Fast Multiscale Reservoir Simulations With POD-DEIM Model Reduction

Yang, Yanfang; Ghasemi, Mohammadreza; Gildin, Eduardo; Efendiev, Yalchin; Calo, Victor M.

doi:10.2118/173271-pa

Cited by 54 publications

(21 citation statements)

References 29 publications

(34 reference statements)

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“…Model reduction by projection using POD modes is easy to implement. The spatial orthogonal POD modes are computed from snapshot data collected from numerical simulator or experiments [18,26], which is called "training step" in reservoir simulation and depends on several runs of a high fidelity model. The method selects the dominant modes that have strong impact on the solution by the rank of energy level.…”

Section: Of 22mentioning

confidence: 99%

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Data-Driven Model Reduction for Coupled Flow and Geomechanics Based on DMD Methods

Bao

Gildin

Narasingam

et al. 2019

Fluids

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Learning reservoir flow dynamics is of primary importance in creating robust predictive models for reservoir management including hydraulic fracturing processes. Physics-based models are to a certain extent exact, but they entail heavy computational infrastructure for simulating a wide variety of parameters and production scenarios. Reduced-order models offer computational advantages without compromising solution accuracy, especially if they can assimilate large volumes of production data without having to reconstruct the original model (data-driven models). Dynamic mode decomposition (DMD) entails the extraction of relevant spatial structure (modes) based on data (snapshots) that can be used to predict the behavior of reservoir fluid flow in porous media. In this paper, we will further enhance the application of the DMD, by introducing sparse DMD and local DMD. The former is particularly useful when there is a limited number of sparse measurements as in the case of reservoir simulation, and the latter can improve the accuracy of developed DMD models when the process dynamics show a moving boundary behavior like hydraulic fracturing. For demonstration purposes, we first show the methodology applied to (flow only) single- and two-phase reservoir models using the SPE10 benchmark. Both online and offline processes will be used for evaluation. We observe that we only require a few DMD modes, which are determined by the sparse DMD structure, to capture the behavior of the reservoir models. Then, we applied the local DMDc for creating a proxy for application in a hydraulic fracturing process. We also assessed the trade-offs between problem size and computational time for each reservoir model. The novelty of our method is the application of sparse DMD and local DMDc, which is a data-driven technique for fast and accurate simulations.

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Section: Of 22mentioning

confidence: 99%

“…Mixed formulation for the two-phase flow. In this paper, we use for the two-phase flow system a mixed formulation of the equation [26]. Previous works have demonstrated that it gives more stable computations, especially after applying the projection matrices.…”

Section: Multi-phase Flow Problemmentioning

confidence: 99%

Data-Driven Model Reduction for Coupled Flow and Geomechanics Based on DMD Methods

Bao

Gildin

Narasingam

et al. 2019

Fluids

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“…A constraint reduction based on POD-TPWL was present in [34]. In [11,35], POD-DEIM model reduction was used to solve a two-phase flow problem with gravity. However, these methods can only deal with cases that the variation in inputs is within a certain range, i.e., the offline procedure should be able to anticipate almost all the the dynamics of the online system.…”

Section: Of 21mentioning

confidence: 99%

“…The pressure equation is solved by mixed finite element method, see [35,44] which produces mass conservative velocity field, and the saturation equation is solved by finite volume method.…”

Section: Single-phase Flowmentioning

confidence: 99%

Online Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media

2016

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Abstract:We propose an online adaptive local-global POD-DEIM model reduction method for flows in heterogeneous porous media. The main idea of the proposed method is to use local online indicators to decide on the global update, which is performed via reduced cost local multiscale basis functions. This unique local-global online combination allows (1) developing local indicators that are used for both local and global updates (2) computing global online modes via local multiscale basis functions. The multiscale basis functions consist of offline and some online local basis functions. The approach used for constructing a global reduced system is based on Proper Orthogonal Decomposition (POD) Galerkin projection. The nonlinearities are approximated by the Discrete Empirical Interpolation Method (DEIM). The online adaption is performed by incorporating new data, which become available at the online stage. Once the criterion for updates is satisfied, we adapt the reduced system online by changing the POD subspace and the DEIM approximation of the nonlinear functions. The main contribution of the paper is that the criterion for adaption and the construction of the global online modes are based on local error indicators and local multiscale basis function which can be cheaply computed. Since the adaption is performed infrequently, the new methodology does not add significant computational overhead associated with when and how to adapt the reduced basis. Our approach is particularly useful for situations where it is desired to solve the reduced system for inputs or controls that result in a solution outside the span of the snapshots generated in the offline stage. Our method also offers an alternative of constructing a robust reduced system even if a potential initial poor choice of snapshots is used. Applications to single-phase and two-phase flow problems demonstrate the efficiency of our method.

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“…For large scale dynamical system, global reduced order models adopting Proper Orthogonal Decomposition method, Krylov subspace projection method, etc, are proposed to approximate the state-space problems. Though both local and global model reduction techniques have been extensively applied in many problems, reduced order models may have complicated forms in the linear case, not mentioning in nonlinear settings [25,4,8,46].Recently, deep learning has attracted growing attention in a rich class of applications. It has gained revolutionary results in image, speech, and text recognition [35,31,29].…”

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confidence: 99%

Efficient deep learning techniques for multiphase flow simulation in heterogeneous porousc media

Wang

Lin

2020

Journal of Computational Physics

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We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete systems and can be served as efficient alternatives to the system solvers at the full order. In particular, for the flow problem, we design a network with convolutional and locally connected layers to perform model reductions. Moreover, we employ a custom loss function to impose local mass conservation constraints. This helps to preserve the physical property of velocity solution which we are interested in learning. For the saturation problem, we propose a residual type of network to approximate the dynamics. Our main contribution here is the design of custom sparsely connected layers which take into account the inherent sparse interaction between the input and output. After training, the approximated feed-forward map can be applied iteratively to predict solutions in the long range. Our trained networks, especially in two-phase flow where the maps are nonlinear, show their great potential in accurately approximating the underlying physical system and improvement in computational efficiency. Some numerical experiments are performed and discussed to demonstrate the performance of our proposed techniques. IntroductionVarious physical phenomena in engineering applications are described by flow and transport problem in porous media, including reservoir engineering, climate dynamics, material science and so on. The underlying problems naturally exhibit heterogeneities covering from large physical scales down to micro-scales. Numerical simulations for these problems are challenging due to a rich class of length scales and potential uncertainties. In the past decades, numerous model reduction techniques and multiscale methods are proposed to design alternative models with great computational efficiency as well as desired accuracy. Local model reduction techniques typically involve building representations of underlying heterogeneity using some basis functions or effective coarse grid properties, and then constructing a form of the coarse level ]. For large scale dynamical system, global reduced order models adopting Proper Orthogonal Decomposition method, Krylov subspace projection method, etc, are proposed to approximate the state-space problems. Though both local and global model reduction techniques have been extensively applied in many problems, reduced order models may have complicated forms in the linear case, not mentioning in nonlinear settings [25,4,8,46].Recently, deep learning has attracted growing attention in a rich class of applications. It has gained revolutionary results in image, speech, and text recognition [35,31,29]. The potential of deep neural networks lies in their great capacity in approximating high-dimensional nonlinear maps. There are extensive efforts devoted to learning the expressivity of deep neural nets theoretically, just to mention a few [21,32,20,42,38], ...

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Fast Multiscale Reservoir Simulations With POD-DEIM Model Reduction

Cited by 54 publications

References 29 publications

Data-Driven Model Reduction for Coupled Flow and Geomechanics Based on DMD Methods

Data-Driven Model Reduction for Coupled Flow and Geomechanics Based on DMD Methods

Online Adaptive Local-Global Model Reduction for Flows in Heterogeneous Porous Media

Efficient deep learning techniques for multiphase flow simulation in heterogeneous porousc media

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