A Hybrid Modeling Approach to Production Control Optimization Using Dynamic Mode Decomposition

Abstract

Model-based field development planning and optimization often require computationally intensive reservoir simulations, where the models need to be run several times in the context of input uncertainty or seeking optimal results. Reduced Order Modeling (ROM) methods are a class of techniques that are applied to reservoir simulation to reduce model complexity and speed up computations, especially for large scale or complex models that may be quite useful for such optimization problems. While intrusive ROM methods (such as proper orthogonal decomposition (POD) and its extensions, trajectory piece-wise linearization (TPWL), Discrete Empirical Interpolation Method (DEIM) etc.) have been proposed for application to reservoir simulation problems, these remain inaccessible or unusable for a large number of practical applications that use commercial simulators. In this paper, we describe a novel application of a non-intrusive ROM method, namely dynamic mode decomposition (DMD). We specifically look at reducing the time complexity involved in well control optimization problem, using a variant of DMD called DMDc (DMD with control). We propose a workflow using a training dataset of the wells and predict the state solution (pressure and saturation) for a new set of bottomhole pressure profiles encountered during the optimization runs. We use a novel strategy to select the basis dimensions to prevent unstable solutions. Since the objective function of the optimization problem is usually based on fluid production profiles, we propose a strategy to predict the fluid production rates from the predicted states from DMDc using machine learning techniques. The features for this machine learning problem are designed based on the physics of fluid flow through well perforations, which result in very accurate rate predictions. We compare the proposed methodology using another variant of DMD called ioDMD (input-ouput DMD) for system identification to predict output production flow rates. The methodology is demonstrated on a benchmark case and a Gulf of Mexico deepwater field that shows significant time reduction in production control optimization problem with about 30 – 40 times speedup using the proposed DMDc workflow as compared to fine scale simulations, while preserving the accuracy of the solutions. The proposed "non-intrusive" method in this paper to reduce model complexity can substantially increase the range of application of ROM methods for practical field development and reservoir management.

Two-Step Predict and Correct Non-Intrusive Parametric Model Order Reduction for Changing Well Locations Using a Machine Learning Framework

“…Some of the non-intrusive methods that have been used for changing well controls are DMD [35], DMDc, and ioDMD [22]. For changing well locations, we propose a new non-intrusive PMOR technique that has been applied in [28,29] for problems that are time-independent or for steady-state systems.…”

“…Other methods were later implemented for this application of changing well controls, such as POD-Trajectory-based DEIM (TDEIM) [18], which is a combination of TPWL and DEIM techniques to utilize their benefits and avoid their shortcomings; bilinear approximation and quadratic bilinear formulation [19,20]; and the Gauss-Newton with Approximated Tensors (GNAT) method [21]. Recently, non-intrusive methods have been developed for a well-control optimization problem-namely, Dynamic Mode Decomposition with control (DMDc) and input-output DMD (ioDMD) in Reference [22].…”

Non-Intrusive Parametric Model Order Reduction With Error Correction Modeling for Changing Well Locations Using a Machine Learning Framework

“…Methods like POD-TPWL [11] are intrusive to some extent as it requires access to Jacobian and residual matrices, that is not easily available for commercial simulators and POD-DEIM [17] is highly intrusive to the source code. One of the non-intrusive methods that has been used for changing well controls is DMD [37] and DMDc [22]. We propose a new non-intrusive PMOR technique that has been applied in [29,28] for problems that are time independent or steady state systems.…”

“…Other methods were later implemented for this application of changing well controls, such as, POD -Trajectory based DEIM (TDEIM) [18] which is a combination of TPWL and DEIM techniques to utilize their benefits and avoid their shortcomings; bilinear approximation and quadratic bilinear formulation [19,20] and Gauss-Newton with Approximated Tensors (GNAT) method [21]. Recently, non-intrusive methods have been developed for well control optimization problem, namely Dynamic Mode Decomposition with control (DMDc) and input-output DMD (ioDMD) in [22].…”