The transport of contaminants has been a problematic issue for many years, mainly due to the adverse impact of the contaminants on the quality of groundwater. In order to analyse this, this study has developed a prediction model that allows the early detection of possible contamination. Firstly, the paper introduces the concept of the modelling of contamination transport through a soil matrix. Then it presents a two-dimensional Convection-Dispersion Equation (CDE) for contaminant transport in a soil matrix. This includes the investigation of different reaction coefficients and time-dependent inlet boundary conditions, from which a numerical solution is derived. The study also verifies recent previous work in this area through the use of numerical programming. The results for soil contamination in two dimensions are presented in this research.