地球科学进展

地球科学进展 ›› 2019, Vol. 34 ›› Issue (4): 414 -423. doi: 10.11867/j.issn.1001-8166.2019.04.0414

地球化学 上一篇    下一篇

水热体系中 Na2SO4/K2SO4 溶解度的热力学计算
张为 1, 2( ),周丽 2( ),唐红峰 2,李和平 2,王力 2, 3   
  1. 1. 贵州师范大学喀斯特生态文明研究中心，贵州 贵阳 550025
    2. 中国科学院地球化学研究所地球内部物质高温高压院重点实验室，贵州 贵阳 550002
    3. 中国科学院大学，北京 100039
  • 收稿日期:2018-11-08 修回日期:2019-03-19 出版日期:2019-04-10
  • 通讯作者: 周丽 E-mail:zhangwei@gznu.edu.cn;zhouli@vip.gyig.ac.cn
  • 基金资助:
    国家自然科学基金项目“独居石和磷钇矿在热液中溶解行为的实验研究：对U-Th-Pb年龄有效性以及稀土元素成矿的约束”(编号：41773058);贵州省科技厅—贵州师范大学联合基金项目“石阡县地热资源可持续利用研究”(编号：黔科合LH字[2017]7339号)

Thermodynamic Calculation of Solubility of Na 2SO 4/K 2SO 4 in Hydrothermal Fluids

Wei Zhang 1, 2( ),Li Zhou 2( ),Hongfeng Tang 2,Heping Li 2,Li Wang 2, 3   

  1. 1. Research Center of Karst Ecological Civilization, Guizhou Normal University, Guiyang 550025, China
    2. Key Laboratory of High-Temperature and High-Pressure Study of the Earth’s Interior, Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550002, China
    3. University of Chinese Academy of Sciences, Beijing 100039, China
  • Received:2018-11-08 Revised:2019-03-19 Online:2019-04-10 Published:2019-05-27
  • Contact: Li Zhou E-mail:zhangwei@gznu.edu.cn;zhouli@vip.gyig.ac.cn
  • About author: Zhang Wei (1988-), male, Wuhan City, Hubei Province, Lecturer. Research areas include experimental and computational geochemistry on water-rock reactions. E-mail: zhangwei@gznu.edu.cn | Zhang Wei (1988-), male, Wuhan City, Hubei Province, Lecturer. Research areas include experimental and computational geochemistry on water-rock reactions. E-mail: zhangwei@gznu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China "Experimental study of the behavior of monazite and xenotime in hydrothermal fluids: Constraints on the usefulness of U-Th-Pb age and the mineralization of REE"(No. 41773058);The Joint Foundation of Guizhou Science and Technology Department and Guizhou Normal University “Study on sustainable utilization of geothermal resources in Shiqian County”(No. QIANKEHE LH [2017] 7339)
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硫酸盐流体是自然界中的常见热液，其盐度可以为成矿流体演化、成矿元素的迁移富集和矿床类型的划分等提供重要信息。但是现有文献报道的Na2SO4和K2SO4溶解度多是在饱和蒸气压条件或超临界条件下，而对于低温成矿热液体系的实验研究较少。热力学计算是研究流体性质的重要手段，特别是在实验结果较少的温压范围内起着重要作用，但是利用热力学模型来计算硫酸盐溶解度的工作却少有开展。使用Pitzer模型，利用Na2SO4和K2SO4溶液高温高压条件下的密度数据，使用非线性最小二乘法拟合，获得了压力对Na2SO4和K2SO4的活度系数及其溶解过程中的标准偏摩尔体积影响的模型参数，评价了压力对其活度系数和标准偏摩尔体积的影响。结合文献中饱和蒸气压下的相关参数，构建了温度范围为0~250 oC，压力范围为0.1~40.0 MPa，Na2SO4和K2SO4溶解度的热力学计算模型。模型计算结果与文献数据吻合较好。计算结果还显示，压力对Na2SO4和K2SO4的平均活度系数和溶度积都有正向的促进作用，但是由于平均活度系数随压力的变化更大，导致Na2SO4和K2SO4的溶解度随压力的增大而降低，并且随着温度的升高这种降低的程度变得更大。

关键词: 硫酸盐流体包裹体, 溶解度, 热力学计算, Pitzer模型

Sulfate fluids are common fluids in nature, and their salinity studies can provide important information for the evolution of ore-forming fluids, migration and enrichment of ore-forming elements, and the classification of deposit types. Considerable research has been carried out to investigate the solubility of Na2SO4 and K2SO4 in hydrothermal fluids, however most of the literature reported experimental data were under saturated vapor pressure or the water supercritical region. A few data have been reported for the low temperature hydrothermal mineralization region. Thermodynamic model is a useful method to study the properties of hydrothermal geofluids, especially for mineral solubility. Pitzer interaction model is one of the most widely used model to calculate the thermodynamic properties of hydrothermal fluids, but few work have ever been carried out to calculate the solubility of sulfate at high temperature and pressure. With Pitzer specific interaction model, using the literature reported density data of Na2SO4 and K2SO4 solutions at high temperature and pressure, the pressure effect on Pitzer activity coefficient of sulfate and the standard partial molar volume change during sulfate dissolution process were evaluated and related parameters were obtained. The standard partial molar volumes of Na2SO4 and K2SO4 calculated with these parameters agreed well with those reported in the literature. Combined with the relevant parameters in the literature under saturated vapor pressure, a thermodynamic model for Na2SO4 and K2SO4 solubility calculation with temperature up to 250 ℃ and pressure up to 40 MPa was developed. The model gave very good agreement with the experimental solubility data. With this model, Na2SO4 and K2SO4 solubility was calculated at high temperature and pressure. The calculation results showed that pressure had a positive effect on both the average activity coefficient and solubility product of Na2SO4 and K2SO4, but the solubility of Na2SO4 and K2SO4 decreased with pressure due to the larger change of the average activity coefficient with pressure. And as the temperature increased, the degree of such reduction became larger. The results herein can provide instructions for the compositional analysis of sulfate fluid inclusions.

Key words: Sulfate fluids inclusion, Solubility, Thermodynamic model, Pitzer model.

中图分类号: 

图1 25 oC不同压力下，模型计算的NaCl的平均活度系数随浓度的变化
Fig. 1 The model calculated NaCl mean activity coefficient at 25 oC as a function of concentration under different pressure
表1 Na2SO4-H2O体系密度实验数据
Table 1 Summary of density data of Na 2SO 4-H 2O system
温度范围/oC 压力范围/MPa 参考文献
25.0~300.0 9.0~30.0 [ 48 ]
25.0~200.0 1.1~68.6 [ 49 ]
5.0~60.0 0.1 [ 50 ]
20.0~200.0 2.0~10.0 [ 51 ]
0~50.0 0.1~80.0 [ 52 ]
50.0~200.0 2.0 [ 53 ]
25.0~100.0 0.6 [ 54 ]
25.0~250.0 0.1~40 [ 55 ]
30.0~300.0 2.4~39.8 [ 56 ]
5.0~100.0 0.1 [ 57 ]
表2 K2SO4-H2O体系密度的实验数据
Table 2 Summary of density data of K 2SO 4-H 2O system
温度范围/oC 压力范围/MPa 参考文献
25.0~300.0 9.0~30.0 [ 48 ]
50.0~200.0 2.0 [ 53 ]
25.0~100.0 0.6 [ 54 ]
0~90.0 0.1 [ 57 ]
20.0~300.0 5.0~40.0 [ 58 ]
图2 水热体系中模型计算的Na2SO4 溶液密度（a）和K2SO4 溶液密度（b）与实验数据的对比
Fig.2 Plot of density deviations between model calculation and literature data of Na2SO4 + H2O (a)and K2SO4 + H2O (b) system
表3 Na2SO4 和 K2SO4 体积性质计算的参数
Table 3 Parameters for the volumetric properties calculation of Na 2SO 4 and K 2SO 4
参数 Na2SO4 K2SO4
m r 1.5 1.0
a 1 9.69382688×102 1.10686112×103
a 2 2.83105828×10-1 -5.98247606×10-1
a 3 -9.00393580×10-4 5.96259241×10-4
a 4 2.57624184×10-6 2.39804594×10-6
a 5 -1.43199512×100 -2.71085716×100
a 6 7.37402186×10-3 1.41493666×10-2
a 7 -1.17539062×10-5 -2.08587301×10-5
a 8 -4.86834961×10-4 5.43596750×10-3
a 9 8.87142143×10-2 4.61245819×10-3
a 10 2.75966178×10-7 -1.21299746×10-5
a 11 2.13350752×10-4 -5.55380818×10-3
a 12 -1.36823713×10-2 6.41685688×10-2
a 13 -2.95936943×10-7 1.44544684×10-5
图3 Na2SO4 （a）和K2SO4 （b）标准偏摩尔体积随温度的变化
Fig.3 The standard partial molar volumes of Na2SO4 (a) and K2SO4 (b)against temperature and pressure
图4 不同温度压力下模型计算的Na2SO4 （a）和K2SO4 （b）平均活度系数随浓度的变化
Fig. 4 The model calculated Na2SO4 (a) and K2SO4 (b) mean activity coefficient as a function of concentration at different temperature and pressure
表4 模型计算的 Na2SO4 和 K2SO4 溶解度和实验结果的对比
Table 4 Comparison between model calculated Na 2SO 4 and K 2SO 4 with experimental data
温度/oC 实验结果/（mol/kg） 模型计算/（mol/kg） 参考文献

Na2SO4

P=P sat

60.0 3.15 3.34 [ 16 , 27 ]
100.0 2.99 3.04
120.0 2.95 2.94
140.7 2.96 2.89
200.7 3.15 3.16

K2SO4

P=P sat

50.00 0.95 0.94 [ 15 ]
80.00 1.23 1.20
100.0 1.40 1.33
150.0 1.69 1.57
190.0 1.97 1.71

Na2SO4

P= 25 MPa

 50.0 3.53 3.19 [ 60 ]
100.0 2.34 2.74
150.0 2.33 2.53
180.0 2.39 2.48
200.0 2.41 2.46
220.0 2.37 2.40
图5 Na2SO4 溶解平衡常数的自然对数（a）和溶解度（b）随温度压力的变化
Fig.5 The natural logarithm of Na2SO4 solubility product (a) and solubility (b) at different temperature and pressure
图6 K2SO4 溶解平衡常数的自然对数（a）和溶解度（b）随温度压力的变化
Fig.6 The natural logarithm of K2SO4 solubility product (a) and solubility (b) at different temperature and pressure
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