Mathematical modelling to establish the influence of pesticides on groundwater contamination

Groundwater contamination due to pesticides used during cultivation was modelled mathematically, assuming that both the soil and the aquifer were initially contaminant free and the source of contamination was constant. A plane-type source was considered to show the impact of pesticides in soil domain, and a crack was considered in the upper part of the aquifer to keep a similarity with the physical system. The concentration of contaminants through the soil was used to obtain the concentration of contaminants in the aquifer. Three-dimensional analytical solutions of the dispersion equation for soil contamination and advection-dispersion equation (ADE) for aquifer contamination were obtained using Laplace transform. Application of analytical solution shows that 50–80% of the shallow aquifer, approximately 0.5 km deep and 5–8 km long, is contaminated irrespective of the concentration level. If the aquifer is 2 km deep and 15–20 km long, then the contaminant concentration in the aquifer asymptotically tends to zero after an average distance of 5 km, and 25–33% of the aquifer is contaminated with one or more pesticides irrespective of the concentration level. Result matches exactly the USGS data.