Three-Phase Permeabilities: Upscaling, Analytical Solutions and Uncertainty Analysis in Elementary Pore Structures

详细信息    查看全文

• 作者：Emanuela Bianchi Janetti (1)
  Monica Riva (1) (2)
  Alberto Guadagnini (1) (2)
  
• 关键词：Three ; phase flow ; Upscaling ; Relative permeability ; Viscous coupling ; Analytical solution ; Global sensitivity analysis
• 刊名：Transport in Porous Media
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：106
• 期：2
• 页码：259-283
• 全文大小：1,902 KB
• 参考文献：1. Al-Futaisi, A., Patzek, T.W.: Three-phase hydraulic conductances in angular capillaries. 2002 SPE/DOE Improved Oil Recovery Symposium, 13/04-17/04/2002, Tulsa, Oklahoma. SPE J. 8(3), 252-61 (2003) CrossRef
  2. Auriault, J.L.: Non saturated deformable porous media. Quasistatic 2, 45-4 (1987)
  3. Auriault, J.L.: Dynamics of two immiscible fluids flowing through deformable porous media. Transp. Porous Media 4, 105-28 (1989) CrossRef
  4. Auriault, J.L., Adler, P.M.: Taylor dispersion in porous media: analysis by multiple scale expansions. Adv. Water Resour. 4, 217-26 (1995) CrossRef
  5. Auriault, J.L., Boutin, C., Geindreau, C.: Homogenization of Coupled Phenomena in Heterogeneous Media. Iste Wiley, London (2009) CrossRef
  6. Avraam, D.G., Payatakes, A.C.: Generalized relative permeability coefficients during steady-state two-phase flow in porous media, and correlation with the flow mechanisms. Transp. Porous Media 20, 135-68 (1995) CrossRef
  7. Aziz, K., Settari, A.: Wettability literature survey-Part 4: effects of wettability on capillary pressure. J. Petrol. Technol. 39, 1283-300 (1979)
  8. Baker, L.E.: Three phase relative permeability correlation. In: SPE Enhance Oil Recovery Symposium, 17-0 Apr, Tulsa, USA (1988)
  9. Beal, C.: The viscosity of air, water, natural gas, crude oil and its associated gases at oil field temperature and pressure. Trans. AIME 165, 94-15 (1946) CrossRef
  10. Bear, J., Cheng, A.H.D.: Modeling Groundwater Flow and Contaminant Transport. Springer, Dordrecht (2010) CrossRef
  11. Bensen, R.G., Manai, A.A.: On the use of conventional cocurrent and countercurrent effective permeabilities to estimate the four generalized permeability coefficients which arise in coupled, two-phase flow. Transp. Porous Media 11, 243-62 (1993) CrossRef
  12. Blunt, M.J.: An empirical model for three-phase relative permeability. Soc. Petrol. Eng. J. 5, 435-45 (2000)
  13. Bravo, M.C., Araujo, M., Lago, M.E.: Pore network modeling of two-phase flow in a liquid-(disconnected) gas system. Physica A 375, 1-7 (2007) CrossRef
  14. Chen, D.L., Li, L., Reyes, S., Adamson, D.N., Ismagilov, R.F.: Using three-phase flow of immiscible liquids to prevent coalescence of droplets in microfluidic channels: criteria to identify the third liquid and validation with protein crystallization. Langmuir 23, 2255-260 (2007) CrossRef
  15. Dehghanpour, H., Aminzadeh, B., Mirzaei, M., DiCarlo, D.A.: Flow coupling during three phase gravity drainage. Phys. Rev. E 83, 065302 (2011a) CrossRef
  16. Dehghanpour, H., Aminzadeh, B., DiCarlo, D.A.: Hydraulic conductance and viscous coupling of three-phase layers in angular capillaries. Phys. Rev. E 83, 066302 (2011b) CrossRef
  17. DiCarlo, D.A., Sahni, A., Blunt, M.J.: The effect of wettability on three-phase relative permeability. Transp. Porous Media 39, 347-66 (2000) CrossRef
  18. Dullien, F
• 作者单位：Emanuela Bianchi Janetti (1)
  Monica Riva (1) (2)
  Alberto Guadagnini (1) (2)
  
  1. Dipartimento di Ingegneria Civile e Ambientale (DICA), Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy
  2. Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ, 85721, USA
  
• ISSN：1573-1634

文摘

Immiscible three-phase flow in a rigid porous medium is upscaled from the pore to the continuum (Darcy) scale through homogenization relying on multiple scale expansion. We solve the Stokes flow problem at the pore level upon imposing continuity of velocity and shear stress at the fluid–fluid interfaces. This enables one to explicitly account for the momentum transfer between the moving phases. A macroscopic model describing the system at the Darcy scale is then rigorously obtained. This allows defining a tensor of three-phase effective relative permeabilities, \(\mathbf{K}_{\alpha \eta ,r}\) , as a function of the distribution of the fluids in the system, phase saturations and fluid viscosity ratios. We present an analytical solution for \(\mathbf{K}_{\alpha \eta ,r}\) corresponding to a scenario where three-phase fluid flow takes place within (a) a plane channel and (b) a capillary tube with circular cross-section. These geometrical settings are typical of microfluidics applications and are archetypal to the analysis of key processes occurring in topologically complex porous or fractured systems. Our results show the relevance of the viscous coupling effects between the three phases on the continuum-scale system behavior and demonstrate that the traditional extension of Darcy’s law to model multiphase relative permeabilities might be inadequate. We then exploit our analytical solutions to investigate the way the uncertainty associated with the characterization of the phase viscosities propagates to \(\mathbf{K}_{\alpha \eta ,r}\) through a global sensitivity analysis approach. We quantify the relative contribution of the considered uncertain parameters to the total variability of \(\mathbf{K}_{\alpha \eta ,r}\) by relying on the variance-based Sobol indices which are derived analytically for the investigated settings.