A numerical study of non-Darcy flow in EGS heat reservoirs during heat extraction

Abstract

Underground non-Darcy fluid flow has been observed and investigated for decades in the petroleum industry. It is deduced by analogy that the fluid flow in enhanced geothermal system (EGS) heat reservoirs may also be in the non-Darcy regime under some conditions. In this paper, a transient 3D model was presented, taking into consideration the non-Darcy fluid flow in EGS heat reservoirs, to simulate the EGS long-term heat extraction process. Then, the non-Darcy flow behavior in water- and supercritical CO₂ (SCCO₂)-based EGSs was simulated and discussed. It is found that non-Darcy effects decrease the mass flow rate of the fluid injected and reduce the heat extraction rate of EGS as a flow resistance in addition to the Darcy resistance which is imposed to the seepage flow in EGS heat reservoirs. Compared with the water-EGS, the SCCO₂-EGS are more prone to experiencing much stronger non-Darcy flow due to the much larger mobility of the SCCO₂. The non-Darcy flow in SCCO₂- EGSs may thus greatly reduce their heat extraction performance. Further, a criterion was analyzed and proposed to judge the onset of the non-Darcy flow in EGS heat reservoirs. The fluid flow rate and the initial thermal state of the reservoir were taken and the characteristic Forchheimer number of an EGS was calculated. If the calculated Forchheimer number is larger than 0.2, the fluid flow in EGS heat reservoirs experiences non-negligible non-Darcy flow characteristic.

Keywords

enhanced geothermal system / non-Darcy flow / heat extraction / Reynolds number / Forchheimer number

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Acknowledgments

This work was supported by the National Key R&D Program of China (2018YFB1501804), the Strategic Priority Research Program of Chinese Academy of Sciences (XDA21060700), the National Natural Science Foundation of China (Grant No. 41702256), and the Natural Science Foundation of Guangdong Province (2017A030310328).

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