Capillary pressure-saturation relation for gas-liquid two-phase fluid in spherical pore

doi:10.11949/j.issn.0438-1157.20160720

Abstract

Abstract:

The relationship between capillary pressure and saturation is one of the most basic and important issues of multiphase flow in porous media. The-state-of-the-art of theoretical models on capillary pressure-saturation relation as well as the progress of Leverett-J function are reviewed and discussed, and then the capillary pressure-saturation equations for liquid-gas two-phase fluid in a single spherical cavity are derived through geometry manipulation. Calculations are performed for solid-liquid contact angles of 10°, 30°, 60° and 90° using such equations, the obtained results are consistent with the experimental data in the literature, providing a rational explanation for the variation characteristics of the capillary pressure-saturation curve.

Key words: porous medium, spherical pore, gas-liquid two-phase fluid, capillary pressure, saturation, porosity

摘要：

毛细压力与饱和度的关系是多孔介质多相流最基本、最重要的关系之一。综述了毛细压力与饱和度关系的研究现状，列举了多种毛细压力与饱和度关系模型，展现了Leverett-J函数的发展历程。在此基础上以单个球形空腔内气液两相流体为研究对象，依据几何分析推导得到了固液接触角分别为10°、30°、60°和90°时毛细压力随饱和度的变化关系，计算结果与文献中的实验结果具有相同的变化趋势，从而很好地说明了毛细压力与饱和度关系曲线的变化特征。

关键词: 多孔介质, 球形空腔, 气液两相流, 毛细压力, 饱和度, 孔隙率

CLC Number:

O359⁺.1

LIU Guiling, MIN Jingchun, TANG Yicun. Capillary pressure-saturation relation for gas-liquid two-phase fluid in spherical pore[J]. CIESC Journal, 2016, 67(S1): 40-46.

刘桂玲, 闵敬春, 汤一村. 球形空腔内气液两相毛细压力与饱和度的关系[J]. 化工学报, 2016, 67(S1): 40-46.

References 20

[1]	张茂林, 梅海燕, 李闽, 等. Young-Laplace方程推导的新方法及应用[J]. 西南石油学院学报, 2002, 24(5):43-45. ZHANF M L, MEI H Y, LI M, et al. A new derivation method and the application of Young-Laplace equation[J]. Journal of Southwest Petroleum Institute, 2002, 24(5):43-45.
[2]	LEVERETT M C. Capillary behavior in porous solids[J]. Transactions of the AIME, 1941, 142(1):152-169.
[3]	MOSELEY W A, DHIR V K. Capillary pressure-saturation relations in porous media including the effect of wettability[J]. Journal of Hydrology, 1996, 178(1):33-53.
[4]	PARKER J C, LENHARD R J. A model for hysteretic constitutive relations governing multiphase flow(1):Saturation-pressure relations[J]. Water Resources Research, 1987, 23(12):2187-2196.
[5]	LENHARD R J, PARKER J C. Experimental validation of the theory of extending two-phase saturation-pressure relations to three-fluid phase systems for monotonic drainage paths[J]. Water Resources Research, 1988, 24(3):373-380.
[6]	GRAY W G, HASSANIZADEH S M. Thermodynamic basis of capillary pressure in porous media[J]. Water Resources Research, 1993, 29(10):3389-3405.
[7]	ROSE W, BRUCE W A. Evaluation of capillary character in petroleum reservoir rock[J]. Journal of Petroleum Technology, 1949, 1(5):127-142.
[8]	UDELL K S. Heat transfer in porous media considering phase change and capillarity-the heat pipe effect[J]. International Journal of Heat and Mass Transfer, 1985, 28(2):485-495.
[9]	KUEPER B H, FRIND E O. Two-phase flow in heterogeneous porous media(1):Model development[J]. Water Resources Research, 1991, 27(6):1049-1057.
[10]	ISHAKOGLU A, BAYTAS A F. The influence of contact angle on capillary pressure-saturation relations in a porous medium including various liquids[J]. International Journal of Engineering Science, 2005, 43(8):744-755.
[11]	HASSANIZADEH S M, GRAY W G. Toward an improved description of the physics of two-phase flow[J]. Advances in Water Resources, 1993, 16(1):53-67.
[12]	GRAY W G, HASSANIZADEH S M. Paradoxes and realities in unsaturated flow theory[J]. Water Resources Research, 1991, 27(8):1847-1854.
[13]	HASSANIZADEH S M, CELIA M A, DAHLE H K. Dynamic effect in the capillary pressure-saturation relationship and its impacts on unsaturated flow[J]. Vadose Zone Journal, 2002, 1(1):38-57.
[14]	FATT I. The network model of porous media (1):Capillary pressure characteristics[J]. Transactions of the AIME, 1956, 207(7):144-159.
[15]	FATT I. The network model of porous media (3):Dynamic properties of networks with tube radius distribution[J]. Transactions of the AIME, 1956, 207(7):164-181.
[16]	FATT I. The network model of porous media(2):Dynamic properties of a single size tube network[J]. Transactions of the AIME, 1956, 207(7):160-163.
[17]	REEVES P C, CELIA M A. A functional relationship between capillary pressure, saturation, and interfacial area as revealed by a pore-scale network model[J]. Water Resources Research, 1996, 32(8):2345-2358.
[18]	陶军, 姚军, 李爱芬, 等. 毛细管压力, 饱和度和相界面积间的关系[J]. 中国石油大学学报:自然科学版, 2008, 32(2):90-92. TAO J, YAO J, LI A F, et al. Relationship among capillary pressure, saturation and phases interfacial area[J]. Journal of China University of Petroleum, 2008, 32(2):90-92.
[19]	BLUNT M J. Flow in porous media-pore-network models and multiphase flow[J]. Current Opinion in Colloid & Interface Science, 2001, 6(3):197-207.
[20]	王达健, 陈书荣, 张雄飞, 等. 多孔介质孔隙模型及其应用——毛细管束模型[J]. 计算机与应用化学, 2001,18(5):429-432. WANG D J, CHEN S R, ZHANG X F, et al. Developement and application of pore structure model-bundle of capillary tubes model[J]. Computers and Applied Chemistry, 2001, 18(5):429-432.