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Finite volume solution for two-phase flow in a straight capillary

Alexander Yelkhovsky1 and W. Val Pinczewski1

  • 1School of Petroleum Engineering, University of New South Wales, Sydney 2052, Australia

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Phys. Rev. Fluids 3, 044003 – Published 27 April, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.044003

Abstract

The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to be important in these displacements but is usually ignored in network models commonly used to predict macroscopic flow properties. This study presents a numerical model for two-phase flow which describes the spatial and temporal evolution of the interface between the fluids. The model is based on an averaged Navier-Stokes equation and is shown to be successful in predicting the complex dynamics of both capillary rise in round capillaries and imbibition along the corners of polygonal capillaries. The model can form the basis for more realistic network models which capture the effect of capillary, viscous, and inertial forces on pore-scale interfacial dynamics and consequent macroscopic flow properties.

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References (32)

  1. M. J. Blunt, B. Bijeljic, H. Dong, O. Gharbi, S. Iglauer, P. Mostaghimi, A. Paluszny, and C. Pentland, Pore-scale imaging and modelling, Adv. Water Resources 51, 197 (2013).
  2. I. Bondino, G. Hamon, W. Kallel, and D. Kachuma, Relative permeabilities from simulation in 3d rock models and equivalent pore networks: Critical review and way forward, Petrophysics 54, 538 (2013).
  3. V. Joekar-Niasar and S. M. Hassanizadeh, Analysis of fundamentals of two-phase flow in porous media using dynamic pore-network models: A review, Crit. Rev. Environ. Sci. Tech. 42, 1895 (2012).
  4. A. Aghaei and M. Piri, Direct pore-to-core up-scaling of displacement processes: Dynamic pore network modeling and experimentation, J. Hydrol. 522, 488 (2015).
  5. A. Q. Raeini, B. Bijeljic, and M. J. Blunt, Generlaized network modelling of capillary dominated two-phase flow, Phys. Rev. E 97, 023308 (2018).
  6. V. H. Nguyen, A. P. Sheppard, M. A. Knackstedt, and W. V. Pinczewski, The effect of displacement rate on imbibition relative permeability and residual saturation, J. Petrol. Sci. Eng. 52, 54 (2006).
  7. N. A. Idowu and M. J. Blunt, Pore-scale modelling of rate effects in waterflooding, Transp. Porous Media 83, 151 (2010).
  8. K. Singh, H. Menke, M. Andrew, Q. Lin, C. R. M. J. Blunt, and B. Bijeljic, Dynamics of snap-off and pore-filling events during two-phase fluid flow in permeable media, Nat. Sci. Rep. 7, 5192 (2017).
  9. F. Moebius and D. Or, Interfacial jumps and pressure bursts during fluid displacement in interacting irregular capillaries, J. Colloid Interf. Sci. 377, 406 (2012).
  10. R. T. Armstrong and S. Berg, Interfacial velocities and capillary pressure gradients during Haines jumps, Phys. Rev. E 88, 043010 (2013).
  11. F. Moebius and D. Or, Inertial forces affect fluid front displacement dynamics in a pore-throat network model, Phys. Rev. E 90, 023019 (2014).
  12. S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J.-O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, Real-time 3d imaging of Haines jumps in porous media flow, Proc. Natl. Acad. Sci. U. S. A. 110, 3755 (2013).
  13. S. Berg, R. T. Armstrong, A. Georgiadis, H. Ott, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, M. Rücker, L. Leu, M. Wolf, F. Khan, F. Enzmann, and M. Kersten, Onset of oil mobilization and nonwetting-phase cluster-size distribution, Petrophysics 56, 15 (2015).
  14. M. Rücker, S. Berg, R. T. Armstrong, A. Georgiadis, H. Ott, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, M. Wolf, F. Khan, F. Enzmann, and M. Kersten, From connected pathway flow to ganglion dynamics, Geophys. Res. Lett. 42, 3888 (2015).
  15. M. Andrew, H. Menke, M. J. Blunt, and B. Bijeljic, The imaging of dynamic multiphase fluid flow using synchrotron-based x-ray microtomography at reservoir conditions, Transp. Porous Media 110, 1 (2015).
  16. R. T. Armstrong, J. E. McClure, M. A. Berill, M. Rücker, S. Schluter, and S. Berg, Flow regimes during immiscible displacement, Petrophysics 58, 10 (2017).
  17. W. B. Haines, Studies in the physical properties of soil. V. The hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith, The Journal of Agri. Sci. 20, 97 (1930).
  18. D. A. DiCarlo, J. I. G. Cidoncha, and C. Hickey, Acoustic measurements of pore-scale displacements, Geophys. Res. Lett. 30, 1901 (2003).
  19. A. Ferrari and I. Lunati, Inertial effects during irreversible meniscus reconfiguration in angular pores, Adv. Water Resources 74, 1 (2014).
  20. R. T. Armstrong, N. Evseev, D. Koroteev, and S. Berg, Modeling the velocity field during Haines jumps in porous media, Adv. Water Resources 77, 57 (2015).
  21. P. Meakin and A. M. Tartakovsky, Modeling and simulation of pore-scale multiphase fluid flow and reactive transport in fractured and porous media, Rev. Geophys. 47, RG3002 (2009).
  22. D. Quéré, É. Raphaël, and J.-Y. Ollitrault, Rebounds in a capillary tube, Langmuir 15, 3679 (1999).
  23. D. Quéré, Inertial capillary, Europhys. Lett. 39, 533 (1997).
  24. M. M. Weislogel and S. Lichter, Capillary flow in an interior corner, J. Fluid Mech. 373, 349 (1998).
  25. M. Dong and I. Chatzis, The imbibition and flow of a wetting liquid along the corners of a square capillary tube, J. Colloid Interf. Sci. 172, 278 (1995).
  26. T. C Ransohoff and C. J Radke, Laminar flow of a wetting liquid along the corners of a predominantly gas-occupied noncircular pore, J. Colloid Interf. Sci. 121, 392 (1988).
  27. R. E. Bank, PLTMG: A software package for solving elliptic partial differential equations, users' guide 11.0, Technical Report (University of California at San Diego, 2012).
  28. J. Szekely, A. W. Neumann, and Y. K Chuang, The rate of capillary penetration and the applicability of the Washburn equation, J. Colloid Interf. Sci. 35, 273 (1971).
  29. D. Duvivier, T. D. Blake, and J. De Coninck, Toward a predictive theory of wetting dynamics, Langmuir 29, 10132 (2013).
  30. O. V. Voinov, Hydrodynamics of wetting, Fluid Dyn. 11, 714 (1976).
  31. R. G. Cox, The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow, J. Fluid Mech. 168, 169 (1986).
  32. F. P. Bretherton, The motion of long bubbles in tubes, J. Fluid Mech. 10, 166 (1961).

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Phys. Rev. Fluids 3, 044003– Published 27 April, 2018
  • Received 6 August 2017
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