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


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.


Tortuosity Enhanced gas recovery Diffusion Electrical resistivity Carbonate rocks 



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.


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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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