A generalized Forchheimer radial flow model for constant-rate tests

Abstract

Models used for data interpretation of constant-rate tests (CRTs) are commonly derived with the assumption of Darcian flow in an idealized integer flow dimension, where the non-Darcian nature of fluid flow and the complexity of flow geometry are disregarded. In this study, a Forchheimer's law-based analytical model is proposed with the assumption of buildup (or drawdown) decomposition for characterizing the non-Darcian flow in a generalized radial formation where the flow dimension n may become non-integer. The proposed model immediately reduces to Barker's (1988) model for Darcian flow in the generalized radial formation and to Mathias et al.'s (2008) model for non-Darcian flow in a two-dimensional confined aquifer. A comparison with numerical simulations shows that the proposed model behaves well at late times for flow dimension n > 1.5. The proposed model is finally applied for data interpretation of the constant-rate pumping tests performed at Ploemeur (Le Borgne et al., 2004), showing that the intrinsic hydraulic conductivity of formations will be underestimated and the specific storage will be overestimated if the non-Darcian effect is ignored. The proposed model is an extension of the generalized radial flow (GRF) model based on Forchheimer's law, which would be of significance for data interpretation of CRTs in aquifers of complex flow geometry in which non-Darcian flow occurs.