# Well-Doublets: A First-Order Assessment of Geothermal SedHeat Systems
### The Geothermal Doublet  
The well-doublet design (Figure 1) is the simplest approach to energy extraction in a closed or limited recharge SedHeat system, whether it is a deep liquid reservoir or a shallow ground-source heat pump system using an unconfined aquifer. From one well equipped with a lifting pump, the SedHeat aquifer supplies hot-water from which energy is extracted by a heat exchanger to be sent for power generation or direct heat use. Cooled geofluid re-injection takes place into another well placed at an optimum distance designed to meet the project's desired power profile (power = electrical and heat energy rate) [25] and sustain flow. The maximum energy rate (work or power) available, ignoring all of the minor hydraulic losses (pumps, fitting, etc.) and irrecoverable heat losses, is  
\[\dot{\text{E}}\ =\Delta\text{T}\cdot\dot{Q}\text{-}\text{c}_{\text{p}} \tag{1}\]  
where \(\dot{\text{E}}\) is the energy rate (power) in J/s, \(\Delta\)T = (T\({}_{\text{in}}\) -T\({}_{\text{out}}\)) in K, \(\dot{Q}\) is the flow rate in kg/s, and c\({}_{\text{p}}\) is the fluid heat capacity in J/kg\(\cdot\)K. T\({}_{\text{in}}\) and T\({}_{\text{out}}\) (units of K) refer to the inlet and exit temperatures in the energy (electricity + heat) extraction system, likely a heat exchanger. The fluid involved may be the natural fluids in the case of SedHeat development, or in the case of EG systems, it is likely to be an introduced fluid such as water or supercritical CO\({}_{2}\)[26]. Specifically, T\({}_{\text{in}}\) is not the original reservoir T\({}_{\text{o}}\); it is the temperature at the surface going into the energy system (the heat exchanger between the primary loop and the secondary power/heat system loop). It will eventually change with time as cool injected fluids begin to impinge upon the production well. Nor is T\({}_{\text{out}}\) equal to the ambient temperature; T\({}_{\text{out}}\) will always be higher because of thermodynamic constraints. Unextracted heat in the primary loop fluid is returned to the reservoir through fluid re-injection; if there are low-grade waste heat sources to increase T\({}_{\text{out}}\) through a downstream heat exchanger, the project life may be extended, and the low-grade heat exploited. The parameter \(\dot{Q}\) is mainly a function of the aquifer's permeability, thickness, and layering, the amount of energy desired or achievable, the aquifer's thermal properties and heat recovery time [8], and several secondary factors. A reasonable value for c\({}_{\text{p}}\) is 4180 J/kg\(\cdot\)K for pure freshwater, somewhat different for geofluids of different salinities. For fluids such as supercritical CO\({}_{2}\), different specific heats, fluid densities, and viscosities must be used, and these may be quite sensitive to P and T, leading to additional non-linear effects in modeling heat extraction. Using a recirculating well-doublet in a binary geothermal system means that remnant useable heat in the geofluid (e.g., 50-70 \({}^{\circ}\)C) is reinjected after electrical power generation, but if space heating is needed, additional heat can be stripped from the fluids, lowering re-injection T. Furthermore, coupling a deep doublet with a shallow ground-source heat pump system allows shallow seasonal heat storage and recovery (a thermal repository) and leads to higher efficiency and lower fossil-fuel use where there is a cooling deficiency in the summer [28], as in northern climates. Using a deep multi-well system allows injection/production strategies to be devised to maximize the system's value, while also exploiting the shallow heat repository in the winter when high heat demand exists. The  
Figure 1: Schematic illustration of a typical shallow geothermal well-doublet system with a single primary loop, no heat exchanger, in an unconfined aquifer (modified from [27]). design of such a system depends on the estimated power/thermal energy profiles for the year, combined with a safety factor, and noting that design in Canada (for example) must be to meet November-March energy needs.