Tortuosity is a key parameter for fluid flow and mass transport in porous media. Geodesic reconstruction (GR) and fluid velocity field (FVF) are techniques that allow tortuosity estimation. Essentially, tortuosity is the ratio of the geodesic length by the Euclidian length of the pore inlet-outlet in the region of interest. However, its estimation is not trivial, especially for 3D porous medium samples, such as for reservoir rock core samples. Digital rock physics has made much progress recently, providing estimates of several quantities and improving the understanding of the pore-scale processes of reservoir rocks.

This paper briefly discusses the GR and FVF techniques and their computational implementions to estimate the directional tortuosity of a pore network. The GR estimates the geometric tortuosity while the FVF estimates the hydraulic tortuosity. An application of these techniques is done for four carbonate and twelve sandstones reservoir rock core samples, provided by the MicroCT Images and Networks of Imperial College London database.

The results show that the tortuosity estimates in the x, y and z -directions, for all but one direction, have the FVF values slightly higher than the GR values, with a mean relative error around 10%. When the specific directional tortuosities are compared, the mean relative error for τx, τy and τz are, 9.8%, 10.3% and 10.5%, respectively. The mean GR and FVF tortuosities for the carbonate and sandstone samples are <τC> = 1.6, <τS> = 1.4 and <τC> = 1.8, <τS> = 1.6, respectively. The mean porosity for the carbonate and sandstone samples are <φC> = 0.16 and <φS> = 0.22, respectively. From these results, it can be noticed that the FVF tortuosity estimates are higher than the GR estimates, which is expected to be as in general hydraulic tortuosity is larger than the geometric one. On the other hand, it is observed that high porosity correlates to low tortuosity, which is consistent with results in the literature. The two techniques have very high Pearson correlation ρ = 0.9, and by Bland-Altman analysis they are within the limits of agreement (LoA), which means that both techniques are essentially equivalent to estimate the tortuosity, even though neither technique is considered as a gold standard measure for tortuosity.

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