Analytical solution for aquifer decontamination by pumping

Abstract

Rehabilitation of polluted aquifers is an important issue in groundwater study. The use of withdrawal wells to extract dissolved solutes from contaminated aquifers is a possible mechanical remedial technique. A mathematical model dealing with aquifer decontamination by pumping is developed. The pumping well with a constant flow rate is taken into account as a mathematical sink located at the center of the plume to be removed. This plume is assumed to have a circular geometry inside which the solute concentration is axial symmetric with respect to the well and is incorporated into the model as an initial condition that can be formulated in an analytic or a sectionally continuous function capable of representing a wide range of uniform or nonuniform profiles. It assumes advection and longitudinal mechanical dispersion to be the transport mechanisms on a radially converging groundwater flow field. The analytical solution detecting concentration variation inside the aquifer is determined in closed forms with the Green's function approach and the Laplace transform technique. Using the field data presented by Pickens and Grisak (1981), the analytical solution obtained very accurately reproduces the reported concentration history at the well during the withdrawal phase of the single‐well injection‐withdrawal tracer test. It is found that if the initial conditions are expressed in functions presenting noticeable concentration gradients at the plume boundary, adverse dispersion against the converging groundwater movement would cause spreading of solutes beyond the original extent of plume during pumping. If the initial conditions gradually decrease to zero concentration at the plume boundary where negligible concentration gradients exist, concentration distributions do not extend beyond the initial condition envelopes during the withdrawal process. Since the well is placed at the center of the plume where maximum concentration occurs, the analytical solution evaluated at the well bore can be employed to indicate the decontamination level achieved at various pumping times. Graphical relations are presented for approximating the pumping time required to lower the concentration at the well bore to 1% of the maximum initial concentration. In general, neglecting dispersion in estimating the total cleanup times yields shorter pumping times.