An implementation of mimetic finite difference method for fractured reservoirs using a fully implicit approach and discrete fracture models

Zhang, Na; Abushaikha, Ahmad

doi:10.1016/j.jcp.2021.110665

Cited by 21 publications

(2 citation statements)

References 59 publications

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“…where Ω E denotes the cell volume. The expression for the interface fluxes in equation ( 8) is all in all similar to that generated by a Mimetic finite difference discretization (see, for instance, [27,40]).…”

Section: Weak Formulationmentioning

confidence: 99%

Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements

Nardean¹,

Ferronato²,

Abushaikha³

2023

Preprint

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This work proposes an original preconditioner that couples the Constrained Pressure Residual (CPR) method with block preconditioning for the efficient solution of the linearized systems of equations arising from fully implicit multiphase flow models. This preconditioner, denoted as Block CPR (BCPR), is specifically designed for Lagrange multipliers-based flow models, such as those generated by Mixed Hybrid Finite Element (MHFE) approximations. An original MHFE-based formulation of the two-phase flow model is taken as a reference for the development of the BCPR preconditioner, in which the set of system unknowns comprises both element and face pressures, in addition to the cell saturations, resulting in a 3 × 3 block-structured Jacobian matrix with a 2 × 2 inner pressure problem. The CPR method is one of the most established techniques for reservoir simulations, but most research focused on solutions for Two-Point Flux Approximation (TPFA)-based discretizations that do not readily extend to our problem formulation. Therefore, we designed a dedicated two-stage strategy, inspired by the CPR algorithm, where a block preconditioner is used for the pressure part with the aim at exploiting the inner 2 × 2 structure. The proposed preconditioning framework is tested by an extensive experimentation, comprising both synthetic and realistic applications in Cartesian and non-Cartesian domains.

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Section: Weak Formulationmentioning

confidence: 99%

Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements

Nardean¹,

Ferronato²,

Abushaikha³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Its extension, the multi-point flux approximation (MPFA) variant, [5][6][7] is another popular strategy along with the mimetic finite difference (MFD) scheme, which has been recently used in a two-phase flow model in fractured media. 8 Nevertheless, the approximation accuracy in determining the fluid pressure and velocity, even on unstructured meshes with full tensor medium properties, and the continuity of the normal component of the fluxes through the interfaces of the grid, while honoring the mass conservation at the element level, 9,10 have made the MHFE an alternative robust approach. Despite a few drawbacks, such as the enlargement of the stencil or the breach of the discrete maximum principle, 11 MHFE and the pioneering nonhybridized version, the mixed finite element (MFE) method, have witnessed an increasing popularity in the last decade.…”

Section: Introductionmentioning

confidence: 99%

A block preconditioner for two‐phase flow in porous media by mixed hybrid finite elements

Nardean

Ferronato

Abushaikha

2021

Comp and Math Methods

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In this work, we present an original block preconditioner to improve the convergence of Krylov solvers for the simulation of two-phase flow in porous media. In our modeling approach, the set of coupled governing equations is addressed in a fully implicit fashion, where Darcy's law and mass conservation are discretized in an original way by combining the mixed hybrid finite element (MHFE) and the finite volume (FV) methods. The solution to the sequence of large-size nonsymmetric linearized systems of equations that stem during a full-transient simulation represents the most time and resource consuming task, thus motivating the need for efficient preconditioned Krylov solvers. The proposed preconditioner exploits the block structure of the Jacobian matrix while coping with the nonsymmetric nature of the individual blocks. Both academic and realistic applications have been used to challenge the preconditioner, allowing to point out its robustness, stability and overall computational efficiency.

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Numerical Simulation of Water-Flooding Reservoirs Considering Permeability Time Variation Base on Mimetic Finite Difference Method

Wang,

Zhang,

Sun

et al. 2023

Mechanisms and Machine Science

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An implementation of mimetic finite difference method for fractured reservoirs using a fully implicit approach and discrete fracture models

Cited by 21 publications

References 59 publications

Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements

Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements

A block preconditioner for two‐phase flow in porous media by mixed hybrid finite elements

Numerical Simulation of Water-Flooding Reservoirs Considering Permeability Time Variation Base on Mimetic Finite Difference Method

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