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Implications of Wellbore Heat Transfer for Conductive Closed-Loop Geothermal Systems Roland HORNE [Stanford University, USA] |
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Closed-loop, or “advanced”, geothermal systems circulate a working fluid through a sealed conduit in hot rock, taking up heat by conduction alone and never producing formation fluid. The concept appears to be attractive because it removes the requirement for permeability, and with it the dry-hole risk, the scaling problems of produced fluid, and the pressure disturbance that accompanies injection. This paper examines what such a conduction-only system can deliver, using the standard single-phase wellbore heat transmission equations. In a coaxial well the two legs form a countercurrent heat exchanger, and the governing equations become a two-point boundary value problem whose linearized form has one growing eigenmode. A closed-form solution is given for uniform properties, together with an affine backward sweep that accommodates arbitrary variation of the conductances along the flow path and avoids the ill-conditioning that defeats a shooting method. With a perfectly insulated return leg the delivered heat is exactly the heat gain that an injection well experiences on its way down, and its ceiling is the formation conductance multiplied by the temperature difference available along the path, independent of circulation rate. This defines the “conduction ceiling”, which is the maximum heat output attainable, and which is easily calculable in advance. The conduction ceiling is almost exclusively a function of the formation properties, and the design of the completion only determines how much of the ceiling can be recovered. The consequences are restrictive. A 3000 m vertical well continued 3000 m as a lateral in rock at 150ºC delivers 765 kW of heat at 131ºC with perfect insulation and 568 kW at 108ºC with good vacuum-insulated tubing, against a conduction ceiling of 1660 kW. Thermal energy in the rock more than about 20 m from the hole is barely disturbed after ten years, and the system recovers under three percent of the heat lying within 50 m of the wellbore over its first decade. The ratio of leg-to-leg to leg-to-formation conductance determines how much of the ceiling survives. The U-loop configuration evades the short circuit by separating the legs with rock, at the cost of a second well and of an ordinary production heat loss on the return. Closed-loop designs suit direct use, heat storage and shallow borehole heat exchangers with heat pumps; for power generation they would require tens of kilometers of hole.
Topic: Reservoir Engineering