Flowing partially penetrating well: solution to a mixed-type boundary value problem

A new semi-analytic solution to the mixed-type boundary value problem for a ̄owing partially penetrating well with in®nitesimal skin situated in an anisotropic aquifer is developed. The solution is suited to aquifers having a semi-in®nite vertical extent or to packer tests with aquifer horizontal boundaries far enough from the tested area. The problem reduces to a system of dual integral equations (DE) and further to a deconvolution problem. Unlike the analogous Dagan's steady-state solution [Water Resour. Res. 1978; 14:929±34], our DE solution does not su€er from numerical oscillations. The new solution is validated by matching the corresponding ®nite-di€erence solution and is computationally much more ecient. An automated (Newton±Raphson) parameter identi®cation algorithm is proposed for ®eld test inversion, utilizing the DE solution for the forward model. The procedure is computationally ecient and converges to correct parameter values. A solution for the partially penetrating ̄owing well with no skin and a drawdown±drawdown discontinuous boundary condition, analogous to that by Novakowski [Can. Geotech. J. 1993; 30:600±6], is compared to the DE solution. The D±D solution leads to physically inconsistent in®nite total ̄ow rate to the well, when no skin e€ect is considered. The DE solution, on the other hand, produces accurate results. Ó 1999 Elsevier Science Ltd. All rights reserved.