Groundwater flow in an inhomogeneous aquifer

An analytic solution is obtained for the groundwater head in a confined inhomogeneous and isotropic aquifer of constant thickness. The vertical z and horizontal y direction components of the groundwater flow are assumed to be zero. The specific storage S s is assumed to be a constant, but the hydraulic conductivity K is taken to be K = k o [1 − ( x/a )], where k o and α are constants. Initial and boundary conditions imposed on the groundwater head h(x, t) are h(x, 0) = 0 for 0 < x ≤ a and h(0, t ≥ 0) = h o , where h o is a constant. The solution for h(x, t) is found for 0 ≤ x ≤ a and t > 0. The solution is compared graphically with the solution for the case where K = k o and an impermeable boundary exists at x = a . The comparison shows that h(x, t) approaches its final value h o more rapidly for K = k o than for K = k o [1 − ( x/a )].