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Transport in Porous Media

, Volume 130, Issue 3, pp 847–865 | Cite as

Quantitative Tortuosity Measurements of Carbonate Rocks Using Pulsed Field Gradient NMR

  • Kaishuo Yang
  • Ming LiEmail author
  • Nicholas N. A. Ling
  • Eric F. May
  • Paul R. J. Connolly
  • Lionel Esteban
  • Michael B. Clennell
  • Mohamed Mahmoud
  • Ammar El-Husseiny
  • Abdulrauf R. Adebayo
  • Mahmoud Mohamed Elsayed
  • Michael L. Johns
Article
  • 153 Downloads

Abstract

Tortuosity is an important physical characteristic of porous materials; for example, it is a critical parameter determining the effective diffusion coefficient dictating mixing between miscible fluids in porous rock structures as is relevant to enhanced gas recovery processes. Accurate measurement of tortuosity remains challenging, resulting in various definitions dictated largely by the measurement protocol applied. Here, we focus primarily on ‘diffusive’ tortuosity (τd), which is defined as the ratio of the bulk fluid diffusion coefficient to the restricted diffusion coefficient applicable to the porous media under study. Specifically, we consider carbonate rock cores ranging in permeability from 2 to 5300 mD and adapt pulsed field gradient (PFG) NMR methodology such that accurate measurements of tortuosity are obtained over a sufficiently representative length scale of the porous media. To this end, we deploy supercritical methane as a probe molecule exploiting both its high mobility and proton density. Tortuosity measurements are shown to be independent of both pressure and diffusion observation time, conclusively proving that our measurements are in the asymptotic regime in which all of the pore space is adequately sampled by the diffusing methane molecules. The resultant ‘diffusive’ tortuosity measurements (which ranged from 3.1 to 5.6) are then compared against independent electrical conductivity measurements of tortuosity using a two-electrode impedance technique applied to the carbonate samples saturated with brine solution. Agreement between the ‘diffusive tortuosity,’ as measured by PFG NMR, and ‘electrical’ tortuosity was remarkably good (within 10%), given the very different measurements techniques used, for most of the carbonate rock samples considered.

Keywords

Tortuosity Enhanced gas recovery Diffusion Electrical resistivity Carbonate rocks 

Notes

Acknowledgement

Funding from the College of Petroleum Engineering and Geosciences, King Fahd University of Petroleum and Minerals, is gratefully acknowledged. PhD financial support from the Program of China Scholarship Council (No. 201708190001) for Kaishuo Yang is also gratefully acknowledged.

References

  1. Adler, P.M.: Porous media: geometry and transports. Butterworth-Heinemann series in chemical engineering. Butterworth-Heinemann, Boston (1992)Google Scholar
  2. Akpa, B.S., Holland, D.J., Sederman, A.J., Johns, M.L., Gladden, L.F.: Enhanced 13C PFG NMR for the study of hydrodynamic dispersion in porous media. J. Magn. Reson. 186(1), 160–165 (2007).  https://doi.org/10.1016/j.jmr.2007.02.001 CrossRefGoogle Scholar
  3. Alyafei, N., Blunt, M.J.: The effect of wettability on capillary trapping in carbonates. Adv. Water Resour. 90, 36–50 (2016).  https://doi.org/10.1016/j.advwatres.2016.02.001 CrossRefGoogle Scholar
  4. Archie, G.E.: The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. AIME. 146(1), 54–62 (1942).  https://doi.org/10.2118/942054-G CrossRefGoogle Scholar
  5. Bijeljic, B., Blunt, M.J.: Pore-scale modeling and continuous time random walk analysis of dispersion in porous media. Water Resour. Res. (2006).  https://doi.org/10.1029/2005WR004578 CrossRefGoogle Scholar
  6. Bijeljic, B., Mostaghimi, P., Blunt, M.J.: Signature of non-Fickian solute transport in complex heterogeneous porous media. Phys. Rev. Lett. (2011).  https://doi.org/10.1103/PhysRevLett.107.204502 CrossRefGoogle Scholar
  7. Bona, N., Rossi, E., Capaccioli, S., Lucchesi, M.: Electrical measurements: considerations on the performance of 2- and 4-contact systems. SCA paper 2008–07, 1–12 (2008)Google Scholar
  8. Callaghan, P.T.: Principles of nuclear magnetic resonance microscopy. Clarendon Press, Oxford (1991)Google Scholar
  9. Carman, P.C.: Fluid flow through granular beds. Transactions of the Institute of Chemical Engineers 15, S32–S48 (1937).  https://doi.org/10.1016/S0263-8762(97)80003-2 CrossRefGoogle Scholar
  10. Carman, P.C.: Flow of gases through porous media. Butterworths Scientific Publications, London (1956)Google Scholar
  11. Clennell, M.B.: Tortuosity: a guide through the maze. Geol. Soc. Lond. Spec. Publ. 122(1), 299–344 (1997).  https://doi.org/10.1144/GSL.SP.1997.122.01.18 CrossRefGoogle Scholar
  12. Coats, K.H., Whitson, C.H., Thomas, K.: Modeling conformance as dispersion. SPE Reserv. Eval. Eng. 12(1), 33–47 (2009).  https://doi.org/10.2118/90390-PA CrossRefGoogle Scholar
  13. Cotts, R.M., Hoch, M.J., Sun, T., Markert, J.T.: Pulsed field gradient stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems. J. Magn. Reson. 83(2), 252–266 (1989).  https://doi.org/10.1016/0022-2364(89)90189-3 CrossRefGoogle Scholar
  14. Dawson, R., Khoury, F., Kobayashi, R.: Self-diffusion measurements in methane by pulsed nuclear magnetic resonance. AIChE J. 16(5), 725–729 (1970).  https://doi.org/10.1002/aic.690160507 CrossRefGoogle Scholar
  15. Davies, C.J., Griffith, J.D., Sederman, A.J., Gladden, L.F., Johns, M.L.: Rapid surface-to-volume ratio and tortuosity measurement using difftrain. J. Magn. Reson. 187(1), 170–175 (2007).  https://doi.org/10.1016/j.jmr.2007.04.006 CrossRefGoogle Scholar
  16. Dullien, F.A.L.: Porous media: fluid transport and pore structure, 2nd edn. Academic Press, San Diego (1992)Google Scholar
  17. Frosch, G.P., Tillich, J.E., Haselmeier, R., Holz, M., Althaus, E.: Probing the pore space of geothermal reservoir sandstones by nuclear magnetic resonance. Geothermics 29(6), 671–687 (2000).  https://doi.org/10.1016/S0375-6505(00)00031-6 CrossRefGoogle Scholar
  18. Ghanbarian, B., Hunt, A.G., Ewing, R.P., Sahimi, M.: Tortuosity in porous media: a critical review. Soil Sci. Soc. Am. J. 77(5), 1461–1477 (2013).  https://doi.org/10.2136/sssaj2012.0435 CrossRefGoogle Scholar
  19. Harris, K.R.: The density dependence of the self-diffusion coefficient of methane at − 50, 25 and 50 °C. Phys. A 94(3–4), 448–464 (1978).  https://doi.org/10.1016/0378-4371(78)90078-X CrossRefGoogle Scholar
  20. Heller, R., Zoback, M.: Adsorption of methane and carbon dioxide on gas shale and pure mineral samples. J. Unconv. Oil Gas Resour. 8, 14–24 (2014).  https://doi.org/10.1016/j.juogr.2014.06.001 CrossRefGoogle Scholar
  21. Hidajat, I., Mohanty, K.K., Flaum, M., Hirasaki, G.: Study of vuggy carbonates using NMR and X-ray CT scanning. SPE Reserv. Eval. Eng. 7(5), 365–377 (2004).  https://doi.org/10.2118/88995-PA CrossRefGoogle Scholar
  22. Ho, T., Criscenti, L.J., Wang, Y.: Nanostructural control of methane release in kerogen and its implications to wellbore production decline. Sci. Rep. 6, 28053 (2016).  https://doi.org/10.1038/srep28053 CrossRefGoogle Scholar
  23. Honari, A., Hughes, T.J., Fridjonsson, E.O., Johns, M.L., May, E.F.: Dispersion of supercritical CO2 and CH4 in consolidated porous media for enhanced gas recovery simulations. Int. J. Greenh. Gas Con. 19, 234–242 (2013).  https://doi.org/10.1016/j.ijggc.2013.08.016 CrossRefGoogle Scholar
  24. Honari, A., Bijeljic, B., Johns, M.L., May, E.F.: Enhanced gas recovery with CO2 sequestration: the effect of medium heterogeneity on the dispersion of supercritical CO2–CH4. Int. J. Greenh. Gas Con. 39, 39–50 (2015).  https://doi.org/10.1016/j.ijggc.2015.04.014 CrossRefGoogle Scholar
  25. Hughes, T.J., Honari, A., Graham, B.F., Chauhan, A.S., Johns, M.L., May, E.F.: CO2 sequestration for enhanced gas recovery: new measurements of supercritical CO2–CH4 dispersion in porous media and a review of recent research. Int. J. Greenh. Gas Con. 9, 457–468 (2012).  https://doi.org/10.1016/j.ijggc.2012.05.011 CrossRefGoogle Scholar
  26. Hürlimann, M.D., Latour, L.L., Sotak, C.H.: Diffusion measurement in sandstone core: NMR determination of surface-to-volume ratio and surface relaxivity. Magn. Reson. Imaging 12(2), 325–327 (1994).  https://doi.org/10.1016/0730-725X(94)91548-2 CrossRefGoogle Scholar
  27. Johnson, J.F., Cole, R.H.: Dielectric polarization of liquid and solid formic acid. J. Am. Chem. Soc. 73(10), 4536–4540 (1951).  https://doi.org/10.1021/ja01154a012 CrossRefGoogle Scholar
  28. Kim, T., Cho, J., Lee, K.: Evaluation of CO2 injection in shale gas reservoirs with multi-component transport and geomechanical effects. Appl. Energy 190, 1195–1206 (2017).  https://doi.org/10.1016/j.apenergy.2017.01.047 CrossRefGoogle Scholar
  29. Kozeny, J.: Ueber kapillare Leitung des Wassers im Boden. Sitzungsber Akad. Wiss., Wien, 136(2), 271–306 (1927)Google Scholar
  30. Latour, L.L., Mitra, P.P., Kleinberg, R.L., Sotak, C.H.: Time-dependent diffusion coefficient of fluids in porous media as a probe of surface-to-volume ratio. J. Magn. Reson. Ser. A 101(3), 342–346 (1993).  https://doi.org/10.1006/jmra.1993.1056 CrossRefGoogle Scholar
  31. Latour, L.L., Kleinberg, R.L., Mitra, P.P., Sotak, C.H.: Pore-size distributions and tortuosity in heterogeneous porous media. J. Magn. Reson. Ser. A 112(1), 83–91 (1995).  https://doi.org/10.1006/jmra.1995.1012 CrossRefGoogle Scholar
  32. Li, L., Shikhov, I., Zheng, Y., Arns, C.H.: Experiment and Simulation on NMR and electrical measurements on Liège chalk. Diffus. Fundam. 22(6), 1–7 (2014)Google Scholar
  33. Li, M., Vogt, S.J., May, E.F., Johns, M.L.: In situ CH4–CO2 dispersion measurements in rock cores. Transp. Porous Med. 129(1), 75–92 (2019).  https://doi.org/10.1007/s11242-019-01278-y CrossRefGoogle Scholar
  34. Liu, S., Song, Y., Zhao, C., Zhang, Y., Lv, P., Jiang, L., Liu, Y., Zhao, Y.: The horizontal dispersion properties of CO2-CH4 in sand packs with CO2 displacing the simulated natural gas. J. Nat. Gas Sci. Eng. 50, 293–300 (2017).  https://doi.org/10.1016/j.jngse.2017.12.019 CrossRefGoogle Scholar
  35. Lucia, F.J.: Carbonate Reservoir Characterization. Springer, Berlin (2007)Google Scholar
  36. Mair, R.W., Wong, G.P., Hoffmann, D., Hürlimann, M.D., Patz, S., Schwartz, L.M., Walsworth, R.L.: Probing porous media with gas diffusion NMR. Phys. Rev. Lett. 83(16), 3324–3327 (1999).  https://doi.org/10.1103/PhysRevLett.83.3324 CrossRefGoogle Scholar
  37. Mantle, M.D., Enache, D.I., Nowicka, E., Davies, S.P., Edwards, J.K., D’Agostino, C., Mascarenhas, D.P., Durham, L., Sanker, M., Knight, D.W., Gladden, L.F., Taylor, S.H., Hutchings, G.J.: Pulsed-field gradient NMR spectroscopic studies of alcohols in supported gold catalysts. J. Phy. Chem. C 115(4), 1073–1079 (2011).  https://doi.org/10.1021/jp105946q CrossRefGoogle Scholar
  38. Mitra, P.P., Sen, P.N., Schwartz, L.M., Le Doussal, P.: Diffusion propagator as a probe of the structure of porous media. Phy. Rev. Lett. 68(24), 3555–3558 (1992).  https://doi.org/10.1103/PhysRevLett.68.3555 CrossRefGoogle Scholar
  39. Mitra, P.P., Sen, P.N., Schwartz, L.M.: Short-time behavior of the diffusion coefficient as a geometrical probe of porous media. Phy. Rev. B. 47(14), 8565–8574 (1993).  https://doi.org/10.1103/PhysRevB.47.8565 CrossRefGoogle Scholar
  40. Oldenburg, C.M., Pruess, K., Benson, S.M.: Process modeling of CO2 injection into natural gas reservoirs for carbon sequestration and enhanced gas recovery. Energy Fuel. 15(2), 293–298 (2001).  https://doi.org/10.1021/ef000247h CrossRefGoogle Scholar
  41. Oldenburg, C.M., Stevens, S.H., Benson, S.M.: Economic feasibility of carbon sequestration with enhanced gas recovery (CSEGR). Energy. 29(9–10), 1413–1422 (2004).  https://doi.org/10.1016/j.energy.2004.03.075 CrossRefGoogle Scholar
  42. Pape, H., Tillich, J.E., Holz, M.: Pore geometry of sandstone derived from pulsed field gradient NMR. J. Appl. Geophys. 58(3), 232–252 (2006).  https://doi.org/10.1016/j.jappgeo.2005.07.002 CrossRefGoogle Scholar
  43. Patel, M.J., May, E.F., Johns, M.L.: High-fidelity reservoir simulations of enhanced gas recovery with supercritical CO2. Energy. 111, 548–559 (2016).  https://doi.org/10.1016/j.energy.2016.04.120 CrossRefGoogle Scholar
  44. Patel, M.J., May, E.F., Johns, M.L.: Inclusion of connate water in enhanced gas recovery reservoir simulations. Energy. 141, 757–769 (2017).  https://doi.org/10.1016/j.energy.2017.09.074 CrossRefGoogle Scholar
  45. Perkins, T.K., Johnston, O.C.: A review of diffusion and dispersion in porous media. Soc. Petrol. Eng. J. 3(1), 70–84 (1963).  https://doi.org/10.2118/480-PA CrossRefGoogle Scholar
  46. Satterfield, C.N., Sherwood, T.K.: The Role of Diffusion in Catalysis. Addison-Wesley, Boston (1963)Google Scholar
  47. Samson, G., Deby, F., Garciaz, J., Perrin, J.: A new methodology for concrete resistivity assessment using the instantaneous polarization response of its metal reinforcement framework. Constr. Build. Mater. 187, 531–544 (2018).  https://doi.org/10.1016/j.conbuildmat.2018.07.158 CrossRefGoogle Scholar
  48. Schlumberger.: Carbonate reservoirs. (2019). Retrieved from https://www.slb.com/services/technical_challenges/carbonates.aspx Accessed 31 July 2019
  49. Sen, P.N.: Time-dependent diffusion coefficient as a probe of geometry. Concepts Magn. Reson., Part A 23A(1), 1–21 (2004).  https://doi.org/10.1002/cmr.a.20017 CrossRefGoogle Scholar
  50. Setzmann, U., Wagner, W.: New equation of state and tables of thermodynamic properties for methane covering the range from the melting line to 625 K at pressures up to 100 MPa. J. Phys. Chem. Ref. Data 20(6), 1061–1155 (1991).  https://doi.org/10.1063/1.555898 CrossRefGoogle Scholar
  51. Shi, Y., Jia, Y., Pan, W., Huang, L., Yan, J., Zheng, R.: Potential evaluation on CO2-EGR in tight and low-permeability reservoirs. Nat. Gas Indu. B. 4(4), 311–318 (2017).  https://doi.org/10.1016/j.ngib.2017.08.013 CrossRefGoogle Scholar
  52. Shikhov, I., Arns, C.H.: Tortuosity estimate through paramagnetic gas diffusion in rock saturated with two fluids using T2 (z, t) low-field NMR. Diffus. Fundam. 29(5), 1–7 (2017)Google Scholar
  53. Stalkup, F.I.: Status of miscible displacement. J. Petrol. Technol. 35(4), 815–826 (1983).  https://doi.org/10.2118/9992-PA CrossRefGoogle Scholar
  54. Stejskal, E.O., Tanner, J.E.: Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J. Chem. Phy. 42(1), 288–292 (1965).  https://doi.org/10.1063/1.1695690 CrossRefGoogle Scholar
  55. Stoller, S.D., Happer, W., Dyson, F.J.: Transverse spin relaxation in inhomogeneous magnetic fields. Phy. Rev. A. 44(11), 7459–7477 (1991).  https://doi.org/10.1103/PhysRevA.44.7459 CrossRefGoogle Scholar
  56. Takahashi, S.: The diffusion of gases at high pressures IV. The diffusion of CTH3 in the CH4-CO2 system. Bull. Chem. Soc. Jpn 45(7), 2074–2078 (1972).  https://doi.org/10.1246/bcsj.45.2074 CrossRefGoogle Scholar
  57. Taylor, G.: Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. Ser. A 219(1137), 186–203 (1953).  https://doi.org/10.1098/rspa.1953.0139 CrossRefGoogle Scholar
  58. Taylor, G.: Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular diffusion. Proc. R. Soc. Lond. Ser. A 225(1163), 473–477 (1954).  https://doi.org/10.1098/rspa.1954.0216 CrossRefGoogle Scholar
  59. Thomas, S.: Enhanced oil recovery—an overview. Oil Gas Sci. Technol. Rev. IFP 63(1), 9–19 (2008).  https://doi.org/10.2516/ogst:2007060 CrossRefGoogle Scholar
  60. Vogt, C., Galvosas, P., Klitzsch, N., Stallmach, F.: Self-diffusion studies of pore fluids in unconsolidated sediments by PFG NMR. J. Appl. Geophys. 50(4), 455–467 (2002).  https://doi.org/10.1016/S0926-9851(02)00195-7 CrossRefGoogle Scholar
  61. Wang, H., Li, G., Shen, Z.: A feasibility analysis on shale gas exploitation with supercritical carbon dioxide. Energy Sour. A: Recov. Util. Environ. Eff. 34(15), 1426–1435 (2012).  https://doi.org/10.1080/15567036.2010.529570 CrossRefGoogle Scholar
  62. Wang, R., Pavlin, T., Rosen, M.S., Mair, R.W., Cory, D.G., Walsworth, R.L.: Xenon NMR measurements of permeability and tortuosity in reservoir rocks. Magn. Reson. Imaging 23(2), 329–331 (2005).  https://doi.org/10.1016/j.mri.2004.11.044 CrossRefGoogle Scholar
  63. Wyllie, M.R.J., Rose, W.D.: Some theoretical considerations related to the quantitative evaluation of the physical characteristics of reservoir rock from electrical log data. J. Petrol. Technol. 2(4), 105–118 (1950).  https://doi.org/10.2118/950105-G CrossRefGoogle Scholar
  64. Yildirim, H., Ilica, T., Sengul, O.: Effect of cement type on the resistance of concrete against chloride penetration. Constr. Build. Mater. 25(3), 1282–1288 (2011).  https://doi.org/10.1016/j.conbuildmat.2010.09.023 CrossRefGoogle Scholar
  65. Zecca, M., Vogt, S.J., Connolly, P.R.J., May, E.F., Johns, M.L.: NMR measurements of tortuosity in partially saturated porous media. Transp. Porous Med. 125(2), 271–288 (2018).  https://doi.org/10.1007/s11242-018-1118-y CrossRefGoogle Scholar
  66. Zhang, L., Li, X., Zhang, Y., Cui, G., Tan, C., Ren, S.: CO2 injection for geothermal development associated with EGR and geological storage in depleted high-temperature gas reservoirs. Energy. 123, 139–148 (2017).  https://doi.org/10.1016/j.energy.2017.01.135 CrossRefGoogle Scholar
  67. Ziauddin, M.E., Bize, E.: The effect of pore scale heterogeneities on carbonate stimulation treatments. In: SPE middle east oil and gas show and conference, Manama, Bahrain. (2007).  https://doi.org/10.2118/104627-MS

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Engineering, Faculty of Engineering and Mathematical SciencesThe University of Western AustraliaCrawleyAustralia
  2. 2.College of Petroleum Engineering and GeosciencesKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia
  3. 3.CSIRO EnergyKensingtonAustralia

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