Two-phase water flooding simulations on dynamic adaptive octree grids with two-point nonlinear fluxes

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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“…where quantities Υ f,K and Υ L, f , also known as half transmissibility coefficients, are given by [93]…”

Section: Appendix a Tpfa Transmissibility Computationmentioning

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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“…(2.1) is discretized for every control volume, i.e., matrix and fracture. In the classical two-point flux approximation scheme [28], implemented in this work, the discrete system reads for every cell i:…”

Section: Fine-scale Discretized Systemmentioning

confidence: 99%

Multiscale Finite Volume Method for Discrete Fracture Modeling with Unstructured Grids

Bosma

Hajibeygi

Ţene

2017

Day 3 Wed, February 22, 2017

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A multiscale method for Discrete Fracture Modeling (DFM) using unstructured grids is developed. The fine-scale discrete system is obtained by imposing tetrahedron (triangular for 2D domains) shaped grid cells, while lower-dimensional fractures are imposed at the grid interfaces. The DFM approach is then used to describe the transmissibility coefficients for all the interfaces, including those with the lower-dimensional fractures. On this fine-scale discrete system, a new algebraic multiscale formulation is developed, which first imposes two sets of coarseand dual-coarse grids. The former grid is essential for conservative multiscale formulations, while the second one is used for the calculation of local multiscale basis functions. The coarse-scale partitioning of the fracture and matrix domains is flexible and totally independent. Moreover, the multiscale basis functions are constructed for both the matrix and fracture domains. By construction, the basis functions are a partition of unity. For 2D and 3D test cases, the performance of the multiscale method is systematically assessed. It is shown that the method (with no multiscale iterations) provides accurate results, even for complex fractured systems. The presented multiscale method is a promising framework for real-field application of DFM models.

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“…Most of the existing literature about nonlinear finite‐volume schemes focuses on linear elliptic equations. Only a few publications exist that consider multi‐phase flow in porous media . However, they do not account for compositional and nonisothermal effects.…”

Section: Introductionmentioning

confidence: 99%

“…Most of the existing literature about nonlinear finite-volume schemes focuses on linear elliptic equations. Only a few publications exist that consider multi-phase flow in porous media [31,32]. However, they do not account for compositional and nonisothermal effects.A main constituent of this work is the numerical analysis of accuracy and efficiency of a nonlinear finite-volume scheme for the nonisothermal two-phase two-component flow equations.…”

mentioning

confidence: 99%

Monotone nonlinear finite‐volume method for nonisothermal two‐phase two‐component flow in porous media

Schneider

Flemisch

Helmig

2016

Numerical Methods in Fluids

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Summary This article presents a new nonlinear finite‐volume scheme for the nonisothermal two‐phase two‐component flow equations in porous media. The face fluxes are approximated by a nonlinear two‐point flux approximation, where transmissibilities nonlinearly depend on primary variables. Thereby, we mainly follow the ideas proposed by Le Potier combined with a harmonic averaging point interpolation strategy for the approximation of arbitrary heterogeneous permeability fields on polygonal grids. The behavior of this interpolation strategy is analyzed, and its limitation for highly anisotropic permeability tensors is demonstrated. Moreover, the condition numbers of occurring matrices are compared with linear finite‐volume schemes. Additionally, the convergence behavior of iterative solvers is investigated. Finally, it is shown that the nonlinear scheme is more efficient than its linear counterpart. Copyright © 2016 John Wiley & Sons, Ltd.

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Two-phase water flooding simulations on dynamic adaptive octree grids with two-point nonlinear fluxes

Cited by 15 publications

References 20 publications

A two-stage preconditioner for multiphase poromechanics in reservoir simulation

A two-stage preconditioner for multiphase poromechanics in reservoir simulation

Multiscale Finite Volume Method for Discrete Fracture Modeling with Unstructured Grids

Monotone nonlinear finite‐volume method for nonisothermal two‐phase two‐component flow in porous media

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