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Mechanism of seepage heat transfer in thermal reservoirs of high temperature metamorphic rocks in the Yanggao-Tianzhen basin
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Abstract: A typical high-temperature metamorphic rock geothermal reservoir was newly discovered in the Tianzhen geothermal field in Datong City, China. However, due to the complex geological structure and thermal properties, the seepage heat transfer mechanism of metamorphic rock reservoirs is still unclear, seriously impeding the efficient development and sustainable utilization of geothermal resources. This study established a percolation-heat transfer model through tracer testing and numerical simulation to reveal the percolation mode and heat transfer mechanism of high-temperature metamorphic rock reservoirs during the reinjection process. We also predicted the distribution characteristics of various physical fields in the geothermal reservoir after the geothermal system has been in operation for 100 a, analyzed the influence of different reinjection schemes on seepage heat transfer in the geothermal reservoir, and proposed an optimization strategy for the reinjection scheme. The results show that: (1) The connectivity between production and injection wells is poor, and there are water-conducting fractures connecting the shallow and bottom layers; (2) The seepage channels through fractures guide the migration of the reinjected fluid and form a cold front surface with a protruding shape towards the mining well in the temperature field, resulting in temperature changes in the production well; (3) Seepage heat transfer in thermal reservoirs is greatly affected by the reinjection flow rate and the distance between production and reinjection wells, but less by the reinjection temperature. As the reinjection temperature drops, the flow rate increases, the well spacing decreases, and the temperature variation range of the production well becomes greater; (4) Under the current reinjection test conditions, the temperature of the mining well decreased by approximately 4°C after 100 a of geothermal reinjection operation, and a thermal breakthrough occurred at 78 a. Under the condition of maintaining a reinjection flow rate of 60 m3/h and a reinjection temperature of 80°C unchanged, the well spacing should be no less than 470 m to ensure that the well temperature does not cause a thermal breakthrough during the reinjection operation for 100 a. This research provides a theoretical basis and optimization methods for the efficient development of high-temperature metamorphic rock thermal reservoirs.
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Figure 1. (a) Location of the North China Craton, with a red box indicating the Datong Basin; (b) Tectonic background of the Datong Basin (blue box indicating the study area) (Kusky and Li, 2003; Zhou et al., 2020)
Figure 4. Schematic diagram of the seepage channel model of a deep thermal reservoir (Li et al., 2020)
Figure 6. Numerical simulation results, analytical Equation (2), and on-site test results
Figure 7. Tracer concentration detection (left axis) and temperature detection (right axis) in well GR1
Figure 13. Average temperature variation of production well under different reinjection schemes
Table 1. Governing equations for each physical field
Description Governing equation Seepage equations in thermal reservoirs $ \dfrac{\partial }{\partial t}({\rho }_{\mathrm{f}}\varphi )+\nabla \cdot ({\rho }_{\mathrm{f}}{\mathbf{u}}_{\mathrm{f}})={Q}_{\mathrm{m}} $ Heat transfer equation in thermal reservoir $ (\rho {C}_{p}{)}_{\text{eff}}\dfrac{\partial T}{\partial t}+{\rho }_{\mathrm{f}}{C}_{\mathrm{p},\mathrm{f}}{\mathbf{u}}_{\mathrm{f}}\cdot \nabla T-\nabla \cdot \left({k}_{\text{eff}}\nabla T\right)={q}_{f} $ Solute transport equations in thermal reservoirs $ \dfrac{\partial C}{\partial t}=D\dfrac{{\partial }^{2}C}{\partial {x}^{2}}-u\dfrac{\partial C}{\partial x} $ Heat transfer equation of wellbore $ {\rho }_{\mathrm{f}}{A}_{\mathrm{w}}{C}_{\mathrm{p},\mathrm{f}}\dfrac{\partial T}{\partial t}+{\rho }_{\mathrm{f}}A{C}_{\mathrm{p},\mathrm{f}}{\bar{u}}_{\mathrm{w}}\cdot \nabla T=\nabla \cdot Ak\nabla T+{f}_{\mathrm{D}}\dfrac{{\rho }_{\mathrm{f}}A}{2{d}_{\mathrm{i}}}{\left| u\right| }^{3}+{Q}_{\text{wall}} $ Notes: Where: t is time (s), $ {\rho }_{\mathrm{f}} $ is the fluid density (kg/m3), Qm is the fluid mass source (kg/(m3∙s)), $ {C}_{\mathrm{p},\mathrm{f}} $ is the specific heat capacity of the fluid under constant pressure (J/kg/K), T is the temperature (K), $ {q}_{f} $ is the heat source (W/m3), and (ρCp)eff is the equivalent volumetric heat capacity of the reservoir rock mass keff is the effective thermal conductivity of the reservoir rock mass (W/m/K), C is the tracer concentration/(kg/m3); t is time (s), x is the channel axial coordinate (m); D is the tracer axial dispersion coefficient (m2/s); u is the average flow rate of the fluid (m/s); Aw is the cross-sectional area of the geothermal well (m2); uw is the average flow velocity along the shaft axis (m/s); Qwall is the heat exchange between the fluid and the surrounding rocks through the geothermal well wall, and f D is the Darcy friction factor. 
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Table 2. Model parameter table
Parameters Value Parameters value Reinjection temperature 80°C Reservoir density 2,689 kg/m³ Thermal reservoir temperature 169°C Reservoir porosity 2.5% Reinjection flow 60 m3/h Thermal conductivity of reservoir rock 7 W/(m·K) Fluid density 1,000 kg/m³ Reservoir permeability 2×10−16 m2 Fluid heat capacity 4,200 J/(kg·°C) Reservoir heat capacity 920 J/(kg·°C)
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Table 3. Grid sensitivity analysis
Grid division mode Number of grids Calculate the peak concentration of tracer in the mining well (t = 40 d) (×10−3/m3) Refine the mesh 46,371 1.4525 Ultra-fine grid 135,351 1.4523 Extremely fine grid 224,470 1.4519
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Table 4. Tracer concentration statistics of observation wells and well GR1
Time(d) Tracer concentration by well (×10−6 kg/m3) K4 K6 K13 GR1 8 8.10 50.34 24.82 Tracer was not detected 16 13.39 49.42 12.95 Tracer was not detected 26 28.07 29.00 17.17 480.24 42 10.05 21.16 12.09 1,320.08 61 9.93 23.90 11.23 890.88 69 12.85 16.84 10.90 809.68 78 10.25 15.45 12.30 679.76 86 10.58 13.50 11.23 621.76
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Table 5. Seepage channel parameter table
Parameter Inversion result Tracer recovery rate 15.1% Channel length 468 m Seepage velocity 11.6 m/d Longitudinal dispersion 35 m Dispersion coefficient 0.00413 m2/s Channel cross-sectional area 7.91 m2
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Table 6. Parameter description of the reinjection scheme
Parameter/unit Value Reinjection temperature/°C 25 50 80 Reinjection flow/(m3/h) 60 100 140 Production and reinjection well spacing/m 240 440 640
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Table 7. Temperature variation and thermal breakthrough time of the mining well after 100 a of the geothermal system operation under different reinjection schemes
Well spacing Reinjection flow Reinjection temperature 25°C 50°C 80°C 340 m 60 m3/h 152°C/38a 154°C/41a 157°C/46a 100 m3/h 143.9°C/28a 146.3°C/29a 150.7°C/33a 140 m3/h 135.8°C/23a 139.6°C/24a 145.49°C/30a 440 m 60 m3/h 163.7°C/70a 164.5°C/74a 165.6°C/78a 100 m3/h 159.9°C/54a 161.3°C/58a 163°C/65a 140 m3/h 155.8°C/46a 157.8°C/49a 160.2°C/55a 540 m 60 m3/h 168.1°C/No thermal breakthrough 168.3°C/No thermal breakthrough 168.5°C/No thermal breakthrough 100 m3/h 167.2°C/No thermal breakthrough 167.5°C/No thermal breakthrough 167.9°C/No thermal breakthrough 140 m3/h 166.2°C/90a 166.7°C/96a 167.2°C/No thermal breakthrough Notes: "165.6°C/78a" represents the temperature value of the extraction well after the geothermal system has been in operation for 100 a, the time of thermal breakthrough under the current reinjection scheme.
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