Semi-analytical solutions for groundwater flow dynamics in confined aquifers under constant-rate injection considering clogging of aquifers around well

To investigate the effect of clogging of aquifers around well on the flow dynamics in the well vicinity during the constant-rate recharge using a partially penetrating injection well, an analytical model for well hydraulics was proposed with special consideration of the clogging-related permeability reduction, which was assumed to reduce exponentially with time. By means of the variable substitution and the Laplace and finite Fourier cosine transforms, the solutions for the hydraulic head increment in the Laplace domain were derived and then the solutions in the real-time domain were obtained using the Stehfest numerical inversion method. A parametric study indicates that: a smaller asymptotic hydraulic conductivity K-r,K-infinity can not only increase the hydraulic head increment and the injection pressure during the recharge process but also accelerate the flow dynamics of the recharged aquifer at the quasi-steady state, whereas a larger permeability reduction exponent lambda only result in larger hydraulic head increment and the injection pressure during the recharge process but doesn't affect the flow dynamics at the quasi-steady state. The hydraulic head difference distribution due to various K-r,K-infinity and lambda values reaches its maximum value in the wellbore and then decreases gradually with the radial distance. The findings of this study can offer theoretical reference for the estimation and prediction of the clogging in the aquifer around well during the constant-rate injection test.