Estimation of distribution algorithms applied to history matching

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. Copyright 2011, Society of Petroleum Engineers.