Model to interpret pulsed-field-gradient NMR data including memory and superdispersion effects.

We propose a versatile model specifically designed for the quantitative interpretation of NMR velocimetry data. We use the concept of mobile or immobile tracer particles applied in dispersion theory in its Lagrangian form, adding two mechanisms: (i) independent random arrests of finite average representing intermittent periods of very low velocity zones in the mean flow direction and (ii) the possibility of unexpectedly long (but rare) displacements simulating the occurrence of very high velocities in the porous medium. Based on mathematical properties related to subordinated Lévy processes, we give analytical expressions of the signals recorded in pulsed-field-gradient NMR experiments. We illustrate how to use the model for quantifying dispersion from NMR data recorded for water flowing through a homogeneous grain pack column in single- and two-phase flow conditions.