11-interval PFG pulse sequence for improved measurement of fast velocities of fluids with high diffusivity in systems with short T2(∗)

Quantitative measurement of solid fraction in a silo using SPRITE

The purpose of this study is to develop MRI methods to measure the solid fraction in granular flows quantitatively. It is increasingly recognised that solid fraction plays a key role in granular rheology, but experimental characterisation of it during flow is challenging. Here centric sectoral-SPRITE imaging is applied to image mustard seeds discharging from a 3D-printed hopper. Quantitative images are obtained after considering and correcting artefacts that may arise from flow and relaxation. The image intensity is then further corrected for spatial variations in the B₁ field. Various maps of nominally homogeneous samples were tested to correct for variations in the B₁ field. The B₁ field was found to be sensitive to the geometry of the sample and the material in the sample. Hence, here static images of the seeds in the hopper were used to correct for B₁ field variations. Moreover, small signal variations were observed from measurements performed on different days owing to subtle differences in the spectrometer operation. Here an internal standard was used to scale the signal intensity and correct for these variations. Following these corrections, a linear correlation (R² = 0.999) was observed between the scaled image intensities and the known solid fractions of packed samples with solid fractions between 0.55 and 0.64. This correlation was used as a calibration of the 3D image of the hopper to extract quantitative time-averaged spatial maps of solid fraction during steady flow. The measurements were confirmed to be quantitative by also measuring the velocity of the particles. Together these measurements were used to calculate a mass flow rate in the hopper, which was consistent with the mass flow measured gravimetrically.

Accuracy of phase-contrast velocimetry in systems with skewed intravoxel velocity distributions

Phase contrast velocimetry (PCV) has been widely used to investigate flow properties in numerous systems. Several authors have reported errors in velocity measurements and have speculated on the sources, which have ranged from eddy current effects to acceleration artefacts. An often overlooked assumption in the theory of PCV, which may not be met in complex or unsteady flows, is that the intravoxel displacement distributions (propagators) are symmetric. Here, the effect of the higher moments of the displacement distribution (variance, skewness and kurtosis) on the accuracy of PCV is investigated experimentally and theoretically. Phase and propagator measurements are performed on tailored intravoxel distributions, achieved using a simple phantom combined with a single large voxel. Asymmetric distributions (Skewness ≠ 0) are shown to generate important phase measurement errors that lead to significant velocimetry errors. Simulations of the phase of the spin vector sum, based on experimentally measured propagators, are shown to quantitatively reproduce the relationship between measured phase and experimental parameters. These allow relating the observed velocimetry errors to a discrepancy between the average phase of intravoxel spins considered in PCV theory and the vector phase actually measured by a PFG experiment. A theoretical expression is derived for PCV velocimetry errors as a function of the moments of the displacement distribution. Positively skewed distributions result in an underestimation of the true mean velocity, while negatively skewed distributions result in an overestimation. The magnitude of these errors is shown to increase with the variance and decrease with the kurtosis of the intravoxel displacement distribution.

Accurate phase-shift velocimetry in rock

Spatially resolved Pulsed Field Gradient (PFG) velocimetry techniques can provide precious information concerning flow through opaque systems, including rocks. This velocimetry data is used to enhance flow models in a wide range of systems, from oil behaviour in reservoir rocks to contaminant transport in aquifers. Phase-shift velocimetry is the fastest way to produce velocity maps but critical issues have been reported when studying flow through rocks and porous media, leading to inaccurate results. Combining PFG measurements for flow through Bentheimer sandstone with simulations, we demonstrate that asymmetries in the molecular displacement distributions within each voxel are the main source of phase-shift velocimetry errors. We show that when flow-related average molecular displacements are negligible compared to self-diffusion ones, symmetric displacement distributions can be obtained while phase measurement noise is minimised. We elaborate a complete method for the production of accurate phase-shift velocimetry maps in rocks and low porosity media and demonstrate its validity for a range of flow rates. This development of accurate phase-shift velocimetry now enables more rapid and accurate velocity analysis, potentially helping to inform both industrial applications and theoretical models.