Semi-analytical finite element method for simulating chemical dissolution-front instability problems in fluid-saturated porous media
ISSN: 0264-4401
Article publication date: 30 November 2021
Issue publication date: 3 May 2022
Abstract
Purpose
The objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.
Design/methodology/approach
The porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.
Findings
The direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.
Originality/value
Analytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.
Keywords
Acknowledgements
This work is financially supported by the National Natural Science Foundation of China (Grant Nos: 42030809 and 72088101). The authors express sincere thanks to the anonymous referees for their valuable comments, which led to a significant improvement over an early version of the paper.
Citation
Zhao, C., Hobbs, B.E. and Ord, A. (2022), "Semi-analytical finite element method for simulating chemical dissolution-front instability problems in fluid-saturated porous media", Engineering Computations, Vol. 39 No. 5, pp. 1781-1801. https://doi.org/10.1108/EC-05-2021-0286
Publisher
:Emerald Publishing Limited
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