Quantitative Assessment of Calcite Scaling of a High Temperature Geothermal Production Well: Two-Phase Flow—Application to the Yangbajing Geothermal Fields, Tibet
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摘要: 高温地热生产井碳酸钙结垢定量评价涉及到复杂的物理和化学过程，其中井筒中的两相流研究是评价的基础.本文首先基于质量守恒、能量守恒和动量守恒方程，建立了CO2-H2O体系井筒两相相变稳定流动模型，提出了稳健的求解方法，并验证了其计算结果的可靠性.然后，在西藏羊八井地热田典型井开展了静止和放喷状态下的井筒中的温度和压力测试，并结合放喷试验，采用开发的模型成功评价了高温地热生产井筒两相流动过程.结果显示：气相和液相之间的速度差对井筒中温度和压力的分布有决定性的影响，不考虑气相和液体之间的速度差，会使模型计算结果远远偏离测量值.在开采速率19.10 kg/s的条件下，计算的井口温度和压力分别约为128 ℃和2.6 bar；井口的气相质量分数在6%~7%之间，对应的井口气相饱和度约为0.84；从闪蒸点往上大概20~30 m气相和液相中CO2质量分数变化较为剧烈，也是碳酸钙结垢严重井段.Abstract: The quantitative evaluation of calcite scaling in high temperature geothermal production wells involves complex physical and chemical processes, in which the two-phase flow in the wellbore is the basis for the evaluation. Based on mass, energy and momentum conservations, this paper firstly constructs a model for governing the two-phase steady flow with phase transition in the presence of CO2 in the wellbore. A robust calculation method is presented and the calculation is validated. Then the temperature and pressure measurements in a typical geothermal well were carried out during discharge tests including static and dynamic test in the Yangbajing geothermal field, Tibet. Combined with the discharge test, the model is successfully used to evaluate the two-phase flow process in a high temperature production well. The results show that the velocity difference between the gas and liquid phase has a decisive impact on the profiles of temperature and pressure in the wellbore. If the velocity difference is not considered in the model, the calculations will deviate far from the measurements. At the production rate of 19.10 kg/s, the calculated wellhead temperature and pressure are about 128 ℃ and 2.6 bar, respectively. The wellhead gas mass fraction is between 6% and 7%, and the corresponding gas phase saturation is about 0.84. The CO2 mass fractions in both gas and liquid phases change sharply about 20-30 m up from the flash point, indicating that serious calcite scaling will occur in this well section.
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Key words:
- geothermal energy /
- two-phase flow /
- CO2 /
- numerical simulation /
- Yangbajing /
- hydrogeology
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图 2 程序可靠性验证：(a)、(b)和(c)为与Khasani et al.(2021)的对比，(d)和(e)为与T2Well-EWASG(Vasini et al., 2018)的对比
Fig. 2. Verification of the code: comparison (a, b and c) with Khasani et al.(2021) and comparison (d and e) with T2Well-EWASG(Vasini et al., 2018)
图 3 研究区位置和地质概况：(a)平面，(b)剖面
根据许多龙等(2018)和多吉(2003)修改
Fig. 3. The location and geological profile of the study area: (a) plan, (b) cross section
图 4 温度和压力测试结果：(a)压力，(b)温度
Fig. 4. Temperature and pressure measured results: (a) pressure, (b) temperature
图 6 模型计算与测试结果对比: 均质速度模型(a)压力，(b)温度，漂移流(DFM)模型(c)压力，(d)温度
Fig. 6. Comparison of calculation and measurement: (a) pressure and (b) temperature with homogeneous model, (c) pressure and (d) temperature with DFM model
图 7 模型计算结果：(a)气相质量分数，(b)气相体积分数，(c)气相中CO2的质量分数，(d)液相中CO2的质量分数，(e)气体速度，(f)液体速度
Fig. 7. Calculated results: (a) gas mass fraction, (b) gas volume fraction, (c) CO2 mass fraction in the gas phase, (d) CO2 mass fraction in the liquid phase, (e) gas velocity, (f) liquid velocity
表 1 井口蒸汽组分特征(Zhao et al., 1998)
Table 1. Wellhead steam composition characteristics (Zhao et al., 1998)
井名 蒸汽中CO2含量
(mmol/kg)非凝析气体体积含量(%) CO2 N2 O2 H2S H2 Ar ZK303 66.1 (0.29%)a 92.7 5.02 0.92 0.23 0.034 0.14 ZK304 26.4 (0.12%) a 93.8 4.67 0.47 0.33 0.041 0.47 ZK309 34.0 (0.15%) a 85.7 11.7 2.28 0.27 0.028 0.21 ZK313 21.6 (0.10%) a 81.3 15.6 1.96 0.43 0.035 0.23 ZK325 21.4 (0.10%) a 92.5 6.17 0.59 0.22 0.035 0.16 注：数据在一个大气压下测量；a括号中的数值为换算的CO2质量分数. 
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表 2 流动模型参数
Table 2. Model parameters for flow
参数 取值 井筒套管长度(m) 120 井筒直径(m) 0.34 套管底部位置压力(bar) 7.31 套管底部位置温度(℃) 154.3 质量速率(kg/s) 19.10 套管底部位置CO2质量分数 三种情况：饱和CO2含量，饱和CO2含量的一半和没有CO2 套管摩擦系数(m) 4.5×10-5
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