Publications [#58010] of Zbigniew J. Kabala

Papers Published

1. Cassiani, G. and Kabala, Z.J. and Medina, M.A. Jr., Flowing partially penetrating well: solution to a mixed-type boundary value problem, Advances in Water Resources, vol. 23 no. 1 (1999), pp. 59 - 68 [S0309-1708(99)00002-0]
   (last updated on 2007/04/09)

   Abstract:
   A new semi-analytic solution to the mixed-type boundary value problem for a flowing partially penetrating well with infinitesimal skin situated in an anisotropic aquifer is developed. The solution is suited to aquifers having a semi-infinite 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 suffer from numerical oscillations. The new solution is validated by matching the corresponding finite-difference solution and is computationally much more efficient. An automated (Newton-Raphson) parameter identification algorithm is proposed for field test inversion, utilizing the DE solution for the forward model. The procedure is computationally efficient and converges to correct parameter values. A solution for the partially penetrating flowing 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 infinite total flow rate to the well, when no skin effect is considered. The DE solution, on the other hand, produces accurate results.

   Keywords:
   Flow of water;Boundary value problems;Aquifers;Mathematical models;Finite difference method;Algorithms;Boundary conditions;