The SPE Foundation through member donations and a contribution from Offshore Europe

Transcription

1 Primary funding is provided by The SPE Foundation through member donations and a contribution from Offshore Europe The Society is grateful to those companies that allow their professionals to serve as lecturers Additional support provided by AIME Society of Petroleum Engineers Distinguished Lecturer Program

2 How to Predict Reservoir Performance with Subsurface Uncertainty at Multiple Scales? Xiao-Hui Wu ExxonMobil Upstream Research Company Society of Petroleum Engineers Distinguished Lecturer Program

3 Outline Why Predict Reservoir Performance? What Makes It Challenging? The Common Approach and Its Flaws Taking a Step Back Goal and Data Driven Modeling Technologies That Makes It Happen Summary and Recommendations 3

4 Why Predict Reservoir Performance? Understanding Subsurface Optimizing Project Economics Delivering Product 4

5 Pressure Oil Rate What Makes It Challenging? Geologic Model Flow Simulation Predictions Cumulative Oil Analogs Flow Properties Rock-Fluid Properties Seismic Logs Sequence Stratigraphy Core Wells & Facilities Recovery Process Temperature 5

6 Vertical Resolution/Range (ft) What Makes Prediction Challenging? 10, Well Log Seismic Data Core Data Field & Well Performance Reservoir Model , ,000 Areal Resolution/Range (ft) 6

7 Filling the Gaps Uncertainty at Multiple Scales Seismic Low Vertical Resolution 3 Dimensional Stratigraphy Reservoir Model Core Logs High Vertical Resolution 1 Dimensional (Very Sparse) Analogs / Concepts 7

8 Common Approach and Its Problems Interpolate at the finest scale feasible, commonly through spatial statistical methods, to incorporate sparse fine-scale field data Reservoir model with fine-scale cells everywhere regardless of data availability Some fine-scale feature still missing or misrepresented The process is often slow (12-18 months for one model) Many highly uncertain model parameters introduced (e.g., model parameters away from well controls) Aggravating the curse of dimensionality 8

9 Curse of Dimensionality 2 parameters 3 parameters 10 parameters H M L L M H 3 2 = 9 cases 3 3 = 27 cases 3 10 = cases gle.com/?gws_rd =ssl#q=image+of +hypercube P inside P inside P inside

10 Uncertainty Propagation Subsurface Input Project Decision Uncertainty in geology and fluid descriptions at multiple scales Modeling errors Numerical approximation errors Physical model errors Uncertainty in flow prediction Uncertainty in decision variables Reduce source of uncertainty by reducing modeling and numerical errors 10

11 Flux in X Direction Impact of modeling method on numerical accuracy Finite Volume Finite Element 10 Net to Gross = 0.5, l x = l y = 0.1 L z = 0.05 N x = N y = N z = Number of Cells in Each Direction Original geologic model A million cells Large numerical errors due to piece-wise constant permeability field Significant impact of modeling method on numerical accuracy Ref: XW, Parashkevov, Stone, Lyons, J. Algorithms & Computational Technology 2(2),

12 Dealing with Curse of Dimensionality Subsurface Input Project Decision Med. - High Very High Very High Medium Low Med. Apparent dimensions Low - Med. Low - Med. Medium Low Med. Low Med. Effective or observable dimensions in many practical cases Reduce dimension of uncertainty space by focusing on parameters observable in flow stream & decision variables 12

13 Observable Input Large-Scale Trends VS Base case More complex model, more parameters Higher numerical uncertainty Large-scale Trend Simpler model, fewer parameters Lower numerical uncertainty Water, Oil, Gas Pore Volume Injected Ref: XW, Bi, Kalla, International J. of Uncertainty Quantification, 2(3),

14 Observable Input Large-Scale EOD geometry Seismically-delineated Shale Plug Water Injector Water Injector Producer Producer Adjustment of environment of deposition necessary for history matching 14

15 Observable Input Fine-Scale Barriers Abreu, et al. 2003, identifies Lateral Accretion Packages as key reservoir elements in deepwater sinuous channels Similar features are observed in a 4D dataset from a deepwater reservoir offshore Angola Abreu, et al 2003 Gonzalez-Carballo, et al

16 Observable Input Fine-Scale Heterogeneity Smooth trend Base case Near well adjustment Localized fine-scale modeling for effective parameterization Pore Volume Injected Water, Oil, Gas Pore Volume Injected 16

17 Goal-Driven Model Selection: An Example Deep Water Environment Distal Section 17

18 Goal-Driven Model Selection: An Example (cont.) Base Case w. Full Details Storey, Storey-set, Complex Level Shales Water Drive Gas Drive Ref: XW, Bi, Kalla, International J. of Uncertainty Quantification, 2(3),

19 Goal-Driven Model Selection: An Example (cont.) Base Case w. Full Details Storey, Storey-set, Complex Level Shales Water Drive Gas Drive Ref: XW, Bi, Kalla, International J. of Uncertainty Quantification, 2(3),

20 Water Rate Pressure Water Rate Probability Pressure Modeling Approaches Goal-driven Data-driven Decision Variable Major compartments Time Main flow units Time Increased details Time Fine-scale realistic model Time 20

21 Data-Driven Modeling Simpler explanations are, other things being equal, generally better than more complex ones --Sir William of Ockham Occam s razor in the form of Bayesian model selection P(H 1 D) P(H 2 D) = P H 1 P(D H 1 ) P(H 2 )P(D H 2 ) P D H i = P D w, H i P( w H i ) dw from Bayes theorem evidence for H i H i = i th Hypothesis, D = Data, P = Probability Occam s razor penalizes complex models with many parameters models that have to be finely tuned to fit the data See also: Elsheikh, Wheeler, Hoteit, Water Resources Research, 49(12),

22 Hierarchical Geometric Modeling Channel complex set Flexible Parameterization Geometric Primitives Geologic Primitives Concept Model Plan View X Cross-Section Long Axis Short Axis Channel-bar system Modeling hierarchical surfaces to better capture geologic concepts and continuous flow barriers, baffles, and conduits Ref: Gai, XW, Branets, Sementelli, Robertson, SPE , 2012 Flexibility Multiple scenarios Efficient parametrization 22

23 Functional Form Modeling 23

24 Reduce Modeling and Numerical Errors Additional Technology Flexible unstructured gridding Multiscale functional property modeling Ref: Branets, Kubyak, Kartasheva, Shmyrov, Kandybor, SPE ,

25 Summary Challenge: strong effects of subsurface features at different scales on reservoir performance predictions Key to resolution: effective multiscale parameterization of subsurface heterogeneity Recommendations Reduce dimension of uncertainty space by focusing on parameters impacting business decisions and observable from field data Reduce source of uncertainty by reducing numerical and modeling errors 25

26 Thank you! All models are wrong, but some are useful -- George E. P. Box 26

27 Your Feedback is Important Enter your section in the DL Evaluation Contest by completing the evaluation form for this presentation Visit SPE.org/dl Society of Petroleum Engineers Distinguished Lecturer Program 27