A Simplified Solution Using Izbash's Equation for Non-Darcian Flow in a Constant Rate Pumping Test.

Abstract

This paper derives an equivalent of Darcian Theis solution for non-Darcian flow induced by constant rate pumping of a well in a confined aquifer. The derivation, which is valid at later times only, is original. It utilizes Izbash's equation. This introduces an additional parameter to Darcian condition, namely, empirical exponent. The solution is a non-Drcian equivalent of Jacob straight line method for analyzing pumping tests at late times. It can be used to determine aquifer parameters: storativity, analogous hydraulic conductivity, and empirical exponent. However, while the Jacob method requires a minimum of only one pumping test with one observation well, the additional parameter in the present solution means that a minimum of two observation wells in one test or two pumping tests at different rates with one observation well are required. The derived solution is applied to a case study at Plomeur in Brittany, France, and is shown to provide a practical and efficient method for analyzing pumping tests where non-Darcian groundwater flow occurs.