Skip to main content
Log in

Combining Mercury Intrusion and Nuclear Magnetic Resonance Measurements Using Percolation Theory

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

Nuclear magnetic resonance (NMR) relaxation time distributions are frequently combined with mercury intrusion capillary pressure (MICP) measurements to allow determination of pore or pore throat size distributions directly from the NMR data. The combination of these two measurements offers an advantage over high-resolution imaging techniques in terms of cost and measurement time, and can provide estimates of pore sizes for pores below imaging resolution. However, the methods that are typically employed to combine NMR and MICP measurements do not necessarily honor the way in which the two different measurements respond to the size distribution and connectivity of the pore system. We present a method for combining NMR and MICP data that is based on percolation theory and the relationship between bond occupation probability and the probability that a bond is part of a percolating cluster. The method yields results that compare very well with pore sizes measured by high-resolution microtomography, and provides particular improvement in media with broad pore size distributions and large percolation thresholds.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

References

  • Arns, C.: A comparison of pore size distributions derived by NMR and X-ray-CT techniques. Phys. A 339(1–2), 159–165 (2004). doi:10.1016/j.physa.2004.03.033

    Article  Google Scholar 

  • Bloch, F.: Nuclear induction. Phys. Rev. 70(7/8), 460–474 (1946). doi:10.1103/PhysRev.70.460

    Article  Google Scholar 

  • Brownstein, K.R., Tarr, C.E.: Importance of classical diffusion in NMR studies of water in biological cells. Phys. Rev. A 19(6), 2446–2453 (1979). doi:10.1103/physreva.19.2446

    Article  Google Scholar 

  • Butler, J.P., Reeds, J.A., Dawson, S.V.: Estimating solutions of the first kind integral equations with nonnegative constraints and optimal smoothing. SIAM J. Numer. Anal. 18(3), 381–397 (1981). doi:10.1137/0718025

    Article  Google Scholar 

  • Carr, H.Y., Purcell, E.M.: Effects of diffusion in free precession in nuclear magnetic resonance experiments. Phys. Rev. 94(3), 630–638 (1954). doi:10.1103/PhysRev.94.630

    Article  Google Scholar 

  • Chatzis, I., Dullien, F.A.L.: Modelling pore structure by 2-D and 3-D networks with application to sandstones. J. Can. Petrol. Technol. 16(1), 97–108 (1977). doi:10.2118/77-01-09

    Google Scholar 

  • Coates, G., Xiao, L., Prammer, M.G.: NMR Logging Principles and Applications. Halliburton Energy Services, Houston (1999)

    Google Scholar 

  • Daigle, H., Johnson, A., Thomas, B.: Determining fractal dimension from nuclear magnetic resonance data in rocks with internal magnetic field gradients. Geophysics 79(6), D425–D431 (2014a). doi:10.1190/GEO2014-0325.1

    Article  Google Scholar 

  • Daigle, H., Thomas, B., Rowe, H., Nieto, M.: Nuclear magnetic resonance characterization of shallow marine sediments from the Nankai Trough, Integrated Ocean Drilling Program Expedition 333. J. Geophys. Res. Solid Earth 119(4), 2631–2650 (2014b). doi:10.1002/2013JB010784

    Article  Google Scholar 

  • Dullien, F.A.L.: Porous Media Fluid Transport and Pore Structure, 2nd edn. Academic Press, San Diego (1992)

    Google Scholar 

  • Dullien, F.A.L., Dhawan, G.K.: Bivariate pore-size distributions of some sandstones. J. Colloid Interf. Sci. 52(1), 129–135 (1975). doi:10.1016/0021-9797(75)90309-4

    Article  Google Scholar 

  • Fisher, M.E., Essam, J.W.: Some cluster size and percolation problems. J. Math. Phys. 2(4), 609–619 (1961). doi:10.1063/1.1703745

    Article  Google Scholar 

  • Fleury, M., Santerre, Y., Vincent, B.: Carbonate rock typing from NMR relaxation measurements. In: Transactions of the \(48^{{\rm th}}\) Annual Logging Symposium SPWLA, paper EEE (2007)

  • Foley, I., Farooqui, S.A., Kleinberg, R.L.: Effect of paramagnetic ions on NMR relaxation of fluids at solid surfaces. J. Magn. Reson. Ser. A 123(1), 95–104 (1996). doi:10.1006/jmra.1996.0218

    Article  Google Scholar 

  • Gallegos, D.P., Smith, D.M.: A NMR technique for the analysis of pore structure: determination of continuous pore size distributions. J. Colloid Interface Sci. 122(1), 143–153 (1988). doi:10.1016/0021-9797(88)90297-4

    Article  Google Scholar 

  • Hürlimann, M.D., Helmer, K.G., Latour, L.L., Sotak, C.H.: Restricted diffusion in sedimentary rocks. Determination of surface-area-to-volume ratio and surface relaxivity. J. Magn. Reson. Ser. A 111(2), 169–178 (1994). doi:10.1006/jmra.1994.1243

    Article  Google Scholar 

  • Ingels, J.J.C.: Geometry, paleontology, and petrography of Thornton Reef complex, Silurian of northeastern Illinois. AAPG Bull. 47(3), 405–440 (1963). doi:10.1306/bc743a53-16be-11d7-8645000102c1865d

    Google Scholar 

  • Johnson, A.: Investigations of porous media using nuclear magnetic resonance secular relaxation measurements and micro-CT image analysis. MS thesis, University of Texas, Austin, Texas (2015)

  • Katz, A.J., Thompson, A.H.: Prediction of rock electrical conductivity from mercury injection measurements. J. Geophys. Res. 92(B1), 599–607 (1987). doi:10.1029/JB092iB01p00599

    Article  Google Scholar 

  • Kleinberg, R.L.: Utility of NMR \(\text{ T }_{2}\) distributions, connection with capillary pressure, clay effect, and determination of the surface relaxivity parameter \({\uprho }_{2}\). Magn. Reson. Imaging 14(7/8), 761–767 (1996)

    Article  Google Scholar 

  • Kleinberg, R.L., Horsfield, M.A.: Transverse relaxation processes in porous sedimentary rock. J. Magn. Reson. 88(1), 9–19 (1990). doi:10.1016/0022-2364(90)90104-h

    Google Scholar 

  • Larson, R.G., Morrow, N.R.: Effects of sample size on capillary pressures in porous media. Powder Technol. 30(2), 123–138 (1981). doi:10.1016/0032-5910(81)80005-8

    Article  Google Scholar 

  • Lindquist, W.B., Venkatarangan, A.: Investigating 3D geometry of porous media from high resolution images. Phys. Chem. Earth Pt. A 24(7), 593–599 (1999). doi:10.1016/S1464-1895(99)00085-X

  • Lindquist, W.B., Lee, S., Oh, W., Venkatarangan, A.B., Shin, H., Prodanović, M.: 3DMA-Rock: A software package for automated analysis of rock pore structure in 3-D computed microtomography images. http://www.ams.sunysb.edu/~lindquis/3dma/3dma_rock/3dma_rock.html. Accessed 3 September 2015 (2005)

  • Lindquist, W.B., Venkatarangan, A., Dunsmuir, J., Wong, T.: Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainebleau sandstones. J. Geophys. Res. 105(B9), 21509–21527 (2000). doi:10.1029/2000JB900208

    Article  Google Scholar 

  • Liu, H., Zhang, L., Seaton, N.A.: Determination of the connectivity of porous solids from nitrogen sorption measurements—II. Generalisation. Chem. Eng. Sci. 47(17/18), 4393–4404 (1992). doi:10.1016/0009-2509(92)85117-t

    Article  Google Scholar 

  • Liu, H., Zhang, L., Seaton, N.A.: Analysis of sorption hysteresis in mesoporous solids using a pore network model. J. Colloid Interface Sci 156(2), 285–293 (1993). doi:10.1006/jcis.1993.1113

    Article  Google Scholar 

  • Marschall, D., Gardner, J.S., Mardon, D., Coates, G.R.: Method for correlating NMR relaxometry and mercury injection data. In: Transactions of the 1995 Symposium SCA, paper 9511 (1995)

  • Mishra, B.K., Sharma, M.M.: Measurement of pore size distributions from capillary pressure curves. AIChE J. 34(4), 684–687 (1988). doi:10.1002/aic.690340420

    Article  Google Scholar 

  • Øren, P., Bakke, S.: Reconstruction of Berea sandstone and pore-scale modelling of wettability effects. J. Petrol. Sci. Eng. 39(3–4), 177–199 (2003). doi:10.1016/S0920-4105(03)00062-7

    Article  Google Scholar 

  • Purcell, W.R.: Capillary pressures—their measurement using mercury and the calculation of permeability therefrom. J. Petrol. Technol. 1(2), 39–48 (1949). doi:10.2118/949039-g

    Article  Google Scholar 

  • Sahimi, M.: Applications of Percolation Theory. Taylor and Francis, Bristol, PA (1993)

    Google Scholar 

  • Swanson, B.F.: Visualizing pores and nonwetting phase in porous rock. J. Petrol. Technol. 31(1), 10–18 (1979). doi:10.2118/6857-PA

    Article  Google Scholar 

  • Talabi, O., AlSayari, S., Iglauer, S., Blunt, M.J.: Pore-scale simulation of NMR response. J. Petrol. Sci. Eng. 67(3–4), 168–178 (2009). doi:10.1016/j.petrol.2009.05.013

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hugh Daigle.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Daigle, H., Johnson, A. Combining Mercury Intrusion and Nuclear Magnetic Resonance Measurements Using Percolation Theory. Transp Porous Med 111, 669–679 (2016). https://doi.org/10.1007/s11242-015-0619-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-015-0619-1

Keywords

Navigation