Lattice Boltzmann framework for accurate NMR simulation in porous media

Nuclear magnetic resonance (NMR) responses of fluids saturating porous media arise from complex relaxation-diffusion dynamics of polarized spins. These constitute a sensitive probe of the microstructure and are described by the Bloch-Torrey equations. An NMR simulation framework based on an augmented lattice Boltzmann method aimed at the fine-scale resolution of nuclear polarization density is presented. The approach encapsulates the time evolution of the full magnetization vector and naturally incorporates the mechanisms of diffusional transport. Spin dephasing mechanisms are fully resolved at tomogram voxel scale to account for magnetic field inhomogeneity. The approach is validated against analytical solutions of spin-echo decays for simple pore geometries. An application to a nano-computed-tomography image of chalk with inhomogeneous internal fields yields T_{2} spectral measures in good agreement with experiment and illustrates the spatial pore-scale dynamics of net magnetization. Findings establish the feasibility of the framework for pure diffusion and present an approach vector to modeling the evolution of magnetization under flow conditions.