Addressing nonlinear transient diffusion in porous media through transformations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.2516/ogst/2021064

R. Raghavan, Chih-Cheng Chen

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Abstract

The nonlinear differential equation describing flow of a constant compressibility liquid in a porous medium is examined in terms of the Kirchhoff and Cole-Hopf transformations. A quantitative measure of the applicability of representing flow by a slightly compressible liquid – which leads to a linear differential equation, the Theis equation – is identified. The classical Theis problem and the finite-well-radius problem in a system that is infinite in its areal extent are used as prototypes to address concepts discussed. This choice is dictated by the ubiquity of solutions that depend on these archetypal examples for examining transient diffusion. Notwithstanding that the Kirchhoff and Cole-Hopf transformations arrive at a linear differential equation, for the specific purposes of this work – the estimation of the hydraulic properties of rocks, the Kirchhoff transformation is much more advantageous in a number of ways; these are documented. Insights into the structure of the nonlinear solution are provided. The results of this work should prove useful in many contexts of mathematical physics though developed in the framework of applications pertaining to the earth sciences.

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通过变换处理多孔介质中的非线性瞬态扩散

用Kirchhoff变换和Cole-Hopf变换研究了描述恒压缩性液体在多孔介质中流动的非线性微分方程。确定了用微可压缩液体来表示流动的适用性的定量测量方法——这导致了一个线性微分方程，即忒伊斯方程。用经典的Theis问题和有限井半径问题作为原型来解决所讨论的概念。这种选择是由无处不在的解决方案决定的，这些解决方案依赖于这些原型例子来检查瞬态扩散。尽管Kirchhoff变换和Cole-Hopf变换得到的是线性微分方程，但对于这项工作的具体目的——估计岩石的水力特性，Kirchhoff变换在许多方面都更加有利;这些都是有记录的。提供了对非线性解的结构的见解。这项工作的结果将在许多数学物理的背景下证明是有用的，尽管它是在与地球科学有关的应用框架中发展起来的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.