Chalk formations constitute important targets for CO2 geological storage in depleted oil fields, yet their complex pore networks spanning nanometer to micron scales pose significant challenges for NMR characterization. Understanding how internal magnetic field gradients and multi-scale porosity heterogeneity influence relaxation responses is essential for reliable interpretation of NMR measurements in these formations. This presentation details a sophisticated dual-scale numerical simulation approach designed to capture these effects in chalk microstructure.
The simulation methodology combines micro-CT imaging at 3.62 μm resolution with Gaussian Random Field (GRF) reconstruction of nano-CT data at 64 nm resolution. The micro-CT image is segmented into three phases: resolved macroporosity (vugs), intermediate unresolved porosity, and semi-solid inclusions. The GRF approach enables periodic generation of the fine-scale microporosity, matched to experimental nano-CT images through two-point correlation functions. This dual-scale representation is utilized by a random walk algorithm where the microstructure is generated on-the-fly rather than storing the complete high-resolution volume.
To ensure smooth transitions between scales, an 800³ voxel micro-CT subdomain is interpolated to 900 nm resolution (creating a 3200³ image), with a 1920³ periodic GRF model overlayed at a 14:1 voxel ratio. The internal fields are computed using dual-scale FFT methods, capturing both fine-scale heterogeneity within microporosity and long-range gradients from larger-scale susceptibility variations.
Results demonstrate significant effects of paramagnetic inclusions on T₂ relaxation distributions. Even at low field strength (2 MHz), moderate inclusion fractions with susceptibility contrasts of up to 0.01 SI produce significant distribution shape changes. At 43 MHz, high-susceptibility inclusions generate internal gradients of ~200 G/cm in microporous regions (compared to ~30 G/cm without inclusions) and ~700 G/cm in microporous regions. CPMG simulations at multiple echo spacings (0.1-1.0 ms) reveal the echo-spacing dependence of gradient refocusing, distinguishing fine-scale from large-scale internal field effects, and enabling quantitative assessment of their relative contributions to observed relaxation behaviour.

References
[1] Arns, C.H., AlGhamdi, T. and Arns, J.Y. (2011). Numerical analysis of nuclear magnetic resonance relaxation–diffusion responses of sedimentary rock. New Journal of Physics 13(1), 015004.
[2] Cui, Y., Shikhov, I. and Arns, C.H (2022). NMR Relaxation Modelling in Porous Media with DualScaleResolved Internal Magnetic Fields. Transport in Porous Media 142(), 453-474.
[3] Rybin, I., Shikhov, I. and Arns, C.H. (2022). Lattice Boltzmann framework for accurate NMR simulation in porous media. Physical Review E 105(5), 055304.