Reviewing numerical simulation methods of nuclear magnetic resonance signals in porous media.

Low-field nuclear magnetic resonance (NMR) is a minimally-invasive geophysical method often used to characterize pore spaces, water content, and fluid transport and distribution in geologic materials. NMR measurements are based on the magnetization and relaxation behavior of the spin magnetic moment of hydrogen atoms in external magnetic fields. These measurements can be taken in the field, such as from a borehole or the surface of the Earth, or in the laboratory using a bench-top apparatus. Numerical simulations of NMR signals are great tools to better understand the relaxation behavior of pore water under different scenarios, explore the effect of changes in the composition or geochemical characteristics of the geologic material, verify experimental findings, and improve the interpretation of field measurements. They can also be used to examine situations where traditional interpretation of NMR signals fails, such as in complex, heterogeneous geometries with pore coupling effects. In a pore coupled system, significant magnetization exchange between pores of different sizes occurs during the measurement time, which makes it difficult to independently characterize the pore environments. Using numerical simulations, it is possible to explore the factors that control pore coupling, such as surface relaxivity, pore-network connectivity and other pore-network characteristics, can be explored independently in a controlled setting. In this work, we introduce common numerical modelling approaches used for simulating NMR responses in geologic materials, along with their limitations and traditional workflows. We present two specific examples: a Random Walk (RW) simulation to test the effect of different pore-network connectivity features on pore coupling in a simplified pore geometry, and a Finite Element Method (FEM) simulation approach to visualize the distribution of magnetization density within a single pore. NMR is a promising hydrogeophysics tool gaining popularity and finding new applications for near-surface exploration. A better understanding of the NMR signals in diverse and complex scenarios is essential for the adequate design of experiments and field campaigns and for the correct interpretation of NMR measurements at different scales. The use of numerical modelling strategies can help improve this understanding, leading to more accurate and reliable measurements and interpretations.