Pore connectivity, permeability, and electrical formation factor: A new model and comparison to experimental data

Overview & Synopsis

This paper is a follow up on Bernabé et al.'s (2010) study of the effect of pore connectivity and pore size heterogeneity on permeability. In the permeability model initially proposed, pore connectivity was characterized by means of the average coordination number z, a parameter rarely included in experimental investigations of the transport properties and microstructure of porous rocks. Obviously, lack of information on z makes it difficult to apply the model. One way around this problem is to eliminate z from the model by introducing the resistivity formation factor, an approach previously used by Paterson (1983), Walsh and Brace (1984), and many others. Using the network simulation approach of Bernabé et al. (2010), we extended the model to include the electrical formation factor. The new joint permeability-formation factor model consists of three equations, the first two expressing the relation of permeability and formation factor to z and the last one, obtained by elimination of z, linking permeability and formation with each other. We satisfactorily tested the model by comparison with published experimental data on a variety of granular materials and rocks. Furthermore, we show that, although our model does not explicitly include porosity, it is consistent with Archie's law.