Sedimentary rocks display complex spatial distribution of both pore space and solid components, impacting the directional dependence of physical phenomena such as electrical conduction, fluid flow, heat transfer, and molecular diffusion. The complexity of the pore space is often quantified by the concept of tortuosity, which measures the sinuosity of the connecting paths in the pore space. Tortuosity is an important quantity in formation evaluation as it impacts petrophysical properties such as permeability and formation factor. However, the existence of various techniques can lead to nonuniqueness in assessment of tortuosity. Furthermore, spatial variation of the solid components of the rocks occurring at the core-scale domain reflected in the connectivity and distribution of the minerals is typically not quantified. The objectives of this paper are (a) to quantify tortuosity and tortuosity anisotropy of porous media through estimation of electrical, diffusional, hydraulic, and geometrical tortuosity at the pore scale and core scale and (b) to compare electrical, diffusional, hydraulic, and geometrical tortuosity.

We estimate tortuosity in the pore space of microcomputed tomography (micro-CT) scan images and in the most connected and abundant solid phase of whole-core CT scan images. We conduct numerical simulations of electric potential distribution, diffusion, and fluid flow and velocity distribution to estimate electrical, diffusional, and hydraulic tortuosity, respectively. To calculate geometrical tortuosity, we use the segmented pore space from micro-CT scan images to extract a pore network model and compute the shortest path of all opposing pores of the samples. Finally, tortuosity values obtained with each technique are used to assess the anisotropy of the samples.

We applied the documented workflow to core- and pore-scale images. The CT scan images in the core-scale domain belong to a siliciclastic formation. Micro-CT scan images in the pore-scale domain were obtained from Berea Sandstone, Austin Chalk, and Estaillades limestone formations. We observed differences in estimates of direction-dependent electrical, diffusional, hydraulic, and geometrical tortuosity for both types of images. The highest numerical differences were observed when comparing streamline electrical and hydraulic tortuosity with diffusional tortuosity. The observed differences were significant in anisotropic samples. Differences in tortuosity estimates can impact the outcomes of rock physics models for which tortuosity is an input. The documented comparison provides insight in the selection of techniques for tortuosity estimation. Use of core-scale image data provides semicontinuous estimates of tortuosity and tortuosity anisotropy, which are typically not attainable using pore-scale images. Additionally, the semicontinuous tortuosity anisotropy estimates from whole-core CT scan images provide a tool for selection of best locations to take core plugs.

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