The Transition from Darcy to Nonlinear Flow in Heterogeneous Porous Media: I—Single-Phase Flow
The Transition from Darcy to Nonlinear Flow in Heterogeneous Porous Media: I—Single-Phase Flow
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DOI：
10.1007/s11242-024-02070-3
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发表时间：
2024-03
影响因子：
2.7
通讯作者：
S. Arbabi;Muhammad Sahimi
中科院分区：
文献类型：
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作者：
S. Arbabi;Muhammad Sahimi
利用广泛的数值模拟的Navier-Stokes方程，我们研究了从达西定律的流体缓慢流动通过无序多孔介质的非线性流动制度，其中的惯性的影响不能忽略的过渡。多孔介质由砂岩的三维图像的二维切片表示。我们研究的问题在很宽的范围内的孔隙度和雷诺数，以及两种类型的边界条件，并计算流体流动的基本特征，即，涡的强度，孔隙空间的有效渗透率，摩擦阻力，和宏观压力梯度和流体速度v之间的关系。结果表明，当雷诺数Re足够低，使达西定律成立时，涡量接近于零。然而，当Re增加时，Re也增加，并且它从接近零的Re开始增加，在相同的Re处，达西定律失效。我们还表明，宏观压力梯度和流体速度v之间的非线性关系，给出，提供了精确的数值数据表示，其中和是流体的粘度和密度，是有效的达西渗透率在线性政权，和是一个广义的非线性阻力。的关系的理论依据，其预测也与Forchheimer的方程。
Using extensive numerical simulation of the Navier–Stokes equations, we study the transition from the Darcy’s law for slow flow of fluids through a disordered porous medium to the nonlinear flow regime in which the effect of inertia cannot be neglected. The porous medium is represented by two-dimensional slices of a three-dimensional image of a sandstone. We study the problem over wide ranges of porosity and the Reynolds number, as well as two types of boundary conditions, and compute essential features of fluid flow, namely, the strength of the vorticity, the effective permeability of the pore space, the frictional drag, and the relationship between the macroscopic pressure gradientand the fluid velocityv. The results indicate that when the Reynolds number Re is low enough that the Darcy’s law holds, the magnitudeof the vorticity is nearly zero. As Re increases, however, so also does, and its rise from nearly zero begins at the same Re at which the Darcy’s law breaks down. We also show that a nonlinear relation between the macroscopic pressure gradient and the fluid velocityv, given by,, provides accurate representation of the numerical data, whereandare the fluid’s viscosity and density,is the effective Darcy permeability in the linear regime, andis a generalized nonlinear resistance. Theoretical justification for the relation is presented, and its predictions are also compared with those of the Forchheimer’s equation.