A simplified model for heat extraction by circulating fluid through a closed-loop multiple-fracture enhanced geothermal system

Multiple hydraulic fractures have been proposed for improving the performance of an enhanced geothermal system (EGS) by providing conductive flow pathways and increased contact area between flowing fluid and surrounding rock formation. Use of more fractures incurs a higher drilling and hydraulic fracturing cost, but the additional cost can be offset by improved operation performance of an EGS. In this paper, a model is presented for efficiently predicting the output temperature so as to optimize the number of fractures and fracture spacing to maximize the EGS lifetime under a constant circulation rate. This optimal spacing is shown to arise due to the interplay among number of fractures, fracture spacing, well depth, and the pre-existing geothermal gradient. Specifically, under a typical geothermal gradient associated with EGS for a 5km total vertical depth of the well, the number of fractures N and the equal fracture spacing d have optimal values: 6⩽N⩽13 and 30m⩽d⩽90m. In addition, the semi-analytical solution method presented is effective and efficient in computation and, for this reason, is useful for optimizing the design of a geothermal reservoir with multiple layers at equal or non-equal spacing.

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