Analytical Models for Predicting the Formation Resistivity Factor and Resistivity Index at Overburden Conditions

Abstract

In this study, new parameters referred to as rock resistivity modulus (RRM) and true resistivity modulus (TRM) were defined. Analytical models were developed based on RRM, TRM, and Archie’s equation for predicting formation resistivity factor (FRF) and resistivity index (RI) under overburden pressure conditions. The results indicated that overburden FRF is dependent on FRF at initial pressure (ambient FRF), RRM, and net confining pressure difference. RRM decreases with cementation factor and rock compressibility. The proposed FRF model was validated using 374 actual core data of 79 plug samples (31 sandstone and 48 carbonate plug samples) from three sandstone reservoirs and four carbonate reservoirs, measured under four to six different overburden pressures. The developed FRF model fitted the experimental data with an average relative error of 2% and 3% for sandstone and carbonate samples, respectively. Moreover, the applications and limitations of the models have been investigated and discussed. Further theoretical analysis showed that overburden RI is a function of RI at initial pressure, TRM, and net confining pressure difference. The developed models supplement resistivity measurements and can be applied to estimate FRF, RI, and saturation exponent (n) variations with overburden pressure.