Research Ideas and Outcomes : Research Article

Corresponding author: Adewale Amosu (adewale@tamu.edu)
Received: 13 Feb 2018  Published: 21 Feb 2018
© 2018 Adewale Amosu, Hamdi Mahmood, Paul Ofoche
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation: Amosu A, Mahmood H, Ofoche P (2018) Estimating the Permeability of Carbonate Rocks from the Fractal Properties of Moldic Pores using the KozenyCarman Equation. Research Ideas and Outcomes 4: e24430. https://doi.org/10.3897/rio.4.e24430

Reservoir modeling of carbonate rocks requires a proper understanding of the pore space distribution and its relationship to permeability. Using a pigeonhole fractal model we characterize the fractal geometry of moldic pore spaces and extract the fractal dimension. We apply the KozenyCarman equation and equations relating the tortuosity and the porosity to the fractal dimension to derive an empirical relationship between permeability and porosity.
Porosity; Permeability; Tortuosity; Carbonate Rocks; KozenyCarman Equation; Pigeon Hole Fractal Model; Fractal Geometry
Scale invariance of intrinsic patterns is an important concept in geology that can be observed in numerous geological objects and phenomena. These geological objects and phenomena are described as containing statistically selfsimilar patterns often modeled with fractal geometry. Examples include the perimeter of coastlines (
The Happy Spraberry Field Texas is located in Garza County on the northern part of the Midland Basin (Fig.
We make use of thin section photomicrographs of the reservoir facies from a well in the Happy Spraberry Field. We use a newly developed program to interactively model the pore paces as tubular cylinders and apply the boxcounting method to extract the porosity and the MinkowskiBouligand fractal dimension (For more geoscience programs, see
\(k={ \phi \over {8T}} r_{eff}^2 \)
\(T= {1.34 \left ({r_{grain} \over r_{eff} } \right)^ {0.67(D2)}} \)
\(\phi= {0.5 \left ({r_{grain} \over r_{eff} } \right)^ {0.39(D3)}} \)
In the above equations, T is tortuosity, r_{grain} is average grain size, r_{eff} is the effective pore radius, D is the fractal dimension, k is permeability and ø is porosity.
Fig.
\(T= {1.34 \left ({r_{grain} \over r_{eff} } \right)^ {0.07}} \)
\(\phi = {0.5 \left ({r_{grain} \over r_{eff} } \right)^ {0.35}} \)
Combining these two two equations with the first equation, we obtain:
\(k ={4.3 *10^{11} r_{grain}^2 \phi^{7/5}}\)
Using an average value of grain size radius = 250000 nm and porosity ranging from 0 to 35%, we compare the estimated permeabilities to laboratorymeasured core permeabilities from the field. Fig.
The pigeonhole fractal is used to successfully characterize the moldic pores in the reservoir facies of carbonate rocks and extract the fractal dimension. We then apply the KozenyCarman equation and equations relating the tortuosity and the porosity to the fractal dimension to establish an empirical relationship between permeability and porosity.