当前位置: X-MOL 学术J. King Saud Univ. Sci. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Derivation of fractional-derivative models of multiphase fluid flows in porous media
Journal of King Saud University-Science ( IF 3.8 ) Pub Date : 2021-01-21 , DOI: 10.1016/j.jksus.2021.101346
Mohamed F. El-Amin

This paper is devoted to deriving several fractional-order models for multiphase flows in porous media, focusing on some special cases of the two-phase flow. We derive the mass and momentum conservation laws of multiphase flow in porous media. The mass conservation-law has been developed based on the flux variation using Taylor series approximation. The fractional Taylor series's advantage is that it can represent the non-linear flux with more accuracy than the first-order linear Taylor series. The divergence term in the mass conservation equation becomes of a fractional type. The model has been developed for the general compressible flow, and the incompressible case is highlighted as a particular case. As a verification, the model can easily collapse to the traditional mass conservation equation once we select the integer-order. To complete the flow model, we present Darcy’s law (momentum conservation law in porous media) with time/space fractional memory. The modified Darcy’s law with time memory has also been considered. This version of Darcy’s law assumes that the permeability diminishes with time, which has a delay effect on the flow; therefore, the flow seems to have a time memory. The fractional Darcy’s law with space memory based on Caputo's fractional derivative is also considered to represent the nonlinear momentum flux. Then, we focus on some cases of fractional time memory of two-phase flows with countercurrent-imbibition mechanisms. Five cases are considered, namely, traditional mass equation and fractional Darcy’s law with time memory; fractional mass equation with conventional Darcy’s law; fractional mass equation and fractional Darcy’s law with space memory; fractional mass equation and fractional Darcy’s law with time memory; and traditional mass equation and fractional Darcy’s law with spatial memory.



中文翻译:

多孔介质中多相流体流的分数-导数模型的导数

本文致力于推导多孔介质中多相流的几个分数阶模型,重点是两相流的一些特殊情况。我们推导了多孔介质中多相流的质量和动量守恒律。质量守恒定律是基于使用泰勒级数近似的通量变化而开发的。分数阶泰勒级数的优势在于,与一阶线性泰勒级数相比,它可以更精确地表示非线性通量。质量守恒方程中的散度项变为分数类型。该模型是针对一般可压缩流开发的,不可压缩的情况作为特殊情况突出显示。作为验证,一旦我们选择整数阶,该模型就很容易崩溃为传统的质量守恒方程。为了完成流动模型,我们提出了具有时间/空间分数记忆的达西定律(多孔介质中的动量守恒定律)。还考虑了带有时间记忆的修正达西定律。此版本的达西定律假设渗透率随时间而减小,这对流动有延迟作用。因此,流程似乎具有时间记忆。基于Caputo分数导数的带有空间记忆的分数达西定律也被认为代表了非线性动量通量。然后,我们将重点介绍具有逆流吸收机制的两相流分数时间存储的某些情况。考虑了五种情况,即传统的质量方程和带时间记忆的分数达西定律。具有传统达西定律的分数质量方程;具有空间记忆的分数质量方程和分数达西定律;具有时间记忆的分数质量方程和分数达西定律;以及传统的质量方程和具有空间记忆的分数达西定律。

更新日期:2021-02-02
down
wechat
bug