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.

中文翻译：

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多裂隙增强地热库三维传热的积分方程解

为了预测多裂隙地热储层的能量生产，以前的模型基本上集中于岩石中一维传导，该岩石包含等比例分布的均匀裂缝。在这里，描述了一个新颖的模型，以数值方式研究地热储层中三维热传递，这些热储层具有不均匀分布的，包括孔径和半径在内的各种尺寸的盘状裂缝。对于通过每条裂缝的水流，假设在裂缝（注水）井中心和裂缝内的不同位置，由裂缝裕度和开采（注入）操作引起的水压扰动得到了近似的解析解。注（采）井范围大致相等。通过二维平面裂缝的积分方程方案，模拟了三维热交换问题，而无需进行储集层离散化。在极坐标中分析计算出奇异积分，而在笛卡尔坐标中通过高斯求积法对非奇异积分进行数值估计。与一维简化相比，三维热传导显着改变了提取温度的预测。另外，储层温度场还受到裂缝的间距和尺寸的显着影响。本模型可用于地热储层的估计，设计和优化。在极坐标中分析计算出奇异积分，而在笛卡尔坐标中通过高斯求积法数值估算非奇异积分。与一维简化相比，三维热传导显着改变了提取温度的预测。另外，储层温度场还受到裂缝的间距和尺寸的显着影响。本模型可用于地热储层的估计，设计和优化。在极坐标中分析计算出奇异积分，而在笛卡尔坐标中通过高斯求积法对非奇异积分进行数值估计。与一维简化相比，三维热传导显着改变了提取温度的预测。另外，储层温度场还受到裂缝的间距和尺寸的显着影响。本模型可用于地热储层的估计，设计和优化。三维热传导显着改变了提取温度的预测。另外，储层温度场还受到裂缝的间距和尺寸的显着影响。本模型可用于地热储层的估计，设计和优化。三维热传导显着改变了提取温度的预测。此外，储层温度场还受到裂缝间距和尺寸的显着影响。本模型可用于地热储层的估计，设计和优化。