Coevolution of Simulator Proxies and Sampling Strategies for Petroleum Reservoir Modeling

Transcription

1 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

2 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

3 Reservoir Modeling In the petroleum business, reservoir models are used to estimate hydrocarbon reserve, and help making production management decisions. Initial model is built using geological data: Well logs data Cores data Seismic data The model is updated using: Production data collected from the field.

4 History Matching Process History Match Geological model created with geological data Field Oil Production Rate Select a set of reservoir parameter values to run computer simulations Forecast With Uncertainty Select models with simulation outputs that best match production data Field Oil Cumulative Prod Historical Field Oil Prod. Rate 4.0 SBOPD Field Oil Prod. Rate FOPC - Millons of SBO Forecasting future production Historical Field Oil Cummulative Prod. Time - days

5 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 historymatched models has a high degree of uncertainty.

6 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.

7 Sampling Strategies and Simulator Proxies Training Methods Design of Experiment (DOE) Plackett-Burman Central composite D-optimal design Uniform design. Model training methods: Kirging Neural network Genetic programming Splines

8 A Competitive Co-evolution System Reservoir Samples: Evolved by a GA An individual is a vector of reservoir parameter values, on which computer simulation is performed The fitness of a sample is its ability to make the evolved proxies disagree with their prediction. Simulator proxies: Evolved by a GP An individual is a symbolic regression, which determines if a reservoir model is a good or bad match to the production data. The fitness of a proxy is its ability to predict the evolved samples correctly.

9 Enhanced Techniques GA Three genetic operators are designed to create samples that induce more disagreement among the GP simulator proxies. Attractor mutation Repeller mutation Average crossover GP A test-bank is used to temporary store GA evolved samples which are too difficult for the GP population to learn. These samples will be re-introduced to the GP training set in later cycles.

10 System Flow

11 Case Study Reservoir Descriptive Parameters name min max name min max Krw_A ZPERM_A -2 0 Krw_B ZPERM_B -2 0 Krw_C ZPERM_C -2 0 Krw_D ZPERM_D -2 0 XPERM 1 2 Falut_A_B simulation data obtained in a previous work were used to evaluate the robustness of the final proxies.

12 Experimental Setup Setup a Samples Selection Random sampling Proxies Training GP b c d e f Random Sampling GA with point crossover & bit mutation GA with point crossover & bit mutation GA with the 3 designed genetic operators GA with the 3 designed genetic operators GP with test-bank GP GP with test-bank GP GP with test-bank

13 Results In all 6 setups, a small number of reservoir samples (<= 40) were selected for GP to train simulator proxies.

14 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.

15 Random Sampling GP GP with test bank

16 GA with One Point Crossover & Point Mutation GP GP with test bank

17 GA with 3 Designed Genetic Operators GP GP with test bank

18 Simulation Data Sample Distribution The 10 parameter values are sampled evenly among the 5 ranges.

19 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 testbank to remove and re-introduce training data.

20 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.

21 Concluding Remarks Our case study shows that the competitive coevolutionary system is able to select a very small number of reservoir samples to construct highaccuracy 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 testbank technique helped mitigating the situation. We continue investigating test-bank and other fitness measures to improve the system performance.