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**Compositional flow modeling using a multi-point flux mixed finite element method.**
*(English)*
Zbl 1395.65091

Summary: We present a general compositional formulation using multi-point flux mixed finite element (MFMFE) method on general hexahedral grids. The mixed finite element framework allows for local mass conservation, accurate flux approximation, and a more general treatment of boundary conditions. The multi-point flux inherent in MFMFE scheme allows the usage of a full permeability tensor. The proposed formulation is an extension of single and two-phase flow formulations presented by the second author and I. Yotov [SIAM J. Numer. Anal. 44, No. 5, 2082–2106 (2006; Zbl 1121.76040)] with similar convergence properties. Furthermore, the formulation allows for black oil, single-phase and multi-phase incompressible, slightly and fully compressible flow models utilizing the same design for different fluid systems. An accurate treatment of diffusive/dispersive fluxes owing to additional velocity degrees of freedom is also presented. The applications areas of interest include gas flooding, CO\(_2\) sequestration, contaminant removal, and
groundwater remediation.

### MSC:

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

76S05 | Flows in porous media; filtration; seepage |

86-08 | Computational methods for problems pertaining to geophysics |

### Keywords:

hexahedral grids; oil recovery; mixed finite element framework; gas flooding, CO\(_2\) sequestration; groundwater remediation### Citations:

Zbl 1121.76040
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\textit{G. Singh} and \textit{M. F. Wheeler}, Comput. Geosci. 20, No. 3, 421--435 (2016; Zbl 1395.65091)

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