Sequential Bayesian Optimization Coupled with Differential Evolution for Geological Well Testing

Abstract

Summary This paper presents a novel approach for updating the reservoir model from well test data. A sequential Bayesian optimization technique, i.e. Gaussian Process, is coupled with the Differential Evolution (DE) algorithm, for guided sampling from the parameter space. The Gaussian process assumes the simulation outputs are normally distributed, and aims at modelling the current model and misfit data to predict the best next sampling locations. The next samples are chosen by maximizing the expected improvement gained by sampling from a new location. Differential evolution is used in the maximization process of the expected improvement. This procedure is successfully tested in matching a noisy well test data from a multi-layered faulted reservoir model. The samples from multiple well-test simulations are pooled together, and the Markov chain Monte Carlo (McMC) techniques are used to estimate the posterior distributions over the parameter space. The computational cost of McMC process is reduced by implementing a bootstrap Multivariate Adaptive Regression Spline.