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0.8 Sahimi et al.

Recovery

0.4

0
0.4 0.8 1.2
Pore volume injected

Figure 8.3. Comparison of the simulation results of Araktingi and Orr (1990) (curves) with the experi-
mental data (symbols) of Blackwell et al. (1959). The results are, from top to bottom, for M = 5, 86, 150,
and 375

Araktingi and Orr (1990) compared their results with the experimental data of
Blackwell et al. (1959). Figure 8.3 compares their results with the data; the agreement
is very good. Although this model suffers from fluctuations due to the limited number
of particles used in the simulation, the ensemble-averaged properties over several real-
izations compare well with the data of Blackwell et al. (1959). Generalization of this
model to irregular computational grids was achieved by Ebrahimi and Sahimi (2004).

8.9 STABILITY ANALYSIS OF MISCIBLE DISPLACEMENTS

Theoretically, miscible displacements are very efficient EOR processes. Because
capillary forces, which are usually responsible for oil entrapment, are absent, the dis-
placement can potentially be 100% efficient. In practice, however, complete recovery
is usually not realized due to the instability phenomena mentioned above, which leads
to macroscopic fingering of the solvent.
Over the past many decades, many stability analyses of miscible displacements
have been carried out (see, e.g., Perrine, 1963; Dumore, 1964, Schowalter, 1965;
Heller, 1966; Gardner and Ypma, 1982; Lee et al., 1984; Peters et al., 1984). Among
the unsolved problems is the question of what causes the disturbances that propagate
as the fingers. It is widely believed that reservoir heterogeneities are the source of
the disturbances. However, the presence of a porous space is not necessary for the
development of the fingers. Indeed, pioneering studies of viscous fingering did not
even use a porous medium. Instead, they used the Hele-Shaw cell. It may seem
that the uniformity of a Hele-Shaw cell should preclude any cell-related source of
instability. This is actually seen in the early time radial behavior at the inlet of a