Analytical Solution for Darcy Flow in a Bounded Fracture-Matrix Domain

IF 2.7 3区工程技术 Q3 ENGINEERING, CHEMICAL

Transport in Porous Media Pub Date : 2024-10-19 DOI:10.1007/s11242-024-02130-8

Jan Březina, Pavel Burda

引用次数: 0

Abstract

We derive an analytical solution to a Darcy flow problem in a discrete 1D fracture coupled to a 2D continuum matrix. Separate unknowns for the fracture and matrix domain are considered, coupled by a Robin-type condition. The solution, in the form of a Fourier series, applies to a wide range of problem parameters, covering both conductive and barrier fracture cases. The evaluation procedure and convergence properties are discussed. To validate the solution, we compare it against a numerical solution using second-order finite differences in a parametric study. Our results demonstrate the accuracy and effectiveness of the analytical solution, making it a valuable tool for testing numerical schemes for discrete fracture-matrix models.

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有界断裂矩阵域中达西流的解析解

我们推导出了离散一维断裂与二维连续介质耦合的达西流问题的解析解。我们考虑了断裂和矩阵域的独立未知数，并通过罗宾型条件进行耦合。傅立叶级数形式的解决方案适用于广泛的问题参数，包括导电和阻挡断裂情况。我们讨论了评估程序和收敛特性。为了验证该解决方案，我们在参数研究中将其与使用二阶有限差分的数值解决方案进行了比较。我们的结果表明了分析解决方案的准确性和有效性，使其成为测试离散断裂矩阵模型数值方案的重要工具。

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

Transport in Porous Media 工程技术-工程：化工

CiteScore

5.30

自引率

7.40%

发文量

155

审稿时长

4.2 months

期刊介绍： -Publishes original research on physical, chemical, and biological aspects of transport in porous media- Papers on porous media research may originate in various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering)- Emphasizes theory, (numerical) modelling, laboratory work, and non-routine applications- Publishes work of a fundamental nature, of interest to a wide readership, that provides novel insight into porous media processes- Expanded in 2007 from 12 to 15 issues per year. Transport in Porous Media publishes original research on physical and chemical aspects of transport phenomena in rigid and deformable porous media. These phenomena, occurring in single and multiphase flow in porous domains, can be governed by extensive quantities such as mass of a fluid phase, mass of component of a phase, momentum, or energy. Moreover, porous medium deformations can be induced by the transport phenomena, by chemical and electro-chemical activities such as swelling, or by external loading through forces and displacements. These porous media phenomena may be studied by researchers from various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering).