by a facies probability cube, which permitted the use of a single training image for different stratigraphic intervals of the reservoir, with different combinations and proportions of the seven facies. Multiple versions of the facies probability cube were produced to model the uncertainty in the occurrence of reservoir quality rock units. In modelling the reservoir properties, uncertainties in porosity, permeability and water saturation (‘PKS’) were taken into account. Five models were produced reflecting the combinations of high- and low-case reservoir facies, high- and low-case PKS properties and an intermediate-case. The high-, intermediate- and low-case models were then dynamically tested to ensure different flow behaviours, prior to upscaling, and the flow behaviours compared to analogue producing fields. In order to utilize DoE simulation, upscaling of the five fine-grid models was required. Flow-based simulation was chosen as the best tool to validate the behaviour of the coarse-grid models against the fine-grid models. However, this effort demonstrated that the conventional scale-up methods utilized in other reservoir models did not adequately capture the behaviour of the fine-grid models in this heterogeneous reservoir. A new method that adjusts the Dykstra–Parsons coefficient was investigated and successfully employed to tune the coarse-scale models. Twelve development alternatives for the field were defined and deterministic economics, based on results from the mid-case simulation model, were run in order to narrow down the number of alternatives to be carried forward into probabilistic analysis to five. The DoE approach allowed us to undertake a thorough evaluation of the key subsurface uncertainties and design an overall development plan. The probabilistic simulation results along with full Decision Analysis (DA) allowed us to identify a phased development, which would mitigate potential downside risks while preserving the ability to capture upside potential.

This study of the Mafumeira oilfield, offshore Angola, was conducted over a period of about six months in 2003 and was part of a larger effort to evaluate development options prior to front-end engineering design. In preparation for the work described here, extensive geological, geophysical,

petrophysical and engineering work had been performed to provide the necessary data for modelling, but this is beyond the scope of this paper. Here, we will concentrate on describing the process for static geological modelling, including uncertainty analysis, the dynamic flow simulation of multiple

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 161– 179. DOI: 10.1144/SP309.12 0305-8719/08/$15.00 # The Geological Society of London 2008.

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models, economic evaluation using a Decision Analysis methodology and the decisions made on the basis of this modelling. The integration of geological and reservoir engineering techniques with an underlying theme of identifying and managing uncertainty throughout the whole modelling and simulation process were fundamental in this work; this is considered to be industry best practice.

Summary of the geology The reservoir studied is within the Cretaceous Pinda Formation; published literature is very limited on the structure and the mixed clastics and carbonate stratigraphy of this formation but limited discussion can be found in Rouby et al. (2003) and Brice et al. (1982) with a passing reference (and stratigraphic column) in Brownfield & Charpentier (2006). The deposition of the Pinda is interpreted to be in a fluvial to shallow-marine environment with the strike of the palaeocoastline at approximately N208W. In the east of our study area, deposition was primarily continental red-beds and in the west, a fully marine shelf; these environments are separated by shoreface deposits, from lower shoreface in the west to beach sediments of barrier islands in the east; behind the barrier complex, a

lagoon developed. These facies belts migrated roughly from east to west and back again in line with eustatic sea-level changes. The climate was generally arid, but ephemeral river channels cut through the red-bed section in times of heavy rainfall, depositing fluvial sands and, as they entered the lagoon, bay-head deltas. In times of less rainfall, the lagoons became the site of carbonate deposition; there is evidence of tidal inlets and washover fans. Figure 1a is a simplified map illustrating these facies for a single reservoir zone. A stratigraphic study identified sequence boundaries and flooding surfaces, and these were used to subdivide the Pinda into 15 reservoir zones. In the Tertiary, the Cretaceous succession was deformed by the characteristic rift – raft tectonics of the area: Pinda-age fault blocks detached on the underlying Aptian Loeme salt section and were highly rotated. Deformation in the south of the study area was particularly intense, and there the fault blocks are difficult to map with confidence, even with the benefit of 3D seismic data. The Pinda is now buried to a depth of 8500 to 12 000 feet. Figure 2 illustrates the structural style of the field and shows a structure map of the top reservoir with three representative cross-sections.

Fig. 1. Multiple point geostatistical training image. (a) Map view illustrating depositional facies relationships; (b) transverse cross-section flattened on base; (c) cut-away the block diagram.

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Fig. 2. Structure map and three seismic lines: illustrating the Pinda rift-raft tectonics.

Static geological model The static geological model was constructed in three phases: construction of the geocellular stratigraphic grid; the modelling of depositional facies; and the modelling of the reservoir properties of the depositional facies. Six boreholes penetrated the reservoir with one further well used for structural control. Two of the six wells were extensively cored and this core was used to control the stratigraphic studies; facies were identified in core and these were simplified into seven main depositional facies: shelf, shoreface, lagoon, red-beds, channels and proximal/distal delta-lobes; well logs were calibrated with core and then the facies interpretation was extended by log-character interpretation to the uncored well sections.

Construction of the geocellular stratigraphic grid The hydrocarbon-bearing units of the Pinda are confined to an elongated fault-block with N208W strike and are compartmentalized with multiple gas –oil and oil– water contacts; for simplicity, however, the stratigraphic grid used for modelling was not itself faulted. Seismic horizons and faults were mapped, depth corrected and imported into Gocad (Paradigm’s visualization and modelling package); surfaces were constructed to honour the faults and were used to constrain the structure of

the stratigraphic grid; fault scarps were honoured by steeply dipping beds in the grid; individual fault blocks were identified as separate regions in the grid and were assigned different hydrocarbon contacts later in the process. The grid cells were 100 m square areally and the average cell thickness was 1– 2 feet, giving a total stratigraphic grid size of 13.5 million cells; for computational efficiency, the grid was split into three sections (termed Reservoirs 1, 2, and 3 below) which were joined together again during the scale-up process.

Modelling of depositional facies Strebelle & Levy (2008) have described the techniques used in this step of the process and Harding et al. (2004) have discussed their application to this particular field, so here we will only present a summary. We have used multiple-point geostatistical simulation (MPS) to model the depositional facies. The advantage of using depositional facies over any other categorical characterization of the rock units is that our geological understanding of each depositional facies allows us to describe their shape and the spatial association with the other facies present. This information is compiled into a ‘training image’ which is a 3D idealized model containing the facies shapes with their appropriate dimensions and associations; the training image was constructed using an object modelling technique,

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Fig. 3. Facies probability cube. One horizontal slice of the cube is shown to illustrate the geological control provided with the probability of facies occurrence. Unit is facies fraction.

proprietary to Chevron. Figure 1c is a cut-away 3D view of the training image which has been flattened at top and base. The training image used in the simulation has the same horizontal and vertical cell dimensions as the modelling grid but it is only 20 cells in thickness. The MPS process uses the training image to calculate the probability of a facies occurring, given the known facies occurrences, and uses this in a sequential simulation with the facies in the wells as conditioning data. With that degree of control

however, a realization can be produced which has, for example, a shelf facies where our geological sense would tell us that it is not appropriate. We have circumvented this problem by adding a facies probability cube as additional control; this is constructed for each reservoir zone modelled and is made from facies depocentre maps and vertical proportion curves, based on our geological interpretation of the zone. Figure 3 shows maps of the facies probabilities for each facies at one particular stratigraphic grid layer in the model and

Fig. 4. Depositional facies realizations for three stratigraphical grid layers of model.

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Figure 4 shows the resulting facies realization for three grid layers. The early part of the simulation draws heavily on the information in the probability cube – as only a few cells have been populated – so the facies belts we see in the probability cube are reproduced; later in the simulation, when more cells have been populated, MPS draws on the probability information in the training image so that the facies associations are reproduced in the fine structure of the model. With only six boreholes penetrating the reservoir, there is insufficient information on the facies proportions – controlling net-to-gross ratio – to be confident that the interpretations we have made for facies distributions are reliable. We have therefore postulated two further scenarios for our facies probability cube in addition to our preferred interpretation case; these represent the high and low net-to-gross ratio cases. While the low and high cases do not represent true P10 and P90 probability scenarios, they were constructed based on regional analysis of depositional facies and capture the range of net-to-gross seen in analogue Pinda fields; the sensitivity of the oil-in-place distribution to the probability assignments can be analysed using experimental design techniques but that is beyond the scope of this paper. We then performed multipoint simulations using the high and low net-to-gross-ratio facies-probability cubes but with the same training image as before. An example of a grid layer for the three cases is shown in Figure 5; the shoreface, fluvial channels

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and bay-head delta-lobe facies are shown to be increasing in abundance at the expense of the marine shelf, lagoon and red-bed facies. The difference in facies proportions, within the same reservoir architecture has an impact on the oil-in-place volumes and the reservoir connectivity. The high net-to-gross cases have strong north-to-south connectivity, whereas the low case may well consist of several isolated reservoirs. To assess this quantitatively, we must first populate the model with the reservoir properties of porosity, permeability and water saturation (‘PKS’), and this is discussed below.

Modelling of reservoir properties Standard geostatistical tools were used to populate each depositional facies with reservoir properties; first, permeability was populated using Sequential Gaussian Simulation (SGS), Deutsch & Journel 1992; secondly, porosity was simulated by p-field cloud transform (described by Bashore et al. 1994) using permeability as an independent property; finally, irreducible water saturation was modelled using a cloud transform from permeability. The workflow of modelling permeability followed by porosity was adopted for the Pinda Formation in order to capture the heterogeneous permeability structure as a key characteristic of the model affecting fluid flow. Use of the cloud transform allows the representation of the multivalued porosity– permeability relationship, though because of the

Fig. 5. Three depositional facies realizations for one layer of the model. Different facies probability cubes are used to produce scenarios for a high-case, intermediate (base)-case and low-case of reservoir of facies development.

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order of simulation, the heterogeneity of the porosity model will be exaggerated; this effect is not considered significant because reservoir volume is governed by the porosity histogram, which is implicit in the scattergram of the cloud transform process. Horizontal permeability was estimated at the wells using a transformation of mineral-based, well-log-derived, petrophysical properties calibrated to core measurements; the values were then corrected for overburden and fluid flow effects. All six boreholes used in this study had a full suite of modern logs (spectral gamma-ray, resistivity, neutron-density, sonic and nuclear-magnetic resonance [NMR] logs) and these were calibrated with excess of 2000 ft of core and the log-derived permeability-height values were compared with five DST intervals in three wells and found to have a good correlation; the NMR interpretation was calibrated by core scans. The SGS was conditioned to the calculated well permeability values; a separate anisotropic variogram was used for each facies with variable azimuth to conform to the interpreted trends in depositional facies. Figure 6 shows the histograms of permeability for the entire reservoir, classified by depositional facies on a log10 scale; although the histograms of some facies are similar, such as Shelf and Distal Lobe, the morphology of these facies and their associations with other facies are different and this justifies the need to model them separately. Whilst the permeability statistics of the facies are sufficient for stochastic modelling, the sparse well control suggests that we may not have adequately

sampled the true distribution. We have used the histograms shown for a base case model but we have also generated scenarios with a higher permeability case and a lower permeability case. Estimating the histogram for these cases is subjective; in our example, we chose to inspect the facies permeability distributions for each of the 15 zones modelled, and grouped together those zones showing the higher average permeability and those showing the lower average permeability. The resulting histograms were then used to control high-case and low-case realizations of the permeability model. Figure 7 shows the high-case, global-case and low-case histograms used to perform the normal-score transformation in SGS and these statistics are preserved in the output models. We considered modelling additional permeability uncertainty by perturbing the well log values; we had not investigated the uncertainties in these values, therefore we elected not to do this but used instead one set of well permeability values for each scenario. The cloud transform process requires a scattergram relating permeability (the independent variable) to porosity (the modelled variable); the permeability–porosity pairs were derived from the petrophysical analysis; Figure 8 shows the scattergrams used for each facies. We considered several options to model the effect of porosity uncertainty, including perturbation of the well log values and the generation of multiple scenarios for the permeability–porosity scattergram, however, because of a lack of firm grounding for these cases, we elected simply to allow the high and

Fig. 6. Histograms of permeability for reservoir facies and non-reservoir facies rocks (millidarcy on a log10 scale).

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Fig. 7. Histograms of high-case, global-case and low-case for reservoir facies permeability (millidarcy on a log10 scale).

Fig. 8. Scattergrams to convert permeability to porosity for reservoir facies (millidarcy vs. porosity fraction).

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low permeability histograms to drive high- and low-case porosity scenarios using only the scattergrams shown in Figure 8. For the static model, irreducible water saturation was modelled using a p-field cloud transform of permeability; cross-plots of log-derived water saturation above the hydrocarbon–water contact for each facies were made and the data from these were used in the cloud transform. For the sake of brevity, we have not illustrated these cross-plots; they show, however, an inverse trend of water saturation with permeability but with a high degree of scatter. The uncertainty in permeability histogram was again used to derive high, medium and low cases of water saturation.

Model construction and volumetric calculations The structural complexity of the field has resulted in multiple oil and gas pools and the limited well control leaves considerable uncertainty on the gas–oil –water contacts. For each hydrocarbon pool, we assigned high, intermediate and low case contacts and calculated volumes for each case. For the Pinda reservoir, we typically define net reservoir with a permeability cut-off but there is uncertainty over which is the most appropriate; we therefore used three different cut-offs to assess volumes: 1 mD, 5 mD and 10 mD. A range of formation-volume-factors (FVF) was applied, based on gas–oil ratio and PVT data from drill stem tests. These are a simple multiplier on hydrocarbon

volume so this step did not require construction of models. Depth conversion velocity is a further source of uncertainty and was modelled separately from the other parameters for comparison purposes. A probabilistic range of velocity models was constructed based on available seismic and well velocity data. The top reservoir time map for each of three main reservoir intervals was depth converted with the low-, intermediate- and high-case velocity models to test the sensitivity of gross rock volume above the oil –water–contact to velocity variance. The Gocad earth models were constructed using the intermediate-case depth surfaces for each reservoir. Figure 9 shows the sensitivity of hydrocarbon volume to each uncertainty parameter in the form of a ‘tornado chart’. This chart is constructed for each parameter by varying its values over the expected range and measuring the resulting hydrocarbon volume while keeping all other parameters constant at the base-case values. The three main sources of uncertainty are PKS, reservoir facies proportion and hydrocarbon contacts, with net-gross ratio cut-offs also important. The combination of depositional facies cases and PKS property cases resulted in nine models; the addition of net-pay cut-offs, hydrocarbon contacts and formation-volume-factor uncertainties resulted in 243 estimates of hydrocarbon volume. A smoothed cumulative curve of the hydrocarbons for all these models is shown in Figure 10, and this is based on the assumption that each of the high, medium and low parameter values are

Fig. 9. Tornado chart showing sensitivity of hydrocarbon volume to each uncertainty parameter.

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Fig. 10. Field total OOIP and geological models investigated with reservoir simulation.

equiprobable; the technical basis of this was that we had no a priori justification to assume a probability distribution so the least-biased option was selected. The key geologically based uncertainties of reservoir depositional facies occurrence and PKS reservoir properties can be represented by five models which are combinations of high and low PKS parameters and high and low reservoir facies proportions, and the addition of the ‘mid-mid’ model (mid-case facies and mid-case PKS): these were carried forward into the flow simulation phase of the study. The cumulative curve shows that the ‘mid-mid’ model is indeed close to the P50, the ‘high-high’ is close to the P90 (with mid-case hydrocarbon contacts), but the low case is represented by no single model. The five models

Fig. 11. Reservoir simulation workflow.

were taken forward to the reservoir simulation phase of the study.

Reservoir simulation modelling The five fine-scale models described in the previous section (representing combinations of high and low reservoir volumes and high and low reservoir continuity) are shown in Figure 10. High/intermediate/ low models were identified for both facies (for sand quantity) and petrophysics or PKS (for sand quality and connectivity); various combinations of facies and PKS models could be identified. The reservoir simulation modelling followed the workflow shown in Figure 11.

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Geological model validation To ensure that the fine-scale models were indeed capturing different dynamic flow behaviour, reservoir simulation tests were conducted early in the modelling effort. The geological models were first tested in fine scale to verify whether the models captured a broad-enough range of reservoir performance variability (for both primary and water flooding). A sector of the core area (c. 930 000 cells) was cut from the low-intermediate- and high-case fine-scale models, Figure 12. These three models with high, intermediate, and low PKS, respectively, were tested. The models were tested using Frontsim (Schlumberger’s 3D streamline simulator: http:// www.oilfield.slb.com/content/services/software/ geo/petrel/frontsim.asp) under realistic operating conditions. Some of the results are shown in Figs 13 and 14. These indicate that the models have captured a broad-enough range of reservoir performance variability for both primary depletion and waterflooding.

Scale-up In order to carry both facies and PKS into the uncertainty modelling, four geological models were

Fig. 12. Reservoir 1 sector model.

chosen to capture the extremes in these parameters, (Table 1). These fine-scale geostatistical models were each comprised of a Reservoir 1 (R1) model with approximately three million cells and Reservoirs 2 and 3 (R23) models with approximately 10 million cells. The models were scaled-up separately using SCP (Chevron proprietary reservoir scale-up software). The mid-case R1 (MM) model was scaled-up and tested first. The areal dimension was mostly left unchanged (100 m  100 m) with some coarsening at the edges of the model. Several scale-up methods were investigated: † † † †

Manual versus automatic layering; Vertical layering (16, 20, 29 and 43 layers); Default versus border region option; and Near wellbore scale-up.

Using standard scale-up diagnostics (based on single phase flow comparisons), the fine-scale and coarse-scale (scaled-up) models looked reasonably similar. Some differences were observed between these scale-up methods, but not significant enough to choose one coarse model over another. To further investigate the quality of

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Fig. 13. Primary case: production at 10 000 barrels/day.

scale-up, dynamic flow behaviour comparisons were undertaken.

Dynamic flow validation Dynamic testing (two phase flow) and comparison of the fine- and coarse-scale models were undertaken, using conceptual primary and waterflooding scenarios. All dynamic testing was conducted using a 3D streamline simulator (Frontsim).

Under the primary case, conceptual producers were placed approximately 1200 m apart to cover most of the field area. Simulation runs were made to test the coarse models generated with the different scale-up options. It was concluded that for the primary recovery case, model performance was not sensitive to scale-up method and the fine and coarse models were in close agreement. Under the waterflood case, conceptual producers and injectors, approximately 1000 m apart, were

Fig. 14. Waterflooding case: 500 m spacing, max. liquid 5000 barrels/day.

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Table 1. Facies extremes 1 2 3 4 5

Mid-Facies, Mid-PKS Low-Facies, Low-PKS Low-Facies, High-PKS High-Facies, Low-PKS High-Facies, High-PKS

(MM) (LL) (LH) (HL) (HH)

placed to cover most of the field area. It was found that the coarse model which performed best (29-layer model) still remained optimistic compared to the fine-scale model as shown in Figure 15. In order to improve the match, adjustments to Kv/Kh (multipliers), relative permeability (straight lines), and near wellbore scale-up methodology were attempted, but without success. Finally, the heterogeneity of the system was investigated via calculation of the Dykstra –Parsons (DP) coefficient. It was found that the fine-scale R1 model had a DP coefficient of approximately 0.99 which indicated a very heterogeneous system, while the coarse-scale 29-layer R1 model had a lower DP coefficient indicating some loss of heterogeneity due to scale-up. By increasing the coarse scale DP coefficient to 0.85, a better dynamic match was obtained (Fig. 15). Adjustments to DP coefficient adjusts the permeability contrast in the model without changing the model Kh. The adjustments required for the match did not change the overall ‘geology’ of the system compared to the fine-scale

Fig. 15. Coarse-scale model dynamic behaviour.

model. The standard scale-up diagnostics were repeated and showed good comparisons as before. This process of dynamic model validation via the adjustment of the DP coefficient was repeated for the R23 reservoir units and the remaining four fine-scale models (HH, HL, LH and LL). All validated coarse-scale models were then taken into the DoE analysis.

DoE analysis Probabilistic analysis of the reservoir was undertaken using the DoE methodology. First, the key subsurface uncertainty parameters and their likely ranges were identified as shown in Table 2. The faults connections meant that smaller faults remained unchanged or were connected longitudinally to create longer faults and, thus, transmissible flow across faults. Using a Plackett–Burman (Plackett & Burman 1946) design, the experimental design table below (Table 3), was constructed. Thirteen simulation decks, based on this combination of uncertainty parameters, were constructed and run. The DoE simulations were conducted for two realistic development scenarios: (1) Northern Area Primary and (2) Northern Area waterflood (Fig. 16). This allowed the selection of separate P10/50/90 models for the primary and waterflood recovery processes. The DoE analysis allows the calculation of the statistical P10/50/90 recoveries and identification of the key or most significant parameters that

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Table 2. DoE parameters and ranges Parameter

Low

Facies PKS Faults

High case High case Not connected and transmissible 0.15/0.17 0.22/0.15/0.08 0.35 0.0001/0.001 Viscosity * 0.9

Sorw/Sorg Krw (3 Kr regions) Krg Kv/Kh (R1/R23) PVT

influence the recoveries. The simulation data were sampled at year 2015 and 2030, and the corresponding DoE results of the Northern Area primary and waterflood scenarios are shown in Figures 17 & 18. It is clear from the above Pareto charts that facies and PKS are the most significant uncertainty parameters and account for 70–80% of the variance in recoveries for both primary depletion and waterflooding. The next most influential parameter is faulting for primary depletion and Kv/Kh for waterflooding. Also, there is significant upside to waterflooding provided the reservoir quality is P50 or more. For P10 quality reservoirs, there is little upside to waterflooding and this would translate into significant downside risk for the additional investment, i.e. a ‘trainwreck’ scenario. Using the most significant uncertainty parameters – facies and PKS – as the primary choices, simulation models were constructed and tested to match the representative DoE P10/P50/P90 recoveries during mid- and late-time. These simulation models now represented the DoE P10/50/90 models for primary and waterflood developments (Table 4) and were subsequently used for

Mid

High

Mid case Mid case Connected and transmissible 0.27/0.23 0.33/0.24/.08 0.47 0.001/0.01 Viscosity * 1.0

optimization of the probabilistic analysis.

Low case Low case Connected and non-transmissible 0.37/0.33 0.42/0.32/0.08 0.65 0.01/0.1 Viscosity * 1.1

developments

and

for

Reservoir development modelling The reservoir development modelling followed the workflow shown in Figure 19.

Alternatives selection Twelve development alternatives were initially defined. It would have been too much effort to conduct full probabilistic analysis of each alternative. Instead, deterministic runs were first made for each alternative using the mid-case simulation model (run 13, Table 3). Economic analyses were then conducted using results from the mid-case simulation models, Figure 20. Based on the above economics, the five best alternatives (cases 1, 4, 6, 10 and 12) were selected.

Optimization of preferred alternatives The optimizations of the five preferred alternatives were conducted using the DoE P50 model. The

Table 3. Plackett –Burman Experimental Design table

1 2 3 4 5 6 7 8 9 10 11 12 13

Facies

PKS

Faults

Sorw/g

Krw/g

Kv/Kh

PVT

H H L H H H L L L H L L M

L H H L H H H L L L H L M

H L H H L H H H L L L L M

L H L H H L H H H L L L M

L L H L H H L H H H L L M

L L L H L H H L H H H L M

H L L L H L H H L H H L M

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Fig. 16. Development scenarios for DoE analysis.

optimization was conducted only with ‘controllable’ parameters (i.e. well type/count, placement, timing, rates, etc.); the subsurface uncertainty parameters which are ‘uncontrollable’ remained unchanged as defined by the DoE P50 parameter combination (Table 4). Various development and

production strategies for primary and waterflood scenarios were investigated: † Horizontal wells; † Well spacing and infill wells (400 and 200 acres);

Fig. 17. DoE results from Northern Area primary development.

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Fig. 18. DoE results from Northern Area waterflood development.

† Alternative well locations (at 400 acres); † Perforation stand off (15 ft and 50 ft from GOC and OWC); † Dual and commingled wells; † Flow tables/gas lift; † Peripheral and infield injection; † Water injection timing; † Water flood with infill wells; † Completion strategy (selective and full completions); and † Producer-to-injector ratios (2:1 and 3:1) Based on the findings of the above sensitivities, optimized models of the five preferred alternatives were constructed.

Probabilistic forecasts The optimized preferred alternatives (based on the DoE P50 model optimization) were then run with the DoE P10 & P90 models (Table 4). In this way, the probabilistic effects of the ‘uncontrollable’ subsurface parameters could be determined. These results were also benchmarked against existing well test results and data from analogue fields to ensure consistency in the spread of results. The P10/50/90 reserves at year 2015 and 2030 for the five preferred alternatives are shown in Figure 21. The maximum spread between primary and waterflood cases are indicated by the horizontal arrows. It can be observed (not surprisingly) that the

Table 4. Uncertainty parameter combinations for DoE P10/50/90 simulation models Primary

P10 Model P50 Model P90 Model

Facies

PKS

Faults

Sorw/g

Krw/g

Kv/Kh

PVT

OOIP Bstb

L M H

L M H

L M M

L M H

L M H

L M L

M M M

0.544 1.217 1.757

M M L

M M M

0.476 1.241 1.794

Waterflood P10 Model P50 Model P90 Model

L M H

L M H

L M M

L M H

M M H

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Fig. 19. Reservoir development workflow.

spread in reserves between primary and waterflood cases increases with reservoir quality. However, waterflood increments in poor reservoirs (c. P10) are significantly lower and this highlights significant downside risks.

Decision analysis The P10/50/90 production profiles for each of the five alternatives were carried forward into

probabilistic analysis. These profiles provided the essential input for probabilistic Decision Analysis (DA). The DA model included the following probability nodes: † † † † †

Production forecast; Facilities capital expenditure; Drilling capital expenditure; Operating expenditure; and Crude price scenario.

Fig. 20. Deterministic economic analysis of the 12 development alternatives.

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Fig. 21. Comparison of probabilistic reserves for optimized preferred alternatives.

The probabilistic results are shown below in Figure 22. Probabilistic economic analysis clearly distinguishes the five development alternatives from each other while highlighting the pros and cons of each case. Case 10 (full-field waterflood) – the highest expected value NPV10, but has negative NPV in the event of a poor reservoir outcome. Case 1 (northern area sweet spot primary) – the highest capital efficiency and no probability of negative NPV, but has considerably lower reserves, especially in a P90 reservoir outcome. As standalone projects, none of the current cases captures the best aspects of all decision criteria: high NPV, low probability of negative NPV, high capital efficiency, and high reserves recovery. Reservoir quantity and quality uncertainties are the largest factors influencing the P10/50/90 range in economic

Fig. 22. Preliminary probabilistic economic results.

results and should be addressed early in any development strategy. The challenge is to develop a hybrid alternative which would capture, as much as possible, the best aspects of each of the five stand-alone cases and develop the incremental reserves (to Case 1) at acceptable capital efficiencies.

Phased development A notional phased development strategy was therefore recommended, which will allow for sequential upside capture and mitigate downside risks due to large reservoir uncertainties, as shown in Figure 23. The phases are represented by: † Phase 1 – Northern Area Sweet Spot development utilizing existing infrastructure;

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Fig. 23. Notional phased development results.

† Phase 2 – Expand to Northern Area Primary development. We would proceed to Phase 2 if the reservoir appeared to be high quality; † Phase 3 – Implement Northern Area Water flood (and test Southern Area). We would proceed to Phase 3 if the reservoir appeared to be high quality and a pilot waterflood was successful; and † Phase 4 – Expand to Full-field Waterflood. We would proceed to Phase 4 if the Southern Area of the reservoir is much higher quality than expected.

phased development strategy was subsequently recommended, which will allow for sequential upside capture and mitigate downside risks due to large reservoir uncertainties. The authors would like to thank Sonangol, Cabinda Gulf Oil Co., ENI Angola Production B.V. and Total Petroleum Angola Ltd for permission to publish this paper. We received generous support from the management of Chevron Africa & Latin America Exploration & Production Co., and Chevron Energy Technology Co. Special thanks go to Bryan Bracken, Jennifer Ayers, Sebastien Leigh, Rachel Preece, Sharon Unser, Surat Thurachen and others who were part of the Chevron team.

Conclusions This paper highlights a methodology currently for defining and modelling geological uncertainty in fine-scale models, carrying it through to reservoir simulation, to access subsurface uncertainties with DoE to generate probabilistic forecasts. In this fashion, key subsurface ‘uncontrollable’ uncertainties were identified along with development risks. Probabilistic Decision Analysis clearly distinguished the five development alternatives from each other while highlighting the pros and cons of each case. This process helped formulate a hybrid alternative which would capture, as much as possible, the best aspects of each of the five stand-alone cases and develop the incremental reserves at acceptable capital efficiencies. A

References B ASHORE , W. M., A RAKTINGI , U. G., L EVY , M. & S CHWELLER , W. G. 1994. Importance of a geological framework and seismic data integration for reservoir modeling and subsequent fluid-flow predictions. In: Y ARUS , J. M. & C HAMBERS , R. L. (eds) Stochastic Modeling and Geostatistics: Principles, Methods and Case Studies. American Association of Petroleum Geologists. B RICE , S. E., C OCHRAN , M. D., P ARDO , G. & E DWARDS , A. D. 1982. Tectonics and sedimentation of the South Atlantic rift sequence, Cabinda, Angola. In: W ATKINS , J. S. & D RAKE , C. L. (eds) AAPG Memoir. Studies in Continental Margin Geology, 34, 5–18. B ROWNFIELD , M. E. & C HARPENTIER , R. R. 2006. Geology and Total Petroleum Systems of West-Central

INCORPORATING UNCERTAINTY INTO MODELLING Coastal Province West Africa. United States Geological Survey Bulletin, 2207-B. D EUTSCH , C. V. & J OURNEL , A. G. 1992. GSLIB: Geostatistical Software Library and Users Guide. Oxford University Press. H ARDING , A. W., S TREBELLE , S. & L EVY , M. ET AL . 2004. Reservoir Faces Modelling: New Advances in MPS. Proceedings of the Seventh International Geostatistics Congress, 2, 559–568. P LACKETT , R. L. & B URMAN , J. P. 1946. The Design of Optimal Multifactorial Experiments. Biometrika, 33, 305–325.

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R OUBY , D., G UILLOCHEAU , F., R OBIN , C., B OUROULLEC , R., R AILLARD , S., C ASTELLTORT , S. & N ALPAS , T. 2003. Rates of deformation of an extensional growth fault/raft system. Basin Research, 15, 183– 200. S TREBELLE , S. & L EVY , M. 2008. Using multiple-point statistics to build geologically realistic reservoir models: the MPS/FDM workflow. In: R OBINSON , A., G RIFFITHS , P., P RICE , S., H EGRE , J. & M UGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 67– 74.

Addressing uncertainty and remaining potential in a mature field. A case study from the Tertiary of Lake Maracaibo, Venezuela CHARLOTTE A. L. MARTIN Shell Development (Australia) Pty Ltd., Level 28 QVI Building, 250 St. George’s Terrace, Perth, WA 6000, Australia (e-mail: [email protected]) Abstract: The Urdaneta West Field is located on the western margin of Lake Maracaibo in northern Venezuela. Biodegraded oil (12– 158 API) is reservoired in Tertiary sandstones and produced through a series of lateral wells. The productive sandstones of the Icotea and Misoa Formations are thin, calculated as 0.5–4.5 m (1.5–15 ft) vertical thickness, and of limited lateral extent. This heterogeneity, coupled with heavy oil, results in poor fluid communication and low recovery efficiency. During 2004, a full field review was undertaken to address future development. Despite production from the Icotea and Misoa Formations, subsurface uncertainty was identified as a major issue due to the clustered nature of field development, complex depositional and structural environments, and reservoir fluid characteristics. In order to rank and mitigate reservoir uncertainties, a series of static models were built. The first phase of static modelling used a simple structural framework and reservoir interval averages to generate minimum, mid- and maximum volume cases. Dynamic simulation of these identified two major areas of uncertainty impacting oil-in-place and productivity – net sandbody connectivity and hydrocarbon contact. Two further phases of static and dynamic modelling concentrated on evaluating the full range of these uncertainties within a detailed structural framework.

The Urdaneta West Field (UDW) was discovered in 1955 and is operated by Shell Venezuela on behalf of Petro´leos de Venezuela SA (PdVSA). The field is located in the western part of Lake Maracaibo, Venezuela, as illustrated in Figure 1. Oil, sourced from the Cretaceous La Luna Formation, is produced from Cretaceous, Jurassic and Tertiary reservoirs. The Tertiary sandstone reservoirs of UDW form the subject of this paper. Two separate reservoirs are developed – the Misoa and Icotea Formations of Eocene and Oligocene age respectively (Fig. 2). Top seal for the reservoir sandstones is provided by the Miocene mudstones of the La Rosa Formation (Fig. 2) and hydrocarbon trapping is through a combination of structural and stratigraphic mechanisms. Multiple hydrocarbon contacts, in the form of oil-down-to, are measured from the reservoirs, ranging in depth from 8772 to 9455 ft (2707–2918 m) sub-sea. The Tertiary oils of UDW are degraded, with a gravity of 11 –148 and a Gas : Oil Ratio (GOR) of 50 scf/stb. Reservoir sandstones are thin, typically varying between 1.5–15 ft (0.5–4.5 m) in vertical thickness, and reservoir quality is variable, with sandstone porosity ranging from ,5–35%. The combination of heavy oil with thin sandstones of variable quality results in a highly heterogeneous reservoir. To maximize oil recovery, UDW has been developed by a series of lateral wells as illustrated in Figure 1. A total of 17 production

wells have been drilled on the field to form five production clusters. During 2004, the Tertiary reservoirs of UDW were assessed for further development potential. Due to the heterogeneous nature of the reservoirs and the clustered nature of the development, a level of uncertainty still existed in the subsurface understanding of the Icotea and Misoa Formations. Sandbody geometry/connectivity and fluid contacts were perceived to be the factors of high risk. In order to mitigate risk and incorporate uncertainty into development scenarios, a phase of static and dynamic reservoir modelling work was undertaken. The objective of this modelling work was to build a series of full-field 3D models capturing the range of identified subsurface uncertainties.

Geological setting During the Eocene, the Maracaibo Basin lay within a large foreland basin (Lugo 1991; Lugo & Mann 1995; Parnaud et al. 1995). The Misoa Formation was deposited in a series of deltas that were sourced from the south and west and flowed to a marine depocentre in the north of the present-day Lake Maracaibo. As illustrated in Figure 2, a series of unconformities is evident within the Misoa Formation interpreted as the result of tectonic movements during deposition (Ghosh et al. 1996; Mele´ndez et al. 1996).

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 181– 192. DOI: 10.1144/SP309.13 0305-8719/08/$15.00 # The Geological Society of London 2008.

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Fig. 1. Location of Urdaneta West Field in Lake Maracaibo, Venezuela. Line A–A’ indicates location of Figure 4; line B– B’ indicates location of Figure 7.

The end of the Eocene was a period of basinwide uplift reflected in the development of a regional unconformity between the Eocene and Oligocene. In the Urdaneta West Field, the Eocene –Oligocene unconformity is correlated with SB36-39.5 of Mele´ndez et al. (1996). The Icotea Formation is preserved overlying SB 3629.5. This sand-rich unit is limited in distribution to the western part of Lake Maracaibo, reaching a maximum thickness of 500 ft (152 m) in UDW. The sandstones of the Icotea Formation were deposited within small delta systems that were sourced from uplifted Misoa Formation strata exposed to the east of Urdaneta West (Lugo 1991). The end of the Oligocene was marked by regional flooding of Lake Maracaibo and the mudstone-dominated La Rosa Formation was deposited across the area. Although the La Rosa Formation is attributed to the Miocene (Fig. 2), Oligocene mudstones are also included in the lithostratigraphic unit. Thus, the contact between the Icotea and La Rosa

Formations is a diachronous one; sandstonedominated lithologies are here assigned to the Icotea Formation and mudstone to the La Rosa Formation.

Database Urdaneta West Field is covered by a 3D seismic survey that was used to derive structural and sedimentological information for reservoir evaluation as detailed by Poupon et al. (2004). A total of 115 wells drilled and logged between 1955 and 2004 were used in this study. The majority of these wells targeted Jurassic and Cretaceous reservoir intervals and hence the wireline evaluation of Tertiary reservoirs was limited to gamma and resistivity logs. Thorough Tertiary wireline evaluations were made in approximately 60 wells and image logs and dipmeter data of varying quality were made available for seven wells. Conventional core

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Fig. 2. Urdaneta West Field stratigraphy. Shaded area indicates missing section.

was cut in nine wells with approximately 1920 ft (592 m) of material available from the Icotea Formation and 560 ft (173 m) cut from the Misoa Formation. Biostratigraphic samples were taken from eight of the cored wells and qualitative petrographic description, porosity and permeability measurements were available for six of the cored wells.

Geological modelling workflow The workflow used to model the Icotea and Misoa Formation sandstones of Urdaneta West consisted of three phases, each progressively more complex. An initial coarse-scale full-field static model was passed through to dynamic simulation to identify and rank static and dynamic uncertainties in the modelling parameters for the Icotea and Misoa Formation reservoirs. The second iteration of static models was built to address these uncertainties with updated seismic interpretation, finer grid resolution and a greater number of well data points. Feedback from dynamic modelling was used to develop ‘history matchable’ maximum and minimum static scenarios. The third iteration

of static models combined all available stratigraphic, sedimentological and seismic data with detailed petrophysical inputs. Within a single structural scenario, minimum, mid- and maximum cases for the connectivity of the reservoir were deterministically developed. Multiple realizations of petrophysical models were then generated for each of these facies cases. These detailed models enabled the development of a range of development scenarios for use in well planning and field management.

Iteration 1: static modelling – identification of uncertainties A database of 41 wells with good-quality wireline data was used for the first iteration of staticdynamic modelling. As shown in Figure 3, four surfaces were identified at wells based on lithology and log shape criteria: (1) base of the La Rosa Formation, i.e. first downhole occurrence of sandstone; (2) top of the Icotea Formation upwards-fining gamma log motif; (3) unconformity between Icotea and Misoa Formations; and (4) an IntraMisoa Formation marker, termed the SB 44

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Fig. 3. Reservoir subdivision scheme used in static modelling iterations 1, 2 and 3. Shaded area indicates missing section.

(cf. Mele´ndez et al. 1996) corresponding to an uphole increase in sandstone volume. These surfaces defined three reservoir intervals: the Misoa Formation; a lower Icotea Formation unit characterized by an upwards-fining gamma log motif; and an upper Icotea unit characterized by an upwards-coarsening log motif. These three units had clearly defined porosity and permeability characteristics. The unconformity between the Icotea and Misoa Formations forms a clear seismic marker that was mapped across UDW. This single seismic horizon was combined with simple fault polygons to develop a structural model for iteration 1 modelling. The well-derived intra-reservoir picks were used to build true vertical thickness (TVT) isochores for each of the three reservoir intervals identified – Icotea Marine Unit, Icotea Fluvial Unit and Misoa (Fig. 3). These isochores were used to generate faulted depth structural horizons for the surfaces not constrained by seismic. Interval average porosity cut-offs were used to calculate net-to-gross (NTG) for each interval. To create a minimum-case model, only sandstone with porosity .25% was defined as net. In the mid-case model, a porosity cut-off .22% was used, and in the maximum case .20% porosity sandstone was considered net. NTG and average net porosity were then calculated for the minimum, mid- and maximum models in each of the three reservoir layers from well data. A series

of maps was then generated from these well data. The reservoir layer maps for NTG and average net porosity were sampled directly into the simulation grids where a single equation was used to transform net porosity to permeability. Hydrocarbon saturation was calculated above a range of oil–water contacts (OWC). Following dynamic simulation of the three firstpass model realizations, a number of key uncertainties were identified: (1) definition of net pay rock, i.e. the porosity/permeability cut-off at which oil would flow through sandstone; (2) reservoir heterogeneity and hydrocarbon pay connectivity; (3) position of fluid contacts; and (4) the role of faults in reservoir compartmentalization. In order to address these uncertainties, two further iterations of static modelling were required, each progressively more detailed.

Iteration 2: capturing the range of uncertainty In the second phase of static-dynamic modelling, a database of some 97 wells was used. Wireline log data and all available conventional cores were used to define a sequence stratigraphic reservoir correlation scheme and facies. Porosity evaluations were made available for 52 wells. Two static models were built – low and high cases.

UNCERTAINTY AND REMAINING POTENTIAL IN A MATURE FIELD

Framework modelling – addressing fluid contact and compartmentalization In order to understand and therefore mitigate uncertainties of OWC and fault compartmentalization, detailed structural models were required for UDW. During the second iteration of static modelling, well and seismic data were used to define additional correlation surfaces within the Icotea Formation. Two important surfaces were defined from conventional core and wireline data and mapped on seismic: (1) a maximum flooding surface (MFS) within the La Rosa Formation; and (2) a major stratigraphic break within the Icotea Formation interpreted as a transgressive surface of erosion (TSE). The TSE divides the Icotea Formation into two units here referred to informally as the upper and lower Icotea. Based on core and wireline log response, the upper Icotea Formation was further subdivided into upwards-coarsening cycles bounded by flooding events. Within the cored intervals of the lower Icotea Formation, a sudden influx of extra-formational gravel-sized clasts was noted. This event was clear on wireline as a break in sandbody stacking pattern and was correlated across the field as surface Erosion 1, thus subdividing the unit into two (Figs 3 and 4).

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An updated seismic interpretation of faults was made available for static modelling and these were used to generate a series of dipping fault planes tied to wells. These surfaces enabled more detailed analysis of fault seal potential, and hence reservoir compartmentalization. Analysis of fluid contact data suggested that the oil –water contacts within the Icotea and Misoa Formation reservoirs were independent. In each Formation, the fluid level was reflected by oil-down-to, and water-up-to, measurements. To capture the range of possible oil– water contacts indicated by the oil-down-to and water-up-to data ranges, independent deterministic low, high and base case contacts were defined in the Icotea and Misoa Formations.

Facies modelling – addressing reservoir heterogeneity and connectivity In order to address uncertainty around vertical and lateral reservoir heterogeneity and the connection between oil-bearing sandbodies, a range of detailed facies models were required for both the Icotea and Misoa Formations. The second iteration of static modelling incorporated detailed sedimentological

Fig. 4. Well correlation of Icotea Formation in Urdaneta West Field. Line of section defined in Figure 1. Vertical scale in feet.

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studies, and tied these to petrophysical properties. Cored wells were used as reference points, and away from cored sections sedimentological facies were defined through the use of wireline log response, log stacking character (i.e. coarseningor fining-upwards profiles), and porosity. Conceptual geological models were constructed, based on previously published information as described below. The Misoa Formation is typified by fine – medium-grained sandstone interbedded with mud-rich lithofacies. Cross-bedded sandstones are most commonly preserved in erosively based fining-upwards units 7 –25 ft (2–7.6 m) in thickness, with multistorey units reaching a maximum of 65 ft (19.8 m). Clay clasts are abundant within the base of sandstone packages. Mud-draped reactivation surfaces, flasar ripples and multiple thin mud layers draping clean sand are commonly preserved in the upper portion of fining-upwards units, indicating alternating high and low energy conditions (cf Reineck & Singh 1973). Less commonly, sandstone is preserved in upwards-coarsening units ,5 ft (,1.5 m) thick with evidence of hummocky cross-stratification and bioturbation including Ophiomorpha, Planolites, Asterosoma and Teichichnus. Mudstone-rich units are preserved in intervals of up to 50 ft (15.5 m) in thickness. These are characterized by massive linsen – flasar bedding. The sediments of the Misoa Formation are interpreted as the deposits of fluvial-dominated channels and mouth bars. Biostratigraphic studies of mudstone samples indicate deposition in coastal to marginal marine environments of fluctuating salinity. The mudstone-dominated lithofacies are therefore attributed to deposition within an interdistributary bay with limited marine influence. According to Ghosh et al. (1996), the sedimentary environment for the Misoa Formation corresponds to that of a lower delta plain with sandstones deposited within fluvial-dominated distributary channels. Higgs (1996) interprets a tidal shelf model for the Misoa Formation due to the absence of desiccation cracks and coals, indicative of delta emergence. The lower delta plain model (Ghosh et al. 1996) would appear to be more appropriate for the Misoa Formation preserved in UDW, although tidal influence is indicated in interdistributary areas and within channels with the preservation of mud-draped reactivation surfaces. Using regional published studies (Ghosh et al. 1996) and dipmeter interpretations, it is possible to conclude that fluvially dominated channels flowed from the south and southwest towards a depocentre in the northeast. The lower Icotea Formation is characterized by erosively based, fining-upwards units of mediumto very fine-grained sandstone interbedded with

thick, massive siltstone intervals. Internally, the sandbodies are massive with only limited preservation of cross-stratification. Pedogenesis is common in the upper portion of sandbodies and commonly has removed all evidence of primary structures. Individual sandbodies vary from 1– 15 ft (0.3–4.5 m) in thickness and are stacked to form multistorey units that reach 38 ft (11.5 m). The sandstones of the lower Icotea Formation are interpreted as the deposits of fluvial channels with the multistorey nature of the sand packages suggesting a braided system. Floodplain areas were composed of siltstone and fine sandstone expelled from fluvial channels during periods of flooding. Abandoned channels and floodplain areas were subaerially exposed for significant amounts of time, resulting in deep weathering and vegetation. This prolonged exposure resulted in enrichment of clay minerals within the interchannel units. During deposition of the lower Icotea Formation, UDW lay in upper delta plain environments. Seismic data (Poupon et al. 2004) and dipmeter data indicate that the fluvial channels flowed southwestwards. The upper Icotea Formation and La Rosa Formation strata preserved below the MFS (Fig. 3) are highly heterogeneous. To the north and northeast of the study area, fining-upwards sandbodies, 0.5–9 ft (0.15– 2.7 m) in thickness, are preserved and interbedded with clay-enriched siltstone units reaching 45 ft (13.7 m) characterized by finely disseminated organic mater, ilmenite and authigenic siderite nodules. Evidence of pedogenesis is ubiquitous in sandstones and siltstones. Bioturbation is common within the lower part of sandstone packages with Rhizocorralium, Ophiomorpha, Arenicolites, Planolites and Thallassinoides preserved. The fining-upwards sandstone units are interpreted here as the deposits of fluvial–brackish channels, similar to those preserved in the lower Icotea Formation. Channel sandstones are interbedded with pedogenically modified floodplain areas, as in the lower Icotea Formation. Coarsening-upwards sandstone units 2–10 ft (0.6–3 m) thick, composed of fine to medium grains, are preserved in the southern portion of the study area. The units are characterized by extensive bioturbation with forms Planolites, Arenicolites, Rhizocorallium, Ophiomorpha, Thallassinoides, Teichichnus and Skolithos identified. Rare cross-stratification is preserved in the upper part of individual coarsening-upwards cycles. Coarsening-upwards sandbodies, interpreted as distributary mouth bars, are interbedded with massive, laminated and bioturbated mudstone containing abundant pyrite and siderite. Biostratigraphic analyses from the mudstones indicate deposition in paralic –lacustrine environments with limited marine influence. The presence of pyrite,

UNCERTAINTY AND REMAINING POTENTIAL IN A MATURE FIELD

goethite and siderite indicate proximity to low oxygen or anoxic bottom conditions. During deposition of the upper Icotea Formation and La Rosa Formation, the UDW area is interpreted to have lain on a low-lying lower delta plain, progressively inundated by brackish, poorly oxygenated waters. Seismic data and well image logs indicate that fluvial channels flowed from the northeast and east, feeding mouth bars that prograded westward into a standing shallow body of brackish water with local anoxic conditions. By the La Rosa MFS (Figs 3 and 4), the UDW area was completely flooded. For the second iteration of static modelling, net facies were defined as channel or mouth bar (Fig. 4) and non-net facies were defined as interdistributary bay or interchannel. Aerial probability trend maps were developed for each facies by reservoir layer. Facies percentages calculated from well data points were incorporated with published data on regional palaeotransport directions (Ghosh et al. 1996; Lugo 1991) and well-based dipmeter interpretations to develop sandstone depositional axes for each reservoir layer. Vertical facies proportions were also identified for each reservoir layer from well-based facies logs. These vertical proportion curves make it possible to model coarsening-upwards or fining-upwards trends by layer. In order to capture the vertical reservoir heterogeneity, grid cell resolution was defined as 2–10 ft (0.6–3 m). The facies log defined in the wells was scaled to this grid resolution without loss of heterogeneity. For each reservoir interval, minimum and maximum connected sandbody characteristics were developed. In the absence of seismic information, analogue datasets and statistical analysis were used to estimate sandbody lateral extent. Outcrop analogues studies such as Reynolds (1999) suggest that the fluvial channels 7–25 ft

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(2– 7.6 m) in thickness such as those preserved in the Misoa Formation would be 80–3000 m in width. In the Misoa Formation, it is therefore possible to correlate channel sandstones between closely spaced wells. The fluvial channels of the Icotea Formation are, however, 1.5–15 ft (0.5–4.5 m) in thickness and analogues would indicate such channels to be 8–500 m wide. Hence, although some of the larger fluvial channels in the Icotea Formation may be correlated between wells, there is little support for correlation of channels ,10 m in thickness. Mouth bar sandstones in the upper Icotea Formation vary between 2– 10 ft (0.6–3 m) in thickness and would correspond to bar width of approximately 800 m and length of approximately 2000 m (Reynolds 1999). Well test data and palaeogeographic reconstructions from UDW suggest that the mouth bar sandstones can be correlated over distances of up to 6000 m. The channel and mouth bar width and length relationships calculated from variograms are shown in Table 1. The minimum case correlation lengths correspond to the outcrop analogue data described. The maximum case lateral correlation lengths are larger than would be expected for single channel and mouth bar units, indicating that facies bodies are amalgamated. This observation is supported by conventional core descriptions and field analogue data. The facies models for iteration 2 were built using Sequential Indicator Simulation (SIS) with lateral and vertical trends. This algorithm was chosen over kriging because of the desire to capture heterogeneity for dynamic simulation purposes. Although SIS does not result in geological bodies, elongation direction can be imposed through use of the variogram model. In the minimum connected case, a small lateral correlation distance was used (Table 1), and the large correlation distance modelled in the maximum case. For all reservoir layers, the percentage of each

Table 1. Sandstone facies correlation distances used in iteration 2 modelling Facies

MFS – CSB 25.2 Ma CSB 25.2 Ma – FS11 FS11 – FS10 FS10 – FS7 FS7 – TSE TSE – EROSION 1 EROSION 1 – SB 39.5–36 Ma Misoa Formation

Channel Channel Channel Channel Mouth Bar Channel Channel Channel Channel

Minimum case

Maximum case

Length (m)

Width (m)

Length (m)

Width (m)

985 775 790 675 1970 630 620 760 675

960 670 770 610 1810 520 590 740 570

1700 1980 1200 1175 2295 1335 1085 1125 910

1350 1390 1030 965 2175 1180 965 1070 790

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facies within the minimum model honoured the field mean percentage of that facies preserved in wells. In the maximum connected model, an additional 5% of sandstone was added to the static model. This 5% increase honoured the volume of sand facies preserved in net pay ‘sweet spots’.

Addressing uncertainty associated with net-to-gross The Icotea and Misoa Formation reservoirs are highly heterogeneous in reservoir properties, with conventional core plug measurements of sandstone porosity ranging from ,5–35% and permeability from 0.02 –10,000 mD. The best quality reservoir sandstone is generally preserved within mouth bars and the lower part of fluvial channels. Rock quality variability and hence heterogeneity is most pronounced in the fluvial channels and overbank deposits of the Icotea Formation as illustrated in Figure 5. Pedogenesis and bioturbation of Oligocene sandstones has resulted in modification of reservoir quality in the upper part of fluvial channel with degradation of porosity and permeability. Poor quality sandstone is preserved within interchannel areas where subaerial weathering resulted in clay enrichment and hence permeability degradation (Fig. 5). The combination of heavy oil and this rock quality variation makes the definition of net pay difficult in the Icotea Formation. The simplistic approach followed for petrophysical property modelling in the first phase of static modelling was not able to capture the level

of heterogeneity required for uncertainty analysis of net pay. Therefore, detailed facies models, as built for iterations two and three, were required to assess rock quality and hence net sandstone distribution. In the second iteration of static modelling, calculated porosity curves for some 52 wells were used for property modelling of Icotea and Misoa sandstone facies. Porosity data were checked for trends related to depth and/or lateral relationships. Vertical variograms were developed for each facies from well data, with the lateral correlation distances derived from sandbody geometry (Table 1). Sequential Gaussian Simulation was then used to populate grid cells between wells. This algorithm was chosen in order to capture heterogeneity for dynamic simulation. For both the minimum and maximum static models, 100 porosity realizations were generated by varying seed number alone. These were ranked by pore volume and the P50 case picked as a representative porosity model. A permeability log was calculated at each well control point using a facies-based porosity – permeability transform. A single permeability realization was generated for each of the static models by co-kriging with porosity. In both the Icotea and Misoa Formations, the volume of net rock was calculated from permeability cut-off values as part of the dynamic simulation. After a number of trails, a range of net pay cut-offs between 500 mD and 10 mD was established. These cut-offs allowed for matching of reservoir production behaviour whilst capturing a wide range of uncertainty for development planning.

Fig. 5. Conventional core measurements of porosity and permeability of Icotea and Misoa Formation sandstone facies.

UNCERTAINTY AND REMAINING POTENTIAL IN A MATURE FIELD

Results The maximum and minimum connected sandstone static models were both supported by history match to production data. In this way, dynamic modelling was able to corroborate the end-member cases built during iteration 2. Feedback from dynamic simulation of the second pass structural models indicated further definition of intra reservoir layering was required to fully explain fluid and pressure behaviour in the Misoa Formation. Field development planning also required a reference case model to be built.

Iteration 3: adding detail to improve history match A total of 113 wells were used in the structural and facies modelling for iteration 3. Of these, 60 wells were used for porosity and permeability modelling. In the third iteration of structural modelling, the subdivision of the upper Icotea Formation was increased with the addition of two further flooding surfaces (Fig. 3). Within the lower Icotea Formation, an additional erosion/incision event was identified and correlated across well data (Figs 3 and 4). Progressive onlap of the lower Icotea Formation (Fig. 4) was captured in the structural modelling with the integration of pinch-outs mapped on seismic data (Poupon et al. 2004).

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Figure 6 illustrates the final structural model of the Icotea Formation. Traditionally, the Misoa Formation of Lake Maracaibo is subdivided into the B and C members (Fig. 2) using biostratigraphy and log response (e.g. Ambrose & Ferrer 1997). In areas of significant Eocene erosion, such as UDW, these intra reservoir picks can be difficult to make. However, sedimentological and biostratigraphic evaluation of core indicated a clear break associated with influx of intraformational clasts in the upper Misoa Formation of UDW. The surface, which is clear on wireline logs (Fig. 7) and seismic data, was tentatively assigned to Misoa Formation SB 42.5 (Mele´ndez et al. 1996). The CSB 42.5 Ma surface was mapped on seismic data to give an additional control surface for iteration 3 structural modelling. CSB 42.5 Ma was not preserved across all parts of Urdaneta West Field, being locally removed due to erosion of the overlying unconformity – SB 39.5 –36 as illustrated in Figure 7. Below CSB 42.5, a series of flooding surfaces were identified from well data using gamma ray and resistivity log character and sandbody stacking pattern. Figure 3 illustrates the final layering scheme developed for the Misoa Formation. The flooding events were correlated across UDW to further subdivide the Misoa Formation as shown in Figure 7. With the completion of the third structural modelling iteration, the measured oil levels in the Misoa

Fig. 6. Structural cross-section through Icotea Formation of Urdaneta West Field showing reservoir layers pinching out onto top Eocene unconformity surface. OWC illustrates the mid-case oil–water contact for the Icotea Formation. Vertical scale in feet.

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Fig. 7. Well correlation of Misoa Formation in Urdaneta West Field. Line of section defined in Figure 1. Vertical scale in feet.

Formation could be fully explained in terms of stratigraphic trapping and fault sealing. CSB 42.5 acted as a top seal, resulting in two distinct hydrocarbon columns in the Misoa Formation where the surface was preserved. A deterministic range of OWC surfaces were generated for the two Misoa stratigraphic units to capture the range in oil– water contact possible with the measured oil-down-to and water-up-to data. Iteration 3 facies modelling was undertaken with the updated structural and stratigraphic model. The increased stratigraphic control resulted in improved vertical facies probability modelling. Seismic facies data were made available for the Icotea Formation at this time and these were used to identify fluvial

channel orientation and the lateral facies relationships between mouth bar and fluvial channel sandbodies within the upper Icotea Formation (Poupon et al. 2004). The iteration 3 static modelling involved the building of three facies scenarios – a base case and minimum and maximum connected sandstone models. For the minimum and base cases, the percentage of sandstone within the models was that defined from well data. In the maximum connected, the additional 5% sandstone was incorporated into the model as in iteration 2. Lateral correlation distances were established for individual sandbodies through variogram modelling as in the iteration 2 models. Sequential Indicator Simulation was again

Fig. 8. Icotea Formation facies distributions between Flooding Surfaces 7 –8 (a) minimum, (b) base and (c) maximum connected sandstone cases.

UNCERTAINTY AND REMAINING POTENTIAL IN A MATURE FIELD

used to populate the facies models. Figure 8 details results from the Icotea Formation illustrating the increase in lateral correlation within mouth bar sandstones from the minimum to maximum static. As stated above, SIS does not result in geological bodies, but has the advantage of being a relatively simple algorithm to use where many well data must be matched. The use of lateral trends and appropriate variogram models has resulted in elongation of channel facies and the placement of distributary mouth bars at the conceptual coastal margin (Fig. 8). Great correlation distances result in more laterally extensive facies models as illustrated (Fig. 8). For iteration 3, petrophysical property modelling followed the same workflow as iteration 2, using Sequential Gaussian Simulation to populate a series of grids. For each of the three facies scenarios, minimum, mid-case and maximum, 100 stochastic porosity realizations were generated. These were then ranked using pore volume and three models – high, mid and low (P15, P50 and P85) – were selected for each facies model. For each of these nine porosity models, permeability grids were generated following the same workflow as described in iteration 2 modelling. Nine static models were therefore passed for dynamic simulation. Within the dynamic models, the NTG cut-off range was established as in iteration 2. Cut-off range for iteration 3 was narrower, with net sandstone defined by 200 mD, 100 mD and 25 mD in the minimum, base and maximum cases respectively.

Conclusions An initial set of simple static models can be used early in project life to establish realistic minimum and maximum cases for recognized subsurface uncertainties such as structural definition, sandstone distribution/geometry and rock quality. Early models can then be used to identify and rank the subsurface uncertainties in terms of impact of oil-in-place and productivity. Using the results of simple dynamic simulation models, more detailed static modelling work can be planned to address key uncertainties in a timely manner. In this case study, the structural definition of reservoirs had large impacts on oil– water contacts and the movement of fluids through the reservoir. It was therefore important to define a detailed structural/stratigraphic model for the Urdaneta West Field. This was achieved through use of detailed sedimentological work, seismic stratigraphy and petrophysical evaluations. At the onset of the study, a single oil –water contact was used for UDW. In the final static and dynamic models,

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structural and stratigraphic compartments were identified across UDW and within each fluid compartment a deterministic range of fluid contacts was defined to capture the remaining uncertainty. Net pay definition was another major uncertainty identified during the initial phase of static and dynamic modelling. Through the use of progressively more detailed stratigraphic and facies models in iterations 2 and 3, a range of possible sandstone connection models were developed. Multiple realizations of porosity and permeability for each of the three facies scenarios resulted in the range of uncertainty being captured in dynamic simulation. The multiple dynamic models resulted in a range of reservoir production forecasts that were then used to aid decision making for the future management of Urdaneta West reservoirs. The author thanks PdVSA and Shell Venezuela SA for permission to present this work and Schlumberger for permission to publish images derived from PETREL. The static reservoir modelling described here incorporates the efforts of many individuals from the Urdaneta West team in Maracaibo, Venezuela, and the field studies team based in Houston, USA. Special thanks are extended to Bice Cortiula, Irua Euribe, Ysabel Nava, Tim Woodhead, Manuel Poupon and Maria Balzarini.

References A MBROSE , W. A. & F ERRER , E. R. 1997. Case History: Seismic stratigraphy and oil recovery potential of tide-dominated depositional sequences in the Lower Misoa Formation (Lower Eocene), LL-652 area, Lagunillas Field, Lake Maracaibo, Venezuela. Geophysics, 62, 1483– 1495. G HOSH , S., P ESTMAN , P., M ELE´ NDEZ , L. & Z AMBRANO , E. 1996. El Eoceno en la Cuenca de Maracaibo: Facies Sedimentarias y Paleogeografia. Vo Congreso Venezolano de Geofı´sica. H IGGS , R. 1996. A new facies model for the Misoa Formation (Eocene), Venezuela’s main oil reservoir. Journal of Petroleum Geology, 19, 249– 269. L UGO , J. M. 1991. Cretaceous to Neogene Tectonic Control on Sedimentation; Maracaibo Basin, Venezuela. Unpublished PhD Thesis, The University of Texas at Austin. L UGO , J. M. & M ANN , P. 1995. Jurassic-Eocene Tectonic Evolution of Maracaibo Basin, Venezuela. In: T ANKARD , A. J., S UAREZ , R. & W ELSINK , H. J. (eds) Petroleum Basins of South America. American Association of Petroleum Geologists Memoir, 62, 699– 725. M ELE´ NDEZ , L., G HOSH , S., P ESTMAN , P. & Z AMBRANO , E. 1996. El Eoceno en la Cuenca de Maracaibo: Evolucion Tectonosedimentaria. Vo Congreso Venezolano de Geofı´sica. P ARNAUD , F., G OU , Y., P ASCUAL , J.-C., C APELLO , M. A., T RUSKOWSKI , I. & P ASSALACQUA , H.

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1995. Stratigraphic Synthesis of Western Venezuela. In: T ANKARD , A. J., S UAREZ , R. & W ELSINK , H. J. (eds) Petroleum Basins of South America. American Association of Petroleum Geologists Memoir, 62, 681– 698. P OUPON , M., G IL , J., V ANNAXAY , D. & C ORTIULA , B. 2004. Tracking Tertiary delta sands (Urdaneta West, Lake Maracaibo, Venezuela): An integrated seismic

facies classification workflow. The Leading Edge, 23, 909–912. R EINECK , H. E. & S INGH , I. B. 1973. Depositional Sedimentary Environments – with reference to terrigenous clastics. Springer-Verlag, Berlin. R EYNOLDS , A. D. 1999. Dimensions of paralic sandstone bodies. American Association of Petroleum Geologists, 83, 211–229.

A method for quantifying geological uncertainties in assessing remaining oil targets: a case study from the Glitne Field, North Sea K. J. KEOGH1, F. K. BERG2 & GLITNE PETEK3 1

StatoilHydro ASA, TNE SST RGG GRC, 4035 Stavanger, Norway (e-mail: [email protected])

2

StatoilHydro ASA, TNE SST REST RMS, 7501 Stjørdal, Norway

3

Glitne Petroleum Technology Team, StatoilHydro ASA, 5020 Bergen, Norway Abstract: Evaluating the static volume potential of a field from a single geological reservoir model can be a risky business. Each piece of input data used to build the model carries an uncertainty that is not expressed in a single deterministic realization. In evaluating the technical and economic feasibility of drilling a new production well on the StatoilHydro operated Glitne Field, a quantified assessment of the range in expected volumes was undertaken. A geological uncertainty study was initiated to identify and quantify the input parameters of greatest impact on static volumetric uncertainty in the reservoir model and to identify potential upsides or downsides that would strongly affect the economics of the potential well target areas. For each geological input parameter, a high-case and low-case scenario was established to capture the end members (approximating to P90–P10) in that parameter uncertainty. IRAP RMS was used in combination with an in-house Microsoft Excel macro together with @Risk to produce a quantitative analysis of the uncertainty range in STOIIP and a ranking of the parameters most affecting the uncertainty in this range. This study has contributed to making a better-informed decision for drilling a new production well on the Glitne Field and thus increasing ultimate recovery and field life further. The workflow used has its limitations but this study shows that a geological uncertainty study can be performed relatively simply using only a limited number of software applications. This study also hopes to highlight the importance of having these studies undertaken by company asset teams as part of their reservoir characterization routines.

Uncertainty studies concerning the analysis of all input parameters used to build a static geological model are not often performed within an oil company asset team. The reason may be that the asset team often lacks the specialist personnel to perform the study and also that there are currently very few commercially available tools that can deal with testing and analysing uncertainty for a whole range of input parameters. Corre et al. (2000) is an example where static model uncertainties have been combined and tested in a single software application environment. More often, these studies have to be carried out by specialists within the company where both the expertise is available and that expert is also technically capable of running the multiple software tools needed for testing all the required input parameters. This study focused on the Glitne Field in the Norwegian North Sea as an example where an uncertainty study incorporating all geological model inputs has been performed. Only two non-specialist software applications have been utilized for first defining and quantifying the effects of the various uncertainty parameters and secondly for integrating and statistically analysing the effect on total

uncertainty of both individual and a combination of input parameters. This study was performed as a requirement for assessing a remaining oil target and the results gained from this study were used actively in making a well-informed economic decision.

The Glitne Field The Glitne oilfield is located west of Stavanger, Norway, on the border with the United Kingdom Continental Shelf (UKCS), 40 km north of Sleipner (Fig. 1). Glitne is Norway’s smallest stand-alone field development, put into production in August 2001 with an estimated economic life of 26 months. Recoverable oil in the Plan for Development and Operation (PDO) was estimated to be 4 million Standard Cubic Metres (Sm3). Production of oil is from Palaeocene turbidite deposits in the upper part of the Heimdal complex. In August 2003, the total production from Glitne exceeded 4 million Sm3 and an infill well, A-5H, was put into production. During the autumn of 2003, a technical and economic evaluation of a further infill well, A-6H, was initiated. The purpose of this well would be to ‘explore’ and

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 193– 203. DOI: 10.1144/SP309.14 0305-8719/08/$15.00 # The Geological Society of London 2008.

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Fig. 1. Location map of the Glitne Field in relation to Stavanger, Norway and the Sleipner fields (inset).

produce the potential in the southern end of the field (Fig. 2), an area with previously little production or data from which to evaluate the potential of remaining reserves. This uncertainty in potential economic reserves was the catalyst for undertaking the technical and economic evaluation, of which a static volume uncertainty study would be part.

Base case geological model Prior to the uncertainty study, the static geological model of the Glitne Field was a fully deterministic 3D reservoir model that comprised a single, deterministic facies model with each facies given a single, deterministic petrophysical value for NTG, porosity and permeability. For the purpose of the uncertainty study, this model was treated as the base case (Fig. 3). Input data for building the model comprised seismic-interpreted top reservoir surface, stratigraphic isochores, based on well

picks, for internal zonation, well log data from 11 wells and facies interpretation from cored intervals. The stratigraphic evolution of the Glitne fan system, facies inter-relationships and geometrical constraints on facies associations have benefited from the use of an outcrop analogue: the Permian Tanqua Karoo fan system, South Africa. These outcrops have been studied by a number of workers in the recent past (Johnson et al. 2001; van der Werff & Johnson 2003). Hodgetts et al. (2004) describe the recent collection of digital data from the Tanqua Karoo fan complex and highlight how this data has helped better constrain the stratigraphic understanding of the Glitne fan system.

Aims and objectives of the uncertainty study The main driver for performing the uncertainty study was to re-evaluate the static volumetric

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Fig. 2. Location of the proposed A-6H infill well and the previously drilled wells, the majority of which penetrate areas in the northern sector of the field.

Fig. 3. Visualization of the Glitne Field deterministic, base case 3D reservoir model. The colours identify the different facies associations mapped over the field. View looking NE. The reservoir model covers an area of 8  5 km.

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potential for drilling a new production well on the Glitne Field (Fig. 2). In order to achieve this, the asset team set the following objectives: † Identify and qualify the geological input parameters that are contributing to uncertainty in the base case, deterministic geological model on the Glitne Field; † Use IRAP RMS to define the sensitivities and calculate volumes; † Use the variation in STOIIP (Stock Tank Oil Initially In Place) as the main measure for uncertainty quantification (i.e. the response variable); † Use Microsoft Excel and an in-house macro called ProReg together with Palisade Decision Tools @Risk to compile all variables and run a full Monte Carlo loop and provide quantitative statistical analysis and ranking of the importance of the input parameters; and † Analyse and report the effect of the input parameters on a per-field-segment basis as well as on a full field basis. The approach taken to assessing and managing uncertainty is highlighted in Figure 4 and the geological parameters identified as contributing to potential uncertainty in the Glitne Field static geological model are listed in Table 1.

Fig. 4. Conceptual workflow defining the important steps for undertaking an uncertainty study. This was the concept used in helping to define the workflow for the Glitne Field study.

Scenario building and response variable calculation Methodology The workflow employed for this study involved the use of two software programs instead of the host of programs often used to perform such studies (Fig. 5). The workflow was developed as a tool for allowing for updates of the model input parameters and re-analysis of uncertainty without requiring assistance from specialists. A reason for setting up this workflow was so that the Glitne asset team could later update the workflow without requiring assistance from a specialist. The workflow can be divided into the components of the two software packages, Roxar’s IRAP RMS and Microsoft Excel with Palisade Decisions @Risk plug-in. These are described separately below. The design of this experiment is that of a one-at-a-time set-up whereby each parameter under investigation is changed whilst every other parameter remains constant. The advantage of this type of set-up is that the change in the response variable value can be directly related to the parameter under investigation. However, a disadvantage with this method is that a large number of experimental runs must be set up to test all parameters.

The workflow set up is essentially a scenario-based workflow (Egeland et al. 1992; Sandsdalen et al. 1996; Bentley & Woodhead 1998) where ‘high’ and ‘low’ cases around the base case are defined for each of the parameters under investigation (Fig. 6). As a requirement for the ProReg macro in Microsoft Excel, these high and low case scenarios should approximately equate to P90 and P10 percentiles. Given that this is only an estimation and therefore itself uncertain, this can be accounted for as part of the input to ProReg. For those parameters where high and low are relative to the mean values of a distribution function of that parameter (i.e. porosity distribution), then these cases are also run through multiple stochastic realizations. This is to determine whether the variance between the stochastic realizations of the same distribution function is significantly less than the variance around shifting the mean value of the distribution. In IRAP RMS, the workflow consists of a series of IPL (Internal Programming Language) scripts that execute a series of modelling jobs whereby the parameter under investigation is varied whilst all other parameters are held to the base case model. This kind of investigation is known as a ‘one-at-a-time’ experimental set-up.

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Table 1. List of geological parameters incorporated in the static uncertainty study together with an explanation on the source of uncertainty within each parameter on the Glitne Field Geological parameter Velocity modelling uncertainty

Seismic interpretation uncertainty

Isochore mapping Facies volume fractions from geological interpretation uncertainty

Average net-to-gross estimation Average porosity per facies estimation Permeability mapping uncertainty

Oil –water contact (OWC) Alternative water saturation J-function equation Bo factor value from measurement uncertainty

Source of uncertainty The velocity model can be defined differently when analysis uses different groups of wells. These form the basis for the alternative scenarios. For each of the defined scenarios, the same time interpretation map is used to isolate the effect of only the velocity model. Surface interpretation: different seismic vintages and different cubes can give different results. Three different time interpretations depth converted with the same velocity model to isolate the effect of time interpretation. The mapping of stratigraphic zone thicknesses away from data. Given strong constraints on the Glitne fan system mapping from seismic amplitude information, it is difficult to propose alternative scenarios for mapping the Glitne fan system. Therefore, sensitivity analysis was defined on uncertainty in volume fractions estimation for the sand-rich facies associations. Multiple realizations of each scenario are also produced. The calculation of average net-to-gross values per facies, per zone is uncertain so low and high case scenarios are tested. Calculation of average porosity values per facies, per zone. Low and high case scenarios defined as þ/2 10% from the base case. Multiple realizations of each scenario produced. Mapping of the same per facies distribution modelled using a conditional simulation method with multiple realizations. P90, P50 & P10 values are calculated from the output range in volumes. Data from four wells spread around the field showed that the OWC was not a significant uncertainty and was therefore not tested in this study. The effect of implementing an alternative J-function equation is evaluated in this study whereby the constant values defined in the SWIRR and SW functions are now facies dependent. A PVT study had reported a base case Bo factor with a þ/2 3% uncertainty.

Each IPL workflow job involves the building of a full model, from grid building, to facies modelling, to petrophysical modelling and water saturation modelling and finally to volume calculations to give the response variable for that particular scenario. Volumes are output on a per-segment basis (Fig. 7) as required for evaluation purposes. At the end of each workflow job, the IPL script runs an external script that takes the volume calculation output file and converts it such that only rows and columns of number remain for ease of import and manipulation in Microsoft Excel. Table 2 details the workflow steps in IRAP RMS for the various uncertainty categories in the study. In order for the workflow to be easily set up and repeatable, some assumptions have to be made regarding the building of the geological grids and these assumptions are discussed below.

Assumptions in the workflow method † All grids are built with proportional layering and all have the same IJK values. † With the exception of water saturation modelling, all parameters are resampled from the base case model except when that parameter is the parameter of interest. By building the grids with proportional layering and with the same IJK values each time, the resampling of parameters from the base case model is consistent between the uncertainty parameter model building runs. Water saturation is modelled using a J-function that is a function of porosity, permeability and height above the oil–water contact. Given that in each scenario a parameter is varied that affects the outcome of these J-function inputs, the water saturation parameter

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Fig. 5. Workflow diagram highlighting the numerous specialist software applications and scripting languages used by the specialist Static Uncertainty Group in StatoilHydro when undertaking an uncertainty study. It is the complexity of this workflow that often hinders the possibility of uncertainty analysis being undertaken within asset groups.

Fig. 6. Flowchart of the total workflow used in the uncertainty study. The software application used in each workflow step is shown on the right-hand side of the diagram. Diagram modified from Hodgetts et al. (2005).

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Fig. 7. Top reservoir map of the Glitne Field showing the segment boundaries defined for this study. The coloured contours indicate area of top reservoir map above the oil– water contact.

cannot be simply resampled from the base case grid but must instead be recalculated every time a new scenario is run. † All grids are built with the exclusion of faults. Faulting is an uncertainty, however, with different time interpretations revealing differing fault patterns. Correctly honouring varying fault locations in RMS is not easily automated. A trial run was therefore set up where unfaulted and faulted grids were built with the same parameters. Calculation of gross rock volume (GRV) showed the difference to be less than 1% between the unfaulted and faulted grids. It was therefore deemed acceptable to model with unfaulted grids for the whole study. This may not be a plausible solution if dealing with the dynamic impact of the parameter uncertainties on the reservoir.

Monte Carlo simulation and statistical analysis The output from IRAP RMS is a series of calculated STOIIP values reported on a per-segment basis in

which each value reflects the change in STOIIP from the base case as a result of varying the single parameter under investigation. The ProReg Microsoft Excel macro is used to combine these results and to estimate the total STOIIP uncertainty range using multivariate linear regression analysis and Monte Carlo simulation in @Risk (Fig. 6). The reason for running a Monte Carlo simulation in this context is to derive a smooth volume distribution with the correct uncertainty range by capturing the tails of the distribution. This can hopefully reveal potential upside volumes that have previously not been captured by conventional volume calculation. The data are compiled in a worksheet in which each uncertainty parameter tested is defined in one row (Fig. 8). For each uncertain parameter, the low-base-high range is defined together with the resulting STOIIP value for each of the corresponding scenarios. This low-base-high range value refers to the input value of the parameter and is used in ProReg and @Risk for defining the skewness of the uncertainty distribution histogram for that

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Table 2. IRAP RMS modelling steps completed in the workflow for running the one-at-a-time experiment set-up. The workflow consists of a series of scripts that control the import/export of data, the execution of modelling or resampling jobs within RMS and also executes external scripts. An IPL workflow job exists for each of the geological parameters tested in the uncertainty study Structural uncertainty: seismic interpretation, depth conversion, isochore modelling.

Facies volume fractions:

NTG/porosity/permeability/water saturation/Bo factor:

Load alternative top maps from external directory Set top map in Project to ‘Low Case’ map Run modelling loop: Stratigraphic Modelling ! Create Grid ! Resample Facies/Petrophysics ! Run Sw Script ! Calculate STOIIP Volumes ! Run external volume file conversion script Set Top Map to ‘High Case’ ! Repeat above run Reset Top Map to ‘Base Case’ Build ‘Base Case’ grid Run facies modelling for Base, Low & High Case sensitivities Each sensitivity run 10 realizations Resample Base Case petrophysics for each facies Run SW script for Low/Base/High Case sensitivities Calculate STOIIP volumes & run external volume file conversion script Build ‘Base Case’ grid Resample Base Case parameters into grid Run modelling jobs for Base, Low & High case sensitivities Run 10 stochastic realizations for petrophysical parameters Run Sw modelling script for each parameter sensitivity level Run alternative Sw script for Base Case model parameters Calculate STOIIP volumes & run external volume file conversion script

Fig. 8. Example of the spreadsheet set-up for utilizing the ProReg macro. The user lists the parameters and inputs the relevant ‘Low’, ‘Ref’ and ‘High’ values. ProReg then performs the multivariate regression analysis, completes the values in the remaining columns and defines the relevant columns as @Risk input and output. The user then sets the desired number of iterations to be run and reporting formats of the output before running the Monte Carlo simulation in @Risk.

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particular parameter. Once these values are input, the ProReg macro then runs through various steps listed below, in order to set up the data for @Risk. 1. 2.

3.

Generate Tornado plot (STOIIP numbers from sensitivities). Perform multivariate linear regression on STOIIP numbers taking into account: (a) Combination runs. (b) Multiple realizations. (c) Validation of regression. Prepare for @RISK set-up for simulation of STOIIP: (a) Generate @RISK formulas. (b) Define discrete parameters and skewed distributions. (c) Define correlation matrices allowing dependencies between parameters to be assigned.

The STOIIP equation defined as an @Risk output (Fig. 8) is thus defined as: STOIIP ¼ C0 þ a  P1 þ b  P2 þ c  P3 þ . . . . . . þ x  PX

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where: P1 to PX ¼ parameters P1 to PX under investigation; a, b, c, x ¼ regression coefficients from multivariate regression analysis; C0 ¼ intercept from multivariate regression analysis plot. @Risk is then set to run 10 000 iterations and produces output in the form of descriptive statistics, histograms and tornado plots (Fig. 9a– c). These outputs can then be used to identify the parameter(s) contributing most significantly to the uncertainty range in STOIIP for each field segment (Fig. 9d). For evaluation of the full field uncertainties, a separate ProReg worksheet is constructed by combining the individual worksheets for the field segments, constructing correlation matrices for parameter dependencies both within and between segments and redefining the STOIIP equation according to the data range of the parameters required in the calculation. The statistical and graphical output from this workflow provides a wealth of information regarding the range in possible STOIIP outcomes and the uncertainty factors contributing most to the spread of that distribution (Fig. 9). Following the conceptual flowchart of Fig. 4, this analysis helps the geological

Fig. 9. Example of reporting output from @Risk. (a) Histogram showing the total range in STOIIP, P90, mean and P50 value locations; (b) descriptive statistics table output; (c) Tornado style plot ranking each parameter in terms of their contribution to total uncertainty range in STOIIP with most significant at the top to least significant at the bottom; and (d) list of ‘top 4’ highest contributors to uncertainty range in STOIIP as identified in the Tornado plot.

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impact on remaining volumes to be better understood, evaluated and integrated into other evaluation exercises, thus allowing for better decision making. In this particular study, a large upside potential was found to exist in one of the target segments that had previously not been realized and this quantification added value to the economics of the evaluation. The analysis can also highlight geological factors that have associated high uncertainty ranges and consideration can be given to further reduce the range in uncertainty on these parameters.

Limitations of the Glitne uncertainty study workflow The workflow described above is set up in such a way that many various uncertainty parameters and factors can be assessed and analysed with the minimum of software applications yet still produce complex analysis of the outcomes. The analysis nevertheless has limitations. † The study only deals with the uncertainty associated with static volumes; no dynamic analysis was applied to the volumes. This was partly a function of the project remit and partly a function of the software functionality at the time. It should be mentioned that a dynamic reservoir study was simultaneously ongoing, and results from this study were used to steer the simulation model inputs. A more integrated study where the scenarios under investigation were directly tested in a simulator would have been more optimal, and software solutions in IRAP RMS now exist for allowing a more seamless integration of static and dynamic analysis. † The structural modelling is limited. Nonautomation of fault modelling limits the rebuilding of grids where fault patterns have changed due to interpretation or velocity modelling effects. Again, given that this study concentrated on only static effects, this proved to be a limited problem, but if a dynamic analysis was employed, this uncertainty would have to be accounted for. † No experimental design analysis is incorporated in the workflow. The inclusion of experimental design would benefit the workflow in that it would be possible to assess parameter combination effects and to optimize possible scenario streamlining. As the workflow is currently set up, having to run every scenario and factor one-at-a-time is a time-consuming process. † Historically, routine uncertainty modelling in RMS only dealt with variations associated with mapping of parameters (i.e. seed variation). Although scenarios could be set up in IRAP RMS, it was not an easy or quick task. Other commercially available geological modelling

tools have some uncertainty modelling capabilities and Roxar has recently developed its uncertainty module for IRAP RMS.

Conclusions The following lessons were learnt from this study: † The workflow utilized in this study successfully integrated all geological uncertainty scenarios and produced meaningful results in a relatively simple working environment (i.e. combining IRAP RMS with ProReg Microsoft Excel macro and @Risk). † A modelling workflow has been established that is able to handle both multiple scenarios and multiple realizations of a given scenario with recognized limitation. † Combining the IPL scripting language and Workflow Manager in IRAP RMS has allowed geological uncertainties/scenarios to be handled. However, initial workflow definition requires a good knowledge of the scripting language and can be time-consuming. Despite this, subsequent updating of the uncertainty study requires little effort or knowledge of the actual workflow set-up. † This study contributed to making a wellinformed geological decision concerning the volumetric potential of previously unproducing areas in the Glitne Field and the production well drilled is now producing successfully. † Simple uncertainty/scenario modelling should more readily be performed within company asset groups as an integral part of the geological reservoir model-building process and the tools available within a company’s portfolio should support this vision. The first author would like to express his thanks to the partners of License PL048B (Glitne); StatoilHydro ASA, Total E&P Norge AS, DNO ASA og DONG Norge AS, for permission to publish this paper and also to colleagues within the static uncertainty analysis team in StatoilHydro for support and useful discussions during the execution of this project. Mark Bentley and Charlotte Martin are thanked for reviewing the article. Their comments and suggestions have helped sharpen the content of the final manuscript. Opinions stated in this paper are those of the author and not of StatoilHydro.

References B ENTLEY , M. R. & W OODHEAD , T. J. 1998. Uncertainty Handling through Scenario-Based Reservoir Modelling. SPE n8 39717. C ORRE , B., T HORE , P., DE F ERAUDY , V. & V INCENT , G. 2000. Integrated Uncertainty Assesment for Project Evaluation and Risk Analysis. SPE n8 65205.

A METHOD FOR QUANTIFYING GEOLOGICAL UNCERTAINTIES E GELAND , T., H ATLEBAKK , E., H OLDEN , L. & L ARSEN , E. 1992. Designing Better Decisions. SPE n8 24275. H ODGETTS , D., D RINKWATER , N., H ODGSON , D., K AVANAGH , J., F LINT , S. S., K EOGH , K. J. & H OWELL , J. A. 2004. Three-Dimensional Geological Models from Outcrop Data using Digital Data Collection Techniques: An Example from the Tanqua Karoo Depocentre, South Africa. In: C URTIS , A. & W OOD , R. (eds) Geological Prior Information: Informing Science and Engineering. Geological Society London, Special Publications, 239, 57–75.

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J OHNSON , S. D., F LINT , S. S., H INDS , D. & D E V ILLE W ICKENS , H. 2001. Anatomy, Geometry and Sequence Stratigraphy of Basin Floor to Slope Turbidite Systems, Tanqua Karoo, South Africa. Sedimentology, 48, 987–1023. S ANDSDALEN , C., B ARBIERI , M., T YLER , K. & A ASEN , J. 1996. Applied Uncertainty Analysis Using Stochastic Modelling. SPE n8 35533. VAN DER W ERFF , W. & J OHNSON , S. D. 2003. High Resolution Stratigraphic Analysis of a Turbidite System, Tanqua Karoo Basin, South Africa. Marine and Petroleum Geology, 20, 45– 69.

The Schiehallion Field: lessons learned modelling a complex deepwater turbidite PAUL FREEMAN1,5, SEAN KELLY2,6, CHRIS MACDONALD3, JOHN MILLINGTON4,5 & MIKE TOTHILL1 1

BP Exploration Operating Company, Sunbury, UK

2

Petroleum Development Oman, PO Box 81, 113 Muscat, Oman

3

BP Exploration Operating Company, Aberdeen, UK (e-mail: [email protected]) 4

Shell UK Exploration & Production, Aberdeen, UK

5

Now at: Nexen Petroleum UK Ltd., Charter Place, Vine Street, Uxbridge, Middlesex, UB8 1JG, UK 6

Now at: Mærsk Olie og Gas AS, Esplanaden 50, DK-1263, Copenhagen K, Denmark Abstract: The need for a new Schiehallion full field reservoir simulation model was driven by the requirement to re-evaluate the reserves in the field: the existing model indicated that the modelled volumes were potentially too conservative. This, coupled with a 50% increase in the wells database through ongoing development drilling, was the main reason for building the new model. An integrated multidisciplinary team consisting of BP and Shell staff was set up to build a new full-field reservoir simulation model for reserves re-evaluation. The paper outlines the workflow employed in building the new model, FFM2003, and describes elements of this workflow in more detail, concentrating on lessons learned during the process.

The Schiehallion Field, situated 200 km to the west of the Shetland Islands in the southwestern part of the Faeroe– Shetland Basin (shown in Fig. 1). This basin formed as a result of the Late Jurassic/ Early Cretaceous rifting of the northwestern margin of Europe (Knott et al. 1993; Mitchell et al. 1993; Carr & Scotchman 2003). During Palaeogene times, the Faeroe –Shetland Basin was a major depocentre, controlled by NW– SE orientated transfer zones: the Erland Complex to the north and the Judd Fault to the south, and divisible into two sub-basins: the Flett to the northeast and Foinaven to the southwest. The latter, in which the Schiehallion oilfield is located, was controlled by thermal sag and faulting that remained active throughout Paleocene times during which a thermal plume generated volcanic activity and uplift of the Scottish Highlands and West Shetland Platform that, in turn, created a coarse clastic supply to the west of Britain (Lamers & Carmichael 1999; Morton et al. 2002). The bulk of the clastic input occurred in the Early Palaeocene (T30) which is approximately equivalent to the Andrew Member of the Lista Group in the North Sea. The T30 sequence comprises siliciclastic turbidite sands transported from the shelf in seismically resolvable channels to the basin floor. The sequence has been subdivided using well and biostratigraphic data into a number of subsequences (Lamers & Carmichael

1999; Ebdon et al. 1995; Mitchell et al. 1993). Within Schiehallion, the main oil-bearing sands occur in the T25, T28, T31, T34 and T35 sequences (shown in Fig. 2). The trap is delineated by stratigraphic pinch-out in the east and dip closure along the northern and western margins. Reservoir sands are sealed on the up-dip, southern edge by east–west normal faults that completely offset the reservoirs. The principal reservoirs are T25/T28, T31, T34 and T35 in age. The field is developed through a FPSO facility which is shared with the Loyal Field. To date, 17 producers and 17 injectors have been drilled and linked back to the FPSO from three subsea drill centres. Crude is exported via shuttle tankers to Sullom Voe terminal in Shetland. At the end of 2004, Schiehallion had produced 212 Million Stock Tank Barrels (mmstb) of an estimated 2 billion barrels of Stock Tank Oil Initially In Place (STOIIP).

Summary of modelling workflow The methodology used in the construction of the new model drew upon previous experience of modelling in the west of Shetland and elsewhere by using object modelling combined with seismic conditioning. Figure 3 summarizes the workflow diagrammatically.

From: ROBINSON , A., GRIFFITHS , P., PRICE , S., HEGRE , J. & MUGGERIDGE , A. (eds) The Future of Geological Modelling in Hydrocarbon Development. The Geological Society, London, Special Publications, 309, 205– 219. DOI: 10.1144/SP309.15 0305-8719/08/$15.00 # The Geological Society of London 2008.

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Fig. 1. Location of the Schiehallion Field and regional structural elements.

The workflow starts with data preparation. Preparation of the well data involved the integration of biostratigraphic tops with log data and the picking of depositional elements (facies associations) in the non-cored intervals. The definition of depositional elements is covered in more detail in the ‘facies modelling’ section below. In parallel with this, reservoir horizons and faults were mapped on a number of different seismic volumes in order to capture the maximum extents of potential reservoir sand development; these horizons were termed ‘seismic envelopes’. This approach is in contrast to previous studies which had tended to utilize amplitude-defined bodies. The seismic envelopes and associated faults were depth converted and imported to the modelling software where they were tied to the well picks. When all the tops and depositional elements had been finalized, they were combined with the petrophysical database. Property transforms for porosity and horizontal permeability were generated from the core data and net-to-gross transforms from log analysis for each depositional element. With all the horizon envelopes and well data now fully integrated, the faults

and horizons were combined to make the structural model. Horizon juxtaposition across faults was carefully checked and locally (due to the smoothing and extrapolation algorithms used during structural modelling) manual adjustments needed to be applied. At this stage, the faulted horizons were exported from the modelling software, converted back to time horizons and checked against the seismic data. This iterative step ensured that the geocellular grid that was constructed using these horizons accurately captured all the amplitude data for each reservoir unit. Once all the quality control checks had been completed, the simulation grid was constructed. The construction of the simulation grid first was a key step in the model build workflow as model size (cell count) had been identified as a potential problem to the efficiency of flow simulation. The static model grid was then constructed as a direct integer subdivision of the simulation grid (using the LGR gridding capabilities in RMS). Inverted seismic volumes and 4D difference products were depth converted and re-sampled into the static model grid. In order to generate the object-based

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Fig. 2. Schiehallion field outline showing the principal reservoirs.

facies models, well and seismic data were combined to create facies probability functions for each depositional element. One-dimensional functions and maps were also used to support the vertical and spatial arrangement of facies objects within the seismic probability functions. Construction of satisfactory facies models is a highly iterative process requiring visual, well, map, volumetric and simulation checks. The facies models were then converted to property models using the depositional element-based transforms derived from core and log data. These models were then upscaled into the simulation grid and effective properties checked against those derived from facies micromodels. Upscaled property models were exported to the simulation software. 4D seismic data provided additional detail on the location and strength of baffles and barriers to fluid flow. Lineaments picked from coherency seismic volumes were combined with 4D difference volumes and maps to

determine potential transmissibility values (open, partially closed and closed). The lineaments were integrated with the simulation grid to ensure the correct alignment and continuity with simulation grid cell faces. These barriers and baffles were key variables to establishing a history-matched model. Synthetic seismic volumes generated at field start-up were also used to check the net-to-gross magnitude and distribution. The final stage in the model workflow was the Reservoir Uncertainty Modelling in order to establish the uncertainty in STOIIP and reserves potential from the current well stock.

Structure mapping and grid design Experience from previous modelling projects west of Shetlands had shown that a key stage of the model-building process was the design and size of

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Fig. 3. Schematic of the workflow used to construct the model. GEOCAP (Shell proprietary); Petrel (Schlumberger), RMS (Roxar), VIP (Landmark Corp.), Sim-to-Seis or MorSyn (BP or Shell proprietary respectively).

the simulation grid and its relative scale to the geological grid. More reservoir sequences have been included in this model than in all previous models and it was identified that the model size could become a significant issue to the efficiency of flow simulation. With these factors in mind, the workflow applied recognized that the simulation grid should be constructed first. The use of seismic envelopes minimized the occurrence of grid pinch-outs and non-neighbour connections which all contribute to simulation inefficiency. The static model grid was constructed as a direct integer subdivision of the dynamic grid – also known as ‘down scaling’ the grid. The benefits of this approach was that both the static and dynamic grids honoured the geological geometry required for accurate flow simulation and, additionally, simplified the upscaling of properties into the simulation grid. The initial simulation grid was built at a high vertical resolution, but with the ability to easily reduce the number of layers

without compromising the original project objectives. As the model build progressed, it became necessary to reduce the number of layers in the simulation grid from 168 to 76. The simulation grid was pushed through the complete workflow as early as possible with ‘dummy’ properties to test the effectiveness of the grid to simulation. The lesson learned from grid design was to build-in the flexibility to generate an appropriately sized simulation model based on early experience of runtimes and memory requirements.

Facies modelling The facies modelling approach applied built on the experience of previous Schiehallion and Loyal models in using probability functions to condition seismic with facies. The previous lithofacies scheme utilized for earlier full-field models was essentially bed-scale (cm– m) and heavily reliant on log character for definition of individual facies

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types (i.e. electrofacies). There are a number of potential drawbacks when using such a log-based electrofacies scheme: 1. Using logs without thickness criteria yields a large number of individual facies units (typically 0.15– 1.0 m thick) that are difficult to group into meaningful associations. This can result in a highly complex heterogeneous model built from a large number of small elements. 2. There is minimal sedimentological processbased interpretation and therefore it is difficult to define sedimentological shapes or bodies suitable for object modeling. Such a scheme does not readily allow the sedimentological insight from the core to be incorporated. 3. Such electrofacies schemes are difficult to apply to horizontal wells due to sampling (typically resulting in a very large number of facies units over relatively short horizontal distances). The reservoir description used for input to this modelling project follows a simplified version of the Depositional Elements scheme (DEs) developed as part of a proprietary equity-related study (Ashton 2002). Depositional Elements are essentially facies associations or genetic units. DEs have sub-seismic resolution (0.9 m to 12.8 m, P90 : P10 range) and give more control over conditioning facies to seismic.

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The facies conditioning methodology varied slightly between reservoir layers depending on the seismic volume or principal conditioning parameter used; however, the following consistency was applied to all reservoir units: 1. The discrete facies or depositional element log (DE log) was rescaled into the geological grid for each reservoir unit. 2. Each DE was assigned object parameters (thickness, width, length, shape, orientation, etc.) unless set as background (Fig. 4). These parameters are chosen following a review of core sedimentology, seismic data and appropriate analogues (e.g. Clark & Pickering 1996). 3. Seismic data were loaded as SEGY data and then rescaled into the geological grid (arithmetic average method). 4. Facies Probability Functions (FPFs) based on inverted seismic data were established for each facies. Apart from the raw seismic and well data, the FPF is probably the most critical input to the seismic conditioning of a model as it drives the distribution of facies bodies. The FPF was estimated from histograms of the seismic attribute (or other parameter) against facies in well locations. The probability was obtained by taking the histogram value for a given facies and dividing by the sum of histogram values over all facies (Lia & Gjerde 1998). In Schiehallion, the FPF typically exhibits

Fig. 4. Depositional Elements (DE) object modelling shape criteria.

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Fig. 5. Facies probability function for facies conditioning to inverted seismic data.

a tripartite distribution (Fig. 5) reflecting the main three DEs: sand-prone channel fill (DE2, high net-to-gross), heterolithic channel fill (DE3 & DE4, moderate to low net-to-gross), and the background mudrocks (DE8, very low NtG). For the main reservoir in Schiehallion, T31, these facies represent approximately 85% of the model cells. Good quality DE2 sands differentiate clearly from DE8 mudrocks with poorer-quality sands and heterolithic lithologies of DE3 overlapping to a greater or lesser extent DE2 sands and DE8 mudrocks. The remaining minor DEs (conglomerates, remobilized units, etc.) were also modelled using seismic conditioning but with more emphasis placed on their stratal position and context (e.g. positions within a channel fill succession). Uncorrected FPFs from well data analysis were generally quite spikey and were smoothed manually in order to get better results. Experience indicated that it was better to use relatively smooth FPFs in order to not overestimate the value of the well data and also to improve the convergence of the algorithm. An FPF can be evaluated for statistical robustness by comparing by FPFs for different subsets of well data using the same seismic input. When this test was done, minor differences were detected but it suggested that the statistical data set for Schiehallion was large enough to limit local bias. However, it was recognized that there are more

consistent regional variations in both reservoir properties (e.g. thickness and net-to-gross) associated seismic character that resulted in FPF variation. This variability meant that the best-fit FPF for one area may not be optimal for other parts of the field. 5. The Seismic Weighting Factor (SWF) was set – this parameter dictated how strongly the seismic influences the facies distribution within the model. Experience indicates that if the SWF was set too low, the resultant model does not reflect the seismic amplitude distribution; if it was set too high, the model will look very much like the seismic but will be different immediately around the wells. 6. Intensity maps or 3D volumes (usually clipped or rescaled impedance/lithology volumes) were also used to focus the distribution of key facies – 3D volumes generally gave better results as 2D weight maps do not indicate how a parameter is distributed vertically. Simple 1D functions (i.e. DE frequency vs. grid layer) were used to control vertical distributions in some cases. 7. Prior to a full facies conditioning, model runs were checked so that the expected volume fraction from the seismic data was consistent with that specified or targeted based on the well data statistics. If this was not the case, the seismic data may predict too high or low volume fraction of a facies.

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8. Facies conditioning was then run and the resultant volume fractions checked. If the fractions were incorrect or had not been reached, the number of iterations (usually around one million) were increased and the simulation repeated or the FPF modified prior to a rerun. 9. Once a facies model was constructed, additional property files (net-to-gross ratio, porosity and permeability) were constructed using transforms and then upscaled into the simulation grid. These property transforms are discussed in detail in the Effective Reservoir Properties section. This approach allowed the generation of multiple geological realizations. Sixteen of the realizations were selected and ‘blind’-tested against historical production data, in the reservoir simulator, with and without the separately mapped barriers and baffles. The models were ranked by means of a goodness of fit to the historical data on a well-by-well basis. This allowed the construction of a hybrid reference model arrived at by splitting the model into different regions and then selecting the most appropriate geological realization for each region. This hybrid model formed the starting point for detailed history matching. The main lesson from the use of Depositional Elements was that their scale allowed more control over conditioning to seismic as described above. In addition, the benefit of blind historymatch tests and the construction of a hybrid reference case was that the subsequent detailed history match was then faster and easier as a result.

Effective reservoir properties A three-stage process was adopted for generating effective reservoir properties. First, the available core and log data were analysed and transforms for porosity (w) and horizontal permeability (kh) were developed for each DE. Secondly, the static or fine-scale facies model was converted to a property model by applying the transforms to each DE. Thirdly, the fine-scale model was upscaled into the simulation grid. Previous models had used both constant values and electrofacies transforms. While porosity is relatively constant for reservoir sands at approximately 27% in Schiehallion, there is a clear depth-related trend caused by progressive compaction and cementation with burial. Consequently, porosity versus depth transforms were developed for each DE from available core data (Fig. 6). The core data were measured at ambient conditions so a burial correction of 0.96*w was applied to reflect in situ conditions. Horizontal permeabilities were calculated using porosity–permeability transforms developed for

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Fig. 6. Porosity trend with depth. Coloured data points represent multiple wells.

each of the depositional elements in the model, using all available core data. In developing the porosity –permeability transforms, the data were viewed both in linear porosity versus log permeability and linear porosity versus linear permeability spaces. Most studies use only the linear porosity versus log permeability plots; however, because the reservoir responds to linear permeability, it was important to see how a transform developed in log-linear space will work in reality. Using both plots to view the data and by using transforms which were fitted by eye rather than relying exclusively on least squares fits, we derived relationships that looked ‘best-fit’ for each of the depositional elements (Fig. 7). Estimating vertical permeability (kv) in the static model proved more problematic and the question of scale was a key issue. When plotted against horizontal permeability, core plug data results in a kv/kh value of 0.98. Depositional elements are a much coarser resolution than core plugs with thicknesses of 0.9 m to 12.8 m, P90 : P10 range. In addition, the static grid has an average resolution of 50 m by 50 m by 1 m. As a result, vertical permeabilities were constructed using simple kv/kh relationships, one for each depositional element. Three different kv/kh values were used to populate the fine-scale geological model: 0.5, 0.1 and 0.01. These values were broadly based on a range of micromodels and outcrop analogue studies (Stephen et al. 2001) and applied to each facies association as follows: DE2 and DE1a ¼ 0.5, DE3 ¼ 0.1, DE4, 5, 7 ¼ 0.01.

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Fig. 7. Porosity – permeability transforms in log-linear and linear-linear spaces. Coloured data points represent multiple wells.

Upscaling porosity and permeability Porosity upscaling was relatively straightforward; however, care must be taken to ensure the upscaled porosity was appropriate for the simulation model. In the geological model, porosity was applied to net sand only and therefore in order to upscale this correctly and preserve volumes, a net sand volume weighting is required as opposed to a bulk rock volume weighting. Upscaling permeabilities from the fine-scale geological model into the simulation model were accomplished using the diagonal tensor method. This led to unrealistically high vertical permeabilities in some of the upscaled cells. Upscaling cells that were composed exclusively of fine-scale cells with a kv/kh value of 0.5 resulted in an upscaled kv/kh value of 0.5. This was felt to be far too high for a simulation model in which the grid cell dimensions were of the order of 100 m by 100 m by 3 m. In addition, when these values were used in the model they resulted in unrealistically high well productivities which in turn caused serious stability problems during simulation. The unrealistically high vertical permeabilities generated by upscaling the fine-scale geological model permeability were adjusted using a simple transform to construct vertical permeability (kv) in the upscaled cells: kv ¼ 0:1  ðNTGÞ2 kh

where NTG is the upscaled net-to-gross ratio and kh the upscaled horizontal permeability. This function and the scale of the values it produces are supported by micromodels of effective properties and modelling based on outcrop analogues (Stephen et al. 2001). An extended well test (EWT) was conducted on the first development well CP01_C01 as part of the field appraisal (Fig. 8). This well test data provided an excellent dataset with which to test the model prior to launching into history matching. Figure 9 shows the result of using the extended well test data to further condition the permeabilities in the model. In Figure 9, the red curve represents the model with horizontal permeabilities generated by upscaling the permeabilities in the fine-scale geological model and vertical permeabilities generated using the functional form given above. The green curve represents the same model except that all the permeabilities have been multiplied by a factor of two to reduce the drawdown computed by the model. The black curve in Figure 9 shows the model with the doubled permeabilities and a reduced skin factor on the well. The overall match is very good considering that the grid is fairly coarse for modelling a single well and that no fixes other than those mentioned were made to the model. As an additional test, the RFT data for the Segment 1 wells drilled after the extended well test, wells CP09_C07, CW11_C02, CP05_C05 and WW06_W03 (Fig. 8), were compared against

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Fig. 8. Schiehallion Field map with well locations.

that calculated by the extended well test model. The model did a very good job in reproducing the depletion seen in these wells. Reviewing the kh transforms with the knowledge gained from the EWT, we noted that in the dominant channel sand facies (DE2) a 1 porosity-unit (pu) change in porosity corresponds, approximately, to a change in permeability by a factor of two (Fig. 10) and this was well within the noise of the core datasets used to generate the original transform. Given the quality of the match to the extended well test data achieved using this factor, a horizontal permeability multiplier of two was applied to the starting-point model for the history match. Although the extended well test dataset supported the increased permeabilities, the model was tested on the full history-match dataset before proceeding using the starting-point model both with and without the factor-of-two multiplier on the

horizontal permeabilities. At the field level, there was little to choose between the two models: they both achieved a similar quality of match indicating that absolute permeability was not going to be the biggest controlling influence in achieving a history match. For an individual well, the two models showed more variation.

Static model assurance tests The principal assurance tests on the model prior to moving into detailed history matching were: (1) checking that the wells in the model were completed in the correct geological zones; (2) confirming the location of gas–oil contacts; and (3) comparing porosity and permeability distributions from the model with those from core data.

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Fig. 9. Match to the CP01_C01 extended well test.

Looking at the completed intervals for every well in the model and comparing this to the known position of the completed intervals brought to light a gridding problem in the area of the well CP07_C13 (Fig. 8). This well lies between two approximately parallel faults in Segment 1. Due to the extrapolation distances applied around the faults in the structural modelling in RMS, the horizon had been smoothed and suppressed the structure between these faults where the well is located. As a consequence, well CP07_C13 did not have any perforations in the reservoir unit (T31 upper) it is

actually completed in. The grid problem was fixed before starting the detailed history match. At various stages during the model build, the whole simulation model was reviewed in cross -sectional view to check that the assumed contacts made sense and that the model was capturing the correct juxtaposition of the sands. The juxtaposition of gas on the downthrown side of a fault against oil on the upside of the fault was also looked for. Detailed mapping and seismic attributes identified that gas is trapped in three-way closures and the gas– oil contact is controlled by spill points across

Fig. 10. Porosity–permeability transformed used to populate the fine-scale geological model.

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Fig. 11. Initial water saturations in the T31 reservoirs.

the faults. When these situations were encountered, they tended to involve a few isolated cells. It was relatively easy to remove these by making changes to the way in which the geological realization was generated. Figure 11 shows the initial water saturations in the T31 upper reservoir as represented in the reference case model. Comparisons between the porosity and permeability distributions from the model with those from core data provided a qualitative check on the static model, especially in regard to permeabilities. A poor match between the permeability distribution in the

model for a particular combination of geological realization and porosity–permeability transform was taken as indicating that the model might be difficult to history match. The hydrocarbon pore volume weighted distribution for the whole final history-match model was compared to the core plug data (Fig. 12).

Seismic coherency data-derived barriers Production data and 4D seismic surveys have shown that the Schiehallion Field is

Fig. 12. Comparison between model and core permeability distributions.

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compartmentalized: fluid movement is strongly impacted by non-fault-related flow barriers. A key learning from previous simulation models of the Schiehallion Field was the importance of faults, baffles and barriers to flow in the reservoir. Using seismic coherency data to map lineaments and cross-checking them with 4D difference volumes permitted us to estimate the strength of potential transmissibility barriers that could be incorporated directly into the simulation model. Identification and use of these barriers proved to be critical in achieving matches to pressures and watercuts. A total of 215 possible barriers were mapped from the seismic coherency data. These were discretized onto the simulation grid for use in history matching. Figure 13 shows a cartoon of the areal grid in (i,j) space, with the structural faults shown as the thick dark lines and all 215 seismic coherency data-derived barriers shown as the thin dark lines. This diagram formed the basis for selecting the active barriers that were used in the history match.

dictated by the production data. The general philosophy was to use as few of the barriers as we could and allow the geology incorporated in the DEs and facies distribution to impact the history match. Varying the ‘strength’ of the barriers (i.e. the degree to which they are transmissive) was also used during the history-matching phase. The field level history match is shown in Figure 14 with the solid lines being the simulation and the points the measured production data. After completing the history match, Shell’s proprietary MorSyn software was used to generate an acoustic impedance map for the T31 upper reservoir from the model. This was compared to the corresponding acoustic impedance map obtained directly from the baseline seismic survey. The comparison process generated a net-to-gross multiplier map to be applied to the model T31 upper reservoir net-to-gross ratios. When this was done, the model was re-history-matched, creating a second model to be used for reserves prediction work.

History matching

Capturing uncertainties for reserves prediction

The overall approach to history matching was to start with an ‘open’ model, i.e. one without active barriers (Fig. 13), and then to add in barriers as

Having generated a manual history match to the production data, we had learned what the major

Fig. 13. FFM2003 vertical transmissibility features displayed on a regular grid; seismic coherency based baffles/ barriers, i.e. channel margins and minor faults (thin lines), structural faults (thick lines) and major faults that segment the field (red lines).

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Fig. 14. Field level history match.

geological controls were in the simulation model. We then used this knowledge to test geological uncertainty that would still generate acceptable history-matched models but which would be likely to behave differently in a predictive mode. These alternative history-match cases were then run against a range of field development scenarios to understand the possible range on production and recovery from the field. The generation of alternative history-matched models was achieved using a genetic algorithm approach: we defined a goodness-of-fit to the historical data and then allowed the genetic algorithm to vary the geological uncertainties to try to improve it. We used a total of 12 different historymatched models to develop the range on expected recovery from the field under different development scenarios. The geological uncertainties that were investigated by the genetic algorithm were: (1) (2) (3)

Relative permeability; Net-to-gross ratio in the T31 lower reservoir; and Barrier strengths.

While we could have extended the methodology to encompass other uncertainties (e.g. horizontal and vertical permeabilities), we had to be conscious of the elapsed time required to generate alternative models. We also had to take a view as to whether,

by doing more model runs, the resultant alternative history matches would behave sufficiently differently in prediction from those we were going to generate by looking at only the three variables mentioned above.

Relative permeability Although the relative permeability curves were not a history-match variable, we felt that it was important to look at the potential impact of relative permeability on future performance: the Schiehallion waterflood is still relatively immature, with field watercut at the end of the history match at approximately 25%. To allow for the possibility of a watercut development that is different from that obtained using the reference case relative permeability curves, we constructed two new sets of water– oil relative permeability curves. Figure 15 shows the alternative relative permeability data in the form of fractional flow curves.

Net-to-gross ratio in the T31 lower reservoir Seismic attribute data are difficult to extract for the T31 lower reservoir due to masking effects caused by the overlying T31 upper reservoir. Consequently, there is considerable uncertainty in the

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Fig. 15. Fractional flow curves used to generate alternative history-matched models.

net-to-gross ratio, as derived from seismic data, for the T31 lower reservoir. This translates into uncertainty in oil in place and potentially into reserves. Recognizing this, we decided to allow the net-to-gross ratio in the T31 lower reservoir to vary everywhere by a factor in the range 0.8 to 1.4, i.e. the genetic algorithm was allowed to multiply the T31 lower net-to-gross ratio values in the reference case model by a constant factor in the range 0.8 to 1.4. Varying the net-to-gross in the model impacts not only horizontal fluid movement (via the standard calculation for horizontal transmissibility), but also vertical flow because the model uses the transform given above to construct vertical permeabilities in the upscaled cells from the upscaled horizontal permeabilities. We did not investigate the impact of varying the net-to-gross ratios in the T31 upper reservoir as part of the genetic algorithm approach: this had already been looked at as part of the original history matching and resulted in an alternative history-matched model.

Barrier strengths The final history-matched model has 43 faults and barriers which are either sealing or are very slightly transmissive, i.e. with fault transmissibility multipliers of 0.001 or less. Given the relatively immature state of the waterflood and the importance of these barriers and faults in achieving a history match, we felt that barrier strength could make quite an impact on future model performance. To explore this possibility, we allowed the genetic

algorithm to set all the faults and barriers with transmissibility multipliers of 0.001 or less to the value 0 or 0.001. Similarly, those faults and barriers which were made completely sealing in order to achieve the reference case history match were allowed to either remain completely sealing or be slightly transmissive (i.e. be given a fault transmissibility multiplier of 0.001).

Conclusions 1. A complete evaluation of all model inputs was a critical step prior to any model building; this included a re-evaluation of all log and core analysis data biostratigraphic data and sedimentological interpretation of the reservoir. In addition, new Amplitude versus Offset (AvO) seismic volumes and 4D difference volumes were derived in order to condition and constrain the model. 2. Careful evaluation of previous modelling efforts proved valuable with the aim of replicating best practice and improving suboptimal workflows. 3. Mapping seismic envelopes rather than strictly amplitude-defined bodies, the reservoir zonation was more closely related to the biostratigraphically constrained sequence stratigraphic framework. This resulted in better preservation of stratal relationships such as abrupt facies transitions (e.g. channel to interchannel) within a stratigraphic unit. The horizons generated also acknowledged the local observation from wells that the seismic data do not always have a clear expression of reservoir sands; the surfaces used allowed greater flexibility in modelling the extent and proportion of reservoir

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in order to match well data and production performance. 4. Early consideration of the simulation grid design proved important. By building the geological model as a ‘grid refinement’ of the simulation grid, upscaling and comparison of the models was efficient and transparent. Care must be taken though when creating structural models at a simulation scale, especially around faulted regions. 5. For a reservoir delineated and developed using 3D seismic, conditioning of the static model to 3D seismic volumes was essential. However, care needs to be taken when using this technique, recognizing seismic data limitations (spatial amplitude variations, masking of amplitudes, tuning and bandwidth issues) and important scaling issues (resampling 12.5 m spacing seismic data into a 50 m by 50 m grid; also relative scale of DEs (around 5 m thick) relative to maximum seismic resolution (around 10–15 m). Checking the final product by creating a synthetic seismic volume is a key step in the QC of the conditioning methodology. 6. The detailed mapping of barriers and integration of 4D data were critical, particularly for history matching. Although time-consuming, this step proved invaluable in modelling water breakthroughs and matching pressure responses. This has been true in every full-field simulation model (of which this is the third) that has been used in understanding Schiehallion dynamic performance. 7. One of the critical history-matching sensitivities is both vertical and horizontal permeability. This study has shown the importance of understanding the scaling relationships between core plugs and simulation grid cells. The Schiehallion EWT proved extremely useful in providing an upfront sense-check of the model properties, and lead to modifications in the estimation in upscaled permeability. 8. On a non-technical side, the collaborative effort between BP and Shell, together with the full support of the partnership, led to a shared sense of ownership (and responsibility) for the results. The authors would like to acknowledge the following for their technical contributions to the execution of this project: Regis Marion (Petrocool) – petrophysics; Mike Ashton (Badley Ashton) – core sedimentology; Andrew Alderson and Nick Holmes (Ichron) – biostratigraphy; Rachel Kenworthy, Graeme Bagley, Tim Primmer (BP) – seismic and geological interpretation; Peter Ashton (Shell) – seismic inversion. Andrew C. Evans, Peter Grant, Damien Scott, Jan Stammeijer (Shell) – 4D analysis and interpretation; and Caz Dudley (BP) – for graphics support. In addition, the support of all Schiehallion partners, particularly the subsurface technical representatives from BP, Shell, Amerada, Murphy, Statoil,

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OMV, who provided technical challenges, guidance and assurance for the final products.

References A SHTON , M. 2002. Sedimentary Organisation and Depositional Models. In: Schiehallion Field, Construction of the Deterministic Benchmark Static Model, Volumetrics and Associated Equity Ranges., Unpublished proprietary BP–Shell Equity Report, vol. 1, 9–33. C ARR , A. D. & S COTCHMAN , I. C. 2003. Thermal history modelling in the southern Faroe– Shetland Basin. Petroleum Geoscience, 9, 333–345. C LARK , J. D. & P ICKERING , K. T. 1996. Submarine Channels: Processes and Architecture. Vallis Press, London. E BDON , C. C., G RANGER , P. J., J OHNSON , H. D. & E VANS , A. M. 1995. Early Tertiary evolution and sequence stratigraphy of the Faeroe-Shetland Basin: Implications for hydrocarbon prospectivity. In: S CRUTTON , R. A., S TOKER , M. S., S HIMMFIELD , G. B. & T UDHOPE , A. W. (eds) The Tectonics, Sedimentation and Palaeoceanography of the North Atlantic Region. Geological Society, London, Special Publications, 90, 51–69. K NOTT , S. D., B URCHELL , M. T., J OLLY , E. S. & F RASER , A. J. 1993. Mesozoic to Cenozoic plate reconstructions of the North Atlantic and hydrocarbon plays of the Atlantic margin. In: P ARKER , J. R. (ed.) Petroleum Geology of Northwest Europe. Proceedings of the 4th Conference. Geological Society, London, 953–974. L AMERS , E. & C ARMICHAEL , S. M. M. 1999. The Paleocene deepwater sandstone play west of Shetland. In: F LEET , A. J. & B OLDY , S. A. R. (eds) Petroleum Geology of Northwest Europe: Proceedings of the 5th Conference. Geological Society, London, 645–659. L IA , O. & G JERDE , J. 1998. A marked point process model conditioned on inverted seismic data. In: IAMG ’98 Proceedings of the Fourth Annual Conference of the International Association for Mathematical Geology, 794– 799. M ITCHELL , S. M., B EAMISH , W. J., W OOD , M. V., M ALACEK , S. J., A RMENTROUT , J. A., D AMUTH , J. E. & O LSON , H. C. 1993. Paleogene sequence stratigraphic framework of the Faroe Basin. In: P ARKER , J. R. (ed.) Petroleum Geology of Northwest Europe: Proceedings of the 4th Conference. Geological Society, London, 1011– 23. M ORTON , A. C., B OYD , J. D. & E WEN , D. F. 2002. Evolution of Palaeocene sediment dispersal systems in the Foinaven sub-basin, west of Shetland. In: J OLLEY , D. W. & B ELL , B. R. (eds) The North Atlantic Igneous Province: Stratigraphy, Tectonics, Volcanics and Magmatic Processes. Geological Society Special Publications, London, 197, 69– 93. S TEPHEN , K. D., C LARK , J. D. & G ARDINER , A. R. 2001. Outcrop based stochastic modelling of turbidite amalgamation and its effects on hydrocarbon recovery. Petroleum Geoscience, 7, 163–172.

Index Note: Page numbers denoted in italics refer to figures and those in bold refer to tables. @ Risk 193, 199, 201 acoustic impedance map 216 analogue modelling 87 scale of 88 anchoring 147, 148–149, 154, 158 auto-ranked models 29–31, 30 azimuth map 69, 72 base case modelling 145–148, 146, 158, 166, 194, 195 basement rooted faults 44, 44 bedset surfaces 108–109, 108, 110, 118 bootstrap method 65 boundary conditions 135, 136, 140, 140 Box-Behnken technique 155 capillary entry pressure 22 carbonate facies 39– 49 diagenetic properties 39–49 fracture properties 39–49 carbonate reservoirs 41 modelling 39 cementation 46, 46 clay content 12, 14, 15, 17, 18, 19, 20, 51 and threshold pressures 22, 23 clay mixing algorithms 17 clay smear 17– 19 calculations 33 permeabilities 17 potential 17–19 value 19 clay smear factor (CSF) 17 clinoform 100, 118 barriers 99– 121 effects on flow 99, 100, 102, 118 geometry 1, 99, 113 length scales 118 model hypotheses 113– 115, 117 shale length 117 –118 and water flood direction 118 cloud transform process 89– 92, 165–168, 166 point field 165–166 coarse scale models 135, 137– 140, 161, 170– 172, 172, 183 flow simulation 143 Cogollo Group 39, 42 conceptual model 42 facies model 43 conceptual modelling 42, 69 critical property relationships 33 critical result traps 26– 29, 27 input parameters 29, 29 D-optimal technique 155 data 1, 99, 205– 206 collection methods 95, 102– 103, 104, 118, 182 –183 hard 1, 75 locally calibrated 36

processing 103 random sampling 138, 139 representativity of 127 sample population 60 sample variance 127 soft 1 types 6, 127 see also digital data; gravity survey data; input data; magnetic survey data; seismic data Decision Analysis 161, 176– 177, 178 deep marine reservoir 51, 54, 64 impact index 63 deepwater turbidite modelling 205–219 deltaic outcrop analogues 99– 121 deltaic reservoir 99 highstand vs. lowstand 118– 119 sedimentary sequence 99 Depositional Elements scheme 209–210, 209, 211 depositional environment 51, 55, 61, 63 sample population 52– 53 depositional facies 67, 163 model parameters 53, 54 modelling 67, 161, 163– 165 realizations 164, 165 relationships 162 depressurization 131 Design of Experiments approach 2, 155– 158, 156, 172–173, 174, 175, 175, 178, 202 advantages 157–158 methodology 161 parameters 173 see also Box-Behnken technique; D-optimal technique; Plackett–Burman design deterministic analysis 173 deterministic economic analysis 176 deterministic facies model 194 deterministic realizations 2 diagenesis 39 burial 47 fault related 43– 45 diagenetic fluid pathways 44 diagonal tensor method 212 digital data 96 acquisition 88–90, 89– 90 outcrop data for calibration 92– 96, 93, 96 survey methods 88 dipping grids 111, 113, 115, 117, 118 discrete smoothed interpolation (DSI) 79, 81 Dispersion Variance 128 distribution function 196 Dykstra–Parsons coefficient 161, 172 dynamic reservoir modelling 2, 145, 181 effective shale gouge ratio (ESGR) 17, 19 elastic rock properties 45 estimation error 9 –11, 10, 13 Experimental Design analysis see Design of Experiments approach

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facies 39, 53, 54, 55, 55, 103 –110 associations 105 correlation 187 depocentre map 71, 71 scenarios 189 see also carbonate facies; sedimentary facies facies belts 111, 112, 115 facies conditioning 210, 210 facies distribution 67, 110, 111, 150, 190, 210 multiple realizations 82–83 facies distribution model (FDM) 67– 74, 71, 73, 74 process 69– 70 facies modelling 41, 106, 111–113, 125, 172, 186–188, 206– 207, 208– 211 see also depositional facies modelling facies permeability distributions 166, 166 facies probability 76, 76 facies probability cube 1, 67, 69–70, 71–73, 71, 74, 75, 76, 161, 164– 165, 164, 165 facies probability functions 209–210, 210 facies proportion 76, 77 non stationary variations 69 facies proportion cubes 80, 82, 82, 83, 83 facies proportion curve 70, 76, 77–79, 79 facies proportion map 80 facies transition zones, uncertainty 77, 78 fault modelling 47, 53– 57, 94 fault property modelling 51, 55–57, 56, 62, 62 fault seal 26– 33 algorithm 51 mapping 5 –38 parameters 54– 55 single fixed relationships 33– 34 Fault Seal Toolbox 5 fault throw 32–33, 51, 53 net offset 9– 11, 10 standard deviation 7 fault tips 44, 45 fault transmissibility 11, 125 multipliers 11, 27, 27, 30, 33, 36, 53, 207, 218 fault zone complexity scale 6 physical properties 6 processes 16 structure 6 fault-horizon intersection geometries 8– 9 fault-horizon projection distances 8, 9 faults 39 classification 1, 7 compartmentalization 185 data 94 density 51, 52, 53 dipping reverse 129 displacement 11, 12, 13 and flow magnitude 1 geohistory 8–9 mislocation 9 patterns 51 permeability 19, 20, 51 principal slip surface 9, 10 and rock thickness 11, 12, 13 sealing nature 19, 22, 26– 33 spacing 129

staircased 129 structural style 8 –9 threshold pressures 22 Y-shaped 129 see also basement rooted faults; growth faults; relay faults Ferron Member 99– 121 bedset surfaces 108 data 103 FFM2003 model, workflow 205– 207 fine scale models 135, 138, 170– 172, 178, 211 fixed volume grid 51 flow barriers 215–216 strength 218 flow equations 59 flow properties macroscopic 126 sedimentary structures 123 flow simulation 51, 52, 57, 57, 99, 112, 113, 114, 115, 116, 117, 123, 161, 207 accuracy 130 coarse scale models 143 global approach 140 parameters 119 single phase 140 software 103 uncertainty 161– 179 and upscaling 135–144 fluid contacts 185–186 fluid pathways 1, 43, 44, 53 fluvial reservoirs 51, 54, 65 impact index 64 folds 3D geometry 95–96 development 95 strain accommodation 9 forward flow modelling 30– 31 fractional flow curves 218 fractures see faults framework modelling, fluid contact 185 –186 gas injection 131, 132 gas–oil contacts 212– 213 geocellular grid 5, 8, 19, 206 incorporating uncertainty 22–26 parameter modifications 22–25 geocellular modelling 8, 39 geocellular stratigraphic grid 163 geological modelling 1– 3 3D 1 calibration 92–96 case study 93– 96 Glitne Field, North Sea 197 realizations 52, 211 uncertainty 161– 179 validation 170 workflow 183 geomechanical model 45, 435 geometric coherency tool 7 geometric parameters 22, 68– 69, 68 macro scale uncertainties 6 –8, 7 relationships 6, 34 uncertainties 6 –11

INDEX geophysical data 87 geospatial data, 3D models 91–92 geostatistical simulation 148 –149, 158 facies 82, 82 gigascopic scale 123 Glitne Field, North Sea 193–203 base case model 195 geological parameters 197 location 193–194, 194 reservoir map 199 well locations 195 global single phase simulation 143–144 global uncertainty 31, 32, 33, 36, 77 Gocad software 68 gravity survey data 87 gridding algorithm 110 gridding software 129 grids 112 construction 129– 131 design for structure mapping 207– 208 manual editing 129– 130 multimillion grid cells 135 resolution 110, 129, 187, 208 strategies 110– 111, 118 unstructured 130 see also dipping grids; fixed volume grid; geocellular grid; geocellular stratigraphic grid; regular grids; simulation grid; stratigraphic grid ground penetrating radar (GPR) 90 growth faults, modelling 113 High Impact Visualization Environment (HIVE) 90–91, 91 history matching 47, 137– 140, 137, 152, 153, 183, 189– 191, 207, 211, 216, 217, 218 automatic 155 dataset 213 tools 152–153 see also multiple history matching horizon, angular discordance 7, 9 hybrid reference model 211 hydrocarbon charge 39, 46 diagenesis 46– 47 modelling charge history 46 hydrocarbon column, cross fault 22 hydrocarbon contact 181 hydrocarbon probability distribution 169 hydrocarbon production fault factors 51, 57 forecast 75, 123, 152 tectonic parameters 51 variable 59– 60, 64 see also oil production hydrocarbon recovery 1 –3, 161 estimating 135 role of modelling 2 see also improved oil recovery (IOR); oil recovery hydrocarbon volume 157, 205 3D 210 cumulative curve 168– 169, 169 potential 194– 196 prediction uncertainty 216– 218

223 sensitivity 168–169, 168 uncertainty 193

Icotea Formation 186 –187 facies distribution 190 impact index 62, 63 improved oil recovery (IOR) 126 indicator simulation 124 input data 1, 87, 148– 149, 193, 194 format 60 IRAP RMS software 103, 110, 193, 196, 196–197, 199, 200 isochores, true vertical thickness 184 juxtaposition analysis 26 laser scan point cloud data 89–90, 90–91, 91 meshing 91, 91 picking 92, 92 see also cloud transform process; terrestrial laser scanning (lidar) leaching zones 44, 44, 45, 46, 48 potential 45 leak probability 20, 21 log based electrofacies scheme 208– 211 magnetic survey data 87 Maracaibo Basin, Venezuela 39, 40 Misoa Formation 186 model parameters bulk values 55 clustering 31 dependence between 154 non stationarity 75 relationships 9 rules 6, 9 modelling 44– 45 assessing discrepancies 8 interpretation 60 results comparison 64 simulation time 72 see also analogue modelling; base case modelling; conceptual modelling; depositional facies modelling; dynamic reservoir modelling; facies modelling; fault modelling; forward flow modelling; geocellular modelling; geological modelling; multiscale modelling; numerical based modelling; object based modelling; probabilistic simulation; scenario based modelling; static modelling; stochastic modelling; variogram based modelling modelling scale 88 modelling software see software models grid 112 resolution 19, 126 scale 1 –2 tectonic parameters 1 testing with well data 212–213, 214 see also coarse scale models; facies distribution model; FFM2003 model; fine scale models; flow simulation; geomechanical model; outcrop models; SPE 10 model

224

INDEX

Monte Carlo simulation 157, 196, 199– 202 multimillion grid cells 135 multiple deterministic scenarios 145, 145– 146, 146, 148, 151 see also scenario based modelling multiple history matching 145, 158 multiple model handling 154– 155, 154 multiple point geostatistical simulation 124, 161, 163– 165 training image 162 multiple point statistics (MPS) 67–74 advantages 72 constraints 69– 72, 72–73 tidal reservoir 73, 73 multiple probabilistic models 158 multiple stochastic modelling 2, 145– 146, 146, 147, 149, 158, 196 multiscale modelling factors 131, 131 million cell model 126 sedimentary structures 123 nearest neighbour resampling algorithm 111 Neighbourhood Approximation algorithm 137– 138 net sandbody connectivity 181 net to gross multiplier map 216 net to gross ratio 165 permeability 217–218 porosity 184 numerical based modelling 87 scale of 88 object based modelling 1, 67, 83, 83, 99, 112, 112, 124, 164, 205, 206– 207, 209 oil production 138, 143 oil recovery 138 oil water contacts 185, 189, 189, 191 oil-in-place 181, 191 uncertainty 217 outcrop analogues 87–98 outcrop data 88–90, 100 digital visualization 90–91 outcrop models 110 quantitative 92, 93 visualization 96 outcrop studies 87– 88 quantitative data 88–90 Panther Tongue Member 99–121 bedset surfaces 109 data 103 flow simulations 115 pattern recognition methods 124 permeability 11, 12, 53, 54, 55, 55, 57, 67, 127, 161, 165, 188– 189, 188 coarse scale 137– 140 curves 141, 142 cut-off 168 data 128, 129 distribution 137, 215 net to gross ratio 190, 217– 218 relative 217 transform 212–213 transmissibility multiplier 34

uncertainty 166, 167 upscaling 211–213 petrophysical properties 106, 110, 112 phased development strategy 177– 178, 178 photo logs 99 calibrated 103, 104, 118 photomontage 103 pilot point approach 137–138 Pinda Formation, geology 162 pixel-based approach 1 Plackett–Burman design 155– 157, 157, 172–173, 173 pore scale modelling, flow properties 123 –124 Pore Volume Weighted (PVW) method 141–142 pores geochemical signature 43 microscopic scale 123 secondary volume 39, 43 space 125 structure 41 systems 39 types 39 porosity 47, 53, 55, 55, 67, 161, 188, 188, 211 distribution 46, 136 economic 41 net to gross ratio 184, 206 profiles 42 realizations 190 uncertainty 166– 168, 167 upscaling 211–213 porosity–permeability transform 189, 211, 212, 214 prediction accuracy 5, 32, 36 pressure solution methods 135, 136, 140, 142 probabilistic distribution curve 157 probabilistic economic analysis 177, 177 probabilistic simulation 161 forecasts 175– 176 see also multiple probabilistic models probability 26, 27– 28, 27, 169 probability density function 138, 139, 149–150, 208 process based modelling 124 property models 207, 211 parameters 11–22 property uncertainties, fault seal analysis 11 prospect analysis, probability 28, 29 rationalist approach see base case modelling Real Time Kinematic GPS 87, 89– 90, 90, 95, 96 realizations 2, 25–26, 52, 82– 83, 112, 140, 164, 165, 211 and auto ranking 29– 30 multiple 2, 35, 183 multiple stochastic 196 recovery factor (RF) 115, 116, 117 regular grids 111, 113, 115, 117, 118 relay faults, displacement patterns 93– 95 Representative Elementary Volume (REV) 126, 127 lithofacies scale 127 permeability 127 reservoir analogues, quantitative 88– 92 reservoir connectivity 186–188 reservoir development alternatives 173– 175, 176, 178 reservoir modelling 169–173, 169, 173 –178 calibration of 87–98 comparison 73–74 construction 110–113

INDEX full field 205 methodology 161– 162 multiscale 123–134 properties 165– 168 resolution 51–52 scale transitions 124–125 scales 75–85, 123, 124–126 scenario models 172–173 simulation grid 125 single realization 146 software 5, 39–49, 52, 68 strategy 118 validation of 87–98 workflow 112, 118, 176 see also modelling reservoir performance 117, 118, 131, 131 structural controls 51–66 reservoir potential, mature field 181– 192 reservoirs assessing targets 193–203 economic feasibility 193 effective properties 211 field development planning 123 heterogeneity 135– 144, 186– 188 management 1 productivity 181, 191 property extrapolation 39 subdivision scheme 184 see also carbonate reservoirs; deep marine reservoir; deltaic reservoir; shallow marine reservoir; tidal reservoir response data 157 response variable calculation 196– 197 Restricted Maximum Likelihood Method (REML) 57 RMS finite difference black oil simulator 113 Roxar RMS software see IRAP RMS software sand net to gross values 21–22 sand–sand windows 33, 34, 35 saturation distributions 142, 142 scenario based modelling 135, 145–159, 148, 158 application of 150– 153 benefits 153– 154 issues 154 scenario building 196– 197 parameter clustering 31 Schiehallion Field 205–219 location 206 model workflow 208 principle reservoirs 207 stratigraphy 205 structural control 205 well locations 213 sedimentary facies 51, 103–110 3D modelling 75– 85 cross section 75, 76–79, 78 interpretation 76–77, 78 parameters 60 sedimentary logs 99, 103, 104 sedimentary structures flow properties 123 scale 123 scale transitions 125

225

seismic coherency, data derived barriers 215– 216, 216 seismic data 6 –7, 8, 53, 69, 87 resolution 9 seismic lines 163 seismic volume 7– 8 seismic weighting factor (SWF) 210 semivariograms 137 sensitivity index 62–63, 63 Sequential Gaussian Simulation (SGS) 124, 137, 165–166, 188, 190 Sequential Indicator Simulation (SIS) 72, 73, 82, 188, 189 shale gouge ratio (SGR) 14–17, 51, 52, 53, 54–55, 57 percentage errors 14– 17, 16 sealing 19– 22, 21 trap sealing nature 19 see also effective shale gouge ratio (ESGR) shale smear factor 51, 52, 53, 54– 55 uncertainties 19 shale volume fraction see VShale shallow marine reservoir 51, 54, 64 impact index 63 simulation grid 130, 206, 207, 218 automated construction 123 construction 129–131 single normal equation simulation (snesim) 72 software 1, 5, 39– 49, 52, 68, 96 see also IRAP RMS software SPE 10 model 135, 136, 136, 141, 143 static modelling 2, 145, 163– 168, 181, 183, 211 assurance tests 213– 215, 215 grid 5, 206, 208 uncertainties 183–185 statistical analysis 57–60, 58– 59, 199–202 methods 124 stereoscopic image 90– 91, 91 stochastic modelling 5, 75 advantages 75 multiple realizations 5 techniques 35 see also multiple stochastic modelling Stock Tank Oil Initially In Place (STOIIP) 193, 196, 207 numbers 201 uncertainty range 199, 201 strain partitioning 9– 11 stratigraphic framework, influence of 79–82, 81 stratigraphic grid 70 stratigraphy 41 cross section 101 settings 51–66 studies 99– 100 variation 12–14 stress ratio 45 stress values 44, 45 structural modelling 1, 130 feature category 130 parameters 60 structure mapping, grid design 207– 208 surface stability index 7, 7, 9 tectonic evolution 39 controlled facies 47 terrestrial laser scanning (lidar) 87, 89–90

226 tidal reservoir 51, 54, 64–65, 68–69, 70, 70, 71 impact index 64 multiple point statistics (MPS) 73, 73 top down approach 135 training image 68– 69, 69, 72, 74, 161, 162, 163–165 transmissibility barriers 216, 216 transmissibility multipliers 11, 27, 27, 30, 33, 53, 207, 218 auto-ranked 30 predictions 32 zero uncertainty 36 Truncated Gaussian Simulations (TGS) 82, 82, 99, 111 uncertainty 5– 38, 23, 65, 76, 135, 139–140, 157, 178, 181– 192 absolute value shifts 22 analysis 161 assessment 82– 83 bias 25–26 distribution profiles 25 fault seal analysis 6, 24 geometric properties 5– 38, 6– 11 handling 146 –150, 146, 158 impact 31–32 incorporation techniques 5, 161– 179 juxtaposition 9, 11 key parameters 172 –173, 175, 184– 185, 201– 202 lists 149–150, 150, 151, 152, 152, 153, 154, 155– 157 management 2 modelling 10– 11, 207 and net to gross 188– 189 parameters 168, 200 percentage shifts 22 principle 151 property parameters 11– 22 quantifying 193– 203 range 185– 189 ranking 77, 149–150, 150, 157, 181, 191 shift application 25 single parameter 36 specific risks 32–33 static modelling 183–185, 197 volumetric 193 workflow method 194– 202, 196, 198 see also global uncertainty upscaling 92, 124, 129, 135–136, 136, 161, 170–171, 170, 207, 211 dynamic 141, 171–172 errors 2 factor 139, 140 global 140

INDEX methods 123, 125, 126, 135, 138, 139, 140– 142, 170 multiphase 126 single phase 126, 135, 140, 141, 170 transmissibilities 140, 141 two phase 135, 141, 171– 172 Urdaneta West Field, Venezuela 39, 181–192 basement rooted faults 44 dataset 40 diagenetic fluid pathways 44 facies and thickness 40– 43 geological setting 39, 181– 182 location 182 modelling 41–43, 44– 45 porosity distribution pattern 47 stratigraphy 183 structural cross section 189 structural history 44 well correlation 185, 187–188, 190 wells 182–183 variance adjustment factor 128 variance analysis 123, 127–129, 129 variance components 57, 58– 59, 59–60, 60–62, 61, 65 variogram based modelling 67 see also semivariograms VClay data 14– 17, 15, 22 volume calculation output 197 VShale distribution 14, 15, 22, 53, 54, 55, 55 water alternating gas injection (WAG) 131 water injection 152–153 water saturation 161, 165 initial 214, 215 water-wet faults 22 waterflooding 171, 171 well drive boundary conditions 140 Well Drive Upscaling (WDU) method 140– 142 well log data 69, 87 averaging 126 model testing 212– 213, 214 West Africa, offshore 161–179 Western Interior Basin, USA 99–121 claystone and siltstone 106 cross section 101 delta front sandstones 106 delta front siltstones 106–107 delta lobes 107– 110 distributary channel facies 107 geological setting 102 location 101