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to model this experiment at the pore scale. To set up our
unsteady-state simulations, we use periodic external boundary
conditions. Both fluids could exit the model, but only the
displacing fluid can enter the model. This makes the velocity
field continuous during the displacement and enhances the
stability of the simulations. The pressure field was controlled by
a body force that was applied equally to both fluids.
6 REFRENCES
Chen H., Chen S. and Matthaeus W. H.,(1992), Recovery of the Navier–
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flows. Annual Review of Fluid Mechanics,30, 329–364.
The body force is regulated to keep a constant total mean
velocity and thus constant capillary number (Ramstad et al.
2010). The effluent composition and pressure drop across the
model
are continuously monitored. Figure 4b
show the evolution
of the wetting phase into the medium and Figure6shows the
experimental relative permeability curve as well as the results of
LB simulation performed at similar capillary number. The
LBM code predicts the trends of the variations of relative
permeabilities correctly however, the discrepancies look more
for unsteady-state relative permeability curves compare to those
of the steady state. One of the sources of uncertainty in the
current numerical results is the unfavorable effects of spurious
velocities. In a SC type LBM simulation, largest spurious
velocities occur near the interfacial region of the fluids (Jia et
al., 2008). Therefore, high spurious velocities may affect the
calculated fluxes especially for very slow or creep fluid flows.
On the other hand, as mentioned before the experimental values
are not measured directly from the tests. They are calculated
using the JBN method. This may also contribute to the
difference that is seen between the experimental and
numerically-derived values.
Ghassemi A., Pak A.,(2011),
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5 CONCLUSIONS
A newly developed Lattice Boltzmann-based numerical code
has been described in this paper. This model is based on Shan &
Chen (SC) formulation which is capable of simulating the
simultaneous flow of two immiscible fluids at the pore scale
considering all the important interacting effects such as
interfacial tension and capillary. Using this code the variation of
relative permeabilities of two-fluid flow under steady state and
unsteady sate conditions has been simulated which is of utmost
importance in petroleum reservoir engineering. MRT approach
has been employed in the code to eliminate the problem of the
dependency of the results to the viscosity. The obtained results
indicate that LBM is a powerful method that can simulate
complex problems pertaining flow in porous materials as well
as solving difficult issues in petroleum geomechanics. Results
obtained in this study about the variation of the relative
permeabilities in the reservoir rock reveal that although the
results for steady state two-fluid flow is quite promising, the
modeling of unsteady flow warrants further investigation.
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