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in turn decrease the vertical sweep in horizontal floods. On the other hand, gravity can
be used to advantage in dipping reservoirs to improve the sweep and the displacement
efficiency.
To study the effect of gravity on miscible displacements, two dimensionless
numbers are introduced:
η = (ρ o − ρ s ) /ρ s (8.6)
gk (ρ o − ρ s )
N G = (8.7)
qµ o
where N G is the gravity number. If N G is small, gravity is unimportant and vis-
cous fingering dominates the flooding behavior (see above).As N G increases, viscous
fingering can still occur but gravity influences the growth rates of the individual fin-
gers. If the solvent is lighter than oil, it tends to flow upwards. Hence, more solvent
enters the fingers in the upper part of the porous medium, resulting in faster growth
of these fingers, while the growth of the rest of the fingers is somewhat suppressed,
partly due to gravity drainage and partly because of the shielding effect described ear-
lier. This phenomenon results in early breakthrough and reduced sweep efficiency.
If, however, the solvent is heavier than oil, it is conceivable that, for a range of
N G , gravity might improve the sweep efficiency by delaying the breakthrough of the
fastest-growing finger.
If N G is large enough, a gravity tongue is formed and grows at the top of the porous
medium. Moreover, viscous fingering may occurs near the tongue, while fingering in
the rest of the medium will be suppressed. Under this condition, both gravity override
and viscous fingering are important and affect the displacement. For very large values
of N G , gravity override completely dominates the displacement, suppressing any
fingers that may form at early times. In this case, the gravity tongue breaks through
very early, and the rate of oil recovery will be very low. Therefore, it should be clear
that as N G increases, the breakthrough time decreases, while the rate of oil recovery
after the breakthrough also decreases (Moissis et al., 1989).
The effect of gravity is more pronounced at high viscosity ratios, because the ratio
of gravitational and viscous forces is inversely proportional to the viscosity of the fluid
currently present in the porous medium. This ratio is equal to N G only at time t = 0.
As the displacement proceeds and the lower viscosity fluid (the displacing gas) enters
the porous medium at a constant rate, the ratio of gravitational and viscous forces
increases and, therefore, gravity becomes progressively more important.

8.6 AVERAGED CONTINUUM MODELS OF MISCIBLE
DISPLACEMENTS
One approach to describing miscible displacements and fingering phenomena in a
porous medium is based on averaged continuum equations. This method can describe
any instability that is smooth on the length scale over which of the continuum descrip-
tion is applicable. In the strict absence of dispersion (i.e., the limit that the Peclet