The feasibility of using machine learning to estimate rock permeability from nuclear magnetic resonance T$$_{2}$$ and the role of the surface relaxivity

Abstract

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 ( $$\rho $$ ρ ) parameters. In this work, we investigate the feasibility of using Machine Learning (ML) to estimate permeability from $$T_2$$ T 2 distributions and quantify how $$\rho $$ 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 $$T_2$$ 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 $$\rho $$ ρ . In the first experiment, we simulated $$T_2$$ T 2 distributions by assigning a constant $$\rho $$ ρ value for all synthetic porous media. In the second experiment, we applied a different $$\rho $$ ρ value to each synthetic porous medium to emulate real-world uncertainty, representing the scenario where $$\rho $$ ρ is unknown. The third experiment extends the second by converting the $$T_2$$ T 2 distributions into surface-to-volume ratio distributions using the specific $$\rho $$ 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 $$\rho $$ ρ uncertainty. The main contribution of this work is the systematic quantification of the sensitivity of predictive permeability models to $$\rho $$ 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 $$\rho $$ ρ is unknown.

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