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Insights into non-Fickian solute transport in carbonates.

Bijeljic B, Mostaghimi P, Blunt MJ - Water Resour Res (2013)

Bottom Line: Mostaghimi, and M.Blunt (2013), Insights into non-Fickian solute transport in carbonates, Water Resour.Res., 49, 2714-2728, doi:10.1002/wrcr.20238.

View Article: PubMed Central - PubMed

Affiliation: Department of Earth Science and Engineering, Imperial College London London, UK.

ABSTRACT
[1] We study and explain the origin of early breakthrough and long tailing plume behavior by simulating solute transport through 3-D X-ray images of six different carbonate rock samples, representing geological media with a high degree of pore-scale complexity. A Stokes solver is employed to compute the flow field, and the particles are then transported along streamlines to represent advection, while the random walk method is used to model diffusion. We compute the propagators (concentration versus displacement) for a range of Peclet numbers (Pe) and relate it to the velocity distribution obtained directly on the images. There is a very wide distribution of velocity that quantifies the impact of pore structure on transport. In samples with a relatively narrow spread of velocities, transport is characterized by a small immobile concentration peak, representing essentially stagnant portions of the pore space, and a dominant secondary peak of mobile solute moving at approximately the average flow speed. On the other hand, in carbonates with a wider velocity distribution, there is a significant immobile peak concentration and an elongated tail of moving fluid. An increase in Pe, decreasing the relative impact of diffusion, leads to the faster formation of secondary mobile peak(s). This behavior indicates highly anomalous transport. The implications for modeling field-scale transport are discussed. Citation: Bijeljic, B., P. Mostaghimi, and M. J. Blunt (2013), Insights into non-Fickian solute transport in carbonates, Water Resour. Res., 49, 2714-2728, doi:10.1002/wrcr.20238.

No MeSH data available.


Variograms showing the normalized functions for porosity,, and velocity in the direction of flow, , for the images of (a) Ketton, Mt Gambier, and ME2 and (b) Indiana, Estaillades, and ME1. The variograms are shown as a function of distance x normalized by the characteristic length L.
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fig05: Variograms showing the normalized functions for porosity,, and velocity in the direction of flow, , for the images of (a) Ketton, Mt Gambier, and ME2 and (b) Indiana, Estaillades, and ME1. The variograms are shown as a function of distance x normalized by the characteristic length L.

Mentions: [24] The correlation structure is shown in Figure 5, where the variograms for porosity, , and velocity in the direction of flow, , for the images of (a) Ketton, Mt Gambier, and ME2 and (b) Indiana, Estaillades, and ME1 are plotted. The functions are calculated as(4)(5)where is the indicator function for porosity ( for pore voxels and for grain voxels), are velocities in the direction of flow across faces oriented normal to the x direction, and N is the number of voxels. Plotted are the and values normalized to the theoretical values at infinite range (uncorrelated limit) and . The x axis values are normalized to the characteristic length L estimated for each carbonate sample: the values for L are presented in Table1.


Insights into non-Fickian solute transport in carbonates.

Bijeljic B, Mostaghimi P, Blunt MJ - Water Resour Res (2013)

Variograms showing the normalized functions for porosity,, and velocity in the direction of flow, , for the images of (a) Ketton, Mt Gambier, and ME2 and (b) Indiana, Estaillades, and ME1. The variograms are shown as a function of distance x normalized by the characteristic length L.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3814002&req=5

fig05: Variograms showing the normalized functions for porosity,, and velocity in the direction of flow, , for the images of (a) Ketton, Mt Gambier, and ME2 and (b) Indiana, Estaillades, and ME1. The variograms are shown as a function of distance x normalized by the characteristic length L.
Mentions: [24] The correlation structure is shown in Figure 5, where the variograms for porosity, , and velocity in the direction of flow, , for the images of (a) Ketton, Mt Gambier, and ME2 and (b) Indiana, Estaillades, and ME1 are plotted. The functions are calculated as(4)(5)where is the indicator function for porosity ( for pore voxels and for grain voxels), are velocities in the direction of flow across faces oriented normal to the x direction, and N is the number of voxels. Plotted are the and values normalized to the theoretical values at infinite range (uncorrelated limit) and . The x axis values are normalized to the characteristic length L estimated for each carbonate sample: the values for L are presented in Table1.

Bottom Line: Mostaghimi, and M.Blunt (2013), Insights into non-Fickian solute transport in carbonates, Water Resour.Res., 49, 2714-2728, doi:10.1002/wrcr.20238.

View Article: PubMed Central - PubMed

Affiliation: Department of Earth Science and Engineering, Imperial College London London, UK.

ABSTRACT
[1] We study and explain the origin of early breakthrough and long tailing plume behavior by simulating solute transport through 3-D X-ray images of six different carbonate rock samples, representing geological media with a high degree of pore-scale complexity. A Stokes solver is employed to compute the flow field, and the particles are then transported along streamlines to represent advection, while the random walk method is used to model diffusion. We compute the propagators (concentration versus displacement) for a range of Peclet numbers (Pe) and relate it to the velocity distribution obtained directly on the images. There is a very wide distribution of velocity that quantifies the impact of pore structure on transport. In samples with a relatively narrow spread of velocities, transport is characterized by a small immobile concentration peak, representing essentially stagnant portions of the pore space, and a dominant secondary peak of mobile solute moving at approximately the average flow speed. On the other hand, in carbonates with a wider velocity distribution, there is a significant immobile peak concentration and an elongated tail of moving fluid. An increase in Pe, decreasing the relative impact of diffusion, leads to the faster formation of secondary mobile peak(s). This behavior indicates highly anomalous transport. The implications for modeling field-scale transport are discussed. Citation: Bijeljic, B., P. Mostaghimi, and M. J. Blunt (2013), Insights into non-Fickian solute transport in carbonates, Water Resour. Res., 49, 2714-2728, doi:10.1002/wrcr.20238.

No MeSH data available.