Mathematical modeling of fluid flow and pollutant transport in a homogeneous porous medium in the presence of plate stacks

Abstract

This study aims at investigating the numerical analysis of pollutant transport in homogeneous porous media with solid plate stacks. The investigation was performed for solid/impervious objects of the same size placed in homogeneous porous media. The pollutant transport equation (i.e., steady-state and time dependent advection-dispersion) chosen in mathematical modeling. Three cases arise on the basis of dispersion coefficients: (a) when dispersion is uniformly constant, (b) when dispersion depends upon magnitude of the velocity, and (c) when dispersion depends upon magnitude of the velocity and directional dispersivities, all these are discussed in detail. Generally, analytical solution of such problems doesn't exist, so all the work is done numerically. The governing partial differential equation of pollutant concentration is approximated by using finite difference technique. Central, one-sided, backward and forward finite difference formulae of the same order are used to discretize the domain.Simulations of velocity potential and stream function are approximated by Matlab software. Then equipotential lines and streamlines are visualized in the form of contours. Both, velocity potential and stream function are harmonic and satisfy Laplace's equation. Fluid flow lines and pollutant concentration are represented graphically for several parameters involved in the study.It is found that entrance/exit length, shape, hydraulic conductivity, the number and position of impervious objects affect the fluid flow and pollutant transport. However, there is no significant affect of heated objects on pollutant transport. Moreover, advection and dispersion depend upon permeability of porous media and properties of solid matrix.To authenticate the Matlab scheme of finite difference, it is verified that fluid as well as pollutant fluxes (in and out) are equal. Moreover, time-dependent problem converges to steady-state form after very long time.For monitoring or forecasting the build up of contamination concentration, the pollutant transport model is considerable. As this model is affected by different parameters which are discussed above, can helps to overcome the pollutant accumulation. The solid object is main key to lessen the contamination in the underground. If the entrance or leakage point of the domain is blocked by impermeable object or filled the vertical column with material of low hydraulic conductivity it ultimately slows down or even refrains the pollutant particles to pass through. The pollutant concentration is also minimized by injecting the bioremedial agents with the help of treatment columns.