Flow focusing associated with doublet operation

Heat and cold storage in the subsurface as well as geothermal energy provision intrinsically involve cyclic pumping operations, often in fields of several boreholes. We investigated the pressure and flow-rate fields resulting from the simultaneous periodic operation of two boreholes. The interference in pressure experienced by further (monitoring) boreholes can be assessed by an analytical solution when assuming radial flow from and to the pumping wells. This solution is derived through superposition, relying on the known solution for periodic pumping in a single well. The pressure gradient field, indicative of flow direction, is distorted from radial form, implying dominant flow and consequently heat advection between the two boreholes. We compared the analytical results to observations from field tests conducted in four boreholes located close to the northwestern banks of an artificial freshwater reservoir, the Kemnader See, at the southern city-limits of Bochum, Germany. In the light of the derived solutions, the field observations allow us to assess the role of inhomogeneity and fracture flow for the flow focusing between the pumping wells. Solving and investigating the hydraulic problem constitutes the necessary first step towards devising schemes for the optimization of cold and heat storage or geothermal energy provision by varying the period and phase of pumping coeval operations in several boreholes.