Estimation of the Resistivity Index via Nuclear Magnetic Resonance Log Data Based on Fractal Theory

Abstract

The resistivity index is an important parameter for determining the rock saturation index. However, the saturation index changes greatly in unconventional reservoirs, which leads to oil saturation estimation with great difficulty. Hence, we try to establish the relationship between the resistivity index and log data. Firstly, a novel model of estimating the resistivity index with $T_2$ time was derived based on fractal theory, the relationship between nuclear magnetic resonance (NMR) $T_2$ spectrum and capillary pressure curve ( $T_2$ - $P_c$ ), and Archie formula. It regards the logarithm of the resistivity index as the dependent variable, with $T_2$ time and $T_2$ time when water saturation is 100% as the independent variables. Second, 17 cores were drilled, and $T_2$ spectrum and the relationship between the resistivity index and water saturation ( $I_r$ - $S_w$ ) were jointly measured. Next, the experimental results were substituted into the established model to get the model parameters via the multivariate statistics regression method. Then, the experimental data engaged and not engaged in modeling were used to test the established model. The average relative errors of estimated resistivity indices and experimental results are smaller than 8%, and those of the regressed saturation index are smaller than 5%. Finally, the established model was applied in log data processing and interpretation with good effects. It thus proves that the method of the estimating resistivity index with $T_2$ time is reliable, which provides a novel solution for determining rock electrical parameter of unconventional reservoirs.