Analytical and semi-analytical solutions of horizontal well capture times under no-flow and constant-head boundaries

Abstract

The closed-form analytical solutions and semi-analytical solutions of capture times to horizontal wells are derived for different recovery scenarios. The capture time is the time a fluid particle takes to flow to the well. The first scenario is recovery from a confined aquifer in which the influence of regional groundwater flow upon the capture time is included. The second scenario is recovery from underneath a water reservoir in which the top boundary of the aquifer is constant-head. The third scenario is recovery from a low-permeability layer bounded above and below by much higher permeability media. Closed-form solutions are provided for the cases with: (1) a center or a bottom well for the first scenario; (2) a bottom well for the second scenario; and (3) a center well for the third scenario. Semi-analytical solutions are provided for general well locations for those scenarios. Solutions for both isotropic and anisotropic media are studied. These solutions can be used as quick references to calculate the capture times, and as benchmarks to validate numerical solutions. The limitations of the analytical solutions are analyzed. Our results show that the top and bottom no-flow boundaries of an aquifer constrain the vertical flow, but enhance the horizontal flow, resulting in elongated iso-capture time curves. When constant-head boundaries are presented, water can infiltrate vertically across those boundaries to replenish the aquifers, resulting in less elongated iso-capture time curves.