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Bayesian Optimization Algorithm Applied to Uncertainty Quantification
Abdollahzadeh, Asaad (Heriot-Watt University) | Reynolds, Alan (Heriot-Watt University) | Christie, Mike (Heriot-Watt University) | Corne, David (Heriot-Watt University) | Davies, Brian (BP) | Williams, Glyn (BP)
Summary Prudent decision making in subsurface assets requires reservoir uncertainty quantification. In a typical uncertainty-quantification study, reservoir models must be updated using the observed response from the reservoir by a process known as history matching. This involves solving an inverse problem, finding reservoir models that produce, under simulation, a similar response to that of the real reservoir. However, this requires multiple expensive multiphase-flow simulations. Thus, uncertainty-quantification studies employ optimization techniques to find acceptable models to be used in prediction. Different optimization algorithms and search strategies are presented in the literature, but they are generally unsatisfactory because of slow convergence to the optimal regions of the global search space, and, more importantly, failure in finding multiple acceptable reservoir models. In this context, a new approach is offered by estimation-of-distribution algorithms (EDAs). EDAs are population-based algorithms that use models to estimate the probability distribution of promising solutions and then generate new candidate solutions. This paper explores the application of EDAs, including univariate and multivariate models. We discuss two histogram-based univariate models and one multivariate model, the Bayesian optimization algorithm (BOA), which employs Bayesian networks for modeling. By considering possible interactions between variables and exploiting explicitly stored knowledge of such interactions, EDAs can accelerate the search process while preserving search diversity. Unlike most existing approaches applied to uncertainty quantification, the Bayesian network allows the BOA to build solutions using flexible rules learned from the models obtained, rather than fixed rules, leading to better solutions and improved convergence. The BOA is naturally suited to finding good solutions in complex high-dimensional spaces, such as those typical in reservoir-uncertainty quantification. We demonstrate the effectiveness of EDA by applying the well-known synthetic PUNQ-S3 case with multiple wells. This allows us to verify the methodology in a well-controlled case. Results show better estimation of uncertainty when compared with some other traditional population-based algorithms.
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- Overview > Innovation (0.48)
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- North America > United States > Texas > Permian Basin > Yeso Formation (0.99)
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- Reservoir Description and Dynamics > Reservoir Simulation > History matching (1.00)
- Reservoir Description and Dynamics > Reservoir Simulation > Evaluation of uncertainties (1.00)
- Management > Risk Management and Decision-Making > Risk, uncertainty, and risk assessment (1.00)
- Data Science & Engineering Analytics > Information Management and Systems > Artificial intelligence (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Search (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Optimization (1.00)
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On Population Diversity Measures of the Evolutionary Algorithms used in History Matching
Abdollahzadeh, Asaad (Heriot-Watt University) | Reynolds, Alan (Heriot-Watt University) | Christie, Mike (Heriot-Watt University) | Corne, David (Heriot-Watt University) | Williams, Glyn (BP) | Davies, Brian (BP)
Abstract In history matching, the aim is to generate multiple good-enough history-matched models with a limited number of simulations which will be used to efficiently predict reservoir performance. History matching is the process of the conditioning reservoir model to the observation data; 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 algorithm's control parameters result in different levels of diversity. These behaviours vary from explorative to exploitative. The need to measure population diversity arises from two bases. On the 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 the objective function evaluations in history matching are computationally expensive, algorithms with fewer total number of reservoir simulations in result of a better convergence are much more favourable. Maintaining population'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 reservoir simulation model, PUNQ-S3, as well as on a real North Sea model with multiple wells. We demonstrate that introduced population diversity measures provide efficient criteria for tuning the control parameters of the population-based evolutionary algorithms as well as performance comparison of the different algorithms used in history matching.
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