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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.

Nuclear Magnetic Resonance (NMR) relaxometry is a common technique for petrophysical characterization of sedimentary rocks. The standard interpretation of NMR relaxation response assumes that the fast diffusion limit is valid for the whole pore space, allowing to translate transverse relaxation components into pore apertures. However, porous media naturally exhibit multiple length scales. The diffusion between different sized pores may modify the transverse relaxation rate, weakening the relationship with corresponding pore size populations. Focusing on sandstones, we investigate the impact of diffusion coupling on transverse relaxation depending on kaolinite amount, spatial distribution and temperature. A series of synthetic clayey sandstone models with different clay amounts and morphological distributions (pore-lining, pore-filling and laminated) are generated based on a micro-CT image of an actual Bentheimer sandstone. A dual-scale random walk NMR relaxation simulation with resolved multi-porosity kaolinite models is utilized to avoid problems in near to interface exchange regions typical for effective medium representations. Simulations provide spatially resolved dynamics of magnetization exchange between different porosity populations. The results indicate that increased temperature and kaolinite clay amount with lower micro-porosity allows higher magnetization exchange between micro- and macro- porous regions. Pore-lining clay demonstrates stronger diffusional coupling effects, leading to an overestimation of micro-porosity. We further discuss the impact of diffusion coupling on NMR-estimated permeability via SDR and Coates models.