Model for well hydraulics of constant-head injection using a partially penetrating well considering clogging in well vicinity

To address the issue that the traditional models of well hydraulics for constant-head tests (CHTs) fail to reflect the effects of the clogging in well vicinity on groundwater flow dynamics, a semi-analytical model of the groundwater hydraulics in well vicinity is developed for CHTs using partially penetrating wells. A combination of variable substitution, Laplace transform and finite Fourier cosine transform is used to develop the solutions for the proposed model in the Laplace domain. Then, the solutions in the real-time domain are obtained using the Stehfest numerical Laplace inversion method. A parametric study of the developed solution indicates that a smaller asymptotic hydraulic conductivity K_{r, ∞} leads to the smaller hydraulic head increment s and the less injection flux Q and reduces the quasi-steady flow dynamics of the recharged aquifer, while a larger permeability reduction exponent λ decreases s and Q only in the middle stage of the injection tests but has few effects on the quasi-steady flow dynamics. The hydraulic head difference due to various values of K_{r, ∞} and λ first increases and then decreases with the radial distance and reaches its maximum value at the interface of the clogging region and the formation. The clogging in well vicinity results in an obvious inflection point at the outside boundary of the clogging region on the distribution curve of s and leads to an apparent decreasing stage of the history curve of s, which can offer theoretical reference for the evolution and prediction of the clogging development.