Magnetic Resonance Velocimetry Measurement of Viscous Flows through Porous Media: Comparison with Simulation and Voxel Size Study

Studies that use magnetic resonance velocimetry (MRV) to assess flows through porous media require a sufficiently small voxel size to determine the velocity field at a sub-pore scale. The smaller the voxel size, the less information is lost through the discretization. However, the measurement uncertainty and the measurement time are increased. Knowing the relationship between voxel size and measurement accuracy would help researchers select a voxel size that is not too small in order to avoid unnecessary measurement effort. This study presents a systematic parameter study with a low-Reynolds-number flow of a glycerol–water mixture sent through a regularly periodic porous matrix with a pore size of 5 mm. The matrix was a 3-dimensional polymer print, and velocity-encoded MRV measurements were made at 15 different voxel sizes between 0.42 mm and 4.48 mm. The baseline accuracy of the MRV velocity data was examined through a comparison with a computational fluid dynamics (CFD) simulation. The experiment and simulation show very good agreement, indicating a low measurement error. Starting from the smallest examined voxel size, the influence of the voxel size on the accuracy of the velocity data was then examined. This experiment enables us to conclude that a voxel size of 0.96 mm, which corresponds to 20% of the pore size, is sufficient. The volume-averaged results do not change below a voxel size of 20% of the pore size, whereas systematic deviations occur with larger voxels. The same trend is observed with the local velocity data. The streamlines calculated from the MRV velocity data are not influenced by the voxel size for voxels of up to 20% of the pore size, and even slightly larger voxels still show good agreement. In summary, this study shows that even with a relatively low measurement resolution, quantitative 3-dimensional velocity fields can be obtained through porous flow systems with short measurement times and low measurement uncertainty.