The effect of various lengths of pores and throats on the formation resistivity factor

Abstract

Pore geometry, quantified by the length and size of the pore space, affects the electrical resistivity of the porous media. However, the length described by the geometrical tortuosity and pore topology effect on the resistivity of the model does not thoroughly consider the existing pore geometrical models, which only investigate the pore size, throat length and throat size of the models. A modified capillary model including a pore body and several throats derived the formation factor from the coordination number, the cross-sectional area ratio and geometrical tortuosity of the pores and throats in the model. The derived relationship between the formation factor and porosity of the capillary model compared with the formation factor versus porosity for the various rock types was shown in a plot. The geometrical tortuosity of each rock type almost followed the electrical tortuosity of the related rock type, and the electrical tortuosity was larger than the geometrical tortuosity caused by the variation in the size of the pore and throat. For low porosity, the resistivity of the real porous media was lower than the resistivity of the Archie equation due to the low values of the pore-to-throat cross-sectional area ratio and geometrical tortuosity. The sandstones and interparticle carbonates presented a porosity exponent close to 2.0 and an electrical tortuosity from 1.5 to 4.0 on the plot of the porosity exponent versus electrical tortuosity. The fractured carbonate showed a porosity exponent from 1.0 to 1.6 and an electrical tortuosity ranging from 1.0 to 3.0, while the vuggy carbonates were widely distributed, with a porosity exponent larger than 2.0 and an electrical tortuosity ranging from 2 to 8. This new model correlates the formation factor and porosity to the combination of the coordination number with the geometrical tortuosity and the throat and pore cross-sectional area ratios, thus enhancing the understanding of the pore geometry and topology effect on the electrical resistivity of a porous media with various pore types.