New analytical model for constant-head pumping: Considering rate-dependent factor at well screen

Abstract

Non-Darcy flow due to pumping may occur at the well screen and yields some head loss. Unlike the wellbore skin yielding a constant head loss at the well, the studies in petroleum engineering indicate that the head loss due to the non-Darcy flow is proportional to the pumping rate. The head loss due to non-Darcy flow is quantified by a rate-dependent factor at the well screen. To our knowledge, such a head loss is never considered in the area of groundwater hydraulics. In light of this, this study develops a groundwater flow model for the constant-head pumping with a head loss expressed in terms of a rate-dependent factor at a fully penetrating well in a confined aquifer. A skin factor representing the head loss due to the presence of wellbore skin is also incorporated into the model. The consideration of the rate-dependent factor, however, would make the model nonlinear. The model has a steady-state flow equation with a time-dependent finite outer boundary to approximate the transient groundwater flow in the aquifer system. The solutions to the model for the drawdown and wellbore flowrate are developed and compared with the finite difference solutions. With the help of the present solutions, the sensitivity analyses of the aquifer drawdown and wellbore flowrate are made. The effects of the wellbore skin and non-Darcy flow on the drawdown are also investigated. The wellbore flowrate solution is then applied to estimate the aquifer parameters based on the field data from a constant-head injection test in a confined aquifer. The prediction of the present solution gives the best fit to the field measured data as compared with three existing solutions, indicating that the consideration of the rate-dependent factor improves the aquifer parameter estimation. The results of the parameter estimation also reflect the quality of the well installation.