Two exact solutions for a cylindrical in homogeneity in a multi-aquifer system

Two new exact solutions are presented for steady-state, uniform flow through a cylindrical inhomogeneity in a multi-aquifer system. The solutions are valid for an arbitrary number of aquifers, and all aquifer properties may change from outside to inside the cylinder. The first problem concerns flow in a confined aquifer. The second problem is similar to the first problem, but now the cylinder is bounded on top by a lake with a semi-permeable bottom and a fixed water level; a constant amount of water may be extracted from the lake. The equations are derived in a radial coordinate system and make use of the known solution for uniform flow through a cylindrical inhomogeneity in a single aquifer, and the general theory for flow in leaky, multi-aquifer systems. Separate equations are presented for the head, flow, and leakage inside and outside the cylinder; a complete set of linear equations is presented to solve for the coefficients in the solutions. For each solution a specific example is presented for flow in a system with three aquifers. Rather complicated leakage patterns are obtained when inside the cylinder the transmissivity of the top aquifer is increased, the transimissivity of the middle aquifer is decreased, and the transmissivity of the bottom aquifer is kept constant.