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(ii) On the other hand, when B c > 0, a finite cutoff does not exist, with the rate of
growth increasing indefinitely at large α as Sahimi et al.
√
2
ω ≈ B c (B c + 2 ε)α > 0 (8.39)
Clearly, such is the case for a sufficiently high (but finite) mobility contrasts, so long
as L c = 0, as shown in Figure 8.4. This unexpected and rather remarkable result is
obtained on the basis of a step base state, which is subject to a singular behavior in the
large (as well as in the small) α region. To better understand the proper dependence,
Yortsos and Zeybek (1988) attempted a more rigorous asymptotic analysis valid for
base states near a step profile, namely, for
1
C = erfc(cξ) (8.40)
2
where c 1. Their results showed that the step profile prediction, inequality (8.39),
is invalid at large α when B c > 0 and, in fact, a cutoff wave number does exist.
However, the latter was found to increase monotonically and without bound as c
increases, namely, as the profile becomes step-like, provided that B c > 0.Thus,
the essential prediction that qualitatively different instability behavior is obtained by
changing the sign of B c , remains intact. Most of the above results were confirmed by
the experimental study of Bacri et al. (1991).
The implications of these results are straightforward. Because of the dependence of
the dispersion coefficients on the flow velocity, an essential feature of hydrodynamic
dispersion in porous media, and for mobility ratios that exceed a critical value dictated
by the given process conditions, a miscible displacement is predicted to be unstable
at all wavelengths.
Under such conditions, there is no finite preferred mode and, in fact, the above
continuum description is ill-posed and breaks down. This remarkable result raises
serious doubts about our ability to describe the conditions for the onset of instability
in miscible displacements. Recall that this result is obtained if we make several
hypotheses, including the validity of a continuum description, and with the dispersion
process formulated by a CD equation and the dispersion coefficients represented by
Eqs. (8.21) and (8.22). If these predictions are to be taken seriously, the breakdown
of the continuum hypothesis beyond a finite M calls for an alternative description.

8.10 MAIN CONSIDERATIONS IN MISCIBLE
DISPLACEMENT PROJECTS

Because of their huge cost, field-scale gas-flood projects require careful technical
design. The basic design parameters include the geology of the reservoir; its porosity
and permeability distributions, and temperature and pressure; the relative permeabil-
ity curves characterizing two-phase flow in the reservoir, the amount of residual oil,
and the viscosity and minimum miscibility pressure of the oil-in-place.
The minimum miscibility pressure is typically determined phenomenologically by
measuring displacement of crude oil by CO 2 (or another injection fluid) in a long