An approximate analytical solution for non-Darcian flow in a confined aquifer with a single well circulation groundwater heat pump system

An analytical model is proposed in this study to describe transient drawdown induced by non-Darcian flow in a confined aquifer with a single well circulation groundwater heat pump system. The Izbash equation and a linearization method are employed to describe non-Darcian flow in the horizontal direction of a confined aquifer and to approximate the nonlinear term in the governing equation, respectively. By applying a combination of the Laplace and Fourier cosine transforms, an approximate analytical solution in the Laplace domain is obtained, which is numerically inverted to obtain transient drawdown in the time domain using the Stehfest algorithm method. The results of the derived analytical solution for the special case of Darcian flow (m = 1) correspond well with the existing solution derived using Darcy's law. The steady-state analytical solution in the time domain is obtained by applying the Fourier cosine transform. Moreover, the sensitivity analysis is performed to investigate the influence of selected parameters, such as the power index m, the radial hydraulic conductivity Kr, the aquifer specific storage S, and the length of the sealed section d2, on drawdown. The results show that each parameter has its influence period on drawdown, and that drawdown is more sensitive to the power index m compared to other parameters.