Theory of thermal recovery from a spherically stimulated hot dry rock reservoir

A conceptual model is presented to describe thermal recovery from a semi-infinite hot dry rock (HDR) geothermal reservoir containing an equidimensional permeable zone. Transient behavior may be represented uniquely by five dimensionless parameters. Variation in production temperature TD with time tD is influenced by reservoir throughput QD thermal porosity ϕD and depth ratio a/z. Of these, only throughput QD exercises significant control on transient performance, the parameter being directly proportional to reservoir circulation rate and inversely proportional to the effective radius of the stimulated zone. Steady production temperature TD is indexed to throughput QD and depth ratio a/z, only. Steady production temperatures are always highest for a host medium bounded by a proximal constant temperature surface and lowest for an insulated boundary. Boundary effects are insignificant for reservoir burial depths up to an order of magnitude greater than the reservoir radius. A threshold behavior in time (tDQD) is evident for very large reservoir throughput (QD). This bounding behavior describes, in dimensionless time, the maximum rate at which thermal depletion may occur. This state is evident for large dimensionless throughput magnitudes (QD) corresponding directly with high circulation rates within the reservoir. Predictions compare favorably with results from a 300-day circulation test at the Fenton Hill Geothermal Energy Site, New Mexico.

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