Pore geometrical model for the resistivity of brine saturated rocks

Abstract

In this paper, a theoretical pore geometrical model to mimic a porous body that is fully brine saturated was developed. Analytical equations for porosity and formation resistivity factor, which govern the flow of electricity through the model were derived with no adjustable parameters. The model equations were verified using finite element modelling and the results indicated that pore throat and pore void radii are the most important elements in this model. The porosity of the network model is strongly affected by pore void radius and to a lesser extent by pore throat radius, particularly when pore throat radius is small. The resistivity of the network model when it is fully brine-saturated is strongly affected by pore throat radius and cross-sectional area available to electric current flow and much of the pore void volume can be thought of as electrically dead volume. The formation resistivity factor of the proposed network model is almost entirely controlled by pore throat radius, whereas both pore throat and void radii affect cementation factor. This emphasises that formation resistivity factor and cementation factor are pore geometrical factors only, and more importantly that cementation factor is related to pore geometry rather than cementation.