Flow of groundwater in relatively thick leaky aquifers

Abstract

Solutions to many problems of flow in leaky aquifers are based on a differential equation that includes a leakage term in addition to the usual terms of the equation of groundwater motion. In other words, the effect of leakage on the flow is incorporated in the differential equation rather than expressed as a boundary condition, as it actually occurs in the physical system. Such an approximation is justified when the main aquifer is relatively thin, provided, of course, that the conductivity of the semipervious layer relative to those of the main aquifers of the leaky system is small. Although the latter condition is almost always prevalent in nature, the aquifers are not always relatively thin. In such aquifers, the use of the available solutions may yield poor results, especially when a quantitative criterion for the relative thickness of the aquifers is not available. Solutions are developed by using the usual differential equation of groundwater motion and the pertinent initial and boundary conditions, expressing the effect of leakage on the flow as a boundary condition. Moreover, a quantitative criterion is established for the applicability of the solutions that are already available from the approximate theory now in use. The already available solutions appear to be applicable wherever b/B < 0.10, where b is the thickness of the main aquifer, and is the leakage factor; T is the transmissivity of the aquifer; and (K′/b′} is the leakage coefficient of the flow system. (Key words: Groundwater; hydrologie systems; leaky aquifers; seepage; wells)