An Analytical Model for Computing Ground Water Residence Times Near a Pumping Well

A new analytical solution for calculating the residence time of fluid flowing towards a single pumping well in an unconfined aquifer is developed. The analytical solution was derived based upon a one-dimensional, steady state, Dupuit-Forchheimer flow model. The resulting integral expression involves computing the imaginary error function, for which a simple series expansion is successfully proposed. The validity of the expression is tested against the results from a numerical approximation for an example problem, which demonstrated a good correspondence between the numerical and analytical results. The applications and limitations of the new analytical solution are presented.