Multiphysics Modeling Investigation of Wellbore Storage Effect and Non‐Darcy Flow

Abstract

AbstractThis study presents a comprehensive investigation of wellbore storage effects and non‐Darcy flow in pumping well systems using a multiphysics numerical model. The model incorporates the Reynolds‐averaged Navier‐Stokes equations coupled with a moving free surface to simulate the flow field and drawdown in the wellbore. Hydraulic behavior of the system, including well and aquifer drawdown, pumped water ratio, aquifer flow nonlinearity, and wellbore flow field, is analyzed and compared with simplified 1‐D models. This study highlights the presence of a vortex in the wellbore flow field induced by large Reynolds number and the uneven stress distribution at the screen. This vortex influences the wellbore drawdown and introduces 2‐D flow in the surrounding aquifer, which further contributes to the longer travel paths for groundwater particles and increased hydraulic pressure consumption. The results show that non‐Darcy flow, coupled with wellbore storage effects, leads to higher drawdown in the pumping well compared to Darcy flow cases. The aquifer drawdown exhibits a similar temporal pattern but with decreasing deviation at larger distances due to the cone of depression. The pumped water ratio indicates the challenge of supplying outflow at the intake from aquifer storage, with nonlinear flow resulting in a smaller ratio compared to linear cases. A nonlinearity ratio is defined to illustrate the expansion of nonlinear flow regions over time, their convergence to a predictable quasi‐steady‐state shape, which is influenced by the Forchheimer parameter, and the gradual transition to Darcy flow away from the wellbore.