A Microstructure Description of the Relationship between Formation Resistivity Factor and Porosity

The formation resistivity factor evaluation of brine-filled reservoir rock is an essential part of electrical resistivity log interpretation in petroleum exploration. Empirical relations such as Archie’s law are widely employed to model the relationship between the formation resistivity factor and porosity. Historically, the Archie cementation exponent has been obtained from experimental laboratory measurements. Nowadays, it is possible to approach the formation resistivity factor via numerical calculation on digital images of the microstructure of the reservoir rock. In this paper, we give a direct microstructure description of the relationship between the formation resistivity factor and the porosity, instead of the Archie cementation exponent typically derived from core plug measurements. The pore microstructure effect is defined by a tortuosity and a constriction factor. The combined effect of the calculated tortuosity and constriction, in addition to the porosity, yields the effective formation resistivity factor. To demonstrate the theory we calculate the tortuosity and constriction factor for digital rock images and models of Fontainebleau sandstone, and thereby obtain a microstructurerelated correlation between porosity and the formation resistivity factor in agreement with published experimental data. Such tortuosity and constriction factors provide useful fundamental microstructure parameters allowing evaluation of the pore structure representation in digital rock modeling. INTRODUCTION In this paper, we will investigate the electrical conductivity of a clay-free sedimentary rock filled with brine, where the rock matrix is assumed insulating and the electrical conductivity of the brine is assumed constant. The electrical conductance of the rock is dependent on the porosity and pore microstructure relative to the applied potential. The formation resistivity factor FRF is defined to be the ratio of the electrical resistivity of the rock saturated with brine Ro to the resistivity of the brine Rw: . (1)