Heat extraction efficiency in deep geothermal energy mining and implications for EGS-E
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摘要: 深地熱資源因其儲量大、清潔、可持續等優點在近年受到廣泛關注。不同的深地熱開發系統具有不同的熱儲改造方式，而這些熱儲改造方式決定了其與流體工質的換熱效率及采熱量。通過COMSOL Multiphysics多場耦合軟件系統對比了高滲透率、貫穿裂隙（管道）、隨機裂隙和隨機裂隙+貫穿裂隙熱儲模型的熱能提取效率，研究了水力作用、熱力作用和熱儲裂縫間距對裂隙開度的影響。研究結果表明高滲透熱儲的熱能提取效率最高，其次是隨機裂隙熱儲，隨后是隨機裂隙+貫通裂隙熱儲，最小的是貫通裂隙（管道）熱儲。熱儲裂隙開度演化受基巖冷卻收縮和裂隙流體壓力的競爭影響。增加基巖的冷卻收縮和裂隙流體壓力均能提升總裂隙開度；但是當基巖冷卻收縮起主導作用時（熱力作用），系統的注入能力提升；而當裂隙流體壓力起主導作用時（水力作用），系統的注入能力降低。減小裂隙間距可以顯著增加裂隙的熱力作用開度和總開度。當裂隙間距減小到50 m時，熱力作用開度增加為水力作用開度的4.8倍。因此對EGS-E（基于開挖的增強型地熱系統）的主要啟示為：（1）通過優化爆破或水力壓裂等工藝參數，使崩落的干熱巖盡量破碎，形成高滲透率熱儲，可大幅增加熱交換面積，提高熱能提取效率和采熱量；（2）在EGS-E熱儲分層致裂中，應盡量減小層間距，進而增加熱儲的整體裂隙開度，達到提高換熱效率的目的。Abstract: Geothermal energy has recently attracted substantial attention due to its abundant reserve, cleanness, and sustainability. Geothermal reservoirs can be stimulated via different approaches/techniques that lead to different heat extraction efficiencies and production through heat transfer between the working fluid and the reservoir network. Typical reservoir stimulation strategies include hydraulic fracturing, which is employed in conventional geothermal systems based on drilling, namely, EGS-D; indirect heat exchange using U-shaped pipes, namely, EGS-P; and block caving, which is based on the well-developed mining excavation framework, namely, EGS-E. Although the above three reservoir stimulation modes have been made available, their heat extraction performances for a certain reservoir over the operation lifespan have been unexplored. Selecting the appropriate reservoir stimulation approach and assessing the corresponding heat extraction performance are crucial for the design and subsequent operation of geothermal systems. Here, we systematically compared the heat extraction efficiencies of different stimulated reservoir networks under four typical stimulation modes, including a high-permeability reservoir (representing a reservoir stimulated by EGS-E), a connected fracture (representing a reservoir stimulated by EGS-P) reservoir, a reservoir with randomly distributed fractures (representing a reservoir simulated by EGS-D), and a reservoir with randomly distributed fractures and connected fractures (representing a reservoir simulated by the combination of EGS-D and EGS-P). The mechanical, hydraulic, and thermal coupling among the rock matrix, fracture network, and working fluid was realized in COMSOL Multiphysics. We found that the heat extraction efficiency of the high-permeability reservoir was the highest and that of the reservoir with randomly distributed fractures and connected fractures was the lowest. Crack aperture evolution was modulated by the competition between matrix contraction and hydraulic enhancement. The total crack aperture can be increased by increasing the matrix contraction and the hydraulic pressure of the working flow. Injection capability improved when the matrix contraction (thermal effect) prevailed but decreased when the working flow pressure (hydraulic effect) dominated. We also found that the smaller the matrix spacing, the larger the thermal effect-induced crack aperture and thus the total aperture. When the matrix spacing was reduced to 50 m, the thermal effect-induced crack aperture was nearly five times the hydraulic effect-induced crack aperture. The above findings have the following implications for EGS-E: first, the reservoir should be caved into fractured blocks that are as small as possible to increase permeability. Heat extraction efficiency and heat production can thus be highly promoted. Second, for the EGS-E with multiple reservoir slices, the slice spacing should be appropriately optimized to ensure high crack apertures and thus commensurate heat extraction efficiency.
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圖 1 數值模型. (a) 熱能提取效率研究數值模型; (b) 高滲透率模型; (c) 貫通裂隙（或管道）模型; (d) 隨機裂隙模型; (e) 貫通裂隙+隨機裂隙模型
Figure 1. Numerical model: (a) numerical model for heat extraction efficiency study; (b) high permeability matrix model; (c) connected fracture (pipes) model; (d) random fracture model; (e) connected fracture and random fracture model
圖 2 溫度場演化規律. (a)高滲透率熱儲溫度場演化規律; (b) 貫通裂隙（管道）熱儲溫度場演化規律; (c) 隨機裂隙熱儲溫度場演化規律; (d) 貫通裂隙+隨機裂隙熱儲溫度場演化規律
Figure 2. Temperature field evolution: (a) high-permeability reservoir model; (b) connected fracture (or pipes) model; (c) random fracture model; (d) connected fracture and random fracture model
圖 3 不同換熱方式的熱能提取效率. (a) 不同換熱方式年采熱量對比; (b) 不同注水溫度的年采熱量和出水溫度對比 (散點折線圖為采熱量、折線圖為出水溫度、細線為擬合曲線); (c) 不同基質滲透率入水壓力比較
Figure 3. Performance of different heat extraction approaches: (a) comparison of annual heat production using different heat exchange models; (b) comparison of annual heat production and water outlet temperature at different water injection temperatures (the scatter-line graph is the amount of heat production; the broken-line graph is the water outlet temperature; and the thin-line is the fitting curve); (c) comparison of water inlet pressure at different matrix permeabilities
圖 4 取熱示意圖. (a) 分層取熱EGS-E圖; (b) 分層取熱EGS-E數值模型圖
Figure 4. Schematic diagram of heat extraction: (a) illustration of EGS-E with multiple slices and (b) numerical model of EGS with multiple slices
圖 5 熱力作用與水力作用對裂隙開度的影響. (a) 總裂縫開度; (b) 裂縫開度改變量（水力作用）; (c) 裂縫開度改變量（熱力作用）; (d) 注水量
Figure 5. Influence of thermal and hydraulic effects on fracture opening: (a) total fracture opening; (b) change in fracture opening (hydraulic action); (c) change in fracture opening (thermal effect); (d) water injection volume
圖 6 不同厚度巖體在注入時間為10 a后的溫度分布圖
Figure 6. Temperature distributions of rock masses with different thicknesses after 10 years injection
圖 7 不同裂縫間距下裂縫開度變化趨勢對比圖. (a) 總的裂縫開度; (b) 裂縫開度改變量（水力作用和熱力作用）
Figure 7. Comparison of the change trends of fracture opening at different fracture spacings: (a) total fracture opening; (b) change in fracture opening (hydraulic and thermal effect)
表 1 熱能提取效率研究數值模型中的物理和力學參數
Table 1. Physical and mechanical parameters used in the numerical model
Parameter Value Parameter Value Thermal conductivity of the bedrock /(W·m?1·K?1) 2.75 Dynamic viscosity coefficient of water /(Pa·s) 0.001 Specific heat capacity of the bedrock /
(J·kg?1·K?1)915 Thermal conductivity of water /(W·m?1·K?1) 0.58 Density of the bedrock /(kg·m?3) 2600 Specific heat capacity of water /(J·kg?1·K?1) 4178 Elastic modulus of the bedrock /GPa 10 Density of water /(kg·m?3) 1000 Poisson's ratio of the bedrock 0.3 Injection fluid flow /(kg·s?1) 0.01 Coefficient of thermal expansion of the bedrock/ K?1 1×10?5 Initial temperature of the injected fluid /°C 50 Initial temperature of the bedrock /℃ 200 Initial opening of the fracture /m 1×10?4 Permeability of the bedrock /mD 1 × 10?3 Fracture stiffness /(GPa·m?1) 100 Pore pressure of the bedrock /MPa 5 
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表 2 隨機裂隙屬性
Table 2. Random fracture properties
Number of
random fracturesAverage strike
length /mStandard deviation
of strike length/mAverage trace
length/mStandard deviation
of trace length /m200 150 50 100 50
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表 3 不同注水溫度的采熱量曲線擬合
Table 3. Curve fitting of heat recovery at different water injection temperatures
Water injection temperature /
℃Fitting formula, $y=a-b\cdot {c}^{t}$ a b c R2 20 1559.5967 ± 37.78555 ?3696.40173 ± 77.56903 0.86797 ± 0.00586 0.99073 40 1381.06689 ± 37.58555 ?3256.12666 ± 74.18219 0.8706 ± 0.00637 0.98888 60 1193.38535 ± 28.63278 ?2891.47246 ± 56.77453 0.87029 ± 0.00549 0.99173 80 1030.56764 ± 25.48009 ?2486.14397 ± 51.63048 0.86885 ± 0.0058 0.99086 100 859.89803 ± 21.83143 ?2074.45482 ± 45.10929 0.86753 ± 0.00607 0.99008
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久色视频表 4 裂隙開度演化數值模型中的物理和力學參數
Table 4. Physical and mechanical parameters used in the numerical model
Parameter Value Parameter Value Thermal conductivity of the bedrock /
(W·m?1·K?1)2.75 Dynamic viscosity coefficient of water /(Pa·s) 0.001 Specific heat capacity of the bedrock /
(J·kg?1·K?1)915 Thermal conductivity of water /(W·m?1·K?1) 0.58 Density of the bedrock /(kg·m?3) 2600 Specific heat capacity of water /(J·kg?1·K?1) 4178 Elastic modulus of the bedrock /GPa 10 Density of water /(kg·m?3) 1000 Poisson's ratio of the bedrock 0.3 Injection fluid flow /(kg·s?1) 0.01 Coefficient of thermal expansion of the bedrock /
K?11×10?5 Initial temperature of the injected fluid /℃ 50 Initial temperature of the bedrock /℃ 200 Initial opening of the fracture/m 1×10?4 Permeability of the bedrock /mD 1×10?3 Stiffness of the fracture /(GPa·m?1) 100
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