Random Walk Method to simulate T2 of NMR

Nuclear Magnetic Resonance (NMR) has proven to be a highly valuable tool in the petroleum industry. This non-destructive testing method saves significant costs for expensive rock samples and allows repeated use when further experiments are required.

In petroleum exploration, NMR is commonly used to determine the T₂ relaxation time distribution of fluids within core samples. These distributions can be interpreted to extract information about pore size distribution, porosity, and permeability.

Using micro-tomographic images, which provide an accurate 3D model of the rock sample, these experiments can now be reproduced digitally. One of the main goals of computational science is to replicate real laboratory or in-situ experiments using numerical and computational models. Digital NMR experiments not only offer greater efficiency and lower cost compared to physical experiments but also provide deeper insights into the physical phenomena underlying real NMR measurements.

This tutorial introduces the theoretical background of NMR and its implementation in GeoDict simulations. It demonstrates how to set up NMR simulations, including validation using a spherical pore model, and how to compute T₂ relaxation curves for digital rock samples.

Two examples — Bentheimer Sandstone and Obernkirchen Sandstone — are used to illustrate the simulation workflow and comparison with experimental data.
The Bentheimer Sandstone sample has a size of 1500³ voxels, a voxel resolution of 1.75 μm, and a porosity of 21.1%.