A generalized non-Darcian radial flow model for constant rate test

Models used for data interpretation of constant rate tests (CRTs) are commonly derived with the assumption of Darcian flow in an idealized geometry, hence disregarding the non-Darcian nature of fluid flow and the complexity of flow geometry. In this study, an Izbash's law-based analytical model is proposed by means of Laplace transform and linearization approximation for interpretation of non-Darcian flow in a generalized radial formation where the flow dimension may become fractional between 1 and 3. The source storage and skin effects are also considered in the model development. The proposed model immediately reduces to Barker's (1988) model for Darcian flow in the generalized radial formation and to Wen et al.' s (2008a) model for non-Darcian flow in a two-dimensional confined aquifer. A comparison with numerical simulations shows that the proposed model behaves well in low non-Darcian flow condition or at late times. The proposed model is finally applied for data interpretation of the constant rate pumping tests performed at Ploemeur, showing that the estimated hydraulic properties (i. e., hydraulic conductivity, specific storage coefficient, non-Darcy exponent, and the dimension of flow geometry) are well representative of the hydrogeologic conditions on the field scale at the test site after the exploitation of groundwater. The proposed model is an extension of the generalized radial flow (GRF) model, which would be of significance in the problem of choosing an appropriate dimension of flow geometry in which non-Darcian flow occurs.