Simulations of NMR Relaxation in a Real Porous Structure: Pre-asymptotic Behavior to the Localization Regime

The knowledge of the different physical mechanisms determining the relaxation of the magnetization is crucial to obtain reliable petrophysical parameters from NMR experiments. Some studies have focused on asymptotic mechanisms providing simple expressions for the relaxation rate in terms of parameters of the system. The main difficulties in solving this problem are related to the existence of intrinsic magnetic inhomogeneities, in addition to the complex structure of the porous geometry found in real systems. In this work, simulations of the relaxation of the transverse magnetization were performed on a real pore structure obtained from X-ray microtomography images. Also, a statistical method was used to introduce a local magnetic non-homogeneity, resembling local field distributions discussed in several works in the literature. The conditions of our simulations allowed the study of relaxation processes mainly influenced by local magnetic gradients, while surface relaxation became irrelevant. The dependence of the relaxation rate on the inter-echo spacing was studied, where for low spacings, the results reproduced those expected in the free-diffusion limit. On the other hand, for high inter-echo spacings, the relaxation rate deviates from the expected dependence, indicating the emergence of a new relaxation mechanism. This high-spacing behavior was associated with a pre-asymptotic localization regime. Our data suggest a logarithmic dependence of the relaxation rate with the inter-echo spacing in this transition regime.