A semianalytical approach for solving first‐order perturbation equations of dissolution‐timescale reactive infiltration instability problems in fluid‐saturated rocks

Abstract

Summary This paper presents a semianalytical approach for solving first‐order perturbation (FOP) equations, which are used to describe dissolution‐timescale reactive infiltration instability (RII) problems in fluid‐saturated rocks. The proposed approach contains two parts because the chemical dissolution reaction divides the whole problem domain into two subdomains. In the first part, the interface‐condition substitution strategy is used to derive the analytical expressions of purely mathematical solutions for the FOP equations in the upstream subdomain, where the dissolution chemical reaction is ceased and the FOP equations are weakly coupled. In the second part, the finite element method (FEM) is used to derive the analytical expressions of numerical solutions for the FOP equations in the downstream subdomain, where the dissolution chemical reaction needs to be considered and the FOP equations are strongly coupled so that it is impossible to derive purely mathematical solutions for them. Particular attention is paid to the development of the element‐by‐element forward marching strategy, which is associated with the use of the FEM for solving this new kind of scientific problem. The related analytical results demonstrated that (1) both the dynamic characteristic of a reactive infiltration system and the dimensionless wavenumber can have pronounced influences on the distribution of the FOP dimensionless acid concentration within the entire domain of the dissolution‐timescale RII problems in fluid‐saturated rocks and (2) the FOP dimensionless acid concentration distribution exhibits two significantly different patterns in the upstream and downstream subdomains of the dissolution‐timescale RII system.

Analytical solution for one‐dimensional steady‐state contaminant transport through a geomembrane layer (GMBL)/compacted clay layer (CCL)/attenuation layer (AL) composite liner considering consolidation

“…Increasing the thickness of the AL leads to a larger consolidation advection and a longer consolidation path, which may be the dominant mechanisms for contaminant transport compared to the diffusion process. Two sensitivity coefficients (e.g., X k and $$DI{M_k}$$) are introduced to investigate the effects of various parameters on the performance of the GMBL/CCL/AL composite barrier system. The effects of the variation in parameters Q on the migration of contaminant is the most significant, which is then followed by m v2 , $${\rho _{s2}}{K_{d2}}$$, P g ,$$\;{\rho _{s1}}{K_{d1}}$$, and m v1 . It should be pointed out that extensive studies have demonstrated that the mass (including contaminants in MSW landfills) transport process is strongly coupled with the chemical reaction 59–61 and physical dissolution 62 processes, so that many analytical solutions have been mathematically derived for both of the chemical dissolution front instability problems 63–67 and physical dissolution front instability problems 68 in fluid‐saturated porous media. However, both of the chemical reaction and physical dissolution phenomena are not considered in this study.…”

Numerical investigation of flow control technology for grouting and blocking of flowing water in karst conduits

“…It also should be stated that slurry diffusion process would need to be clearly described by the slurry concentration gradient 20,21 . In addition, due to the nonlinear interactions between underground water flow, mass transport, and chemical/physical reaction processes, the resulting chemical dissolution fronts may have different morphologies 48,49 . Compared with the previous studies associated with chemical dissolution front 50,51 and physical dissolution front instability problems, 21,52 in which the true mass diffusion processes including the medium and fluid compressibility were considered, 53 the numerical simulation method used in this study should be improved in future research.…”

A novel algorithm for implementing perturbations in computational simulations of chemical dissolution‐front instability problems within fluid‐saturated porous media

“…The reason behind this phenomenon has not been revealed so far. This indicates that compared with the porosity‐pressure‐concentration scheme, the porosity‐velocity‐concentration scheme faces more numerically challenging to solve the CDFI problems in the fluid‐saturated porous media 23–34 . On the other hand, the recent studies have demonstrated that in terms of solving reactive mass transport problems involving chemical dissolution in fluid‐saturated porous media with arbitrarily initial porosity distributions, the porosity‐velocity‐concentration scheme can produce higher accurate numerical results than the porosity‐pressure‐concentration scheme does 35 .…”