A semi-analytical model for slug tests considering near-well non-darcy effects

Parameter estimation from slug tests is highly dependent on the physical assumptions underlying the theoretical models used for interpretation. Instantaneous excitation can substantially increase the hydraulic gradient and seepage velocity near the wellbore, thereby inducing Forchheimer-type nonlinear flow. As a result, conventional linear models may implicitly compensate for near-well inertial dissipation by underestimating the permeability coefficient K. To address this issue, a semi-analytical model for slug tests in confined aquifers incorporating near-well non-Darcy effects was developed and solved using the Laplace transform and numerical inversion. The analysis shows that the well water-level response is most sensitive to K, followed by the Forchheimer coefficient \beta , whereas its sensitivity to the storage coefficient S is relatively weak. A pronounced response compensation relationship is also observed between K and β. Using a 1% error threshold as the criterion, the critical boundary radii for the Cooper-Bredehoeft-Papadopulos (CBP) model and the semi-analytical model incorporating near-well non-Darcy effects are 8.31 m and 10.65 m, respectively. Laboratory experiments show that the deviation between measured responses and the CBP model becomes more pronounced with increasing excitation intensity, while the K values estimated by the CBP model decrease. In contrast, the estimates obtained using the semi-analytical model incorporating near-well non-Darcy effects agree better with the independent reference range derived from pumping tests. These findings demonstrate that, when non-Darcy inertial effects are significant, accounting for near-well non-Darcy effects can reduce the bias in K estimation.