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Non‐Darcian flow toward an injection well fully penetrating a leaky confined aquifer with clogging‐induced permeability reduction

Managed aquifer recharge (MAR) using aquifer injection wells is generally developed with the validity of Darcy's law and assumption of a constant hydraulic conductivity, hence ignoring the non‐Darcian nature of groundwater flow and the spatiotemporal permeability reduction owing to well and aquifer clogging. In this study, an Izbash's law‐based analytical model is proposed for constant‐rate recharge (CRR) and constant‐head recharge (CHR) with special consideration of well and aquifer clogging using a time‐dependent hydraulic conductivity (K) function. By means of linearization approximations, variable substitutions and Hankel and Weber transforms, approximate analytical solutions for the model are derived. The early‐time and late‐time solutions and the steady‐state solutions are also derived using the developed approximate solutions. A comparison with numerical solutions indicates that the approximate solutions are highly accurate except during the short period of initial recharge stage. Then, a semi‐log graphic approach based on the developed solutions is tendered for estimating parameters associated with the clogging effect and non‐Darcian aquifer property. The proposed model offers a straightforward way for the quantitative assessment of the non‐Darcian flow dynamics in confined aquifers experiencing clogging and can be adopted for the estimation and prediction of clogging‐related permeability reduction in MAR using aquifer injection wells.