Representative elementary volume for NMR simulations based on X-ray microtomography of sedimentary rock

In porous systems like natural rocks, many phenomenological models have been developed in order to study the correlations between physical properties and the pore structure of these systems. The high resolution obtained with X-ray microtomography (μCT) images (micro or nanometer scales) has allowed exploring in details the complex morphology of the pore space in natural rocks. This has promoted the development of numerical simulations at the pore-scale level aiming to improve our comprehension about the correlations between pore structure and macroscopic physical properties. In this respect, simulations of nuclear magnetic resonance properties performed directly on μCT images are very important, since petrophysical properties can be predicted using a realistic model for the heterogeneous porous structure. Also these simulations can include a specific morphology of the pore geometry, which can be controlled in order to verify the different hypotheses introduced during NMR interpretation of physical properties, like for example, permeability predictions and/or fluid typing. In addition, NMR simulations allow to study the existence of a representative volume of the whole system, whose experimental determination is a major challenge. In this work, nuclear magnetic relaxations are simulated on a pore geometry obtained from microtomography of a natural rock formation, localized in the southeast of Brazil. The simulations were performed through a discrete random-walk algorithm computed at the pore scale. In the simulations bulk relaxation was not considered, while the relaxation rate at the surface of the pores was assumed constant. Our results indicate that the relaxation curves can be considered representatives of the whole system for volumes above a representative volume with dimensions of some cubic millimeters. In addition, this representative elementary volume seems to be of the same order that the one found from the analyses of the porosity on the same digital rock. In summary, this study points out to the importance of verifying the existence of this characteristic volume during NMR simulations directly on images obtained from tomography, in order to ensure the reliability of the information obtained from the numerical simulations.