NMR Relaxation Modelling in Porous Media with Dual-Scale-Resolved Internal Magnetic Fields

Abstract

A pore-scale forward modelling approach for NMR relaxation responses of sandstones incorporating their dual-scale nature is presented. The approach utilises X-ray micro-CT images to capture inter-granular porosity and scanning electron microscopy images to reconstruct clay regions via a resolved clay micro-structure model. A key to calculating the NMR response with resolved clay micro-structure is the development of a dual-scale internal magnetic field calculation. This is achieved by a separation of near- and far-field effects in a dipole approximation of the internal field with periodic clay micro-structures, the latter of which take local clay pocket porosity into account. Tri-linear interpolation of the micro-CT image before calculation of the internal magnetic field further reduces errors in the transition regions between coarse- and fine-scale structure, with final discretisation level matching the fine-scale clay micro-structure model across the whole domain. The method is validated against direct calculations of model media at full resolution and applied to Bentheimer sandstone. Measured and simulated NMR T2 relaxation responses, including relaxation time distribution shape, are in excellent agreement and distributions of internal magnetic field gradients at the highest spatial resolution as well as diffusion-averaged effective gradients are reported.