Analytical Approach to Solute Dispersion along and against Transient Groundwater Flow in a Homogeneous Finite Aquifer: Pulse Type Boundary Conditions

A one-dimensional advective-dispersive equation is analytically solved to predict patterns of contaminant concentration distribution in a homogeneous and finite aquifer. The dispersion of solute along and against transient groundwater flow is considered. Initially the aquifer is assumed to be not clean, which means that some initial background concentration exists and it is represented by uniform concentration. A pulse-type exponentially decreasing temporally dependent source concentration is considered in the intermediate portion of the aquifer and at other end, the concentration gradient is supposed to be zero. The Laplace Transform Technique (LTT) is used to obtain the solution of the problem of contaminant distribution in two different domains. In fact, in one domain the distribution pattern is depicted along groundwater flow and in other domain, it is depicted against groundwater flow. This represents a realistic situation of the contaminant concentration distribution pattern in an aquifer in the presence or absence of temporally dependent source concentration. The time-varying velocity expressions are considered. The dispersion is directly proportional to the seepage velocity used in which the effect of molecular diffusion is not taken into account because the value of molecular diffusion does not vary significantly for different soil and contaminant behaviors. Results of the obtained analytical solution may form useful complements to benchmark numerical models or for their verification. The long-term vertical transport of solute during transient saturated groundwater flow can be described correctly with appropriate analytical models. It may also be used as a preliminary predictive tool for groundwater resource management to estimate transport parameters.