R. R. Yadav

Three-dimensional temporally dependent dispersion through porous media: analytical solution

A three-dimensional model for non-reactive solute transport in physically homogeneous subsurface porous media is presented. The model involves solution of the advection-dispersion equation, which additionally considered temporally dependent dispersion. The model also account for a uniform flow field, first-order decay which is inversely proportional to the dispersion coefficient and retardation factor. Porous media with semi-infinite domain is considered. Initially, the space domain is not solute free. Analytical solutions are obtained for uniform and varying pulse-type input source conditions. The governing solute transport equation is solved analytically by employing Laplace transformation technique (LTT). The solutions are illustrated and the behavior of solute transport may be observed for different values of retardation factor, for which simpler models that account for solute adsorption through a retardation factor may yield a misleading assessment of solute transport in ‘‘hydrologically sensitive’’ subsurface environments.

Analytical solutions for temporally dependent dispersion through homogeneous porous media

Analytical solutions are obtained for advection-dispersion equation in two-dimensional horizontal semi-infinite porous domains. The solute dispersion parameter is considered temporally dependent along uniform flow. The two main characteristic of the porous medium: desorption and reaction, both always some attenuation in solute concentration in liquid phase, are considered by retardation factor and first order decay term, respectively. The solutions are obtained for uniform and increasing input sources. New space and time variables are introduced to reduce the variable coefficients of the advection-dispersion equation into constant coefficients and Laplace transform technique is used to obtain the analytical solutions. The solution of the present problem is also derived in one and three-dimension. Physical significance of the problems is illustrated by different graphs.

Solute-Transport under Fluctuating Groundwater Flow in Homogeneous Finite Porous Domain

Solute-Transport under Fluctuating Groundwater Flow in Homogeneous Finite Porous Domain In this paper a theoretical model is developed for the advection dispersion problem in one-dimensional porous media with two considerations: one the flow is periodic and the second dispersion coefficient is directly proportional to the seepage velocity. The porous domain is homogeneous, isotropic and of adsorbing nature. A time dependent periodic point source is considered at the source boundary. Different boundary conditions are considered at outlet of the domain. In first case, the mixed type and in second case flux type boundary conditions are considered. For both cases, input source are same. We studied the influence on concentration profiles due to different boundary conditions in the domain. The derived solution is also extended in semi-infinite domain. The Laplace Transformation Technique (LTT) is used to get analytical solution. In this process, a new time variables are introduced. Graphical illustrations of concentration profiles versus time and position are presented for different set of data.

Analytical Solutions of One-Dimensional Temporally Dependent Advection-Diffusion Equation along Longitudinal Semi-Infinite Homogeneous Porous Domain for Uniform Flow

Analytical solutions are obtained for one-dimensional advection-diffusion equation with variable coefficients in longitudinal semi-infinite homogeneous porous medium for uniform flow. The solute dispersion parameter is considered temporally dependent while the velocity of the flow is considered uniform. The first order decay and zero-order production terms are considered inversely proportional to the dispersion coefficient. Retardation factor is also considered in present paper. Analytical solutions are obtained for two cases: former one is for uniform input point source and latter case is for increasing input point source where the solute transport is considered initially solute free. The Laplace transformation technique is used. New space and time variables are introduced to get the analytical solutions. The solutions in all possible combinations of increasing or decreasing temporally dependence dispersion are compared with each other with the help of graph. It is observed that the concentration attenuation with position and time is the fastest in case of

One-dimensional solute transport for uniform and varying pulse type input point source through heterogeneous medium

An analytical solution is developed for conservative solute transport in a one-dimensional heterogeneous porous medium. The solute dispersion parameter is considered uniform, while the seepage flow velocity is considered spatially dependent. Retardation factor is considered inversely proportional to square of the flow velocity. The seepage velocity flow is considered inversely proportional to the spatially dependent function. The solution is derived for two cases: the former one is for uniform pulse type input point source and the latter one is for varying pulse type input point source. The second condition is considered at the far end of the medium. It is of the second type (flux type) of homogeneous nature. Laplace transform technique (LLT) is employed to get the analytical solutions to the present problem. In the process, a new space variable is introduced. The solutions are graphically illustrated. The effects of heterogeneity of the medium on the solute transport behaviour, in the presence and absence of the source pollutant, are also studied. Laplace transformation technique is used to solve the present problems analytically.