Exact solutions for one-dimensional transient response of fluid-saturated porous media

2011 ◽  
Vol 35 (4) ◽  
pp. 461-479 ◽  
Author(s):  
Zhendong Shan ◽  
Daosheng Ling ◽  
Haojiang Ding
Keyword(s):  
Porous Media ◽  
Exact Solutions ◽  
Transient Response ◽  
Saturated Porous Media ◽  
One Dimensional ◽  
Fluid Saturated Porous Media

Semi-analytical finite element method for simulating chemical dissolution-front instability problems in fluid-saturated porous media

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chongbin Zhao ◽  
B.E. Hobbs ◽  
Alison Ord
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Chemical Dissolution ◽  
Saturated Porous Media ◽  
Content Type ◽  
Front Instability ◽  
Fluid Saturated Porous Media ◽  
Dissolution Front ◽  
Element Method

PurposeThe 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/approachThe 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.FindingsThe 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/valueAnalytical 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.

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