The utilization of aquifer energy is a new technology closely related to the development of injection and production well technologies. Accurately predicting the effective use of geothermal energy storage in a surrounding aquifer is of great significance. A developed theory of groundwater hydro-geothermal transfer is suggested by analyzing the general features of stored energy in aquifers together with the interactions between flow connections and thermal breakthroughs. Based on the water-heat transfer in an aquifer, a coupled numerical model of groundwater flow and heat transfer is established using FEFLOW software for an injection and production wells system in the city of Xianyang to simulate the flow and temperature field. The results show that the key for the formation of a flow connection is the hydraulic gradient. That is, whether the flow connection will occur can be judged quantitatively according to the hydraulic gradient. Flow connections occur more easily through greater flow quantities and quicker injection and pumping rates, which lead to earlier occurrences of thermal breakthroughs. At an operation time of 120 days, to prevent thermal breakthroughs in the production wells, the reasonable well spacing was between 180 and 200 m, and the optimal well spacing was 180 m. This method is of great