NON-DARCIAN FLOW TOWARDS A FINITE-DIAMETER VERTICAL WELL IN A CONFINED AQUIFER

Most of previous studies on flow to finite-diameter wells were based on a presumption that flow was Darcian. However, under certain circumstances, flow can be non-Darcian, manifested by a nonlinear relationship between the specific discharge and the hydraulic gradient. We have analyzed non-Darcian radial flow towards a finite-diameter well which fully penetrates a confined aquifer on the basis of the Izbash equation with consideration of wellbore storage effect. We have provided semi-analytical solutions of drawdown by using the Boltzmann transformation, and obtained approximate analytical solutions of drawdown at both early and late times. MATLAB programs have been developed to facilitate computation of the semi-analytical solutions, and the results are presented as type curves in log-log plots. It is found that all the type curves at the face of the pumping wellbore with different turbulent factor values are straight lines and approach the same asymptotic values at early times. The pumping rate comes from wellbore storage only at early times, and the wellbore storage effect disappears at late times. The drawdown in the aquifer (outside the well) decreases at early times and increases at late times, respectively, as the turbulent factor increases. Another observation is that at early times the drawdown outside the well is proportional to time with a power of n/(n-1), where n is the power index in the Izbash equation. The drawdown at the face of the pumping wellbore is slightly influenced by n values, while the drawdown in the aquifer decreases at early times and increases at late times, respectively, as the n values increase.