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Approximate solutions are found for a mathematical model developed to predict the heat extraction from a closed-loop geothermal system which consists of two vertical wells (one for injection and the other for production) and one horizontal well which connects the two vertical wells. Based on the feature of slow heat conduction in rock formation, the fluid flow in the well is divided into three stages, that is, in the injection, horizontal, and production wells. The output temperature of each stage is regarded as the input of the next stage. The results from the present model are compared with those obtained from numerical simulator TOUGH2 and show first-order agreement with a temperature difference less than 4°C for the case where the fluid circulated for 2.74 years. In the end, a parametric study shows that (1) the injection rate plays dominant role in affecting the output performance, (2) higher injection temperature produces larger output temperature but decreases the total heat extracted given a specific time, (3) the output performance of geothermal reservoir is insensitive to fluid viscosity, and (4) there exists a critical point that indicates if the fluid releases heat into or absorbs heat from the surrounding formation.

An Approximate Solution for Predicting the Heat Extraction and Preventing Heat Loss from a Closed-Loop Geothermal Reservoir