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Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
K’
end changes and
sand phase index rapidly increases. At this point the flow is
characterized with pronounced formation of packs and clogs
that affect the slurry flow into a channel.
=slurry consistency index,
n’
=slurry flow behavior index and
a
=slurry apparent viscosity.
The plots reveal some interesting trends. The non-Newtonian
slurry index
K’
does not depend on sand concentration while the
index
n’
is (Figs. 9 and 10). Index
n’
appears to decrease with
increase of concentration, but at
c
v
=0.3 the tr
4 CONCLUSIONS
A discrete element study of sand flow in narrow channels with
higher concentrations up to the maximum concentration is
studied. Maximum sand concentration is a value at which the
sand transport is not possible and flow stops. The maximum
sand concentration depends on channel width and particle
diameter ratio, and it has a very low sensitivity to the magnitude
of fluid pressure. At high pressures, slightly higher
concentration than maximum was able to be transported only
for a limited length along the channel. Velocity of the sand and
fluid velocity have different magnitudes, and the sand is being
transported in a slurry at velocities lower than the fluid. At
higher concentrations, sand forms packs and clogs, and fluid
flows around them. Since the two phases, solid phase and fluid
phase, do not have same average velocities, and it is not
possible to simply describe slurry as a mixture of two phases
with and substitute equivalent power-low (non-Newtonian) fluid
parameters. Both fluid and sand average velocities increase
proportionally with the pressure increase. However, if the sand
velocity and fluid velocity ratio is observed, it seems the
generally decrease with pressure increase. In other words, using
higher fluid pressures less difference in sand and fluid flow
velocity can be expected. Power-law behavior of phases can be
captured to describe the flow, but since the two phases have
different average velocites it is hard to average and come up
with unique slurry flow characterization at this point. A more
comprehensive study is needed to address this issue.
e 9. The
K’
fluid index for fluid and sand phase
Figur
Figure 10. The
n’
fluid index for fluid and sand phase
At maximum sand concentration, the flow in the channel is
completely stopped. Observation for both channel widths of
2mm and 4mm and pressures span 100-5000 Pa showed little
dependence of clogging on the pressure difference in the
channel. At higher pressures and higher concentrations, the
initial velocities were larger for a while and then they decreased
to a stabile level at which the flow continued. For the 2 mm
wide channel (
D
/
W
=3.3, where
D
=channel width and
W
=particle diameter) the maximum volumetric sand
concentration that was able to flow with a constant velocity was
0.14 while for the 4 mm wide channel it was 0.39. Attempts of
model runs with higher concentrations showed a little bit of
flowing but the flow stopped. Figs. 11, 12 and 13 show the
clogged sand in a narrow fracture. At limiting value of sand
concentration it can be seen that fluid flows arround the sand
packs formed in
5 ACKNOWLEDGEMENTS
Financial support provided by the U.S. Department of Energy
under DOE Grant No. DE-FE0002760 is gratefully
acknowledged. The opinions expressed in this paper are those of
the authors and not the DOE.
6 REFERENCES
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distributions in a fluidized bed with an immersed obstacle:
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Cundall, P. A., and O. Strack, 1979, A discrete numerical model for
granular assemblies: Geotechnique, v. 29, p. 47-65.
the channel. This study uses numerical model
to observe dense-phase fluid and solids flow in narrow channel,
and more comprehensive laboratory study is recommended for
future research.
Davis, R. H., J. M. Serayssol, and E. Hinch, 1986, The
elastohydrodynamic collision of two spheres: Journal of Fluid
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Patankar, S. V., 1980, Numerical heat transfer and fluid flow,
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Shah, S., 1993, Rheological characterization of hydraulic fracturing
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Figure 11. Clogging of sand in 4mm wide channel at initial volumetric
sand concentration c
v
= 0.49 with particles velocities vectors in
direction opposite to the flow.
Figure 12. Unstable flow with formation of particles packs at initial c
v
=
0.39 in 4mm wide channel with fluid flow velocity vectors around
packs.
Figure 13. Formation of particles packs at initial c = 0.28 in 2mm wide
v
channel.