Numerical study of NMR relaxation responses in synthetic clayey sandstone by dual-scale modeling

Abstract

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.