Semi-analytical solutions for transient flow to a partially penetrated well with variable discharge in a general three-layer aquifer system

Abstract

A general semi-analytical model for transient flow in a three-layered aquifer system with a partial penetration well having a variable discharge of pumping is developed with the consideration of the interface flow on the adjacent layers. This general three-layer system includes the conventional aquitard-aquifer-aquitard system as a subset and does not require that the permeability contrasts of different layers must be greater than a few orders of magnitude and does not ignore any flow components (either vertical or horizontal) in any layer. The pumping well of infinitesimal radius is screened at any portion of the middle layer. Three widely used types of top and bottom boundary conditions are assigned prescribed head (Case 1), zero flux (Case 2), or prescribed head at top and zero flux at bottom (Case 3). Laplace domain solutions for dimensionless drawdown are obtained using Hankel transformation, and associated time-domain solutions are evaluated numerically. The newly obtained solutions include some available solutions for two- or single-layer aquifer systems as subsets. The drawdowns for individual layers caused by a well with an exponentially decreased discharge are explored as an example of illustration. The results indicate that the pumped layer drawdown close to the partially penetrated well is mainly influenced by the variable pumping rate. The late-time drawdown for all layers is remarkably affected by the chosen types of top and bottom boundary conditions, and the drawdown for Case 3 is greater than that for Case 1 and smaller than that for Case 2. Additionally, the effect of the pumped layer anisotropy on drawdowns in the three-layer system is significant, and the anisotropy of the unpumped layers significantly affects the drawdown in the whole aquifer system without large contrast of hydraulic conductivity between the unpumped layers and the pumped layer. The drawdowns in all three layers are greatly affected by the location and length of well screen, and a larger drawdown can be seen at the position that is closer to the middle point of the screen of the partially penetrating pumping well.