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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    $$T_2$$  T 2 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.

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