Hydraulics of a partially penetrating well: solution to a mixed-type boundary value problem via dual integral equations

Abstract

New semi-analytic solutions are obtained for well response to the pumping test and slug test performed on a partially penetrating well. The solutions account not only for the wellbore storage, infinitesimal skin, and aquifer anisotropy, but also for the mixed-type boundary condition at the well face, which is novel. The solutions are obtained via the method of dual integral equations (DE). The new solutions are computationally robust and efficient, about one to two orders of magnitude faster than the corresponding finite difference solutions. Existing approximate solutions obtained with flux–flux discontinuous boundary conditions are compared to our DE solutions. The accuracy of the approximate solutions appears to be adequate for slender well screens. Our DE solution is computationally more efficient than the approximate solutions. In the range where the approximate solutions are less accurate the DE solution is about an order of magnitude faster. More important, the new solutions provide the correct distribution of the point flux (local velocity) along the well screen, unlike all existing solutions. This feature is essential in cases where vertical variations of hydraulic conductivity are sought (e.g. in flowmeter tests), and for tracer tests.