Numerical Modeling of Contaminant Transport with Spatially-Dependent Dispersion and Non-Linear Chemical Reaction

Abstract

A one-dimensional advective-dispersive contaminant transport model with scale-dependent dispersion coefficient in the presence of a nonlinear chemical reaction of arbitrary order is considered. Two types of variations of the dispersion coefficient with the downstream distance are considered. The first type assumes that the dispersivity increases as a polynomial function with distance while the other assumes an exponentiallyincreasing function. Since the general problem is nonlinear and possesses no analytical solutions, a numerical solution based on an efficient implicit iterative tri-diagonal finitedifference method is obtained. Comparisons with previously published analytical and numerical solutions for special cases of the main transport equation are performed and found to be in excellent agreement. A parametric study of all physical parameters is conducted and the results are presented graphically to illustrate interesting features of the solutions. It is found that the chemical reaction order and rate coefficient have significant effects on the contaminant concentration profiles. Furthermore, the scale-dependent polynomial type dispersion coefficient is predicted to obtain significant changes in the contaminant concentration at all dimensionless time stages compared with the constant dispersion case. However, relatively smaller changes in the concentration level are predicted for the exponentially-increasing dispersion coefficient.