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Abstract

Summary

Standard compositional simulators use composition-dependent cubic equations-of-state (EoS), but saturationdependent relative permeability (kr). This discrepancy causes discontinuities, increasing computational time and reduced accuracy. To rectify this problem, kr has been recently defined as a state function, so that it becomes compositional dependent. Such a form of the kr EoS can significantly improve the convergence in compositional simulation, in that time step sizes are near the IMPEC stability limit and flash calculation convergence is improved.

This paper revisits the development of kr EoS by defining relevant state variables and deriving functional forms of the state function via a methodical approach. The state variables include phase saturation, phase connectivity, wettability, capillary number, and pore topology. The developed EoS is constrained to physical boundary conditions. The model coefficients are estimated through linear regression on data collected from a pore-scale simulation study that estimates kr based on micro-CT image analysis. The results show that a simple quadratic expression gives an excellent match with simulation measurements from the literature. The goodness of fit (R2) value is 0.97 for kr at variable phase saturation and phase connectivity, and constant wettability, pore structure, and capillary number (∼10-4). The quadratic response for kr also shows excellent predictive capabilities.

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/content/papers/10.3997/2214-4609.201802125
2018-09-03
2024-04-26

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References

  1. Akhgar, A., Khalili, B., Moa, B., Rahnama, M., and Djilali, N.
    (2017). Lattice-Boltzmann Simulation of Multi-Phase Phenomena Related to Fuel Cells.AIP Conference Proceedings, 1863.https://doi.org/10.1063/1.4992192
     [Google Scholar]
  2. Al-Khulaifi, Y., Lin, Q., Blunt, M. J., and Bijeljic, B.
    (2017). Reaction Rates in Chemically Heterogeneous Rock: Coupled Impact of Structure and Flow Properties Studied by X-ray Microtomography.Environmental Science and Technology, 51(7), 4108–4116. https://doi.org/10.1021/acs.est.6b06224
     [Google Scholar]
  3. Allard, D.
    (1993). Some Connectivity Characteristics of A Boolean Model. In Geostatistics Troia ’92. Quantitative Geology and Geostatistics (pp. 467–478). Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1739-5
     [Google Scholar]
  4. Armstrong, R. T., Mcclure, J. E., Berill, M. A., Rücker, M., Schlüter, S., and Berg, S.
    (2016). Flow Regimes During Immiscible Displacement.Int. Symp. Soc. Core Analysts, 58(1), 1–12. Retrieved from http://www.jgmaas.com/SCA/2016/SCA2016-009.pdf
     [Google Scholar]
  5. Armstrong, R. T., McClure, J. E., Berrill, M. A., Rücker, M., Schlüter, S., and Berg, S.
    (2016). Beyond Darcy’s law: The Role of Phase Topology and Ganglion Dynamics for Two-Fluid Flow.Physical Review E, 94(4), 1–10. https://doi.org/10.1103/PhysRevE.94.043113
     [Google Scholar]
  6. Avraam, D. G.; Payatakes, A. C.
    (1995). Flow Regimes and Relative Permeabilities during Steady-State Two-Phase Flow in Porous Media.Journal of Fluid Mechanics, 293, 207–236. https://doi.org/10.1017/S0022112095001698
     [Google Scholar]
  7. Avraam, D. G., and Payatakes, A. C.
    (1999). Flow Mechanisms, Relative Permeabilities, and Coupling Effects in Steady-State Two-Phase Flow through Porous Media. The Case of Strong Wettability.Industrial and Engineering Chemistry Research, 38(3), 778–786. https://doi.org/10.1021/ie980404o
     [Google Scholar]
  8. Aydogan, D. B., and Hyttinen, J.
    (2013). Contour Tree Connectivity of Binary Images from Algebraic Graph Theory. In 20th IEEE International Conference on Image Processing (ICIP) (pp. 3054–3058). Melbourne, Australia: IEEE.
     [Google Scholar]
  9. (2014). Characterization of Microstructures Using Contour Tree Connectivity for Fluid Flow Analysis.Journal of The Royal Society Interface, 11(95), 20131042–20131042. https://doi.org/10.1098/rsif.2013.1042
     [Google Scholar]
  10. Bachu, S., and Bennion, B.
    (2008). Effects of In-situ Conditions on Relative Permeability Characteristics of CO2-Brine Systems.Environmental Geology, 54(8), 1707–1722. https://doi.org/10.1007/s00254-007-0946-9
     [Google Scholar]
  11. Berg, S., Armstrong, R., Ott, H., Georgiadis, A., Klapp, S. A., Schwing, A., et al.
    , (2014). Multiphase Flow in Porous Rock Imaged Under Dynamic Flow Conditions with Fast X-Ray Computed Microtomography.Society of Petrophysicists and Well-Log Analysts, 55(4), 304–312.
     [Google Scholar]
  12. Berg, S., Ott, H., Klapp, S. A., Schwing, A., Neiteler, R., Brussee, N., et al.
    , (2013). Real-Time 3D Imaging of Haines Jumps in Porous Media Flow.Proceedings of the National Academy of Sciences of the United States of America, 110(10). https://doi.org/10.1073/pnas.1221373110
     [Google Scholar]
  13. Berg, S., Rücker, M., Ott, H., Georgiadis, A., van der Linde, H., Enzmann, F., et al.
    , (2016). Connected Pathway Relative Permeability from Pore-Scale Imaging of Imbibition.Advances in Water Resources, 90, 24–35. https://doi.org/10.1016/j.advwatres.2016.01.010
     [Google Scholar]
  14. Blunt, M. J.
    (2017). Multiphase flow in permeable media : a pore-scale perspective.Cambridge University Press.
     [Google Scholar]
  15. Celauro, J. G., Torrealba, V. A., Karpyn, Z. T., Klise, K. A., and Mckenna, S. A.
    (2014). Pore-Scale Multiphase Flow Experiments in Bead Packs of Variable Wettability.Geofluids, 14(1), 95–105. https://doi.org/10.1111/gfl.12045
     [Google Scholar]
  16. Chang, L. C., Chen, H. H., Shan, H. Y., and Tsai, J. P.
    (2009). Effect of Connectivity and Wettability on the Relative Permeability of NAPLs.Environmental Geology, 56(7), 1437–1447. https://doi.org/10.1007/s00254-008-1238-8
     [Google Scholar]
  17. Cleveland, C. M. C.
    (2014). State Function. In Dictionary of Energy (2nd ed.). Elsevier Science and Technology.
     [Google Scholar]
  18. Delshad, M., Delshad, M., Pope, G. A., and Lake, L. W.
    (1987). Two- and Three-Phase Relative Permeabilities of Micellar Fluids.SPE Formation Evaluation, 2(3), 327–337. https://doi.org/10.2118/13581-PA
     [Google Scholar]
  19. Gerhard, J. I., and Kueper, B. H.
    (2003). Relative Permeability Characteristics Necessary for Simulating DNAPL Infiltration, Redistribution, and Immobilization in Saturated Porous Media.Water Resources Research, 39(8). https://doi.org/10.1029/2002WR001490
     [Google Scholar]
  20. Haines, W. B.
    (1930). 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 Agricultural Science, 20(1), 97–116.
     [Google Scholar]
  21. Herring, A. L., Harper, E. J., Andersson, L., Sheppard, A., Bay, B. K., and Wildenschild, D.
    (2013). Effect of Fluid Topology on Residual Nonwetting Phase Trapping: Implications for Geologic CO2 Sequestration.Advances in Water Resources, 62, 47–58. https://doi.org/10.1016/j.advwatres.2013.09.015
     [Google Scholar]
  22. Herring, A. L., Middleton, J., Walsh, R., Kingston, A., and Sheppard, A.
    (2017). Flow Rate Impacts on Capillary Pressure and Interface Curvature of Connected and Disconnected Fluid Phases during Multiphase Flow in Sandstone.Advances in Water Resources, 107, 460–469. https://doi.org/10.1016/j.advwatres.2017.05.011
     [Google Scholar]
  23. Herring, A. L., Sheppard, A., Andersson, L., and Wildenschild, D.
    (2016). Impact of Wettability Alteration on 3D Nonwetting Phase Trapping and Transport.International Journal of Greenhouse Gas Control, 46, 175–186. https://doi.org/10.1016/j.ijggc.2015.12.026
     [Google Scholar]
  24. Hovadik, J. M., and Larue, D. K.
    (2007). Static Characterizations of Reservoirs: Refining the Concepts of Connectivity and Continuity.Petroleum Geoscience, 13(3), 195–211. https://doi.org/10.1144/1354-079305-697
     [Google Scholar]
  25. Khishvand, M., Akbarabadi, M., and Piri, M.
    (2016). Micro-Scale Experimental Investigation of the Effect of Flow Rate on Trapping in Sandstone and Carbonate Rock Samples.Advances in Water Resources, 94, 379–399. https://doi.org/10.1016/j.advwatres.2016.05.012
     [Google Scholar]
  26. Khorsandi, S., Li, L., and Johns, R. T.
    (2017). Equation of State for Relative Permeability, Including Hysteresis and Wettability Alteration.SPE Journal, 22(6), 1915–1928. https://doi.org/10.2118/182655-PA
     [Google Scholar]
  27. Knill, O.
    (2011). On the Dimension and Euler Characteristic of Random Graphs.Dimension Contemporary German Arts And Letters, 18. Retrieved from http://arxiv.org/abs/1112.5749
     [Google Scholar]
  28. Lamanna, J. M., Bothe, J. V., Zhang, F. Y., and Mench, M. M.
    (2014). Measurement of Capillary Pressure in Fuel Cell Diffusion Media, Micro-Porous Layers, Catalyst Layers, and Interfaces.Journal of Power Sources, 271, 180–186. https://doi.org/10.1016/j.jpowsour.2014.07.163
     [Google Scholar]
  29. Landry, C. J., Karpyn, Z. T., and Ayala, O.
    (2014). Relative permeability of Homogenous-Wet and Mixed-Wet Porous Media as Determined by Pore-Scale Lattice Boltzmann Modeling.Water Resources Research, 50(5), 3672–3689. https://doi.org/10.1002/2013WR015148.
     [Google Scholar]
  30. Landry, C. J., Karpyn, Z. T., and Piri, M.
    (2011). Pore-Scale Analysis of Trapped Immiscible Fluid Structures and Fluid Interfacial Areas in Oil-Wet and Water-Wet Bead Packs.Geofluids, 11(2), 209–227. https://doi.org/10.1111/j.1468-8123.2011.00333.x
     [Google Scholar]
  31. Mohanty, K. K., Davis, H. T., and Scriven, L. E.
    (1987). Physics of Oil Entrapment in Water-Wet Rock.SPE Reservoir Engineering, 2(1). https://doi.org/10.2118/9406-PA
     [Google Scholar]
  32. Nadafpour, M., and Rasaei, M. R.
    (2014). Investigating Drainage Rate Effects on Fractal Patterns and Capillary Fingering in a Realistic Glass Micromodel.Tehnicki Vjesnik, 21(6), 1263–1271.
     [Google Scholar]
  33. Osborne, G. A.
    (1900). Condition for an Exact Differential. In An Elementary Treatise on the Differential and Integral Calculus - with Examples and Applications (pp. 85–86). D. C. Heath and Co.
     [Google Scholar]
  34. Pak, T., Butler, I. B., Geiger, S., van Dijke, M. I. J., and Sorbie, K. S.
    (2015). Droplet Fragmentation: 3D Imaging of a Previously Unidentified Pore-Scale Process during Multiphase Flow in Porous Media.Proceedings of the National Academy of Sciences, 112(7), 1947–1952. https://doi.org/10.1073/pnas.1420202112
     [Google Scholar]
  35. Parker, J. C.
    (1989). Multiphase Flow and Transport in Porous Media.Reviews of Geophysics, 3(27), 311–328.
     [Google Scholar]
  36. Richeson, D. S.
    (2008). Euler’s Gem: The Polyhedron Formula and the Birth of Topology (pp. 63–74). Princeton University Press.
     [Google Scholar]
  37. Roof, J. G.
    (1970). Snap-Off of Oil Droplets in Water-Wet Pores.Society of Petroleum Engineers Journal, 10(1), 85–90. https://doi.org/10.2118/2504-PA
     [Google Scholar]
  38. Rücker, M., Berg, S., Armstrong, R. T., Georgiadis, A., Ott, H., Schwing, A., et al.
    , (2015). From Connected Pathway Flow to Ganglion Dynamics.Geophysical Research Letters, 42(10), 3888–3894. https://doi.org/10.1002/2015GL064007
     [Google Scholar]
  39. Sahimi, M., and Imdakm, A. O.
    (1988). The Effect of Morphological Disorder on Hydrodynamic Dispersion in Flow Through Porous Media.Journal of Physics A: Mathematical and General, 21(19), 3833–3870. https://doi.org/10.1088/0305-4470/21/19/019
     [Google Scholar]
  40. Sandler, S. I.
    (1989). Chemical and Engineering Thermodynamics (Second). John Wiley and Sons.
     [Google Scholar]
  41. Schlüter, S., Berg, S., Rücker, M., Armstrong, R. T., Vogel, H. J., Hilfer, R., and Wildenschild, D.
    (2016). Pore-Scale Displacement Mechanisms as a Source of Hysteresis for Two-Phase Flow in Porous Media.Water Resources Research, 52(3), 2194–2205. https://doi.org/10.1002/2015WR018254
     [Google Scholar]
  42. Singh, K., Menke, H., Andrew, M., Lin, Q., Rau, C., Blunt, M. J., and Bijeljic, B.
    (2017). Dynamics of Snap-off and Pore-Filling Events during Two-Phase Fluid Flow in permeable media.Scientific Reports, 7(1), 5192. https://doi.org/10.1038/s41598-017-05204-4
     [Google Scholar]
  43. Vogel, H.-J.
    (2002). Topological Characterization of Porous Media. Morphology of Condensed Matter, Edited by K.Mecke, D.Stoyan, Lecture Notes in Physics, 600, 75–92. https://doi.org/10.1007/3-540-45782-8_3
     [Google Scholar]
  44. Zhang, P., and Austad, T.
    (2006). Wettability and Oil Recovery from Carbonates: Effects of Temperature and Potential Determining Ions.Colloids and Surfaces A: Physicochemical and Engineering Aspects, 279(1–3), 179–187.
     [Google Scholar]
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On the Development of a Relative Permeability Equation of State
Conference Proceedings 2018, 1 (2018); https://doi.org/10.3997/2214-4609.201802125
/content/papers/10.3997/2214-4609.201802125
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