The feasibility of using machine learning to estimate rock permeability from nuclear magnetic resonance T₂ and the role of the surface relaxivity

Predicting permeability from Nuclear Magnetic Resonance (NMR) data is a fundamental yet challenging task in reservoir characterization, primarily due to the uncertainty associated with surface relaxivity ( ρ ρ ) parameters. In this work, we investigate the feasibility of using Machine Learning (ML) to estimate permeability from T₂ T 2 distributions and quantify how ρ ρ uncertainty affects predictive accuracy. To address this, we generated a dataset of 15,000 synthetic 3D porous media representing granular sedimentary rock samples. We employed efficient in-house implementations of a Random Walk algorithm (governed by Bloch-Torrey physics) to simulate magnetization decay and obtain T₂ T 2 distributions, alongside a Finite Element Method (FEM) solver for the Stokes equations to compute absolute permeability, assuming 100% water saturation. The study comprises three computational experiments designed to isolate the impact of ρ ρ . In the first experiment, we simulated T₂ T 2 distributions by assigning a constant ρ ρ value for all synthetic porous media. In the second experiment, we applied a different ρ ρ value to each synthetic porous medium to emulate real-world uncertainty, representing the scenario where ρ ρ is unknown. The third experiment extends the second by converting the T₂ T 2 distributions into surface-to-volume ratio distributions using the specific ρ ρ value assigned in the second experiment to each medium. We systematically compared the Multilayer Perceptron (MLP) performance against the industry-standard Schlumberger-Doll-Research (SDR) model. Overall, the MLP yielded strong predictive performance. The second experiment presented a performance drop for both models, confirming the impact of ρ ρ uncertainty. The main contribution of this work is the systematic quantification of the sensitivity of predictive permeability models to ρ ρ , establishing a controlled benchmark that addresses and reduces existing uncertainties. Additionally, these findings demonstrate that the MLP provides a robust and competitive alternative for permeability estimation in scenarios where ρ ρ is unknown.