An analytical solution of the seepage field for single-well circulation (SWC) ground water heat pump systems (GWHPs)

The structure of SWC systems is totally different from conventional GWHPs, such as standing column systems or double-well systems with separate pumping and injection wells. A single well is divided into two partially penetrating wells by special clapboards. The upper, partially penetrating well represents an injection section for injecting groundwater at a rate Q to a confined aquifer. The middle section is a sealed section, which prevents injected water from flowing to the pumping section. The lower, partially penetrating well is a pumping section, from which groundwater is pumped at the same rate Q. In this study, groundwater flow around partially penetrating wells in a confined aquifer is investigated. The analytical solution for the drawdown of groundwater is derived first in the Laplace domain and then inverted numerically using the Stehfest algorithm method. The effects of different parameters related to the SWC system on the drawdown are also presented. The results show that the steady drawdown contour is symmetric with the midline of the aquifer and varies tremendously with the distance to the well axis. The contours of the drawdown around the sealed section are dense, indicating that the hydraulic gradient in this area is relatively large. The drawdown increases with the radial saturated hydraulic conductivity (K_r) at early times, while it decreases as K_r increases at late times. The larger specific storage S results in a lager drawdown at early times, while the drawdown remains the same at late times for different specific storage values. The length of the sealed section d₂ also impacts the drawdown. At early times the drawdown increases with d₂, while at late times a smaller drawdown is a result of larger d₂. Additionally, the sensitivity analysis of the results to the system parameters such as the radial and vertical hydraulic conductivities, K_r and K_z, respectively, the length of the sealed section d₂, and the specific storage S of the SWC system was performed. The results show that the drawdown is not sensitive to these parameters at early times, while it is very sensitive to these parameters at late times, particularly to the horizontal hydraulic conductivity, K_r.