Surrogate Reservoir Models

Transcription

1 Quantifying Uncertainties Associated with Reservoir Simulation Studies Using Surrogate Reservoir Models Shahab D. Mohaghegh West Virginia University & Intelligent Solutions, Inc. 1

2 Outline Reservoir Simulation & Uncertainty Surrogate Reservoir Models Case Study: A Giant Oil Field In the Middle East. Quantifying Uncertainty, Using Surrogate Reservoir Model 2

3 Sources of Uncertainty Geological Interpretations Log interpretations Core measurements & Analysis SCAL Rock Typing Seismic measurements and interpretations THE EARTH MODEL 3

4 Quantifying Uncertainty Conventional Approach: Geo-Statistics Multiple Realizations Hundreds & sometimes thousands of simulation runs Response Surface New Approach Surrogate Reservoir Model, SRM 4

5 SRM Development Main tolls for the development of Surrogate Reservoir models: Intelligent Systems Artificial Neural Networks Genetic Algorithms Fuzzy Logic 5

6 Surrogate Reservoir Models A subset of a more general set of models called Surrogate Intelligent Models Real-Time Optimization Real-Time Decision Making Analysis of Uncertainty An absolute essential tool for smart fields (ifields) 6

7 SRM an Engineering Tool Are Surrogate Reservoir Models the same as Response Surface techniques? NO. Unlike purely statistical techniques, SRMs are designed to be engineering tools. SRM is defined within the System Theory while Response Surface is a geostatistical method. INPUT SYSTEM OUTPUT 7

8 SRM an Engineering Tool Depending on the project objectives, SRMs are developed to preserve and respond to the physics of the problem. Honoring the physics is an important validation step in the development process of SRMs and their distinguishing feature from other (geostatistical) techniques. SEE A DEMONSTRATION 8

9 Monte Carlo Simulations entails generating a large number of equally likely random realizations of the reservoir fields with parameter statistics derived from sampling, solving deterministic flow equations for each realization, and postprocessing the results over all realizations to obtain sample moments of the solution. This approach has the advantages of applying to a broad range of both linear and nonlinear flow problems, but has a number of potential drawbacks the computation effort for each realization is usually large, especially for large-scale reservoirs. As a result, a detailed assessment of the uncertainty associated with flow performance predictions is rarely performed. Accurate, Efficient Quantification of Uncertainty for Flow in Heterogeneous Reservoirs Using the KLME Approach. Z. Lu, Los Alamos Natl. Laboratory; D. Zhang, U. of Oklahoma. SPE 93452, SPE Reservoir Simulation Symposium, 31 January-2 February, The Woodlands, Texas. 9

10 Objective Quantify uncertainties associated with reservoir simulation studies, using Monte Carlo Simulation method. Develop a Surrogate Reservoir Model (SRM) based on a Full Field Model (FFM) for a giant oil field in the Middle East for Analysis of uncertainty. 10

11 Methodology Develop an SRM based on the Full Field model. Calibrate and validate the SRM. Select KPIs for uncertainty analysis. Assign PDF to each KPI. Perform Monte Carlo Simulation. 11

12 FFM Characteristics Full Field Model Characteristics: Underlying Complex Geological Model. ECLIPSE TM 165 Horizontal Wells. Approximately 1,000,000 grid blocks. Single Run = 10 Hours on 12 CPUs. Water Injection for Pressure Maintenance. 12

13 SRM Characteristics Accurate replication of Full Field Model Results (for every well in the field): Instantaneous Water Cut Cumulative Oil Production Cumulative Water Production Ability to run in real-time. Remove the bottleneck. 13

14 Very Complex Geology 14

15 Very Complex Geology Reservoirs represented in the FFM. 15

16 Curse of Dimensionality Source of dimensionality: STATIC: Representation of reservoir properties associated with each well. DYNAMIC: Simulation runs to demonstrate well productivity. 16

17 Curse of Dimensionality Representing reservoir properties for horizontal wells. 17

18 Curse of Dimensionality, Static Potential list of parameters that can be collected on a per-grid block basis. Parameters Used on a per segment basis Mid Depth Relative Rock Ttype Initial Water Saturations Horizontal Permeability Reference Point Capillary Pressure/Saturation Function Thickness Porosity Stylolite Intensity Vertical Permeability Reference Point Reference Point IMPORTANT NOTE: Specific objective of the surrogate model must be identified in advance. 18

19 Curse of Dimensionality, Static Potential list of parameters that can be collected on a per-well basis. Parameters Used on a per well basis Latitude Deviation Horizontal Well Length Distance to Free Water Level Flowing Reference Point Cum. Oil Reference Point Distance to Nearest Producer Distance to Major Fault Longitude Azimuth Productivity Index Water Reference Point Oil Prod. Reference Point Cum. Water Reference Point Distance to Nearest Injector Distance to Minor Fault IMPORTANT NOTE: Specific objective of the surrogate model must be identified in advance. 19

20 Curse of Dimensionality, Static Total number of parameters that need representation during the modeling process: 12 parameters x 40 grid block/well = parameter per well Total of 496 parameter per well Building a model with 496 parameters per well is not realistic, THE CURSE OF DIMENSIONALITY Dimensionality Reduction becomes a vital task. 20

21 Curse of Dimensionality, Dynamic Well productivity is identified through following simulation runs: All wells producing at 1500, 2500, 3500, & 4500 bpd (nominal rates) Cap the field productivity No cap on field productivity 21

22 Curse of Dimensionality, Dynamic Well productivity through following simulation runs: Step up the rates for all wells Cap the field productivity No cap on field productivity 22

23 Curse of Dimensionality In order to address the Curse of Dimensionality one must understand the behavior and contribution of each of the parameters to the process being modeled. Not a simple and straight forward task.!!! 23

24 Curse of Dimensionality To address this issue, we use Fuzzy Pattern Recognition technology, based on Fuzzy Cluster Analysis. 24

25 Key Performance Indicator Parameter: Reference 25

26 Key Performance Indicator 26

27 Key Performance Indicators Please Note: The lower the bar, the higher the influence. 27

28 Surrogate Modeling 40% of data was set aside as blind (verification) data. 28

29 Surrogate Modeling 40% of data was set aside as blind (verification) data. 29

30 Optimal Production Strategy Well Ranked No. 1 IMPORTANT NOTE: This is NOT a Response Surface SRM was run hundreds of times to generate these figures. 30

31 Optimal Production Strategy Well Ranked No. 100 IMPORTANT NOTE: This is NOT a Response Surface SRM was run hundreds of times to generate these figures. 31

32 Analysis of Uncertainty Following are the steps involved: 1. Identify a set of key performance indicators that are most vulnerable to uncertainty. 2. Define probability distribution function for each of the performance indicators. a. Uniform distribution b. Normal (Gaussian) distribution c. Triangular distribution d. Discrete distribution 32

33 Analysis of Uncertainty Following are steps involved: 3. Run the neural network model hundreds or thousands of times using the defined probability distribution functions for the identified reservoir parameters. Performing this analysis using the actual Full Field Model is impractical. 4. Produce a probability distribution function for cumulative oil production and the water cut at different time and liquid rate cap. 33

34 P-16 I-12 34

35 Key Performance Indicators 40 producing layers. One million grid blocks. This is the distribution of the parameter being studied in the geologic model. 35

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37 Cumulative Oil Production Uniform Distribution was assigned to the top 5 KPIs. Gaussian Distribution was assigned to the top 5 KPIs. 37

38 Instantaneous Water Cut Uniform Distribution was assigned to the top 5 KPIs. Gaussian Distribution was assigned to the top 5 KPIs. 38

39 B-91 39

40 Cumulative Oil Production Influence of uncertainties associated with top and low ranking KPIs on the well output. 40

41 Instantaneous Water Cut Influence of uncertainties associated with top and low ranking KPIs on the well output. 41

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43 CONCLUSIONS A successful surrogate reservoir model was developed for a giant oil field in the Middle East. The surrogate model was able to accurately mimic the behavior of the actual full field flow model. 43

44 CONCLUSIONS The surrogate reservoir model would provide results in real time. The surrogate model was used to analyze uncertainties associated with the full field flow model. 44

45 CONCLUSIONS Development of successful surrogate reservoir model is an important and essential step toward development of next generation of reservoir management tools that would address the needs of smart fields. 45

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54 Analysis of Uncertainty 54

55 Analysis of Uncertainty 55

56 Analysis of Uncertainty Average S Reference point in Top Layer II Value in the model = 8% Lets use a minimum of 4% and a maximum of 15% with a triangular distribution

57 Analysis of Uncertainty Average Capillary Reference point in Top Layer III Value in the model = 79 psi Lets use a minimum of 60 psi and a maximum of 100 psi with a triangular distribution

58 Analysis of Uncertainty PDF for HB001 Cumulative Oil and Cumulative Water production at the rate of 3,000 blpd cap after 20 years. 58

59 Analysis of Uncertainty Such analysis can be performed for all wells at any rate and any number of years. There is a higher probability of acceptance of the ideas for rate increase by the management, if we show that: We are aware of the uncertainties associated with our analysis. Uncertainties are being accounted for in our decision making process. 59