Numerical simulations of NMR relaxation in chalk using local Robin boundary conditions

TL;DR

This paper applies local Robin boundary conditions to 3D NMR relaxation simulations in chalk, improving accuracy and providing a method for better data processing in NMR analysis.

Contribution

It extends local boundary condition methods to complex 3D porous media and introduces a technique for enhanced NMR data inversion.

Findings

Significant reduction in systematic errors using linear local boundary conditions.

Successful application to real chalk samples from synchrotron CT scans.

Improved data processing method for NMR $T$-inversion.

Abstract

The interpretation of nuclear magnetic resonance (NMR) data is of interest in a number of fields. In \"{O}gren [Eur. Phys. J. B (2014) 87: 255] local boundary conditions for random walk simulations of NMR relaxation in digital domains were presented. Here, we have applied those boundary conditions to large, three-dimensional (3D) porous media samples. We compared the random walk results with known solutions and then applied them to highly structured 3D domains, from images derived using synchrotron radiation CT scanning of North Sea chalk samples. As expected, there were systematic errors caused by digitalization of the pore surfaces so we quantified those errors, and by using linear local boundary conditions, we were able to significantly improve the output. We also present a technique for treating numerical data prior to input into the ESPRIT algorithm for retrieving Laplace components of time series from NMR data (commonly called $T$-inversion).