Influencing patterns of multiple factors on the heat transfer performance of moderately deep geothermal wells
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摘要:
积极推进中深层地热能供暖技术，是践行国家碳达峰碳中和“双碳”目标的重要举措。中深层同轴套管式换热系统可避免对地下水资源和环境造成损害，且影响要素之间存在着复杂的非线性相互作用。基于中深层同轴套管式换热器的理论分析和数学描述，建立地热井分层换热模型，并验证其可靠性；以陕西关中盆地某中深层地热井为依托，采用数值模拟方法对各项因素影响下的地热井换热性能及连续运行过程的取热能力进行系统分析。结果表明：采用均质模型、分层模型计算地热井出水温度与实测值最大相对误差分别为14.08%、11.50%，平均误差分别为7.29%、6.93%，分层模型较均质模型具有较高的计算精度；影响因素中地热井深度、地温梯度及地层导热系数对取热功率影响最为显著，在一定程度上取热功率与地温梯度、进水温度、内管导热系数基本呈线性关系，且固井材料导热系数对传热过程具有热阻效应；中深层地热井取热量随运行年限的增加而降低，前5个供暖季取热量降幅较大，之后取热量降幅减缓，经过50个供暖季，年平均取热功率下降15.59%，将地温下降值超过1℃视为地温场受到影响，地温场平均受影响半径约为65 m，此外，由于地层的差异性，地热井周围地层温度下降及恢复等值线在地层交界面处出现了“阶梯式”变化，岩石导热系数较大的地层在地层交界面附近造成的温度扰动距离更远。研究成果可应用于中深层地热井取热换热能力的评估，同时为中深层同轴套管式换热系统的设计提供借鉴。
Abstract:Vigorously promoting the technology for heating using moderately deep geothermal energy serves as an important measure for China’s pursuit of carbon neutrality and peak carbon dioxide emissions. A coaxial double-pipe heat transfer system for moderately deep geothermal wells can avoid damage to groundwater resources and the environment. Furthermore, the influencing factors of the wells exhibit complicated and nonlinear interactions. Based on the theoretical analysis and mathematical description of a moderately deep well with a coaxial double-pipe heat exchanger, this study established a layered heat transfer model for the geothermal well and verified its reliability. This study investigated a moderately deep geothermal well in the Guanzhong Basin in Shaanxi Province. Through numerical simulations, it systematically analyzed the heat transfer performance of the geothermal well, as well as its heat extraction capacity during continuous operation, under the influence of various factors. The results show that compared to the measured values, the outlet water temperatures calculated using the homogeneous and layered models exhibited maximum relative errors of 14.08% and 11.50%, respectively, and average errors of 7.29% and 6.93%, respectively. Therefore, the layered model enjoyed a higher calculation accuracy than the homogeneous model. Among all influencing factors, geothermal well depth, geothermal gradient, and the thermal conductivity of strata exerted the most significant influence on the heat extraction power of the geothermal well. There existed roughly linear relationships of the heat extraction power with the geothermal gradient, inlet water temperature, and the thermal conductivity of the inner tube. Moreover, the thermal conductivity of well cementing materials produced thermal resistance effects on the heat transfer process. The heat amount extracted from the moderately deep geothermal well decreased with the operating years, with the decreasing amplitude being high in the first five heating seasons and then decreasing. After 50 heating seasons, the annual average heat extraction power decreased by 15.59%. Assuming that a geothermal field is influenced if the geotemperature decreases by more than 1℃, the average influence radius of the geothermal field was about 65 m. In addition, due to the differences in strata, the contour lines illustrating the drop and recovery of formation temperature around the geothermal well exhibited stepped changes at the interface of the strata. Strata with higher thermal conductivity of rocks corresponded to a greater distance of temperature disturbance near the interfaces of strata. The results of this study can be applied to the evaluation of the heat extraction and transfer capacities of moderately deep geothermal wells and also serve as a reference for the design of coaxial double-pipe heat transfer systems for moderately deep geothermal wells.
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图 1 中深层地热分层物理模型
Fig. 1 Layered physical model of coaxial double-pipe heat exchanger for moderately deep geothermal well
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图 3 实测值与均质模型/分层模型模拟值对比
Fig. 3 Comparison between measured values and simulated values of the homogeneous model/layered model
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图 4 地热井深度、地温梯度对取热功率的影响
Fig. 4 Effects of geothermal well depth and geothermal gradient on heat extraction power
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图 5 不同内管导热系数下出口水温随时间的变化
Fig. 5 Time-varying outlet water temperature under different thermal conductivities of the inner pipe
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图 6 不同内管导热系数下的换热器效能
Fig. 6 Heat exchanger efficiency under different thermal conductivities of the inner pipe
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图 7 单个供暖季末管内水温沿地热井纵向分布
Fig. 7 Longitudinal distribution of water temperature in pipes along a geothermal well at the end of a single heating season
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图 8 不同内管导热系数下循环水流量对出口水温和换热功率的影响
Fig. 8 Effects of circulating water flow on outlet water temperature and heat transfer power under different thermal conductivities of the inner pipe
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图 9 不同内管导热系数下循环水流量对换热器效能影响
Fig. 9 Effects of circulating water flow on the heat exchanger’s efficiency under different thermal conductivities of the inner pipe
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图 10 不同地层下固井材料导热系数对取热功率影响
Fig. 10 Effects of the thermal conductivity of well cementing materials on heat extraction power under different strata
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图 11 不同地层下固井材料导热系数对出水温度影响
Fig. 11 Effects of the thermal conductivity of well cementing materials on outlet water temperature under different strata
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图 12 不同流量下进水温度对取热功率的影响
Fig. 12 Effects of inlet water temperature on heat extraction power with different water flow
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图 13 各因素影响下的地热井取热功率变化率
Fig. 13 Rates of change in heat extraction power from the geothermal well under the influence of various factors
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图 14 连续运行50个供暖季取热功率随时间变化
Fig. 14 Time-varying heat extraction power over 50 consecutive heating seasons
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图 15 供暖季末期地层温度分布
Fig. 15 Distribution of formation temperature at the end of heating seasons
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图 16 地热井周围地层温度下降及恢复等值线
Fig. 16 Contour map of stratigraphic temperature drop and recovery around geothermal wells
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图 17 地热井周围地层温度下降及恢复等值线
Fig. 17 Contour maps showing the decrease and recovery of formation temperature around the geothermal well
表 1 地热井井身结构设计
Table 1 Structural design of the casing program of a geothermal well
开钻次序 井段/m 钻头尺寸/
mm套管尺寸/
mm水泥返深/m 一开 0~450 374.7 273.1 0 二开 450~3500 241.3 177.8 0 
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表 2 套管式换热器分析的相关计算参数
Table 2 Calculation parameters for the analysis of the double-pipe heat exchanger
参数 数值 备注 钻孔直径/mm 241.3 内管直径/mm 114.3 外管直径/mm 177.8 内管厚度/mm 19.15 外管厚度/mm 9.19 外管导热系数/(W·m−1·K−1) 40 水的导热系数/(W·m−1·K−1) 0.63 水的比热容/(J·kg−1·K−1) 4.19×103 地层体积比热容/(MJ·m−3·K−1) 2.87×106 用于均质模型地层 地层导热系数/(W·m−1·K−1) 2.7 用于均质模型地层 水的密度/(kg·m−3) 996
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表 3 分层模型地层参数
Table 3 Parameters of strata in the layered model
地层 深度范围/m 体积比热容/
(MJ·m−3·K−1)导热系数/
(W·m−1·K−1)秦川群 0~600.0 2.50 1.85 三门组 600.0~750.8 2.90 1.82 张家坡组 750.8~1 662.3 2.45 2.60 蓝田−灞河组 1 662.3~2 342.0 2.20 2.29 高陵群 2 342.0~3 500.0 2.30 2.22
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表 4 现场试验参数
Table 4 Parameters of field tests
试验
类型实验
时间/d流量/
(m³·h−1)进水
温度/℃运行
方式备注 恒温恒流量 4 30 10 运行9 h
间歇15 h开式系统，
热水排出
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表 5 模拟方案
Table 5 Simulation schemes
方案
序号影响因素 备注 地热井
深度/m地温梯度/
(℃·m−1)地层导热系数/
(W·m−1·K−1)循环水流量/
(m³·h−1)固井水泥导热系数/
(W·m−1·K−1)内管导热系数/
(W·m−1·K−1)进水温度/℃ 1 2000、2500
3000、35000.02、0.03
0.04、0.052.70 30 1.8 0.02 10 2 3500 0.034 3.20 30 1.8 0.02、0.18
0.30、0.5010 3 3500 0.034 3.20 10、20、30、
40、501.8 0.02、0.18
0.30、0.5010 4 3500 0.034 0.83、1.30、
1.80、2.70、3.9830 0.4~4.0 0.02 10 固井水泥导热系数
每隔0.4 W/(m·K)设置
1个导热系数5 3500 0.034 3.20 10、20、30
40、501.8 0.02 5、7
10、12、156 2500×
(60%~160%)0.034×
(60%~160%)3.20×
(60%~160%)25×
(60%~160%)1.8×
(60%~160%)0.02×
(60%~160%)10×
(60%~160%)60%~160%变化率之间
每隔20%设置1个参数7 3500 0.034 30 1.8 0.02 5 地层导热系数见表2
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