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

New semi-analytic solutions are obtained for well response to the pumping t est 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 integra l equations (DE). The new solutions are computationally robust and efficien t, about one to two orders of magnitude faster than the corresponding finit e difference solutions. Existing approximate solutions obtained with flux-f lux discontinuous boundary conditions are compared to our DE solutions. The accuracy of the approximate solutions appears to be adequate for slender w ell screens. Our DE solution is computationally more efficient than the app roximate solutions. Tn the range where the approximate solutions are less a ccurate the DE solution is about an order of magnitude faster. More importa nt, the new solutions provide the correct distribution of the point flux (l ocal velocity) along the well screen, unlike all existing solutions. This f eature is essential in cases where vertical variations of hydraulic conduct ivity are sought (e.g. in flowmeter tests), and for tracer tests. (C) 1998 Elsevier Science B.V. All rights reserved.