Transient-state instability analysis of dissolution-timescale reactive infiltration in fluid-saturated porous rocks: Purely mathematical approach

Zhao, Chong Bin; Hobbs, B. E.; Ord, Alison

doi:10.1007/s11431-018-9448-8

Cited by 23 publications

(25 citation statements)

References 31 publications

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“…The main contribution of this study is to derive semianalytical solutions for the FOP equations of the dissolution‐timescale RII system within the downstream subdomain. This important progress can be considered as the main difference between this study and the previous studies 1–7,28–30,34 …”

Section: Introductionmentioning

confidence: 78%

“…From the mathematical point of view, the derived semianalytical solutions for the FOP equations in the downstream subdomain are much superior to the purely numerical solutions, which are obtained from using the conventional FEM. For this reason, it is logically inappropriate to use the purely numerical solutions to validate analytical or semianalytical solutions for dealing with the same problem 34 . However, the derived semianalytical solutions for the FOP equations in the downstream subdomain can be used to verify the purely numerical solutions, which are directly obtained from using the conventional FEM to solve the same FOP equations in the downstream subdomain of the dissolution‐timescale RII system in a future study.…”

Section: Deducing Analytical Expressions Of Numerical Solutions For Fmentioning

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

Zhao

Hobbs

Ord

2020

Num Anal Meth Geomechanics

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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.

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Section: Introductionmentioning

confidence: 78%

Section: Deducing Analytical Expressions Of Numerical Solutions For Fmentioning

confidence: 99%

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

Zhao

Hobbs

Ord

2020

Num Anal Meth Geomechanics

Self Cite

View full text Add to dashboard Cite

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“…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. This research was based on the simplified assumption above, and the simulation of grouting in flowing water was achieved.…”

Section: Limitations and Discussionmentioning

confidence: 99%

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

Pan

Lin

et al. 2021

Num Anal Meth Geomechanics

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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.

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“…The validation of the proposed numerical procedure should be done by comparing the numerical solution with the analytical solution of a benchmark problem (Zhao et al, 2020). However, since the analytical solution for pore-fluid flow in fractured porous media is not available, a benchmark problem of numerical solutions (Flemisch et al, 2018) is used in this study.…”

Section: Verification Of the Modeling Schemementioning

confidence: 99%

“…First, temperature effects can cause thermal deformation, which can further affect porosity distribution and pore-fluid flow patterns in the fractured porous medium (Zhao et al, 2008b). Second, both the physical dissolution (Zhao et al, 2010) and the chemical dissolution (Zhao et al, 2020) of dissolvable materials in fractured porous media can also cause a significant change in the porosity and permeability of the fractured porous media. This indicates that both the porosity and the permeability should depend strongly on the fractured porous medium deformation (including thermal deformation (Zhao et al, 2015)), physical dissolution and chemical dissolution of dissolvable materials in the fractured porous medium.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of the flow characteristics and permeability of 2D irregular columnar jointed rock masses

Cheng

Wang

et al. 2021

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PurposeThe objective of this paper is to provide a better understanding of the effect of irregular columnar jointed structure on the permeability and flow characteristics of rock masses.Design/methodology/approachAn efficient numerical procedure is proposed to investigate the permeability and fluid flow in columnar jointed rock masses (CJRMs), of which the columnar jointed networks are generated by a modified constrained centroid Voronoi algorithm according to the field statistical results. The fractures are represented explicitly by using the lower-dimensional zero thickness elements. And the modeling scheme is validated by a benchmark test for flow in fractured porous media. The effective permeability and representative elementary volume (REV) size of CJRMs are estimated using finite element method (FEM). The influences of joint density and variation coefficient of columnar joint structure on the permeability of the rock mass are discussed.FindingsThe simulation results indicate that the permeability is scale-dependent and tends to be stable with increase of model size. The hydraulic REV size is determined as 3.5 m for CJRMs in the present study. Moreover, the joint density is a dominant factor affecting the permeability of CJRMs. The average permeability of columnar jointed structures increases linearly with the joint density under the same REV size, while the influence from the coefficient of variation can be neglected.Originality/valueThe present paper investigates the REV size of the CJRMs and the effect of joint parameters on the permeability. The proposed method and the results obtained are useful on understanding the hydraulic characteristic of the irregular CJRMs in engineering projects.

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Transient-state instability analysis of dissolution-timescale reactive infiltration in fluid-saturated porous rocks: Purely mathematical approach

Cited by 23 publications

References 31 publications

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

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

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

Numerical investigation of the flow characteristics and permeability of 2D irregular columnar jointed rock masses

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