Gaussian-based estimation of distribution algorithms for history matching

Numerical reservoir models are used to predict, optimise and improve production performance of the oil and gas reservoirs. History matching is required to calibrate reservoir models to dynamic behaviour of the reservoir. On the one hand, history-matching does not have a unique solution and multiple models can fit observation data, on the other hand, history-matching is a tedious and time-consuming trial and error process as it involves numerous reservoir simulation runs. Modern history matching techniques use optimisation algorithms aim at providing a set of good fitting models in an efficient time.

Many optimisation algorithms are applied in history-matching. Of them, Evolutionary Algorithms (EAs), inspired by natural evolution, do not use gradient information from the optimisation problem and only require the fitness function, usually defined as the sum of squares root deviation of model response from the observation data. Estimation of distribution algorithms (EDAs) are a novel class of EAs developed as a natural alternative to genetic algorithms in the last decade. To date, many EDAs are introduced which differ in the probabilistic model that guides the search process. Most of the EDAs are designed for discrete problems and require discretisation of search space when used for continuous problems, e.g. in history matching. In some cases, discretization error can be significant and deteriorate the search process.

Gaussian-based EDAs use characteristics of Gaussian distribution for multivariate continuous problems. i.e. they make use of mean and covariance matrix of the variables in the promising solutions to generate new solutions which fit better the observation data. In this paper, we introduce and for the first time apply four Gaussian-based EDAs to assisted history-matching of a standard synthetic case. We show our proposed algorithms may produce results more accurately and more efficiently for the continuous problems.