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The Impact of Compaction and Sand Migration on Permeability and Non-Darcy Coefficient from Pore-Scale Simulations

  • Sultan Anbar
  • Karsten E. Thompson
  • Mayank Tyagi
Article
  • 24 Downloads

Abstract

Compaction and sand migration are important problems in loosely consolidated and unconsolidated high-rate gas reservoirs, and proppants in the hydraulic fractures. Their impacts on permeability and non-Darcy flow are important for accurate estimation of well productivity. In this paper, we quantified changes in flow parameters due to simulated compaction and sand migration for computer-generated sphere packing and presented the results in the context of correlations for permeability and non-Darcy coefficient that can be used in reservoir simulations. Compaction effects were simulated by increasing grain diameter in a sphere packing. Permeability and non-Darcy coefficients were calculated using the lattice Boltzmann method (LBM). Findings indicated that the permeability decrease was not directional for compaction simulated by simple grain growth and the change in permeability could be estimated from the porosity change with a power-law relation with an exponent equal to 3.28. An analogous power-law relation between non-Darcy coefficient and permeability was found with the exponent equal to − 1.32. For reservoirs that undergo these compaction-like processes during production, estimation of the inertial effects from traditional correlations developed as a function of permeability and porosity may lead to underestimation of the inertial effects. Sand migration causes pore-throat plugging, which leads to significant permeability reduction. We simulated sand particle-plugged pore-throat locations from network simulations for different values of pore volume reduction, and the corresponding permeability and non-Darcy coefficients were calculated from LBM. It was found that permeability change from sand plugging was directional; permeability decrease in the flow direction was approximately double the other directions. A power-law relation between permeability and porosity could be used to estimate the permeability with a much larger exponent: approximately 10 in the flow direction in the range of plugging studied in this work. Because porosity reduction can depend on other factors besides pore-throat plugging (e.g., compaction or pore surface deposition), a correlation was developed to estimate permeability dependence on the pore-throat sand concentration. Even though permeability change was directional, the permeability and non-Darcy coefficient trends collapsed onto a single power-law relation. The exponent on a power-law relation was greater in magnitude (approximately − 1.84) compared to compaction.

Keywords

Sand migration Compaction Lattice Boltzmann method Kozeny–Carman relationship Permeability and non-Darcy coefficient 

Notes

Acknowledgments

Authors would like to thank Shell E&P Co. for funding this research. LBM was developed by the PALABOS group (www.lbmmethod.org/palabos). We thank the LSU Center for Computation and Technology (CCT) and the Louisiana Optical Network Initiative (LONI) for providing high-performance computing resources. We thank Dongxing Liu for the help with the algorithm that identified sand plugging locations in network modeling simulations.

References

  1. Adler, P.M., Malevich, A.E., Mityushev, V.V.: Nonlinear correction to Darcy’s law for channels with wavy walls. Acta Mech. 224, 1823–1848 (2013)CrossRefGoogle Scholar
  2. Al-Rumhy, M.H., Kalam, M.Z.: Relationship of core-scale heterogeneity with non-Darcy flow coefficients. SPE Form. Eval. (1993).  https://doi.org/10.2118/25649-pa CrossRefGoogle Scholar
  3. Anbar, S.: Multi-scale estimation of inertial effects for frac-pack completed gas reservoirs. (PhD), Lousiana State University (2014). https://digitalcommons.lsu.edu/gradschool_dissertations/1715/. Accessed 6 Aug 2017
  4. Avila, C.E., Evans, R.D.: The effect of temperature and overburden pressure upon the non-Darcy flow coefficient in porous media. In: Paper Presented at the 27th U.S. Symposium on Rock Mechanics (USRMS), Tuscaloosa, AL (1986). http://www.onepetro.org/mslib/app/Preview.do?paperNumber=ARMA-86-0623&societyCode=ARMA. Accessed 5 May 2013
  5. Balhoff, M.T., Wheeler, M.F.: A predictive pore-scale model for non-Darcy flow in porous media. Soc. Pet. Eng. (2009).  https://doi.org/10.2118/110838-pa CrossRefGoogle Scholar
  6. Balhoff, M.T., Mikelic, A., Wheeler, M.F.: Polynomial filtration laws for low Reynolds number flows through porous media. Transp. Porous Media 81, 35–60 (2010)CrossRefGoogle Scholar
  7. Bear, J.: Dynamics of Fluid in Porous Media. Elsevier, New York (1972)Google Scholar
  8. Bhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94(3), 511–525 (1954)CrossRefGoogle Scholar
  9. Bigno, Y., Oyeneyin, M.B., Peden, J.M.: Investigation of pore-blocking mechanism in gravel packs in the management and control of fines migration. In: Paper SPE 27342 Presented at the SPE Formation Damage Control Conference, Lafayette, Louisiana, 7–10 February (1994)Google Scholar
  10. Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena. Wiley, New York (1965)Google Scholar
  11. Borujeni, A.T.: Multi-scale modeling of inertial flows through propped fractures. PhD dissertation, Louisiana State University (2013). https://digitalcommons.lsu.edu/gradschool_dissertations/3031/. Accessed 17 Sept 2014
  12. Carman, P.C.: Fluid flow through granular beds. Trans. Inst. Chem. Eng. Lond. 15, 150–166 (1937)Google Scholar
  13. Cerda, C.M.: Mobilization of kaolinite fines in porous media. Colloids Surf. 27, 219–241 (1987)CrossRefGoogle Scholar
  14. Chukwudozie, C.P.: Pore-scale lattice Boltzmann simulations of inertial flows in realistic porous media: a first principle analysis of the Forchheimer relationship. MS Thesis, Louisiana State University (2011). https://digitalcommons.lsu.edu/gradschool_theses/3220/. Accessed 25 Nov 2012
  15. Civan, F.: Non-isothermal permeability impairment by fines migration and deposition in porous media including dispersive transport. Transp. Porous Media 85, 233–258 (2010)CrossRefGoogle Scholar
  16. Civan, F.: Reservoir Formation Damage: Fundamentals, Modeling, Assessment, and Mitigation, 2nd edn. Gulf Professional Publishing, Elsevier, Burlington (2007)Google Scholar
  17. Civan, F., Evans, R.D.: Non-Darcy flow coefficients and relative permeabilities for gas/brine systems (1991)Google Scholar
  18. Cooper, J.W., Wang, X., Mohanty, K.K.: Non-Darcy-flow studies in anisotropic porous media. SPE J. (1999).  https://doi.org/10.2118/57755-pa CrossRefGoogle Scholar
  19. Cornell, D., Katz, D.L.: Flow of gases through consolidated porous media. Ind. Eng. Chem. 45(10), 2145–2152 (1953).  https://doi.org/10.1021/ie50526a021 CrossRefGoogle Scholar
  20. d’Humieres, D., Ginzburg, I., Krafczyk, M., Lallemand, P., Luo, L.S.: Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 360(1792), 437–451 (2002).  https://doi.org/10.1098/rsta.2001.0955 CrossRefGoogle Scholar
  21. Dong, H.: Micro CT Imaging and Pore Network Extraction. (PhD), Imperial College, London (2007)Google Scholar
  22. Evans, R.D., Hudson, C.S., Greenlee, J.E.: The effect of an immobile liquid saturation on the non-Darcy flow coefficient in porous media. SPE Prod. Eng. (1987).  https://doi.org/10.2118/14206-pa CrossRefGoogle Scholar
  23. Firoozabadi, A., Katz, D.L.: An analysis of high-velocity gas flow through porous media. J. Pet. Technol. (1979).  https://doi.org/10.2118/6827-pa CrossRefGoogle Scholar
  24. Forchheimer, P.: Wasserbewewegung Durch Boden. Z. Ver. Deutsch, Ing. 1781, 45 (1901)Google Scholar
  25. French, L.B.: Multiscale modeling of particle transport in petroleum reservoirs. MS Thesis, Louisiana State University (2015). https://digitalcommons.lsu.edu/gradschool_theses/1795/. Accessed 6 Aug 2017
  26. Gabriel, G.A., Inamdar, G.R.: An experimental investigation of fines migration in porous media. J. Soc. Pet. (SPE) 12168, 1–12 (1983)Google Scholar
  27. Geertsma, J.: Estimating the coefficient of inertial resistance in fluid flow through porous media. Soc. Pet. Eng. J. (1974).  https://doi.org/10.2118/4706-pa CrossRefGoogle Scholar
  28. Gruesbeck, C., Collins, R.E.: Entrainment and deposition of fine particles in porous media. SPE J. 22(6), 847–856 (1982)Google Scholar
  29. Herzig, J.P., Leclerc, D.M., Goff, P.L.: Flow of suspensions through porous media—application to deep filtration. Ind. Eng. Chem. 62, 8–35 (1970)CrossRefGoogle Scholar
  30. Jones, S.C.: Using the inertial coefficient, B, to characterize heterogeneity in reservoir rock. In: Paper Presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas (1987). http://www.onepetro.org/mslib/app/Preview.do?paperNumber=00016949&societyCode=SPE. Accessed 13 Oct 2012
  31. Khilar, K., Fogler, H.: Migrations of Fines in Porous Media. Kluwer Academic Publishers, Dordrecht (1998)CrossRefGoogle Scholar
  32. Kozeny, J.: Ueber kapillare Leitung des Wassers im Boden. Stizungs-ber Akad Wiss Wien 136, 271–306 (1927)Google Scholar
  33. Lao, H., Neeman, H.J., Papavassiliou, D.V.: A pore network model for the calculation of non-Darcy flow coefficients in fluid flow through porous media. Chem. Eng. Commun. 191(10), 1285–1322 (2004)CrossRefGoogle Scholar
  34. Lemley, E.C., Papavassiliou, D.V., Neeman, H.J.: Non-Darcy flow pore network simulation: development and validation of a 3D model. In: ASME. Fluids Engineering Division Summer Meeting, Volume 2: Fora, Parts A and B, pp.1331–1337 (2007).  https://doi.org/10.1115/fedsm2007-37278
  35. Li, Q., Prigiobbe, V.: Numerical simulations of the migration of fine particles through porous media. Transp. Porous. Med. 122, 745 (2018).  https://doi.org/10.1007/s11242-018-1024-3 CrossRefGoogle Scholar
  36. Liu, X., Civan, F., Evans, R.D.: Correlation of the non-Darcy flow coefficient. J. Can. Pet. (1995).  https://doi.org/10.2118/95-10-05 CrossRefGoogle Scholar
  37. Llewellin, E.W.: LBflow: an extensible lattice Boltzmann framework for the simulation of geophysical flows. Part I: theory and implementation. Comput. Geosci. 36(2), 115–122 (2010).  https://doi.org/10.1016/j.cageo.2009.08.004 CrossRefGoogle Scholar
  38. Ma, H., Ruth, D.W.: Physical explanations of non-Darcy effects for fluid flow in porous media. SPE Form. Eval. 12, 122 (1997).  https://doi.org/10.2118/26150-pa CrossRefGoogle Scholar
  39. Mei, C.C., Auriault, J.-L.: The effect of weak inertia on flow through a porous medium. J. Fluid Mech. 222, 647–663 (1991)CrossRefGoogle Scholar
  40. Morita, N., Boyd, P.A.: Typical sand production problems: case studies and strategies for sand control. In: Paper SPE 22739, Presented at the 66th SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA, October 6–9 (1991)Google Scholar
  41. Muecke, T.W.: Formation fines and factors controlling their movement in porous media. J. Pet. Technol. 31, 144–150 (1979)CrossRefGoogle Scholar
  42. Nabzar, L., Chauveteau, G., Roque, C.: A new model for formation damage by particle retention. In: Paper SPE 1283 Presented at the SPE Formation Damage Control Symposium, Lafayette, Louisiana, USA, 14–15 February (1996)Google Scholar
  43. Pan, C., Luo, L.S., Miller, C.T.: An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Comput. Fluids 35, 898 (2006)CrossRefGoogle Scholar
  44. Qian, Y.H., D’Humières, D., Lallemand, P.: Lattice BGK models for Navier–Stokes equation. EPL (Europhys. Lett.) 17(6), 479 (1992)CrossRefGoogle Scholar
  45. Rege, S.D., Fogler, H.S.: A network model for straining dominated capture in porous media. Chem. Eng. Sci. 42(7), 1553 (1987)CrossRefGoogle Scholar
  46. Ruth, D., Ma, H.: On the derivation of the Forchheimer equation by means of the averaging theorem. Transp. Porous Media 7(3), 255–264 (1992).  https://doi.org/10.1007/bf01063962 CrossRefGoogle Scholar
  47. Sukop, M.C., Thorne, D.T.J.: Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers. Springer, Berlin (2007)Google Scholar
  48. Tek, M.R., Coats, K.H., Katz, D.L.: The effect of turbulence on flow of natural gas through porous reservoirs. J. Pet. Technol. 14, 799–806 (1962)CrossRefGoogle Scholar
  49. Thauvin, F., Mohanty, K.K.: Network modeling of non-Darcy flow through porous media. Transp. Porous Med. 31(1), 19–37 (1998).  https://doi.org/10.1023/a:1006558926606 CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Sultan Anbar
    • 1
  • Karsten E. Thompson
    • 1
  • Mayank Tyagi
    • 1
  1. 1.Louisiana State UniversityBaton RougeUSA

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