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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Modeling flow in porous media with double porosity/permeability: A stabilized mixed formulation, error analysis, and numerical solutions
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Modeling flow in porous media with double porosity/permeability: A stabilized mixed formulation, error analysis, and numerical solutions

机译：具有双孔隙率/渗透率的多孔介质中的流动建模：稳定的混合配方，误差分析和数值解

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摘要

The flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon-dioxide sequestration. The flow within numerous natural and synthetic porous materials that contain multiple scales of pores cannot be adequately described by the classical Darcy equations. It is for this reason that mathematical models for fluid flow in media with multiple scales of pores have been proposed in the literature. However, these models are analytically intractable for realistic problems. In this paper, a stabilized mixed four-field finite element formulation is presented to study the flow of an incompressible fluid in porous media exhibiting double porosity/permeability. The stabilization terms and the stabilization parameters are derived in a mathematically consistent manner, and the computationally convenient equal-order interpolation of all the field variables is shown to be stable. A systematic error analysis is performed on the resulting stabilized weak formulation. Representative problems, patch tests and numerical convergence analyses are performed to illustrate the performance and convergence behavior of the proposed mixed formulation in the discrete setting. The accuracy of numerical solutions is assessed using the mathematical properties satisfied by the solutions of this double porosity/permeability model. Moreover, it is shown that the proposed framework can perform well under transient conditions and that it can capture well-known instabilities such as viscous fingering. (C) 2018 Elsevier B.V. All rights reserved.
机译：不可压缩流体通过多孔介质的流动在许多技术应用（例如提高采收率和地质二氧化碳封存）中起着至关重要的作用。经典达西方程式无法充分描述包含许多尺度孔的多种天然和合成多孔材料中的流动。因此，在文献中已经提出了用于在具有多个尺度的孔的介质中的流体流动的数学模型。但是，对于实际问题，这些模型在分析上很难解决。在本文中，提出了一种稳定的混合四场有限元公式，以研究不可压缩流体在具有双重孔隙率/渗透率的多孔介质中的流动。稳定项和稳定参数以数学上一致的方式导出，所有场变量的计算方便的等次插值被证明是稳定的。对所得的稳定弱配方进行了系统误差分析。进行了具有代表性的问题，补丁测试和数值收敛分析，以说明所提出的混合配方在离散环境下的性能和收敛行为。数值解的准确性是使用该双重孔隙度/渗透率模型的解所满足的数学性质来评估的。而且，表明所提出的框架在瞬态条件下可以很好地执行，并且可以捕获众所周知的不稳定性，例如粘性指法。 （C）2018 Elsevier B.V.保留所有权利。

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