Estimation of Distribution Algorithms Applied to History Matching

Abstract

The topic of automatically history-matched reservoir models has seen much research activity in recent years. History matching is an example of an inverse problem, and there is significant, active research on inverse problems in many other scientific and engineering areas. While many techniques from other fields such as Genetic Algorithms, Evolutionary Strategies, Differential Evolution, Particle Swarm Optimisation, and the Ensemble Kalman Filter have been tried in the oil industry, some more recent and effective ideas have yet to be tested. One of these relatively untested ideas is a class of algorithms known as Estimation of Distribution Algorithms (EDAs). EDAs are population-based algorithms, which use probability models to estimate the probability distribution of promising solutions, then to generate new candidate solutions. EDAs have been shown to be very efficient in very complex high-dimensional problems. An example of a state of the art EDA is the Bayesian Optimisation Algorithm (BOA), which is a multivariate EDA employing Bayesian Networks for modelling the relationships between good solutions. The use of a Bayesian Network leads to relatively fast convergence as well as high diversity in the matched models. Given relatively limited number of reservoir simulations used in history matching, EDA-BOA offers the promise of high quality history matches with a fast convergence rate. In this paper, we introduce EDAs and describe BOA in detail. We shows results of EDA-BOA algorithm on two history matching problems. First, we tune the algorithm and demonstrate convergence speed and search diversity on the PUNQ-S3 synthetic case. Secondly, we apply the algorithm to a real, North Sea, turbidite field with multiple wells. In both examples, we show improvements in performance over traditional population-based algorithms.

Estimation of the water–oil–gas relative permeability curve from immiscible WAG coreflood experiments using the cubic B-spline model

“…The estimated result is not only complete but also highly precise (Daoud and Velasquez 2006;Barroeta and Thompson 2010). In recent decades, a variety of numerical inversion methods have been developed to implicitly estimate the relative permeability curve for water-oil or oilgas systems (Chen et al 2008;Li et al 2009;Eydinov et al 2009;Wang et al 2010;Wang and Li 2011;Li and Yang 2011;Abdollahzadeh et al 2011;Zhang and Yang 2013;Xu et al 2013;Miao et al 2014).…”

Fundamental controls on fluid flow in carbonates: current workflows to emerging technologies

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On Population Diversity Measures of the Evolutionary Algorithms used in History Matching

“…In the current study, we used slightly different parameterization for PUNQ-S3 than what we used previously (Abdollahzadeh et al 2011a). We took 38 unknown variables using the given geological description and channel properties.…”