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methods (see, e.g., Falta et al., 1992; Adenekan, 1992; Falta, 2000b; Ochs et al.,
2002). In some cases, analytical solutions can also provide useful estimates of the
condensation front characteristics (Menegus and Udell, 1985; Hunt et al., 1988;
Stewart and Udell, 1988).
22.4.2 Condensation Front Velocity, Steam Velocity, and
NAPL Evaporation Velocity
There are at least three different velocities that are of interest in steam flooding.
The condensation or steam front velocity is the speed at which the steam zone
grows. The steam velocity is the Darcy velocity of the steam behind the conden-
sation front. Because the steam condenses back to liquid water at the condensation
front with a volume change of about a factor of 1600, the steam velocity is much
larger than the steam front velocity. The NAPL evaporation velocity is the speed
at which an evaporation front moves through immobile NAPL trapped at residual
saturation.
Considering a one-dimensional system without any NAPL, Menegus and Udell,
(1985) developed an analytical solution for the condensation front velocity:
Xh
⎡ w ⎤
vap + 1
˙ m in C pl (T s −T 0 )
v sf = ⎣ ⎦ (22.10)
¯
ρ l (1 − φ) ρ R C R + φS l
ρ l C pl
2
where ˙m in is the injected steam mass flux (kg/m s), X is the steam quality (the mass
fraction of water vapor in ˙m in ), C pl is the heat capacity of water, h w is the heat
vap
of vaporization of water, T s and T 0 are the steam zone and ambient temperatures,
¯
respectively, and S l is the water saturation behind the condensation front. Conden-
sation front velocities in field applications are in the range of a few meters per day,
depending on the well geometry, formation thickness, steam injection rates, and
the steam quality. From Eq. (22.10), it is apparent that the one-dimensional steam
front velocity is controlled by the rate of heating of the porous media and residual
water.
The steam darcy velocity behind the condensation front may be estimated from a
simple mass balance as:
˙ m in X
v s = (22.11)
ρ g
3
◦
where ρ g is the steam density, about 0.6 kg/m at 100 C. The steam darcy velocity
behind the steam front is about two orders of magnitude larger than the condensation
front velocity. This very high gas velocity gives the steam a tremendous capability
for evaporation of NAPLs in the steam zone. It is useful to note that noncondensible
gases behave differently from steam because the leading edge of the noncondensible
gas advances at a rate similar to the gas pore velocity behind the leading edge. For
this reason, the addition of air or other gases to steam can substantially change the