多孔介质内气泡Ostwald熟化特性三维孔网数值模拟

张沐安; 王进卿; 吴睿; 冯致; 詹明秀; 徐旭; 池作和

doi:10.7498/aps.72.20230695

摘要

多孔介质内气泡的Ostwald熟化行为广泛存在于CO₂地质封存、多孔材料制备、燃料电池等领域. 为探究孔隙尺度下多孔介质内气泡的熟化特性, 建立了基于浓度耦合计算的三维孔隙网络模型, 该模型考虑了气泡形态、多孔介质结构以及气液之间的传质, 通过求解三维孔隙网络内各孔体的气相浓度, 得到各气泡的演化过程, 并采用四孔隙结构微流体芯片可视化实验验证了模型的可靠性. 为分析多孔介质非均质性对气泡熟化过程影响, 构建了两种不同孔隙尺寸的三维孔网结构, 对两个区域内的气泡熟化过程进行了数值模拟. 结果表明: 气泡初始分布会对熟化过程产生影响, 当气泡非均匀分布时, 气泡从小孔隙区域传输至大孔隙区域的同时, 也会各自向自身区域的大气泡区域传质; 气泡初始尺寸的差异, 会加速熟化进程, 使熟化时间明显短于均匀分布状态. 孔隙数的选取对平均毛细力、饱和度等连续尺度等效参数具有显著影响, 孔隙数增加时毛细力与饱和度呈现更具规律性的非线性变化. 该模型的建立可以预测地质封存过程中CO₂的演化过程, 为CO₂长期封存过程中非均质性的影响机制研究提供指导.

关键词:

Abstract

Ostwald ripening behaviors of bubbles in porous medium are observed commonly in various fields, including CO₂ geological storage, preparation of porous materials, and fuel cells. A three-dimensional pore network model based on concentration coupling calculation has been developed to investigate the ripening characteristics of bubbles in porous medium on a pore scale. This model takes into account the shape of bubble, the structure of porous medium, and mass transfer between gas and liquid. By solving the gas phase concentration of each pore body in the three-dimensional pore network, the model can track the evolution process of each bubble. A microfluidic chip with a four-pore structure is used to validate the reliability of the model through visual experiments. To analyze the effect of porous medium heterogeneity on the bubble ripening process, two different three-dimensional pore network structures with varying pore sizes are constructed and the ripening processes of bubbles in two regions are simulated numerically. The results show that the initial distribution of bubbles can affect the ripening process of porous medium. When bubbles are uniformly distributed, in the ripening process, they exhibit regular and systematic changes in their spacing. However, in the case of uneven bubble distribution, as the bubbles transfer from smaller pore region to larger pore region, they also undergo individual mass transfer towards the larger bubble region in their respective areas. Consequently, the remaining bubbles no longer maintain a spaced distribution pattern. Additionally, the differences in initial size among bubbles can accelerate the ripening process, resulting in a significantly shorter ripening time than that in a uniform distribution. The choice of pore number has a significant influence on continuous-scale equivalent parameters, such as average capillary pressure and saturation. As the number of pores increases, the capillary pressure and saturation exhibit a more regular, nonlinear variation. A relationship between capillary pressure and saturation in the small pore region and in the large pore region are established, which deviate from the assumptions made in the existing literature. This result provides important guidance for constructing the continuous-scale ripening model that can be used to predict the evolution process of CO₂ during geological storage and provide guidance for studying the influence mechanism of heterogeneity during long-term CO₂ storage.

Keywords:

作者及机构信息

1.
中国计量大学计量测试工程学院, 杭州　310018

2.
上海交通大学机械与动力工程学院, 上海　200240

通信作者: 王进卿, jqwang@cjlu.edu.cn

基金项目: 国家自然科学基金(批准号: 52006207)和浙江省自然科学基金(批准号: LQ20E060005)资助的课题.

Authors and contacts

1.
College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou 310018, China

2.
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Corresponding author: Wang Jin-Qing, jqwang@cjlu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 52006207) and the Natural Science Foundation of Zhejiang Province, China (Grant No. LQ20E060005).

文章全文 : translate this paragraph

参考文献

[1]	Chang F M, Sheng Y J, Cheng S L, Tsao H K 2008 Appl. Phys. Lett. 92 264102 Google Scholar
[2]	宋保维, 任峰, 胡海豹, 郭云鹤 2014 63 054708 Google Scholar Song B W, Ren F, Hu H B, Guo Y H 2014 Acta Phys. Sin. 63 054708 Google Scholar
[3]	Feng L, Zhang Z Y, Mai Z H, Ma Y M, Liu B Q, Jiang L, Zhu D B 2004 Angew. Chem. Int. Ed. 43 2012 Google Scholar
[4]	Lautze N C, Sisson T W, Mangan M T, Grove T L 2010 Contrib. Mineral Petrol. 161 331 Google Scholar
[5]	Masotta M, Ni H, Keppler H 2014 Contrib. Mineral. Petrol. 167 976 Google Scholar
[6]	Huang Z D, Su M, Yang Q, Li Z, Chen S R, Li Y F, Zhou X, Li F Y, Song Y L 2017 Nat. Commun. 8 14110 Google Scholar
[7]	严达利, 李申予, 刘士余, 竺云 2015 64 137104 Google Scholar Yan D L, Li S Y, Liu S Y, Zhu Y 2015 Acta Phys. Sin. 64 137104 Google Scholar
[8]	Bachu S 2008 Prog. Energy Combust. Sci. 34 254 Google Scholar
[9]	Singh D, Friis H A, Jettestuen E, Helland J O 2022 Transport Porous Med. 145 441 Google Scholar
[10]	Iglauer S, Pentland C H, Busch A 2015 Water Resour Res. 51 729 Google Scholar
[11]	Rahman T, Lebedev M, Barifcani A, Iglauer S 2016 J. Colloid Interface Sci. 469 63 Google Scholar
[12]	Lifshitz I M, Slyozov V V 1961 J. Phys. Chem. Solids. 19 35 Google Scholar
[13]	Voorhees P W 1992 Annu. Rev. Mater. Sci. 22 197 Google Scholar
[14]	Burlakov V M 2006 Phys. Rev. Lett. 97 155703 Google Scholar
[15]	Schmelzer J, Schweitzer F 1987 J. Non-Equilib. Thermodyn. 12 255 Google Scholar
[16]	Xu R N, Li R, Huang F, Jiang P X 2017 Sci. Bull. 62 795 Google Scholar
[17]	Xu K, Liang T B, Zhu P X, Qi P P, Lu J, Huh C, Balhoff M 2017 Lab. Chip. 17 640 Google Scholar
[18]	Li Y, Garing C, Benson S M 2020 J. Fluid Mech. 889 A14 Google Scholar
[19]	Blunt M J, Bijeljic B, Dong H, Gharbi O, Iglauer S, Mostaghimi P, Paluszny A, Pentland C 2013 Adv. Water Resour. 51 197 Google Scholar
[20]	Golparvar A, Zhou Y, Wu K, Ma J, Yu Z 2018 Adv. Geo. Energy Res. 2 418 Google Scholar
[21]	Kohanpur A H, Valocchi A J 2020 Transport. Porous Med. 135 659 Google Scholar
[22]	Xu K, Mehmani Y, Shang L, Xiong Q 2019 Geophy. Res. Lett. 46 13804 Google Scholar
[23]	Xu K, Bonnecaze R, Balhoff M 2017 Phys. Rev. Lett. 119 264502 Google Scholar
[24]	Mehmani Y, Xu K 2022 J. Comput. Phys. 457 111041 Google Scholar
[25]	de Chalendar J A, Garing C, Benson S M 2017 Energy Procedia. 114 4857 Google Scholar
[26]	Vorst H A 1992 SIAM J. Sci. Stat. Comput. 13 631 Google Scholar
[27]	Pallas N R, Pethica B A 1983 Colloid Surface 6 221 Google Scholar
[28]	Versteeg G F, Van Swaaij W P M 1988 J. Chem. Eng. Data. 33 29 Google Scholar
[29]	周志毅, 王进卿, 王广鑫, 池作和, 翁煜侃 2022 化工进展 41 1265 Google Scholar Zhou Z Y, Wang J Q, Wang G X, Chi Z H, Weng Y K 2022 Chem. Ind. Eng. Prog. 41 1265 Google Scholar
[30]	Blunt M J 2022 Phys. Rev. E 106 045103 Google Scholar
[31]	McClure J E, Berrill M A, Gray W G, Miller C T 2016 Phys. Rev. E 94 033102 Google Scholar

施引文献

图 1 双气泡系统传质过程

Fig. 1. Two-bubble system mass transfer process.

下载: 全尺寸图片幻灯片

图 2 计算程序算法流程图

Fig. 2. Flow chart for the calculation algorithm.

下载: 全尺寸图片幻灯片

图 3 数值计算模型　(a)孔体i内为气泡; (b)孔体i内为液相

Fig. 3. Numerical calculation model: (a) Pore body i with a bubble; (b) pore body i filled with liquid phase.

下载: 全尺寸图片幻灯片

图 4 多孔隙结构熟化模型

Fig. 4. Multi bubble ripening model.

下载: 全尺寸图片幻灯片

图 5 微流控芯片内部结构

Fig. 5. Internal structure of microfluidic chip.

下载: 全尺寸图片幻灯片

图 6 四孔隙结构气泡熟化过程　(a)实验过程; (b)模拟过程

Fig. 6. Four bubble ripening system: (a) Experiments process; (b) simulations process.

下载: 全尺寸图片幻灯片

图 7 四孔隙结构气泡半径随时间变化

Fig. 7. Evolution of curvature radius in four bubble ripening system.

下载: 全尺寸图片幻灯片

图 8 工况1#模拟结果　(a)气泡演化过程, 其中白色区域为CO₂气泡, 蓝色区域为去离子水, 灰色区域为硅颗粒; (b) CO₂气泡曲率半径变化图

Fig. 8. Simulation results of condition 1#: (a) Bubble evolution process, where the white regions are CO₂ bubble, blue regions are filled with DI water, and the gray regions are silicon grains; (b) curvature radius variation diagram of each CO₂ bubble.

下载: 全尺寸图片幻灯片

图 9 一维孔隙结构气泡熟化过程

Fig. 9. Bubble evolution process of one-dimensional structure.

下载: 全尺寸图片幻灯片

图 10 工况2#模拟结果　(a)第1层和第5层气泡演化过程; (b)第1层和第5层CO₂气泡曲率半径变化; (c)第2层和第4层气泡演化过程; (d)第2层和第4层CO₂气泡曲率半径变化; (e)第3层气泡演化过程; (f)第3层CO₂气泡曲率半径变化

Fig. 10. Simulation results of condition 2#: (a) Bubble evolution process in layers 1 and 5; (b) curvature radius variation of each CO₂ bubble in layers 1 and 5; (c) bubble evolution process in layers 2 and 4; (d) curvature radius variation of each CO₂ bubble in layers 2 and 4; (e) bubble evolution process in layer 3; (f) curvature radius variation of each CO₂ bubble in layer 3.

下载: 全尺寸图片幻灯片

图 11 CO₂气泡各参数变化图　(a)毛细力; (b) CO₂饱和度

Fig. 11. Variation diagram of CO₂ bubble parameters: (a) Capillary pressure; (b) CO₂ saturation.

下载: 全尺寸图片幻灯片

图 12 气泡毛细力与CO₂饱和度关系对比图　(a)小孔隙区域; (b)大孔隙区域

Fig. 12. Comparison of capillary pressure with CO₂ saturation curves: (a) Small pore region; (b) large pore region.

下载: 全尺寸图片幻灯片

表 1 模拟工况参数

Table 1. Simulation parameters of three conditions.

工况		行数	列数	层数	孔体总数	各层气泡初始半径 R/μm
工况		行数	列数	层数	孔体总数	1, 2	3	4, 5
1#	大孔隙区域	5	4	5	100	25	25	25
1#	小孔隙区域	9	5	5	225	10	10	10
2#	大孔隙区域	5	4	5	100	25	35	25
2#	小孔隙区域	9	5	5	225	10	15	10
3#	大孔隙区域	10	32	10	3200	25	25	25
3#	小孔隙区域	19	40	10	7600	10	10	10

下载: 导出CSV

表 2 四孔隙及多孔隙结构气泡熟化模拟参数

Table 2. Simulation parameters of four bubble and muti bubble ripening system.

参数	符号 /单位	数值
液相压力	P/Pa	1.013×10⁵
环境温度	T/K	298
CO₂密度	ρ/(kg·m^–3)	1.98
CO₂摩尔质量	M/(g·mol^–1)	44.0
去离子水表面张力^[27]	σ/(mN·m^–1)	71.97
扩散系数^[28]	D/(m²·s^–1)	2.02×10^–9
亨利系数^[28]	H/(Pa·m³·kg^–1)	6.5×10⁴

下载: 导出CSV

map

[1]	Chang F M, Sheng Y J, Cheng S L, Tsao H K 2008 Appl. Phys. Lett. 92 264102 Google Scholar
[2]	宋保维, 任峰, 胡海豹, 郭云鹤 2014 63 054708 Google Scholar Song B W, Ren F, Hu H B, Guo Y H 2014 Acta Phys. Sin. 63 054708 Google Scholar
[3]	Feng L, Zhang Z Y, Mai Z H, Ma Y M, Liu B Q, Jiang L, Zhu D B 2004 Angew. Chem. Int. Ed. 43 2012 Google Scholar
[4]	Lautze N C, Sisson T W, Mangan M T, Grove T L 2010 Contrib. Mineral Petrol. 161 331 Google Scholar
[5]	Masotta M, Ni H, Keppler H 2014 Contrib. Mineral. Petrol. 167 976 Google Scholar
[6]	Huang Z D, Su M, Yang Q, Li Z, Chen S R, Li Y F, Zhou X, Li F Y, Song Y L 2017 Nat. Commun. 8 14110 Google Scholar
[7]	严达利, 李申予, 刘士余, 竺云 2015 64 137104 Google Scholar Yan D L, Li S Y, Liu S Y, Zhu Y 2015 Acta Phys. Sin. 64 137104 Google Scholar
[8]	Bachu S 2008 Prog. Energy Combust. Sci. 34 254 Google Scholar
[9]	Singh D, Friis H A, Jettestuen E, Helland J O 2022 Transport Porous Med. 145 441 Google Scholar
[10]	Iglauer S, Pentland C H, Busch A 2015 Water Resour Res. 51 729 Google Scholar
[11]	Rahman T, Lebedev M, Barifcani A, Iglauer S 2016 J. Colloid Interface Sci. 469 63 Google Scholar
[12]	Lifshitz I M, Slyozov V V 1961 J. Phys. Chem. Solids. 19 35 Google Scholar
[13]	Voorhees P W 1992 Annu. Rev. Mater. Sci. 22 197 Google Scholar
[14]	Burlakov V M 2006 Phys. Rev. Lett. 97 155703 Google Scholar
[15]	Schmelzer J, Schweitzer F 1987 J. Non-Equilib. Thermodyn. 12 255 Google Scholar
[16]	Xu R N, Li R, Huang F, Jiang P X 2017 Sci. Bull. 62 795 Google Scholar
[17]	Xu K, Liang T B, Zhu P X, Qi P P, Lu J, Huh C, Balhoff M 2017 Lab. Chip. 17 640 Google Scholar
[18]	Li Y, Garing C, Benson S M 2020 J. Fluid Mech. 889 A14 Google Scholar
[19]	Blunt M J, Bijeljic B, Dong H, Gharbi O, Iglauer S, Mostaghimi P, Paluszny A, Pentland C 2013 Adv. Water Resour. 51 197 Google Scholar
[20]	Golparvar A, Zhou Y, Wu K, Ma J, Yu Z 2018 Adv. Geo. Energy Res. 2 418 Google Scholar
[21]	Kohanpur A H, Valocchi A J 2020 Transport. Porous Med. 135 659 Google Scholar
[22]	Xu K, Mehmani Y, Shang L, Xiong Q 2019 Geophy. Res. Lett. 46 13804 Google Scholar
[23]	Xu K, Bonnecaze R, Balhoff M 2017 Phys. Rev. Lett. 119 264502 Google Scholar
[24]	Mehmani Y, Xu K 2022 J. Comput. Phys. 457 111041 Google Scholar
[25]	de Chalendar J A, Garing C, Benson S M 2017 Energy Procedia. 114 4857 Google Scholar
[26]	Vorst H A 1992 SIAM J. Sci. Stat. Comput. 13 631 Google Scholar
[27]	Pallas N R, Pethica B A 1983 Colloid Surface 6 221 Google Scholar
[28]	Versteeg G F, Van Swaaij W P M 1988 J. Chem. Eng. Data. 33 29 Google Scholar
[29]	周志毅, 王进卿, 王广鑫, 池作和, 翁煜侃 2022 化工进展 41 1265 Google Scholar Zhou Z Y, Wang J Q, Wang G X, Chi Z H, Weng Y K 2022 Chem. Ind. Eng. Prog. 41 1265 Google Scholar
[30]	Blunt M J 2022 Phys. Rev. E 106 045103 Google Scholar
[31]	McClure J E, Berrill M A, Gray W G, Miller C T 2016 Phys. Rev. E 94 033102 Google Scholar

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