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 ( \(\rho \) ) parameters. In this work, we investigate the feasibility of using Machine Learning (ML) to estimate permeability from \(T_2\) distributions and quantify how \(\rho \) 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 \(T_2\) 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 \(\rho \) . In the first experiment, we simulated \(T_2\) distributions by assigning a constant \(\rho \) value for all synthetic porous media. In the second experiment, we applied a different \(\rho \) value to each synthetic porous medium to emulate real-world uncertainty, representing the scenario where \(\rho \) is unknown. The third experiment extends the second by converting the \(T_2\) distributions into surface-to-volume ratio distributions using the specific \(\rho \) 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 \(\rho \) uncertainty. The main contribution of this work is the systematic quantification of the sensitivity of predictive permeability models to \(\rho \) , 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 \(\rho \) is unknown.
