Study of multispecies convection-dispersion transport equation with variable parameters

Chaudhary, Manish; Singh, Mritunjay Kumar

doi:10.1016/j.jhydrol.2020.125562

Cited by 10 publications

(7 citation statements)

References 48 publications

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“…In a one-dimensional flow field, the general form for a reactive transport system which describes the phenomenon of multi-species migration having spatially and temporally varying parameters can be modelled as follows (Chaudhary and Singh 2020):…”

Section: Governing Equation and Solution Methodologiesmentioning

confidence: 99%

“…It may be noted that the solution methodologies reported here can be adopted for other cases such as the transient migration in steady and unsteady flows (Chaudhary and Singh 2020). However, as our objective is to show the applicability of different homotopy-based methods by extending the work of Chaudhary and Singh (2020), we restrict our analysis for the case of steady migration in steady flow. To that end, we assume:…”

Section: Governing Equation and Solution Methodologiesmentioning

confidence: 99%

“…For the validation of solutions, space and time domains are considered as 0 ≤ x(cm) ≤ 3000 and 0 ≤ t(hr) ≤ 40. The required parameters are chosen as (Simpson and Ellery 2014;Chaudhary and Singh 2020): a 1 2, a 2 0.0025, k 1 0.05 (/hr), k 2 0.01 (/hr), v 0 0.2 (cm/hr), and D 0 0.5 (cm 2 /hr). Also, the other parameters are considered as r 1 2, r 2 2.5, α 1 1, and α 2 0.05 (/cm).…”

Section: Selection Of Expressions and Parametersmentioning

confidence: 99%

“…There are a few works available for the variable transport parameters; however, some are for single species or restricted formulation. Chaudhary and Singh (2020) used the homotopy analysis method (HAM) for two-species convectiondispersion transport equation, considering spatial-temporal varying dispersion coefficient and seepage velocity. They used the standard HAM to deal with the system of PDEs governing the phenomenon.…”

Section: Introductionmentioning

confidence: 99%

“…This paper considers the case of spatially varying transport parameters. Indeed, the methodologies can be adopted for other cases such as the ones provided in Chaudhary and Singh (2020).…”

Section: Introductionmentioning

confidence: 99%

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Approximate analytical solutions for multispecies convection-dispersion transport equation with variable parameters

Kumbhakar

Singh

2023

Front. Earth Sci.

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Multispecies pollutant migration often occurs in polluted groundwater systems. Most of the multispecies problems that have been dealt in the literature assume constant transport parameters, primarily because analytical solutions for varying parameters become a challenge. The present study analytically solves a two-species convection-dispersion transport equation, considering spatially varying dispersion coefficient and seepage velocity, which corresponds to the steady migration in a steady flow domain. Indeed, the methodology can be adopted for other cases, such as the transient migration in a steady flow domain and transient migration in an unsteady flow domain, without any difficulty. Three kinds of homotopy-based methods, namely the homotopy perturbation method (HPM), homotopy analysis method (HAM), and optimal homotopy asymptotic method (OHAM), are used to derive approximate analytical solutions in the form of truncated series. In homotopy analysis method, the convergence-control parameter ℏ plays a key role in the convergence of the series solution. It is observed that for a specific case of this parameter, namely ℏ=−1, the HAM-based solution recovers the HPM-based solution. For the verification of homotopy-based solutions, we utilize the MATLAB routine pdepe, which efficiently solves a class of parabolic PDEs (single/system). An excellent agreement is found between the derived analytical solutions and the numerical solutions for all three methods. Further, a quantitative assessment is carried out for the derived solutions. Also, convergence theorems are proposed for the series solutions obtained using HAM and OHAM.

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Section: Governing Equation and Solution Methodologiesmentioning

confidence: 99%

Section: Governing Equation and Solution Methodologiesmentioning

confidence: 99%

Section: Selection Of Expressions and Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…This paper considers the case of spatially varying transport parameters. Indeed, the methodologies can be adopted for other cases such as the ones provided in Chaudhary and Singh (2020).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Approximate analytical solutions for multispecies convection-dispersion transport equation with variable parameters

Kumbhakar

Singh

2023

Front. Earth Sci.

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Study on multispecies solute transport through heterogeneous porous media

Gupta

Sharma

2023

Arab J Geosci

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The present study focuses on multispecies transport through heterogeneous porous media. An increasing exponential time-dependent dispersion is used to describe the heterogeneity of porous media. A numerical approach to the decomposition method for the study of multispecies solute transport through heterogeneous porous media has been proposed. Governing equations of multispecies solute transport have been solved numerically using the implicit finite difference technique. The effect of time-dependent dispersion has been analyzed using the exponential time-dependent dispersivity function and the same has been validated with the analytical solution. The study illustrates the solute movement involving sequential first-order decay reactions and the analysis has been carried out in three species nitrification chain and migration of radionuclides as four species. The model is used to simulate the breakthrough curves and the analysis has been done using different decay rate constants. Also, this study has been carried out on the behavior of solute concentration using an increasing macro-dispersivity function which accounts for the spatial heterogeneity of porous media. Further, spatial moment analysis has been performed on the concentration of all species and a comparison has been drawn using constant and exponential time-dependent dispersivity functions using various breakthrough curves. This analysis revealed that the mean travel distance and variance are sensitive to the change in the dispersivity function and its transformed species may not have the same transport pattern.

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Exact analytical solutions with great computational efficiency to three-dimensional multispecies advection-dispersion equations coupled with a sequential first-order reaction network

Liao

Suk

Liu

et al. 2021

Advances in Water Resources

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Study of multispecies convection-dispersion transport equation with variable parameters

Cited by 10 publications

References 48 publications

Approximate analytical solutions for multispecies convection-dispersion transport equation with variable parameters

Approximate analytical solutions for multispecies convection-dispersion transport equation with variable parameters

Study on multispecies solute transport through heterogeneous porous media

Exact analytical solutions with great computational efficiency to three-dimensional multispecies advection-dispersion equations coupled with a sequential first-order reaction network

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