On Population Diversity Measures of the Evolutionary Algorithms Used in History Matching (SPE 154488)

In history-matching the aim is to generate multiple good-enough history-matched models in limited number of simulations which will be used to efficiently predict reservoir performance. History-matching is the process of the conditioning reservoir model on the observation data which is mathematically ill-posed, inverse problem and has no unique solution and several good solutions may occur. Numerous evolutionary algorithms are applied to history-matching which operate differently in terms of population diversity in the search space throughout the evolution. Even different flavours of an algorithm behave differently and different values of an algorithmC"s control parameters result in different value of diversity measure. These behaviours vary from explorative to exploitative. The need to measure population diversity arises from two bases. On one hand maintaining population diversity in evolutionary algorithms is essential to detect and sample good history-matched ensemble models in parameter search space. On the other hand, since objective function evaluations in history matching are expensive, algorithms with fewer total number of reservoir simulations in result of a better convergence are much more favourable. Maintaining populationC"s diversity is crucial for sampling algorithm to avoid premature convergence toward local optima and achieve a better match quality. In this paper, we introduce and use two measures of the population diversity in both genotypic and phenotypic space to monitor and compare performance of the algorithms. These measures include an entropy-based diversity from the genotypic measures and a moment of inertia based diversity from the phenotypic measures. The approach has been illustrated on a synthetic model, PUNQ-S3, as well as on a real North Sea model. We demonstrate that introduced diversity measures provide efficient criteria for tuning the control parameters of the algorithms as well as performance comparison of the different algorithms used in history matching.