Sinusoidal pumping of groundwater near cylindrical inhomogeneities

A new analytic-element solution is presented for a well with a sinusoidal discharge pumping near cylindrical inhomogeneities. Both the transmissivity and the storage coefficient may be different inside each cylinder. The solution consists of separate series solutions inside and outside each cylinder; asymptotic expansions are presented for cases where the sinusoidal period is small and the radius and transmissivity of the cylinder are large. The complex coefficients in the series solutions are determined by requiring continuity of head and normal flow across the boundary of each cylinder resulting in a linear system of complex equations that may be solved with standard methods. The solution represents one of the few analytic solutions for two-dimensional transient groundwater flow in an aquifer with inhomogeneities. Computer implementation requires truncation of the series; machine accuracy may be reached when enough terms are used in the series solutions. The effect of cylindrical inhomogeneities on the amplitude and phase of the head are investigated. The complex behavior suggests it may be difficult to determine location and properties of cylindrical inhomogeneities from pump tests, which confirms reported difficulties of interpreting pump test results from heterogeneous aquifers.