A semi-analytical approach to simulate cross-flow effect on the flow behavior of partially penetrating well in two-layer confined aquifer by Green function method

A semi-analytical model for the transient flow problem of a partially penetrating well in three-dimensional anisotropic two-layer confined aquifer is developed by taking the cross-flow between two layers into consideration. Using the Green function and boundary element method in Laplace space, a matrix is established and solved by Gauss’s elimination method. The drawdown solution is inverted to the time domain by using numerical inversion algorithm of Stehfest (1970). Importantly, the time of cross-flow occurrence can be indicated precisely. Moreover, the flow rate on penetrating segments and interfaces between layers at different flow stages are quantitatively investigated. The comparison between the semi-analytical solution and numerical solution shows an excellent agreement. In addition, one case for aquifer with two separate layers and another case for one single layer with an overlying gas cap or an underlying aquifer are also presented to show the differences between that with or without cross-flow effect. Finally, influencing factors including cross-flow coefficient, anisotropic factor, penetrating location, and penetrating ratio on both flow rate and drawdown are analyzed in detail.