Numerical investigation of T2∗-based and T2-based petrophysical parameters frequency-dependent in shale oil

In this paper, the T₂∗-based relaxation theory and numerical simulation method in shale oil were established for the first time, which have been verified through free induction decay (FID) pulse sequence experiments. For the first time, the digital core technology was combined with organic carbon and Rock-Eval analysis, X-ray diffraction quantitative analysis experiments to construct representative digital shale cores. The effects of magnetic field frequency (f), mineral contents and types, as well as the magnetic susceptibilities difference (MSD) on T₂∗ responses were simulated based on the random walk method. For the first time, the frequency conversion cross-plots for T₂∗-based and T₂-based petrophysical parameters were proposed. The results show these effects on NMR-based petrophysical parameters are non-negligible. When T_d = 1 μs, T_E = 0.08 ms, f is 200 MHz, pyrite content is 5.43 %, and MSD is 9 × 10⁻⁵SI, the porosity, $T_{2\text{LM}}^{\ast }$, and organic matter content of T₂∗ distribution is 1.32 %, 0.013 ms, and 9.019 %, which are 1.33 times, 0.006 times, and 1.37 times those of T₂ distribution. This work contributes to frequency conversion of petrophysical parameters between in the laboratory NMR instrument and NMR logging.