Predictions of non-Fickian solute transport in different classes of porous media using direct simulation on pore-scale images

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Predictions of non-Fickian solute transport in different classes of porous media using direct simulation on pore-scale images

Branko Bijeljic, Ali Raeini, Peyman Mostaghimi, and Martin J. Blunt

Phys. Rev. E 87, 013011 – Published 10 January 2013

Abstract

We present predictions of transport through micro-CT images of porous media that include the analysis of correlation structure, velocity, and the dynamics of the evolving plume. We simulate solute transport through millimeter-sized three-dimensional images of a beadpack, a sandstone, and a carbonate, representing porous media with an increasing degree of pore-scale complexity. The Navier-Stokes equations are solved to compute the flow field and a streamline simulation approach is used to move particles by advection, while the random walk method is employed to represent diffusion. We show how the computed propagators (concentration as a function of displacement) for the beadpack, sandstone, and carbonate depend on the width of the velocity distribution. A narrow velocity distribution in the beadpack leads to the least anomalous behavior, where the propagators rapidly become Gaussian in shape; the wider velocity distribution in the sandstone gives rise to a small immobile concentration peak, and a large secondary mobile peak moving at approximately the average flow speed; in the carbonate with the widest velocity distribution, the stagnant concentration peak is persistent, with a slower emergence of a smaller secondary mobile peak, characteristic of highly anomalous behavior. This defines different types of transport in the three media and quantifies the effect of pore structure on transport. The propagators obtained by the model are in excellent agreement with those measured on similar cores in nuclear magnetic resonance experiments by Scheven, Verganelakis, Harris, Johns, and Gladden, Phys. Fluids 17, 117107 (2005).

Received 15 August 2012

DOI:https://doi.org/10.1103/PhysRevE.87.013011

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Branko Bijeljic^*, Ali Raeini, Peyman Mostaghimi, and Martin J. Blunt

Department of Earth Science and Engineering, Imperial College, London SW7 2BP, United Kingdom

^*Corresponding author: b.bijeljic@imperial.ac.uk

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Vol. 87, Iss. 1 — January 2013

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Images

Figure 1
Two-dimensional cross sections of the segmented image of the beadpack (a) and the three-dimensional gray scale images for Bentheimer sandstone (b) and Portland carbonate (c).Reuse & Permissions
Figure 2
Image geometries of the beadpack (a), Bentheimer sandstone (b), and Portland carbonate (c) shown with the pore volume represented by gray color; normalized pressure fields with a unit pressure difference across the model for beadpack (d), Bentheimer sandstone (e), and Portland carbonate (f); normalized flow fields, where the ratios of the magnitude of u at the voxel centers divided by the average flow speed $u_{av}$ are shown using cones (too small to be seen individually) that are colored using a logarithmic scale spanning from 5 to 500 for the beadpack (g), Bentheimer sandstone (h), and Portland carbonate (i). In the images green and red colors indicate high values, while blue color indicates low values.Reuse & Permissions
Figure 3
Variograms showing the normalized functions for porosity, $γ_{p} / γ_{p, \infty}$ , and velocity in the direction of flow, $γ_{u_{x}} / γ_{u_{x, \infty}}$ , for the images of beadpack (a), Bentheimer sandstone (b), and Portland carbonate (c). Indicated by the vertical line is the characteristic length (representing a mean grain size) for all three samples. We find that the porosity and velocity appear to be largely uncorrelated beyond this characteristic length, which is much less than the total system size.Reuse & Permissions
Figure 4
Probability density function of the velocity distributions for the beadpack, Bentheimer sandstone, and Portland carbonate presented on (a) semilogarithmic axes, and (b) doubly logarithmic axes. The solid line is the distribution for a single cylindrical tube, representing the homogeneous limit.Reuse & Permissions
Figure 5
Probability of molecular displacement $P$ (ζ) in the images of (a) beadpack, (b) Bentheimer sandstone, and (c) Portland carbonate as a function of displacement ζ for the set of times $t$ $=$ 0.106, 0.2, 0.45, 1, and 2 s. The coordinates are rescaled by the expected nominal mean displacement ${〈 ζ 〉}_{0} = u_{av} t$ in the direction of flow. The average velocities are $u_{av}$ $=$ 0.91, 1.03, and 1.3 mm/s for the beadpack, Bentheimer sandstone, and Portland carbonate, respectively. These correspond to the flow speeds in the experiments [12] with which we compare our results in Sec. 3b.Reuse & Permissions
Figure 6
Probability of molecular displacements $P$ (ζ) (solid lines) as a function of displacement ζ for the set of times $t$ $=$ 0.106, 0.2, 0.45, 1, and 2 s compared to the propagator obtained in the NMR experiments (dashed lines) by Scheven et al. [12] at the same observation times: (a) the beadpack, (b) Bentheimer sandstone, and (c) Portland carbonate. The coordinates are rescaled by the nominal mean displacement ${〈 ζ 〉}_{0} = u_{av} t$ , $u_{av}$ $=$ 0.91 mm/s for the beadpack, $u_{av}$ $=$ 1.03mm/s for Bentheimer sandstone, and $u_{av}$ $=$ 1.3 mm/s for Portland carbonate, as in the experiments.Reuse & Permissions

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