Magnetic resonance imaging of hydrodynamic dispersion in a saturated porous medium

• Published in: Transport in porous media Vol. 54; no. 2; pp. 145 - 166
• Main Authors: DEURER, M, VOGELER, I, CLOTHIER, B. E, SCOTTER, D. R
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer 01.02.2004; Springer Nature B.V
• Subjects: Beads; Boundary conditions; Convective flow; Dispersion; Earth sciences; Earth, ocean, space; Efflux; Equilibrium flow; Exact sciences and technology; Flow velocity; Hydrogeology; Hydrology. Hydrogeology; Magnetic resonance imaging; Molecular diffusion; NMR; Nuclear magnetic resonance; Porous media; Thickness; Variance; Velocity; experimental studies; diffusion; REV; networks; stochastic-convection; convection; stochastic models; pore water; water content; boundary conditions; boundary condition; models; convection-dispersion; transverse dispersivity; dispersivity; hydrodynamics; transport; Nuclear magnetic resonance imaging; nuclear magnetic resonance; preferential flow; breakthrough curve; correlation; statistical analysis; dispersion; porous media; pore-water velocity
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1023/A:1026358431442

By using nuclear magnetic resonance imaging (NMRI) we have been able to analyse dispersion at the microscopic scale during steady-state flow through water-saturated glass beads. The flow rate through the porous medium was chosen high enough in order to neglect the influence of molecular diffusion on dispersion. Velocity statistics were measured, by NMRI, within slices of increasing thickness perpendicular to the direction of flow. It took more than two bead diameters before a representative elementary volume (REV) for the mean velocity was reached. This was in a region in the middle of the column that was not influenced by the boundary conditions. There the velocity variance decreased exponentially as a function of the slice thickness, due we consider to the formation of an interconnecting streamline network. The exponential decrease in the velocity variance reflects the transition from a local pattern of stochastic–convective flow to a convective–dispersion regime at the scale of the REV. We found that the point-like preferential influx and efflux boundary condition increased velocity variances and thus enhanced longitudinal hydrodynamic dispersion. Using the transverse correlation length of longitudinal velocity variance, we derived a mean transverse dispersivity that agreed well with Saffman’s (1959) model. So we have been able to provide for the first time a direct observation verification of a part of Saffman’s (1959) conjectures. By NMRI we observed this value to be independent of the observation scale of the slice thickness.