Analysis of two-dimensional solute transport through heterogeneous porous medium

Kumar, Abhishek; Kumar, Lav Kush; Shireen, Shireen

doi:10.26855/jamc.2018.03.001

Cited by 2 publications

(3 citation statements)

References 8 publications

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“…Zamani and Bombardelli [16] proposed analytical solutions of nonlinear advection-dispersion equation with spatially and temporally dependent dispersion coefficient and velocity. Kumar et al [17] obtained solution for a two-dimensional solute transport problem with spatially varying dispersion and groundwater velocity. Yadav and Roy [18] studied solute transport phenomena with curved line and curved surface sources in two-and three-dimensional semiinfinite porous media respectively by using Laplace Transformation Technique.…”

Section: Introductionmentioning

confidence: 99%

“…(7) into one-dimensional or single space variable, we introduce a new transformation as Singh and Chatterjee[21]:We further use following transformation to eliminate convective part of Eq. (12)Applying Laplace Transform Technique to Eqns (17)(18)(19)(20),. one can get the solution of the present problem.…”

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confidence: 99%

“…one can get the solution of the present problem. For this purpose, we take Laplace Transform of Eqns (17)(18)(19)(20)…”

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confidence: 99%

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Solute Transport Phenomena with Input Through a Plane Surface in Porous Media

Yadav¹,

Roy²

2019

MMEP

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In the present study, analytical solutions for conservative solute transport, originating from a plane input source, along and against the flow is studied in form of two cases through a threedimensional semi-infinite porous media which is bounded between two infinitely spread planes. Also, flow is considered from one plane to another. In first case, concentration gradient perpendicular to the plane which is free from input is considered zero i.e. (ℎ .) • ∧ = 0 while in second case concentration gradient perpendicular to the plane which is free from input is assumed to be proportional to concentration at that plane i.e. (ℎ .) • ∧ ∝. Here ℎ is second order tensor represents dispersion coefficient and ∧ is unit normal vector to the corresponding plane. In both cases, initially the aquifer is supposed to be uniformly polluted. The temporarily dependent dispersion is assumed proportional to the groundwater velocity. The analytical solution of the advection-dispersion equation is obtained using Laplace Transformation Technique. A transformation is used to change the time-dependent advection-dispersion equation into constant coefficients. Such results may be very useful in predicting the concentration pattern in real scenario where the solute material is injected through a plane in a medium. The prosed model may be used to predict concentration profiles of solute in the laboratory as well as in the field.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%