A Forchheimer's law-based analytical model for constant-rate tests with linear flow pattern

Abstract

Aquifers with quasi-linear flow pattern are frequently envisaged in fractured zones, in oil, gas or enhanced geothermal reservoirs, or in civil engineering where cut-off walls are constructed. The water flow towards a well in this linear aquifer system has been long investigated under Darcian flow condition, but remains an open issue for non-Darcian flow. In this study, a general linearization approximation strategy is suggested for the Forchheimer equation, and an analytical solution is proposed by using Laplace transform for non-Darcian flow towards a well in aquifers laterally bounded by no-flow barriers. Numerical simulations using the finite volume method prove that the linearization approximation performs best when it takes the mean of two commonly-used strategies, and the analytical model is sufficiently accurate at late times for observation wells located moderately far from the source. The proposed model was applied to data interpretation of the pumping tests at the Changheba dam foundation bounded by two cut-off walls in Southwest China, where the drawdown curves can be divided into 1D flow, transitional flow and 2D flow stages as a result of lateral flow through weathered bedrocks at late times. The proposed model provides a valuable tool for characterizing the hydraulic properties of aquifers and reservoirs with a linear flow pattern and for assessing the possible leakage through the lateral barriers by type curve matching.