Search citation statements
Paper Sections
Citation Types
Year Published
Publication Types
Relationship
Authors
Journals
Uncertainty quantification of reservoirs with multiple geological concepts and robust optimization are key technologies for oil/gas field development planning, which require properly characterizing joint distribution of model parameters and/or production forecasts after conditioning to historical production data. In this work, an ensemble of conditional realizations is generated by a multi-realization history-matching (MHM) workflow. The posterior probability-density-function (PDF) of model parameters and/or production forecasts is non-Gaussian and we approximate it by a Gaussian-mixture-model (GMM) using an expectation-maximization (EM) algorithm. This paper first discusses major limitations of the traditional EM algorithm--not robust and converging to suboptimal solutions. We develop a two-loop EM algorithm (EM-EVD-TL) using the compact form of eigenvalue decomposition (EVD) and propose new strategies to overcome these limitations: (1) Reduce the dimension of a Gaussian component if its covariance matrix becomes singular; (2) introduce an inner EM-loop in which only the diagonal matrix in EVD of the covariance matrix is updated. The first strategy improves the stability and convergence of the EM algorithm in dealing with degeneration of Gaussian components. The second strategy reduces the computational cost and further improves the convergence rate. The proposed EM-EVD-TL algorithm was validated on an analytical testing example, and its performance is compared against the single-loop, traditional EM algorithms which use either Cholesky-decomposition (EM-CD) or EVD (EM-EVD). An ensemble of conditional realizations is generated from sampling the actual PDF using the Markov-Chain-Monte-Carlo (MCMC) approach. For the analytical example, the GMMs approximated by three EM algorithms are very close to the actual distribution with negligible difference. Finally, we applied the proposed EM-EVD-TL algorithm to realistic history matching problems with different number of uncertainty parameters and production forecasts. We first generate an ensemble of conditional realizations using either MCMC method or distributed Gauss-Newton (DGN) optimization method. Then, we construct GMMs using different EM algorithms by fitting the conditional realizations, starting from different initial configurations and settings. Our numerical results confirm that the proposed EM-EVD and EM-EVD-TL algorithms performs robustly. In contrast, the traditional EM-CD algorithm without regularization fails to converge for most testing cases. The EM-EVD-TL algorithm converges faster to better solutions than the EM-CD algorithm. The proposed two-loop EM-EVD-TL algorithm has many potential applications and thus helps make better decisions: (1) Close gaps between theoretical formulations of history matching and real applications; (2) characterize posterior distribution of reservoir models having multiple geological concepts or categories; (3) select high-quality P10-P50-P90 representative models; (4) reparametrize gridblock-based properties; and (5) conduct robust well-location and well-control optimization (WLO/WCO) under uncertainty, e.g., through seamless integration of EM-GMM with our advanced multi-objective optimization techniques.
Uncertainty quantification of reservoirs with multiple geological concepts and robust optimization are key technologies for oil/gas field development planning, which require properly characterizing joint distribution of model parameters and/or production forecasts after conditioning to historical production data. In this work, an ensemble of conditional realizations is generated by a multi-realization history-matching (MHM) workflow. The posterior probability-density-function (PDF) of model parameters and/or production forecasts is non-Gaussian and we approximate it by a Gaussian-mixture-model (GMM) using an expectation-maximization (EM) algorithm. This paper first discusses major limitations of the traditional EM algorithm--not robust and converging to suboptimal solutions. We develop a two-loop EM algorithm (EM-EVD-TL) using the compact form of eigenvalue decomposition (EVD) and propose new strategies to overcome these limitations: (1) Reduce the dimension of a Gaussian component if its covariance matrix becomes singular; (2) introduce an inner EM-loop in which only the diagonal matrix in EVD of the covariance matrix is updated. The first strategy improves the stability and convergence of the EM algorithm in dealing with degeneration of Gaussian components. The second strategy reduces the computational cost and further improves the convergence rate. The proposed EM-EVD-TL algorithm was validated on an analytical testing example, and its performance is compared against the single-loop, traditional EM algorithms which use either Cholesky-decomposition (EM-CD) or EVD (EM-EVD). An ensemble of conditional realizations is generated from sampling the actual PDF using the Markov-Chain-Monte-Carlo (MCMC) approach. For the analytical example, the GMMs approximated by three EM algorithms are very close to the actual distribution with negligible difference. Finally, we applied the proposed EM-EVD-TL algorithm to realistic history matching problems with different number of uncertainty parameters and production forecasts. We first generate an ensemble of conditional realizations using either MCMC method or distributed Gauss-Newton (DGN) optimization method. Then, we construct GMMs using different EM algorithms by fitting the conditional realizations, starting from different initial configurations and settings. Our numerical results confirm that the proposed EM-EVD and EM-EVD-TL algorithms performs robustly. In contrast, the traditional EM-CD algorithm without regularization fails to converge for most testing cases. The EM-EVD-TL algorithm converges faster to better solutions than the EM-CD algorithm. The proposed two-loop EM-EVD-TL algorithm has many potential applications and thus helps make better decisions: (1) Close gaps between theoretical formulations of history matching and real applications; (2) characterize posterior distribution of reservoir models having multiple geological concepts or categories; (3) select high-quality P10-P50-P90 representative models; (4) reparametrize gridblock-based properties; and (5) conduct robust well-location and well-control optimization (WLO/WCO) under uncertainty, e.g., through seamless integration of EM-GMM with our advanced multi-objective optimization techniques.
This paper addresses the challenge of optimizing subsurface hydrogen storage in porous media, a crucial component for advancing energy transition. The multifaceted nature of this challenge stems from the complex physics governing the process, coupled with operational limitations, and subsurface geological uncertainties. We apply a stochastic gradient-based optimization method with novel deep-learning acceleration components, tailored to maximize the efficiency of hydrogen storage by tuning well locations while honoring operational constraints. The key objective of optimization is to maximize the amount of recoverable hydrogen while maintaining operational constraints. We adopt a robust optimization approach that maximizes the mean objective function over a set of realizations representing subsurface uncertainty. The objective function, defined as the hydrogen deliverability index, is calculated using a compositional reservoir simulator with high-resolution grids to minimize numerical dispersion. Our approach leverages a deep-learning-accelerated-gradient (DLAG) method alongside these simulations. This method is applied to the Brugge field case study, which is divided into two distinct optimization scenarios. In the first case, we evaluate the effectiveness of the optimization method with only one subsurface realization, optimizing the placement of eight storage wells and comparing outcomes with and without the application of DLAG. In the second case, we extend the analysis to include five different subsurface realizations and impose specific location constraints on each of the storage wells to optimize their placement. In the first case, the application of the DLAG method showed a clear advantage over the non-DLAG approach, resulting in faster convergence. The optimization of hydrogen storage well locations in the Brugge field model yielded notable improvements in storage efficiency, demonstrating the practicality and effectiveness of our approach.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.