A Multipoint Flux Mixed Finite Element Method for Darcy–Forchheimer Incompressible Miscible Displacement Problem

Xu, Wenwen; Dong, Liang; Rui, Hongxing; Li, Xindong

doi:10.1007/s10915-019-01103-0

Cited by 5 publications

(3 citation statements)

References 23 publications

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“…A backward Euler scheme was proposed for the time discretization. The error estimates of the three variables were obtained through strict theoretical derivation, and the results were consistent with the convergence order in a previous incompressible article [15]. In the future, we will study another compressible miscible displacement problem, in which the velocity and pressure are controlled by the nonlinear Darcy-Forchheimer equation, since the non-Darcy and coupling problems actually exist in high-water cut reservoirs and areas with a high flow velocity around the well-bore.…”

Section: Discussionsupporting

confidence: 81%

“…The evolution of the invading fluid is presented in Figure 2. We found the flow was faster in the diagonal direction, which was reasonable and agreed with the simulation results in [15].…”

Section: Single Injection Single Production Casesupporting

confidence: 90%

“…This method was proposed in [13] for a slightly compressible flow in porous media. The authors in [14] considered a multipoint flux MFE method for a compressible Darcy-Forchheimer model, and it was presented again in [15] for an incompressible Darcy-Forchheimer miscible displacement problem. However, most realistic reservoirs are compressible.…”

Section: Introductionmentioning

confidence: 99%

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Multi-Point Flux MFE Decoupled Method for Compressible Miscible Displacement Problem

Guo

et al. 2023

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In this paper, a multi-point flux mixed-finite-element decoupled method was considered for the compressible miscible displacement problem. For this compressible problem, a fully discrete backward Euler scheme was proposed, in which the velocity and pressure equations were decoupled by a multi-point flux MFE method using BDM1 elements combined with a trapezoidal quadrature rule. The concentration equation was handled by a standard FE method. The error analysis for velocity, pressure, and concentration were rigorously derived. Numerical experiments to verify the convergence rates and simulate the miscible displacement problem of a water–oil system were presented.

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Section: Discussionsupporting

confidence: 81%

“…The evolution of the invading fluid is presented in Figure 2. We found the flow was faster in the diagonal direction, which was reasonable and agreed with the simulation results in [15].…”

Section: Single Injection Single Production Casesupporting

confidence: 90%