Analytical Solution for Timedrawdown Response to Constant Pumping from a Homogeneous, Confined Horizontal Aquifer with Unidirectional Flow
Abstract
An exact analytical solution to the ordinary onedimensional partial differential equation is derived for transient groundwater flow in a homogeneous, confined, horizontal aquifer using Laplace transformation. The theoretical analysis is based on the assumption that the aquifer is homogeneous and onedimensional (horizontal); confined between impermeable formations on top and bottom; and of infinite horizontal extent and constant thickness. It is also assumed that there is only a single pumping well penetrating the entire aquifer; flow is everywhere horizontal within the aquifer to the well; the well is pumping with a constant discharge rate; the well diameter is infinitesimally small; and the hydraulic head is uniform throughout the aquifer before pumping. Similar to the Theis solution, this solution is suited to determine transmissivity and storativity for a two dimensional, vertically confined aquifer, such as a long vertically fractured zone of high permeability within low permeable rocks or a long, highpermeability trench inside a lowpermeability porous media. In addition, it can be used to analyze timedrawdown responses to pumping and injection in similar settings. The solution can also be used to approximate the groundwater flow for unconfined conditions if (1) the variation of transmissivity is negligible (groundwater table variation is small in comparison to the saturated thickness); and (2) the unsaturated flow is negligible. The errors associated with the use of the solution to unconfined conditions depend on the accuracies of the above two assumptions. The solution can also be used to assess the impacts of recharge from a seasonal river or irrigation canal on the groundwater system by assuming uniform, time constant recharge along the river or canal. This paper presents the details for derivation of the analytical solution. The analytical solution is compared to numerical simulation results with example cases. Its accuracy is also assessed and discussed for confined and unconfined conditions.
 Publication:

AGU Fall Meeting Abstracts
 Pub Date:
 December 2007
 Bibcode:
 2007AGUFM.H23G1732P
 Keywords:

 1829 Groundwater hydrology;
 1832 Groundwater transport;
 1847 Modeling