Integral equation solution for three-dimensional heat transfer in multiple-fracture enhanced geothermal reservoirs |
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| Authors: | Dong Dong Liu Yan Yong Xiang Jin Lei Zheng |
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| Institution: | School of Civil Engineering, Beijing Jiaotong University, Beijing, China |
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| Abstract: | For the prediction of energy production from multiple-fractured geothermal reservoirs, previous models basically focused on the one-dimensional conduction in the rock containing evenly distributed fractures of equal scale. Here, a novel model is described to numerically investigate the three-dimensional heat transfer in geothermal reservoirs with unevenly spaced disc fractures of various sizes including the aperture and radius. In terms of the water flow through each fracture, an approximate analytical solution is obtained on the assumption that the water pressure disturbances, induced by the fracture margin and extraction (injection) operation, at the injection (extraction) well center and at different locations within the injection (extraction) well range were approximately equal. By the integral equation scheme for two-dimensional planar fractures, the three-dimensional problem of heat exchange is simulated without the reservoir discretization. The singular integral is analytically calculated in polar coordinates whereas the nonsingular integrand is numerically estimated by the Gaussian quadrature method in Cartesian coordinates. Compared with the one-dimensional simplification, the three-dimensional heat conduction remarkably alters the prediction of extraction temperature. In addition, the reservoir temperature field is also significantly influenced by the spacings and dimensions of fractures. The present model may be used for the estimation, design, and optimization of a geothermal reservoir. |
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| Keywords: | enhanced geothermal systems integral equation method multiple fractures |
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