Image-based simulation of molecular diffusion on NMR Pulsed-Field Gradient experiments: Feasibility to estimate tortuosity and permeability of porous media

Abstract

Nuclear Magnetic Resonance (NMR) is an important tool to assess physical quantities that characterize porous media such as reservoir rocks. Information about surface-to-volume ratio and micro-connectivity, for instance, are coded in the time-dependent diffusion coefficient of magnetized spins. In this work, we present an efficient computational implementation to perform image-based simulations of the NMR diffusion experiment in porous media by means of random walks. We enhance our decisions regarding computation that allow us to simulate hundreds of thousands of steps in a large volume of walkers in a matter of seconds on an ordinary personal computer. We validate the implementation against analytical solutions found in the literature and investigate the effects of varying some of the simulation parameters such as number of particles, step length, and image resolution, in the accuracy of results. We then simulate the diffusion in a dataset of digitally generated synthetic media to investigate the correlation of tortuosity, surface-to-volume ratio, and porosity with permeability, and fit exponential curves to explore these correlations. Finally, we perform simulations from microtomographic images of four rock samples and use the results in conjunction with the previously fitted curves to predict the permeability, and compare it to the gas permeability measured experimentally. Our results indicate that the diffusion experiment has the potential of helping in permeability prediction. In particular, they indicate that the tortuosity and the surface-to-volume ratio correlate better with permeability than the porosity. We hope that the present study may serve not only as a reference for those interested in simulating the NMR diffusion experiment but also to help in the design of new permeability prediction models.