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 optimization, and the ensemble Kalman filter have been tried in the oil industry, 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 that use probability models to estimate the probability distribution of promising solutions, and 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 optimization algorithm (BOA), which is a multivariate EDA employing Bayesian networks for modeling 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 the 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 show results of the EDA-BOA algorithm on two historymatching problems. First, we tune the algorithm, demonstrate convergence speed, and search diversity on the PUNQ-S3 synthetic case. Second, 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. MethodologyEstimation of Distribution Algorithms. Stochastic search algorithms, such as genetic and evolutionary algorithms, exploit knowledge of the distribution of good solutions, amongst those already visited, in order to wisely select new points in the search space to evaluate. In the case of genetic algorithms, this knowledge is stored implicitly in the current population. It is exploited through the application of crossover and mutation operators to the solutions in this population, a process which, it is hoped, will lead to the generation of improved solutions.The success of genetic algorithms is sometimes attributed to the so-called building block hypothesis (Goldberg 1989), whereby it is conjectured that the genetic algorithm efficiently identifies and recombines building blocks (i.e., solution components, or schemata) with above-average fitness. However, in practice, genetic operators often break such partial solutions, especially when these schemata are large, spread widely across the solution, or when operators such as uniform crossover are used.This raises the possibility of an alternative approach: one can attempt to explicitly identify high-quality building blocks and

A novel multi-objective estimation of distribution algorithm for solving gas lift allocation problem

“…It should be pointed out that in the field of petroleum engineering, very few works have ever employed any variant of the estimation of distribution algorithms. For instance, Abdollahzadeh et al (2013) utilized an EDA-BOA (Bayesian Optimization Algorithm) for history matching. To the best of the authors' knowledge, there exists no study on applying any multi-objective EDA in the literature of petroleum engineering.…”

Feature selection for reservoir characterisation by Bayesian network

“…In petroleum industry, BN is used to assess situations and conditions probabilistically, e.g. in downstream it is used in circulation monitoring system (Mansure et al, 1999); safety instrumentation and risk reduction at wellsite (Kannan, 2006); identifying candidate wells for gel-polymer treatment (Ghoraishy et al, 2008); drilling industry (Al-yami and Schubert, 2012;Al-Yami et al, 2010;Rajaieyamchee and Bratvold, 2009); production issues and history matching (Abdollahzadeh et al, 2011;Hermann et al, 2011;Khaz'ali et al, 2011); completion (Al-yami et al, 2011); and Enhanced Oil Recovery (EOR) (Zerafat et al, 2011) There are some publications of application of BN in upstream, specifically in basin analysis from economical evaluation of prospects (Van Wees et al, 2008) to studying dependency relationships between geological features (Martinelli et al, 2011;Martinelli et al, 2013;Rasheva and Bratvold, 2011). In addition, there are two recently published papers in the upstream that have used BN in identifying effective logs, i.e.…”