A Laplace-transform boundary element model for pumping tests in irregularly shaped double-porosity aquifers

Abstract

In this paper, a novel Laplace-transform boundary element model for pumping tests in irregularly shaped double-porosity aquifers is presented. The aquifer could be associated with various boundary conditions, such as the general Robin boundary conditions or even the mixed boundary conditions with no-flow boundary on one side and constant head boundary on the other side. The derived solution has analytical characteristics since it is obtained through the Green’s function method within the domain. Unlike traditional numerical methods, the proposed solution using the Laplace-transform boundary element method does not require discretization in spatial and temporal dimensions. In this study, boundary integral equation using Green's second theorem and the fundamental solution of Green function for dual-porosity models are given. A boundary element matrix in Laplace space is established, which allow us to consider irregularly shaped boundary. The drawdown and flux on the boundary can be obtained through solving the boundary element matrix by Gauss's elimination method. The final solution for wellbore drawdown is evaluated using numerical Laplace inversion algorithm of Stehfest (1970). Many previous solutions for transient flow in finite single-porosity aquifers with no-flow outer boundary condition are shown to be special cases of the present solution. Furthermore, the solution with a mixed outer boundary condition is used to investigate the effect of important parameters of aquifers on wellbore drawdown, including fracture storage coefficient, inter-porosity flow coefficient from matrix to fissures, boundary shape, boundary location, and interference of multiple wells.