An interface‐condition substitution strategy for theoretical study of dissolution‐timescale reactive infiltration instability in fluid‐saturated porous rocks

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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.

Section: Introductionmentioning

confidence: 78%

- {\overset{false¯}{x}}_{1} \leq \overset{ξ}{true} \leq 0

) of the dissolution‐timescale RII problem as 1,2,6,30

\nabla^{2} {\overset{false¯}{u}}_{ξ} = 0 ((), - {\overset{false¯}{x}}_{1} \leq \overset{ξ}{true} \leq 0),

\nabla • ([], \nabla \overset{C}{true} - \overset{C}{true} \overset{\overset{false\to}{u}}{true}) = 0 ((), - {\overset{false¯}{x}}_{1} \leq \overset{ξ}{true} \leq 0),

where

{\overset{false¯}{u}}_{ξ}

is the dimensionless velocity component in the ξ direction,

{\overset{false¯}{x}}_{1}

is the location of the planar reference front at the fixed

\overset{x}{true} - o - \overset{y}{true}

coordinate system,

{\overset{false¯}{C}}_{1}

is the dimensionless concentration, and

\overset{\overset{false\to}{u}}{true} = {\overset{false¯}{u}}_{ξ} \overset{i}{true} + {\overset{false¯}{u}}_{y} \overset{j}{true}

is the dimensionless Darcy velocity vector.…”

Section: Brief Derivation Of Fop Equations For Dissolution‐timescale mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

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

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A sequential flow and solidification method was applied to the numerical investigation of flow control technology for grouting and blocking of flowing water in karst conduits. This method accounted for the temporal‐ and spatial‐evolution characteristics of the viscosity. It achieved the visualization of grouting in flowing water in a conduit, and was used to explore a reasonable and effective method for grouting through flow‐control technology. Firstly, the responses of different water tables and flow‐control intensities were studied by establishing a generalized model of flow control at the outlet of a conduit. Secondly, the initial sedimentation location and the distance of down‐flow and counter‐flow of slurries with different intensities of flow control were compared and analyzed. The outlet flow, the loss rate of the slurry, and the distribution laws of velocity and pressure inside the conduit during plugging were further analyzed. In addition, the mechanism of flow control for the grouting and plugging of large‐flow conduits was revealed. The results showed that the most direct effect of flow control on grouting was to decrease the flow rate of flowing water, and the most essential role was to improve the retention rate of slurry. Moreover, the results were applied to the large‐scale water inrush control project of Hejing Limestone Mine, China. The slurry stop devices improved the retention rate of slurry and optimized the grouting technology, which had a certain guiding significance in the treatment of water‐inrush disasters in karst areas.

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

Yan

Xie

Ding

et al. 2022

A composite liner system consisting of a geomembrane layer (GMBL), a compacted clay layer (CCL) and an attenuation layer (AL) is widely used in the modern landfills. The field and experimental observations highlight the potential detrimental effects on breakthrough of contaminants induced by consolidation of soil liner when a relatively high applied stress is caused by the waste placement. A one dimensional steady‐state model is developed to investigate the behaviour of contaminant transport in GMBL/CCL/AL composite liner system considering consolidation. Effects of the consolidation process on the transport of typical contaminants are investigated by the proposed analytical solution. The analytical results show that the magnitude of volume compressibility coefficient in the AL is important in controlling the overall magnitude of the consolidation induced effects. The process of consolidation shows a larger impact on the absorbable pollutants compared to the non‐absorbable pollutants. This may be due to the fact that the migration of solid particles induced by the consolidation may assist the transport of contaminant absorbed on them. The thickness of the AL shows large impacts on the bottom flux for the case with a high volume compressible coefficient. Increasing the thickness of AL from 1 to 3 m can results in a factor of 2.6 increase of the bottom flux. 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.