The effect of a variable pore radius on formation resistivity factor

• A modified capillary model for pores with variable radii has been developed.
• Electrical current flow through a straight pore with variable radius is modeled.
• Experimental data of sediments, sandstones and carbonates are studied.
• Relationships between formation factor and porosity are explained using pore shape.
• Archie's exponent m is controlled by porosity and pore body to pore throat ratio.

Formation resistivity factor F was introduced as the ratio of the resistivity of a rock fully saturated with conductive water to the resistivity of the conductive water based on results of laboratory measurements. It was also found that the formation factor is a function of the type and character of a formation and is related to porosity by a relationship including an exponent m. For model calculations of the formation factor, capillary channel models describing a straight tube with a constant circular cross-sectional area are frequently used. However, the pore channel radius is not constant in natural rocks.A modified capillary model that describes a straight pore channel with a radius varying between its two extreme values rt (pore throat) and rb (pore body) is presented. The proposed model can therefore explain the effect of pore shape upon formation factor and porosity. In this case, exponent m is controlled by the porosity itself and the ratio rb/rt. Different rock types have a specific position in a plot of formation factor versus porosity including a forward calculated grid for varying ratio rb/rt. Sand and gravel are characterized by low ratios rb/rt of 2.5 to 4.5, while sandstones possess intermediate rb/rt of 5.0 to 20.0. Carbonates show the greatest variability with ratios of 1.0 to 40.0.This new approach can be used to derive the ratio rb/rt from a determination of porosity and formation factor and thus enhances the understanding of pore space geometries in different formation types, which is also of importance for hydraulic conductivity.