Constant-head test at a partially penetrating well in an aquifer-aquitard system

An analytical model for describing pumping induced drawdown by constant-head test at a partially penetrating well in a leaky confined aquifer is developed by treating the leakage of aquitard storage as an interface phenomenon rather than an volumetric effect, which is the novel and never developed so far. Three different cases of remote lateral boundaries are considered in the model. The new drawdown solution in Laplace space is obtained and inverted into time-domain solution utilizing the Stehfest method. The (semi-)analytical solutions for well discharge are then obtained under three different cases. Analytical solutions in Laplace and time domains are developed for calculating the (total) leakage rate and volume across the aquitard-aquifer interface due to constant-head test at a partially penetrating well in a leaky confined aquifer, and such solutions are of great use for groundwater resource management. Based on the newly developed solutions, the distribution of wellbore flowrate and aquitard leakage are explored and the sensitivity analysis is conducted to identify the most important controlling factor. The sensitivity analysis shows that the wellbore flowrate and the drawdown in infinite (Case 1), finite (Case 2), and closed (Case 3) leaky confined aquifer systems are both sensitive to the variation of well partial penetration, well radius, and aquifer anisotropic ratio during the whole pumping period and they are most sensitive to the change of outer boundary distance at late time for Case 3. The effect of the outer boundary on the drawdown or wellbore flowrate is more significant for a shorter outer boundary distance.