Reconstruction of porous material geometry by stochastic optimization based on bulk NMR measurements of the dipolar field

The dependence of the bulk signal intensity from a CRAZED NMR pulse sequence on magnetic field gradient strength and direction as a method to probe the geometry of porous materials is investigated. In this article, we report on the reconstruction of three-dimensional media consisting of a void phase and an NMR-observable liquid phase using the bulk intensity of the distant dipolar field. The correlation gradient strength and direction provide the spatial encoding of the material geometry. An integral equation for the total signal intensity is then solved numerically by a simulated annealing algorithm to recover the indicator function of the fluid phase. Results show that cylindrical and spherical structures smaller than the volume contributing to the NMR signal can be resolved using three values of the correlation distance and three orthogonal gradient directions. This is done by minimizing a cost function which measures the distance between the bulk signal dependence on gradient parameters for the simulated configuration and the signal dependence for the target configuration. The algorithm can reconstruct and differentiate their spherical and cylindrical phase-inverted equivalents. It can also differentiate horizontal from vertical cylinders, demonstrating the potential for assessing structural anisotropy and other coarse geometric quantifiers in a porous material.