Pore Space Connectivity in Different Rock-Physics Methods—Similarity and Differences

This study is focused on the analysis of pore space connectivity in reservoir rocks. This parameter is of vital importance for the oil and gas industry since it controls hydraulic permeability. Five methods of rock physics are used for this goal. Three of these methods (self-consistent version of generalized singular approximation, Berryman self-consistent method, and differential scheme) take into account the pore space connectivity implicitly. The other two methods, the f-model of the generalized singular approximation and a similar modification of the Berryman method suggested in this work, allow for quantifying the connectivity via a special parameter (f-parameter). In order to reveal a physical meaning of this parameter, two simple models of carbonate rock (porous-cracked limestone) are considered. The first model is a double porosity model containing spherical pores and cracks. The second model contains only spherical pores, and their connectivity is expressed via the f-parameter. The pores and cracks are filled with brine and gas. Application of the two groups of methods for modeling the effective elastic properties of the carbonate rock gives a possibility of relating the f-parameter to the characteristics of the cracks and pores. The f-parameter is shown to be controlled by the relative crack volume in the total pore space. An increase in crack porosity and crack density leads to an increase in the f-parameter. A good correlation of the f-parameter with crack density is demonstrated. It is shown that for the porosity range 2–20%, a relationship between the f-parameter and crack density ε, in general, has the form f=alog10(ε)2+blog10(ε)+c for ε≤εmin. For the crack density less than εmin the f-parameter can be approximated by a constant value fmin. The values of εmin and fmin and coefficients a, b, and c depend on the porosity of spherical pores, saturation type, and pair of methods used for finding the link. These results give f-models an advantage in searching zones of the enhanced permeability and quantifying the ability of these zones to filtrate fluids.