Relating tortuosity and permeability in microfractured and unfractured porous media

Permeability estimates are key to any subsurface flow prediction. Several methods are available for estimating (relative) permeability either on Darcy scale (lab measurements) or on pore scale (numerical flow simulation, assuming pore space geometry is known). However, relative permeability measurements in particular can be time consuming, and there is a benefit in having a fast estimate. Thus, a number of permeability estimates are available based on the some known porous medium parameters. The famous Carman Kozeny (1937) model represents the pores as parallel tubes of length equal to the sample length and of a range of radii. This single phase permeability model developed for packings of equal spherical grains relates the absolute permeability to the tortuosity of the medium. Fractures or fracture networks, on the other hand, do not lend themselves to an analytical description akin to pores spaces in-between a packing of spheres. Thus far, the study of flow in fractures has for the most part been limited to fractures in rock with impermeable fractures. The simplest models, such as the cubic law, relate fracture permeability to its average aperture and model fracture as parallel planes which are insufficient to extend to multiphase displacement. In this study, we focus on correlating permeability with geometric tortuosity of both pore space and individual fluid phases for a wide variety of homogeneous as well as microfractured porous samples. We use a combination of lattice-Boltzmann simulation and the level set method based progressive-quasistatic (LSMPQS) algorithm to characterize the capillary dominated flow properties (capillary pressure-saturation and relative permeability-saturation relationships) of the matrix, and when present, the fracture, in samples of different compositions. At the same time, we use image analysis tools to characterize the connectivity and tortuosity of the pore space, as well as individual fluid phases at different saturations. Tortuosity distributions were observed to vary in the different samples. Fractures provide the most direct path across the sample (when aligned) and have the narrowest tortuosity distribution, followed by granular packings. Consolidated media and carbonate samples have the widest distribution. The higher the amount of rock cementing material, carbonate or quartz overgrowth, the higher tortuosity (and ultimately the fluid retention time) in both consolidated porous media and partially cemented fractures. When analyzing tortuosity of different fluid phases in the matrix, we observe the non-wetting phase as being more tortuous than the wetting phase. The addition of fracture to the matrix (as a connected system) however, reverses this behavior. Although, imaged samples were necessary for this study, observed tortuosity (and thus permeability) can be correlated to geologic description of the subsurface formations.