Theoretical Simulation of the Resistivity and Fractured–Cavernous Structures of Carbonate Reservoirs

Abstract

Recently, theoretical modeling based on rock physics has emerged as a pivotal approach to studying the resistivity of complex fractured–cavernous microstructures. In this work, to study the effects of fractured–cavernous structures on carbonate reservoir resistivity, electrical conductivity models were developed based on the effective medium theory and Ohm’s Law, and theoretical simulations were performed to examine how the porosity and resistivity of the rock matrix, the formation water resistivity, and the parameters of the fractured–cavernous microstructure affect the resistivity of rocks saturated with petroleum or water. Furthermore, the modeling results revealed the specific relationships between these factors in petroleum-saturated and water-saturated rocks. For vuggy reservoirs, a significant negative correlation between throat diameter and resistivity was revealed when variations in the rock matrix and formation water resistivity were negligible. Furthermore, the pore shape—especially the extension of pores in the direction of the current—severely reduced the resistivity of petroleum-saturated rocks. For fractured reservoirs, the porosity and resistivity of the rock matrix were the primary factors affecting resistivity, with the fracture inclination angle and width also exhibiting pronounced effects on the resistivity of water-saturated rocks. The rock cementation exponent was much smaller when the matrix pores were interconnected through fractures than when they were interconnected through throats. The findings reveal that the effects of the structural parameters of fractured–cavernous carbonate reservoirs on reservoir resistivity differ between petroleum-saturated and water-saturated rocks. The conventional Archie’s equation is insufficient for evaluating fluid saturation in carbonate reservoirs. A saturation evaluation model with a variable rock cementation exponent tailored to the specific reservoir type should thus be developed.