Coevolution of Simulator Proxies and Sampling Strategies for - - PowerPoint PPT Presentation

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

IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009

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

• In the petroleum business, reservoir models are used to

estimate hydrocarbon reserve, and help making production management decisions.

Reservoir Modeling

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.

IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009

History Matching Process

History Match Forecast With Uncertainty Geological model created with geological data Select a set of reservoir parameter values to run computer simulations Select models with simulation outputs that best match production data Forecasting future production

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

Experiment (DOE)

– Plackett-Burman – Central composite – D-optimal design – Uniform design.

• Model training

methods:

– Kirging – Neural network – Genetic programming – Splines

IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009

A Competitive Co-evolution System

• Reservoir Samples:

– Evolved by a GA – An individual is a vector

• f 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.

IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009

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.

IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009

System Flow

IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009

Case Study

• 4

Falut_A_B 2 1 XPERM

• 2

ZPERM_D 0.5 0.1 Krw_D

• 2

ZPERM_C 0.5 0.1 Krw_C

• 2

ZPERM_B 0.5 0.1 Krw_B

• 2

ZPERM_A 0.7 0.3 Krw_A max max min min name name max max min min name name

Reservoir Descriptive Parameters

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

GP with test-bank GA with the 3 designed genetic

• perators

f GP GA with the 3 designed genetic

• perators

e GP with test-bank GA with point crossover & bit mutation d GP GA with point crossover & bit mutation c GP with test-bank Random Sampling b GP Random sampling a Proxies Training Proxies Training Samples Selection Samples Selection Setup Setup

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 GP with test bank

IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 21, 2009

GA with 3 Designed Genetic Operators

GP GP with test bank

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.