Quantitative nuclear magnetic resonance measurements of preasymptotic dispersion in flow through porous media

Abstract

We use pulsed field gradient nuclear magnetic resonance to probe molecular displacements in preasymptotic Stokes flow through a pack of beads with bead diameter d=100±20μm, through a Bentheimer sandstone, and a Portland carbonate rock core, for a common range of flow velocities v and interrogation times Δ. For flow through the bead pack the length scale of the pore is well defined, as are the Peclet number Pe∊[20–80] and the Reynolds number Re<0.1. Probability distributions of molecular displacements P(ζ) are determined. The mean displacement ⟨ζ⟩, the variance σ2≡⟨(ζ−⟨ζ⟩)2⟩ and the skewness γ3≡⟨(ζ−⟨ζ⟩)3⟩ of P(ζ) are determined by a self-consistent cumulant analysis designed to minimize the systematic errors to which any cumulant analysis of non-Gaussian distributions is susceptible. Systematic errors in σ and γ arising from surface relaxation effects and flow displacements through the internal fields of rocks are quantified.