Longitudinal dispersion with time-dependent source concentration in semi-infinite aquifer

Singh, Mritunjay Kumar; Mahato, Nav Kumar; Singh, Piyush Pratap

doi:10.1007/s12040-008-0079-x

Cited by 27 publications

(13 citation statements)

References 8 publications

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“…The work (Park and Zhan 2001) provides analytical solution of contaminant transport from one-, two-, and threedimensional finite sources in a finite-thickness aquifer, using Green's function. The analytical solution was obtained to predict the contaminant concentration along non-uniform groundwater flow in semi-infinite medium (Singh et al 2008). The analytical solutions have been presented to onedimensional advection-diffusion equation with spatially dependent dispersion along non-uniform flow through inhomogeneous medium in which solute dispersion is assumed proportional to the square of velocity (Kumar et al 2009).…”

Section: Introductionmentioning

confidence: 99%

Analytical solution of advection–diffusion equation in heterogeneous infinite medium using Green’s function method

Sanskrityayn

Kumar

2016

J Earth Syst Sci

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Some analytical solutions of one-dimensional advection-diffusion equation (ADE) with variable dispersion coefficient and velocity are obtained using Green's function method (GFM). The variability attributes to the heterogeneity of hydro-geological media like river bed or aquifer in more general ways than that in the previous works. Dispersion coefficient is considered temporally dependent, while velocity is considered spatially and temporally dependent. The spatial dependence is considered to be linear and temporal dependence is considered to be of linear, exponential and asymptotic. The spatio-temporal dependence of velocity is considered in three ways. Results of previous works are also derived validating the results of the present work. To use GFM, a moving coordinate transformation is developed through which this ADE is reduced into a form, whose analytical solution is already known. Analytical solutions are obtained for the pollutant's mass dispersion from an instantaneous point source as well as from a continuous point source in a heterogeneous medium. The effect of such dependence on the mass transport is explained through the illustrations of the analytical solutions.

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Section: Introductionmentioning

confidence: 99%

Analytical solution of advection–diffusion equation in heterogeneous infinite medium using Green’s function method

Sanskrityayn

Kumar

2016

J Earth Syst Sci

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“…The as sess ment of the im pact of pol lu tion source on groundwa ter can be car ried out with the use of pre dic tive mod els (Li et al, 2012), mon i tor ing or geo phys i cal tests (Singh et al, 2008), re search based on an iso to pic multi-tracer ap proach, and lab o ratory tests (Weber et al, 2002;So³tysiak, 2007So³tysiak, , 2009. The most com monly used method is an anal y sis of tem po ral and spa tial vari abil ity of the in di vid ual com po nents of ground wa ter, based on the re sults of mon i tor ing tests (Vilomet et al, 2001(Vilomet et al, , 2003.…”

Section: Introductionmentioning

confidence: 99%

Application of pollution indices for the spatiotemporal assessment of negative impact of a municipal landfill on groundwater (Tychy, southern Poland)

Dąbrowska

Witkowski

Sołtysiak

2018

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Ap pli ca tion of pol lu tion in di ces for the spatiotemporal as sess ment of neg a tive im pact of a mu nic i pal land fill on ground wa ter (Tychy, south ern Po land). Geo log i cal Quar terly, 62 (3): 496-508, doi: 10.7306/gq.1420 As so ci ate ed i tor: Stanis³aw Wo³kowicz Risk as sess ment plays an es sen tial role in the pro tec tion of ground wa ter re sources, es pe cially in the re gions of po ten tial con tam i na tion sources. The pres ent re search was aimed at as sess ing the risk of ground wa ter con tam i na tion in the vi cin ity of the Tychy-Urbanowice mu nic i pal land fill sys tems (south ern Po land), us ing the con tam i na tion in dex tool. Ground wa ter samples from the Qua ter nary Aqui fer were col lected from 22 piezometers lo cated near the for mer land fill site (cur rently closed) and the new sealed land fill site dur ing a mon i tor ing pe riod from 1995 to 2015. Ex tremely high val ues (1700) of the ground water con tam i na tion in dex were ob served in a piezometer that cap tures wa ter be neath the aban doned land fill. Very high in dex val ues (154 or 216) were also no ticed in piezometers lo cated in the ground wa ter out flow from the land fill site. Re sults of in terpo la tion for in di vid ual piezometers, which cap ture only the up per or lower part of an aqui fer, are un rep re sen ta tive. The in terpo la tion for the mean val ues of the con tam i na tion in dex in creased the ground wa ter risk as sess ment. Key words: hydrogeology, ground wa ter risk as sess ment, con tam i na tion in dex, mu nic i pal land fill site, Tychy-Urbanowice.

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“…An Analytical Solution for groundwater transit time through unconfined aquifers was presented [12]. An analytical solution in homogeneous semi-infinite aquifer with Dirichlet boundary condition was presented [13]. Solute transport for one-dimensional homogeneous porous formations with time-dependent point source concentration was presented [14].…”

Section: Introductionmentioning

confidence: 99%

Analytical modeling of solute transport in homogeneous porous media with Cauchy type boundary condition

Singh

Mahato

2012

2012 1st International Conference on Recent Advances in Information Technology (RAIT)

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Analytical solution is obtained to describe the nature of concentration of solute, transported in saturated porous media. The aquifer is assumed to be homogeneous and finite in nature in which groundwater flow is considered unsteady. Initially the aquifer is not supposed to be solute free which means that aquifer is not clean i.e. some initial background concentration exists in the aquifer system which is represented by uniform source of concentration. A Cauchy type input source concentration is considered in the intermediate portion of aquifer system. At the other end, the concentration gradient is supposed to be zero. Two types of temporally dependent velocities are considered. Laplace Transform Technique (LTT) is used to determine the analytical solution. The results are perhaps most useful for benchmarking numerical codes and solutions. It may also be used as a predictive tool of groundwater resource management.

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Longitudinal dispersion with time-dependent source concentration in semi-infinite aquifer

Cited by 27 publications

References 8 publications

Analytical solution of advection–diffusion equation in heterogeneous infinite medium using Green’s function method

Analytical solution of advection–diffusion equation in heterogeneous infinite medium using Green’s function method

Application of pollution indices for the spatiotemporal assessment of negative impact of a municipal landfill on groundwater (Tychy, southern Poland)

Analytical modeling of solute transport in homogeneous porous media with Cauchy type boundary condition

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