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.

Rapid measurements of diffusion using PFG: Developments and applications of the Difftrain pulse sequence

“…The second moment is well fitted by the power law with an exponent Z 0 ¼ À0.22, Eq. [19], in agreement with previous studies on similar rocks using conventional APGSTE measurements (36). The third moment decreases asymptotically toward a small, non-zero value as expected, indicating the probability distributions are becoming more Gaussian at larger displacements.…”

“…This analysis provides the moments of the probability distribution; it is usual to obtain the first, second, and third moments, equivalent to the mean hzi, root-meansquared (rms) width s 2 , and adjusted skewness g 3 as defined in (36). These moments are represented diagrammatically in Fig.…”

“…To compensate for the effects of spin relaxation on the flow propagators, a post-acquisition correction can be applied to the data (36). First, the expected mean displacement hzi 0 is determined using the equation hzi 0 ¼ n p D. The pore velocity v p (the mean velocity of fluid flowing in the pore space) is given by n p ¼ Q/Aj where Q is the imposed volumetric flow velocity, A is the sample cross-sectional area, and j is the porosity.…”

Enhanced gas recovery with CO2 sequestration: The effect of medium heterogeneity on the dispersion of supercritical CO2–CH4

“…This equation is a valid description of transport where the solute molecules quickly sweep over the whole potential velocity field within a chosen representative volume, as it occurs in Fickian processes. A narrow Gaussian spread of flow velocities is a signature of a Fickian process and is classically formed in homogeneous, unconsolidated bead packs (Blunt et al, 2013;Scheven et al, 2005). Thus, it is important to know whether the well-known asymptotic (Fickian) regime has been fully developed in various porous media prior to applying the 1D-AD equation.…”

The Form of Waiting Time Distributions of Continuous Time Random Walk in Dead-End Pores

“…Anomalous dispersion widely exists in solute transport in ground water or in other porous media [1][2][3][4][5][6][7], which makes it difficult to simulate solute transport by traditional advectiondispersion equation. In recent years, scholars have developed a few models to describe the anomalous transport such as continuous time random walk (CTRW) [8][9][10][11][12] and fractional advection-dispersion equation [13][14][15][16].…”