Coevolution of Simulator Proxies and Sampling Strategies for Petroleum Reservoir Modeling Tina Yu Memorial University of Newfoundland, Canada Dave Wilkinson Chevron Energy Technology Company, USA
Outline • Reservoir Modeling and History Matching • Sampling Strategy and Simulator Proxies • A Competitive Co-evolution Framework • Enhanced Techniques • Case Study • Experimental Setup • Results and Analysis • Conclusions and Future Work IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Reservoir Modeling • In the petroleum business, reservoir models are used to estimate hydrocarbon reserve, and help making production management decisions. Initial model is The model is built using updated using: geological data: •Production data • Well logs data collected from the • Cores data field. • Seismic data IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
History Matching Process Select a set of Geological model Select models reservoir parameter created with with values to run geological data simulation outputs computer simulations that best match History production data Forecast With Uncertainty Match Field Oil Production Rate 1400 6.0 Field Oil Cumulative Prod. 1200 5.0 1000 Historical Field Oil Prod. Rate 4.0 800 FOPC - Millons of SBO SBOPD 3.0 600 2.0 Forecasting 400 Field Oil Prod. Rate 1.0 200 future production 0 0.0 0 2000 4000 6000 8000 10000 Historical Field Oil Cummulative Prod. Time - days IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Challenges • Each reservoir simulation takes 2 to 10 hours to complete. • Only a small number of reservoir simulation runs are practically possible. • The reservoir history matching results are normally unsatisfactory. • Consequently, the forecast based on the history- matched models has a high degree of uncertainty. IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Objectives • Select a small number of informative reservoir models to conduct computer simulation. • The simulation data are used to train a good-quality simulator proxy. – This cheap proxy can replace computer simulator to evaluate a large number (millions) of reservoir models to identify more reservoir models that match the production data. – These larger number of good-matched models provide more reliable information about the reservoir and give more accurate forecast with a higher degree of certainty. IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Sampling Strategies and Simulator Proxies Training Methods • Design of • Model training Experiment (DOE) methods: – Plackett-Burman – Kirging – Central composite – Neural network – D-optimal design – Genetic programming – Uniform design. – Splines IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
A Competitive Co-evolution System • Simulator proxies: • Reservoir Samples: – Evolved by a GP – Evolved by a GA – An individual is a vector – An individual is a symbolic regression, of reservoir parameter which determines if a values, on which computer simulation is reservoir model is a good or bad match to performed the production data. – The fitness of a sample is its ability to make the – The fitness of a proxy is its ability to predict the evolved proxies evolved samples disagree with their correctly. prediction. IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Enhanced Techniques • GA • GP – Three genetic operators – A test-bank is used to are designed to create temporary store GA samples that induce evolved samples which more disagreement are too difficult for the among the GP simulator GP population to learn. proxies. – These samples will be • Attractor mutation re-introduced to the GP training set in later • Repeller mutation cycles. • Average crossover IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
System Flow IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Case Study Reservoir Descriptive Parameters name min max name min max name min max name min max Krw_A 0.3 0.7 ZPERM_A -2 0 Krw_B 0.1 0.5 ZPERM_B -2 0 Krw_C 0.1 0.5 ZPERM_C -2 0 Krw_D 0.1 0.5 ZPERM_D -2 0 XPERM 1 2 Falut_A_B -4 0 894 simulation data obtained in a previous work were used to evaluate the robustness of the final proxies. IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Experimental Setup Setup Setup Samples Selection Samples Selection Proxies Training Proxies Training a Random sampling GP b Random Sampling GP with test-bank GA with point crossover & bit c GP mutation GA with point crossover & bit d GP with test-bank mutation GA with the 3 designed genetic e GP operators GA with the 3 designed genetic f GP with test-bank operators IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Results • In all 6 setups, a small number of reservoir samples (<= 40) were selected for GP to train simulator proxies. IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Observations • GA is more intelligent than random search in selecting informative samples for GP to train more accurate simulator proxies on training data. • The 3 designed genetic operators are more effective in selecting difficult samples than the one-point crossover and point mutation for GP to train more accurate proxies on training data. • Using a test-bank to remove and re-introduce GA selected samples to the training set, GP has trained more robust proxies which generalize better on the simulation data. IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Random Sampling GP GP with test bank IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
GA with One Point Crossover & Point Mutation GP with test bank GP IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
GA with 3 Designed Genetic Operators GP with test bank GP IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Simulation Data Sample Distribution The 10 parameter values are sampled evenly among the 5 ranges. IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Observations • GA biases samples with boundary values (high and low), suggesting that they are difficult points and caused high-disagreement among proxy models. • Using these samples as training data, GP evolved proxies do not perform as well on simulation data. • This tendency of over-selecting samples with boundary values no longer exist when GP has a “test- bank” to remove and re-introduce training data. IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Discussions • With competitive co-evolution, the characteristics of samples and proxies impact each other’s evolutionary direction. • The two populations have “conspired” with each other to evolve simulator proxies that only work well on difficult samples but not sample with other values. • When these challenging samples were withdrawn from the training set temporary and re-introduced later, i.e. changing the order of GP learning, the over-sampling phenomenon no longer exist. IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
Concluding Remarks • Our case study shows that the competitive co- evolutionary system is able to select a very small number of reservoir samples to construct high- accuracy proxies. • The designed genetic operators have improved the system performance. • Although the evolved simulator proxies do not generalize very well on a different data set, the test- bank technique helped mitigating the situation. • We continue investigating test-bank and other fitness measures to improve the system performance. IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009
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