NMR Relaxation Modelling in Porous Media with Dual-Scale-Resolved Internal Magnetic Fields

Abstract

A pore-scale forward modelling approach for NMR relaxation responses of sandstones incorporating their dual-scale nature is presented. The approach utilises X-ray micro-CT images to capture inter-granular porosity and scanning electron microscopy images to reconstruct clay regions via a resolved clay micro-structure model. A key to calculating the NMR response with resolved clay micro-structure is the development of a dual-scale internal magnetic field calculation. This is achieved by a separation of near- and far-field effects in a dipole approximation of the internal field with periodic clay micro-structures, the latter of which take local clay pocket porosity into account. Tri-linear interpolation of the micro-CT image before calculation of the internal magnetic field further reduces errors in the transition regions between coarse- and fine-scale structure, with final discretisation level matching the fine-scale clay micro-structure model across the whole domain. The method is validated against direct calculations of model media at full resolution and applied to Bentheimer sandstone. Measured and simulated NMR $$T_2$$ T 2 relaxation responses, including relaxation time distribution shape, are in excellent agreement and distributions of internal magnetic field gradients at the highest spatial resolution as well as diffusion-averaged effective gradients are reported.

Numerical study of NMR relaxation responses in synthetic clayey sandstone by dual-scale modeling

“…To satisfy the clay volume fraction, the mean thickness values of each horizon are different. To reduce discretization effects from the image and force an accurate calculation of the internal magnetic fields [32], a tri-linear interpolation is applied with factor 4 refinement. Thus, the original 800 3 domain is refined to 3200 3 voxels with voxel size of 0.55 𝜇𝜇𝑚𝑚/voxel and smoother solid surface shown in Fig 5.…”

“…The dual-scale NMR relaxation response simulation has been described in detail previously [32]. In this work the simulation approach is extended to clay regions with different porosity.…”

“…However, for the simulation of the NMR transverse relaxation response the internal magnetic field at every location is required. The calculation of high-resolution internal magnetic fields (Bi) is achieved by a separation of near-and far-field effects in a dipole-approximation of the internal field with dual-scale samples [32]. This allows calculating the coarse-scale internal magnetic fields via Fourier methods.…”

Bayesian Optimization With Transfer Learning: A Study on Spatial Variability of Rock Properties Using NMR Relaxometry

“…Arns (2004) introduced the simulation of NMR responses on micro-CT images, acquired on a first-generation instrument. Recently, the combination of fifth-generation high resolution micro-CT imaging with more sophisticated solvers allowed the simulation of realistic NMR responses mimicking experiments over a larger range of relaxation times (Arns et al, 2011;Connolly et al, 2019;Cui et al, 2021Cui et al, , 2022Mitchell et al, 2012) and including partial saturation responses (Shikhov & Arns, 2015;Shikhov et al, 2017); NMR measurements on core plugs were reproduced by simulations based on high-resolution micro-CT images. Given the large number of possible NMR measurements by adaption of different pulse sequences encoding diffusion and relaxation, and associated sensitivity to physical properties, the availability of such solvers is a potential game changer.…”