Estimation of distribution algorithms for reservoir history-matching optimisation

Reservoir modelling is widely used in the oil and gas industry to quantify the risk associated with alternative production scenarios. However, reservoir models themselves still contain a high level of uncertainty because of the typically very limited, sparse and multiscale field knowledge available. History-matching (HM) reduces this uncertainty by constraining the reservoir model to the available dynamic field data. History-matching is an example of a typical non-linear inverse problem which yields the existence of not one but multiple solutions, which all satisfy available data constraints. In inverse problem theory Monte Carlo methods are regarded as the most accurate methods for generating a family of problem solutions and capturing posterior distributions of model parameters by exhaustive exploration of parameter space. However these methods are very rarely applicable to HM problems because they are too time and cost consuming. While other stochastic inversion techniques have successfully overcome the runtime issue Monte Carlo methods have, none of them has provided a deliberate estimation of the posterior probabilities one would expect from Monte Carlo methods. This thesis introduces an innovative application of a member of a class of Estimation of Distribution Algorithms - a histogram-based Population-Based Incremental Learning algorithm, to the problem of reservoir history-matching optimisation. It is shown that while avoiding an exhaustive exploration of parameter space the proposed algorithm is capable of producing the approximations of the marginal posterior distributions of model parameters which can be interpreted as their uncertainty estimates. We also suggest a new extension of histogram-based PBIL for pair-wise conditional probabilities sampling. The developed extended version of the histogrambased PBIL is the first attempt to explicitly capture possible dependencies between reservoir model parameters and use them to perform conditional sampling of the solution space. None of the currently used algorithms and techniques for reservoir history-matching optimisation explicitly utilizes this dependency information