Quantitative Tortuosity Measurements of Carbonate Rocks Using Pulsed Field Gradient NMR

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 (τ_d), 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.