Superdispersion in homogeneous unsaturated porous media using NMR propagators

Abstract

The NMR propagator technique allows the measurements of the variance σ(2)=<(ξ-<ξ>)(2)> of the displacements as a function of time t when flowing in a porous media. The time dependence of σ is a very sensitive test of Gaussian behavior compared to the analysis of the shape of the propagators. Superdispersion occurs when σ(2)[proportionality]t(α) with the exponent α larger than 1. In a homogeneous 30-μm grain pack and 10 < Pe < 35, we observed weak superdispersion in saturated conditions (α = 1.17) and gradually strong superdispersion as the water saturation decreases (up to α = 1.5) during steady-state oil-water two-phase flow. In saturated conditions, the corresponding longitudinal propagators and breakthrough curves are Gaussian or nearly Gaussian, whereas in two-phase conditions, the longitudinal propagators are nonsymmetric and the breakthrough curves show a tail at long times.

Magnetic resonance imaging measurements evidence weak dispersion in homogeneous porous media

“…Various original advanced approaches, relying on flow inversion experiments [8], particle tracking or scattering in matched-index medium [9], tracer concentration displacement [10] or imaging [11], provided further information on the solute distribution in time which apparently confirmed the above results. measurements with this technique generally provided values for smaller than that associated with the average master curve by a factor 2-3 [19][20], 4-5 [13], or 5-10 [21]. Such difference may be attributed to quite limited explored length scales, so that some macroscale effects responsible for higher macroscale dispersivity may be missed.…”

Modeling of super-dispersion in unsaturated porous media using NMR propagators

“…In single phase flow conditions (corresponding to 700 ml/h of Fig. 7 in [4]), we fitted accurately all data available between 0.4 s and 1 s (Fig. 3, only the data at 0.4 s and 1 s are shown).…”

“…The value of K is also very small (0.05 ± 0.02), meaning that molecules are not moving in the mean flow direction only 5% of the time. In two phase flow conditions and in the same grain pack (water flow rate of 50 ml/h in [4]), the data could also be fitted very accurately (Fig. 4).…”

“…We analyzed PFG-NMR data previously published in [4] collected in a homogeneous sand pack column with grains of size 30 lm. In single phase flow, we expect a normal behavior.…”

“…This property has been used by many authors and results from both methods give comparable results (see [2] for a compilation of results), although NMR tend to give lower D values. This simple approach does not apply in porous media with a complex structure such as double porosity carbonates [3], or in two phase flows performed in homogeneous systems [4]. Here, D varies in time and space.…”