Block-preconditioned Krylov Methods for Coupled Multiphase Reservoir Flow and Geomechanics

Klevtsov, Sergey; Castelletto, Nicola; White, Joshua A.

doi:10.3997/2214-4609.201601900

Cited by 7 publications

(5 citation statements)

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“…In order to improve the efficiency of the solution of the system of equations ( 1), an advanced linear solver strategy is required. In White et al (2016), a fixed-stress split concept is used to construct a block-partitioned preconditioner for poromechanics, which was extended for coupled multiphase flow and mechanics in Klevtsov et al (2016). Here we employ the first stage of this approach to construct a preconditioner.…”

Section: Linear Solversmentioning

confidence: 99%

“…In White et al (2016), the authors employ a fixed-stress splitting concept in a sparse approximation of the Schur complement in order to obtain a blockpreconditioned solution strategy. Later this approach was combined with a constrained pressure residual (CPR) preconditioner to construct a robust and effective solution strategy for coupled multiphase flow and mechanics (Klevtsov et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

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A Collocated Finite Volume Scheme for High-Performance Simulation of Induced Seismicity in Geo-Energy Applications

Novikov

Voskov

Khait

et al. 2021

SPE Reservoir Simulation Conference

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We develop a collocated Finite Volume Method (FVM) to study induced seismicity as a result of pore pressure fluctuations. A discrete system is obtained based on a fully-implicit coupled description of flow, elastic deformation, and contact mechanics at fault surfaces on a fully unstructured mesh. The cell-centered collocated scheme leads to convenient integration of the different physical equations, as the unknowns share the same discrete locations on the mesh. Additionally, a multi-point flux approximation is formulated in a general procedure to treat heterogeneity, anisotropy, and cross-derivative terms for both flow and mechanics equations. The resulting system, though flexible and accurate, can lead to excessive computational costs for field-relevant applications. To resolve this limitation, a scalable parallel solution algorithm is developed and presented. Several proof-of-concept numerical tests, including benchmark studies with analytical solutions, are investigated. It is found that the presented method is indeed accurate, stable and efficient; and as such promising for accurate and efficient simulation of induced seismicity.

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Section: Linear Solversmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Collocated Finite Volume Scheme for High-Performance Simulation of Induced Seismicity in Geo-Energy Applications

Novikov

Voskov

Khait

et al. 2021

SPE Reservoir Simulation Conference

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“…Remark 5.3. An algebraic generalization of the fixed-stress approximation was proposed in [83] based on a row-sum lumping (RSL) strategy. Using a probing vector e = {1, .…”

Section: Mechanics / Flow Partitioningmentioning

confidence: 99%

A two-stage preconditioner for multiphase poromechanics in reservoir simulation

White

Castelletto

Klevtsov

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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Many applications involving porous media-notably reservoir engineering and geologic applications-involve tight coupling between multiphase fluid flow, transport, and poromechanical deformation. While numerical models for these processes have become commonplace in research and industry, the poor scalability of existing solution algorithms has limited the size and resolution of models that may be practically solved. In this work, we propose a two-stage Newton-Krylov solution algorithm to address this shortfall. The proposed solver exhibits rapid convergence, good parallel scalability, and is robust in the presence of highly heterogeneous material properties. The key to success of the solver is a block-preconditioning strategy that breaks the fully-coupled system of mass and momentum balance equations into simpler sub-problems that may be readily addressed using targeted algebraic methods. Numerical results are presented to illustrate the performance of the solver on challenging benchmark problems.

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“…The results obtained by FI strategy are shown coupled geomechanical problems requires sophisticated linear solvers [64], and the choice of efficient solvers for large-scale problems is limited. For the following comparison, we employ our in-house iterative linear solver [32], which allows us to deal with the coupled problem in a fully implicit manner and enables a "fair" comparison of the FI and SI approaches within one platform.…”

Section: Water Flooding Problemmentioning

confidence: 99%

“…Since the nonlinearity in the problem is quite mild, the FI method requires 1-2 Newton iterations per time step to achieve convergence, and the overall performance of the FI scheme depends strongly on linear solver capabilities. Here, we employ a special-purpose multi-stage linear solver that exhibits robust and scalable performance; the details are described elsewhere [32]. On the other hand, the overall performance of the SI strategy depends strongly on the number of outer iterations (i.e., the number of times we solve a flow problem followed by a mechanics problem), which is quite sensitive to the coupling strength.…”

Section: Water Flooding Problemmentioning

confidence: 99%

Unified thermo-compositional-mechanical framework for reservoir simulation

et al. 2018

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We present a reservoir simulation framework for coupled thermal-compositional-mechanics processes. We use finite-volume methods to discretize the mass and energy conservation equations and finite-element methods for the mechanics problem. We use the first-order backward Euler for time. We solve the resulting set of nonlinear algebraic equations using fully implicit (FI) and sequential-implicit (SI) solution schemes. The FI approach is attractive for general-purpose simulation due to its unconditional stability. However, the FI method requires the development of a complex thermo-compositionalmechanics framework for the nonlinear problems of interest, and that includes the construction of the full Jacobian matrix for the coupled multi-physics discrete system of equations. On the other hand, SI-based solution schemes allow for relatively fast development because different simulation modules can be coupled more easily. The challenge with SI schemes is that the nonlinear convergence rate depends strongly on the coupling strength across the physical mechanisms and on the details of the sequential updating strategy across the different physics modules. The flexible automatic differentiation-based framework described here allows for detailed assessment of the robustness and computational efficiency of different coupling schemes for a wide range of multi-physics subsurface problems.

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Block-preconditioned Krylov Methods for Coupled Multiphase Reservoir Flow and Geomechanics

Cited by 7 publications

References 0 publications

A Collocated Finite Volume Scheme for High-Performance Simulation of Induced Seismicity in Geo-Energy Applications

A Collocated Finite Volume Scheme for High-Performance Simulation of Induced Seismicity in Geo-Energy Applications

A two-stage preconditioner for multiphase poromechanics in reservoir simulation

Unified thermo-compositional-mechanical framework for reservoir simulation

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