Response Process and Mechanism of Sandstone Geothermal Reservoir Temperature to Reinjection Parameters
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摘要: 研究地热尾水回灌引起的热储层内温度场演化对地热资源的可持续利用具有重要意义.本文通过大型砂槽仿真试验模型的渗透试验、示踪试验和回灌试验结合数值模拟方法，研究了回灌参数与开采井热突破时间的定量关系，并通过非线性拟合和参数敏感性分析讨论了流体粘度与密度对高温流体向低温流体回灌结果的影响，以及回灌参数对开采井热突破时间的影响程度和内在机理与规律.结果显示回灌水在不同渗透率的砂岩层内运移速率不同，开采井热突破时间t分别与Q‒0.85、ΔT‒0.21和R1.4呈线性关系.相关方程和分析结果表明，采灌温差ΔT在大于30 ℃时，其变化对开采井热突破时间t的影响已变得微弱，这是由于ΔT通过影响18.5 ℃等温线在温度过渡区内的相对位置来对开采井热突破时间t产生作用，而试验中采取的高温流体向低温流体回灌产生的误差可以引入粘度修正系数αμ修正.Abstract: The evolution of geo-temperature within the geothermal reservoir induced by reinjection of geothermal cooled water is of great importance for the sustainable utilization of geothermal resources. This study focuses on examining the quantitative relationship between reinjection parameters and the thermal breakthrough time of production wells. A simulation test using a large sand tank combined with numerical simulation methods was conducted. Permeation tests, tracer tests, and reinjection tests were performed in the simulation test model. Additionally, sensitivity analysis and nonlinear fitting were carried out to discuss the impact of fluid viscosity and density on reinjection results, as well as the degree of influence of reinjection parameters on the thermal breakthrough time of production wells and its underlying mechanisms and principles. The results show that the migration speed of reinjection water is different in sand reservoirs with different permeability, and the thermal breakthrough time t is linearly correlated with Q‒0.85, ΔT‒0.21, and R1.4. The correlation equation and analysis show that when the temperature difference between production and reinjection ΔT is more than 30 ℃, the influence of ΔT on the thermal breakthrough time of production well becomes weak, because ΔT exerts an effect on the thermal breakthrough time of production well t by influencing the relative position of the 18.5 ℃ isotherm in the temperature transition region, and the error for reinjection from high temperature fluid to low temperature fluid can be corrected by introducing the viscosity correction coefficient αμ.
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图 5 回灌温度30 ℃时砂槽内部温度云图
a. Z1截面；b. Z3截面
Fig. 5. Temperature cloud diagrams of the sand tank for a reinjection temperature of 30 ℃
图 6 回灌温度50 ℃时砂槽内部温度云图
a. Z1截面；b. Z3截面
Fig. 6. Temperature cloud diagrams of the sand tank for a reinjection temperature of 50 ℃
图 7 示踪试验钼酸铵浓度历时变化散点图
a. Cc1点和Cc3点；b. 开采井
Fig. 7. Change in ammonium molybdate concentration in tracer tests
图 9 不同采灌温差开采井水温变化曲线
Fig. 9. Water temperature variations in production well for different temperature differences between production and reinjection
图 10 不同回灌量开采井水温变化曲线
Fig. 10. Water temperature variations in production well for different reinjection amounts
图 11 不同采灌井间距开采井水温变化曲线
Fig. 11. Variations in water temperature in production well for different spacings between the production and reinjection wells
图 12 回灌量与热突破时间关系
Fig. 12. Relationship between reinjection amount and thermal breakthrough time
图 13 采灌温差与热突破时间关系
Fig. 13. Relationship between the thermal breakthrough time and the temperature difference of production and reinjection
图 14 采灌井间距与热突破时间关系
Fig. 14. Relationship between production and reinjection well spacing and thermal breakthrough time
图 15 回灌量与热突破时间关系
Fig. 15. Relationship between reinjection amount and thermal breakthrough time
图 16 开采井温度对采灌温差的敏感性曲线
Fig. 16. Sensitivity of production well temperature to temperature difference between production and reinjection
图 17 采灌温差与热突破时间关系拟合
Fig. 17. Fitting of the relationship between the thermal breakthrough time and the temperature difference of production and reinjection
图 18 开采井温度对采灌井间距的敏感性曲线
Fig. 18. Sensitivity of production well temperature to the spacing between the production and reinjection wells
图 19 采灌井间距与热突破时间关系拟合
Fig. 19. Fitting of the relationship between the production and reinjection well spacing and the thermal breakthrough time
图 21 回灌量与热突破时间关系拟合
a. 不同采灌温差ΔT；b. 不同采灌井间距R
Fig. 21. Fitting of the relationship between the reinjection amount and the thermal breakthrough time
图 22 不同采灌温差下高温回灌和低温回灌开采井温度变化曲线
Fig. 22. Temperature variation curves of production well with high temperature and low temperature reinjection under different temperature differences between production and reinjection
图 23 不同采灌温差下高温回灌和低温回灌开采井热突破时间散点图
Fig. 23. Scatter diagram of thermal breakthrough time of production well with high temperature and low temperature reinjection under different temperature differences between production and reinjection
图 24 粘性修正系数αμ与采灌流体动力粘度差Δμ关系拟合
Fig. 24. Fitting of the relationship between the viscosity correction factor αμ and the difference of dynamic viscosity Δμ of production and reinjection
图 25 热突破时间与采灌井间距、回灌量关系(采灌温差ΔT=30 ℃)
Fig. 25. Relationships between the thermal breakthrough time and the production and reinjection well spacing and reinjection amount (ΔT=30 ℃)
图 26 不同采灌温差ΔT开采井发生热突破时井筒周边温度云图
Fig. 26. Temperature graph of boreholes surrounding during thermal breakthrough in production well with different temperature difference ΔT
a. ΔT=10 ℃; b. ΔT=20 ℃; c. ΔT=30 ℃; d. ΔT=40 ℃
图 27 不同采灌温差第2.5天时Z3截面中轴线和平面温度分布
Fig. 27. Temperature distribution of central axis and plane of Z3 section at 2.5 d with different temperature difference
表 1 采灌井与水位观测井结构参数表（mm）
Table 1. Structural parameters (mm) of production and reinjection wells and water level monitoring boreholes
井类型 钻孔直径 井壁直径 填充砾料厚度 滤水管孔眼直径 滤水管钢网间距 开采井 100 / / 10 0.5~1.0 回灌井 220 88 66 10 0.5~1.0 水位观测孔 70 / / 5 / 
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表 2 回灌参数敏感性研究取值
Table 2. Values of reinjection parameters for sensitivity analysis
回灌温度（℃） 回灌量（m3/h） 采灌井间距（m） 工况1 30、40、50、60 0.5 10 工况2 30 0.5、1.0、1.5、2.0 10 工况3 30 0.5 4、6、8、10
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表 3 采灌井流量与稳定水位
Table 3. Flow rate and stable water level difference of production and reinjection wells
回灌井水位(m) 开采井水位(m) 采灌井水位差(m) 流量(m3/h) 5.94 3.53 2.41 1.10 5.61 3.72 1.89 0.72 5.38 4.19 1.19 0.52
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表 4 砂槽数值模型参数取值表
Table 4. Parameter values for numerical model of sand tank
参数 单位 数值 孔隙度 中砂岩层 / 0.25 粗砂岩层 / 0.35 渗透率 中砂岩层 mD 3 000 粗砂岩层 mD 5 500 砂岩层热导率 W/(m·K) 2.4 砂岩层体积热容 J/(K·m3) 2 100 000 弥散度 中砂岩层 m 0.2 粗砂岩层 m 0.5 水的热导率 W/(m·K) 0.65 水的密度 kg/m3 998
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表 5 高温回灌与低温回灌参数取值表
Table 5. Parameter values of high temperature and low temperature reinjections
高温回灌 初始温度 15 ℃ 15 ℃ 15 ℃ 15 ℃ 回灌温度 25 ℃ 35 ℃ 45 ℃ 55 ℃ 低温回灌 初始温度 25 ℃ 35 ℃ 45 ℃ 55 ℃ 回灌温度 15 ℃ 15 ℃ 15 ℃ 15 ℃ 采灌温差ΔT 10 ℃ 20 ℃ 30 ℃ 40 ℃
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