Numerical simulation of water flow in three dimensional heterogeneous porous media observed in a magnetic resonance imaging experiment

Abstract

Magnetic resonance imaging (MRI) was used to obtain sequential images of water (i.e., 1H) doped with a paramagnetic tracer as it flowed through a three‐dimensional (3D) flowcell packed with a spatially correlated heterogeneous distribution of 1 cm3 blocks, each containing one of five different sand fractions. Tracer concentration breakthrough curves (BTCs) were obtained from MRI signal intensity profiles at each voxel (0.1875 × 0.1875 × 0.225 cm3). Voxel scale BTCs were averaged over 0.25 × 0.25 cm2, 1 × 1 cm2, and entire flowcell cross‐sections, all at 0.25 cm increments along the main flow direction, and compared with numerical simulations. Hydraulic conductivity (K) and dispersivity values for each of the five sand types were varied, and root‐mean squared error (RMSE) values for mean arrival times and second central moments, and RMSE values between simulated and measured BTCs, at each of the three averaging scales were calculated. Measured values of K with a porosity 5% higher than measured values, and longitudinal dispersivity values on the order of the grain size, yielded simulated BTCs that adequately captured experimental BTCs averaged over the entire flowcell cross‐section, and BTCs at smaller scales (i.e., 1 × 1 cm2 and 0.25 × 0.25 cm2) in regions of the flow cell characterized by more uniform K fields. However, model simulations deviated more from BTCs at smaller scales in regions of the flowcell characterized by greater K contrast, where flow‐bypassing occurred. This may be due to small discrepancies between the experimental and numerical conductivity fields. Comparison of mechanical dispersion and diffusion in low K zones indicates that molecular diffusion is equally important to mechanical dispersion in these zones and transverse dispersion did not have much effect on improving prediction. These results illustrate that predicting water flow at fine scales (relative to permeability variations) is very challenging, even under the most controlled conditions. This may have large implications for modeling reactive transport, where reactant residence time and mixing can be greatly impacted by water flowpaths.