Page 148 - gas transport in porous media

Chapter 8: Gas Injection and Fingering in Porous Media
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be rectilinear, that is, the displacing fluid is injected into the system at one face of
the cell and produced at the opposite face, or it can be radial in which the fluid is
injected into the system at its center, and the system acts as a cylinder of a large
radius and small height. As long as dispersive mixing is absent, the analogy between
formation of fingers in Hele-Shaw cells and a two-dimensional porous medium is
valid, which explains why the study of miscible displacements in Hele-Shaw cells
has been popular. If dispersion is present, the analogy breaks down because transverse
dispersion is always present in a porous medium, whereas a Hele-Shaw cell with its
thin gap between the two plates cannot support significant transverse dispersion in
the third direction.
There have also been many experimental studies of fingering phenomena, both in
miscible and immiscible displacements. Some of these include those of Blackwell
et al. (1959), Benham and Olson (1963), Slobod and Thomas (1963), Greenkorn et
al. (1965), Kyle and Perrine (1965), Perkins et al.(1965), Mahaffey et al. (1966),
Perkins and Johnston (1969), and more recently, those of Paterson (1981, 1983,
1985), Paterson et al. (1982), Chen and Wilkinson (1985), Lenormand et al. (1988),
and Bacri et al. (1991). Most of these experiments were also accompanied by a linear
stability analysis (see Section 8.9).

8.4 FACTORS AFFECTING GAS FINGERING

Let us point out that, in addition to the various factors that affect fingering, which
will be described below, three types of interesting phenomena occur during fingering
which are worth describing here. The first one is tip splitting in which the tip of a
finger becomes unstable and splits into two branches that compete with each other
for further growth. The second phenomenon is spreading, which usually occurs in a
porous medium when the flow velocity is not large. Under this condition, transverse
dispersion causes lateral spreading of the fingers which helps them to join and,
therefore, increase the efficiency of the displacement process. However, due to the
spreading phenomenon the tips of the fingers can become unstable since their typical
breadth exceeds the cutoff length scale for stability (see Section 8.9), which is also
set by transverse dispersion. Thus, tip splitting occurs only if the Peclet number Pe
exceeds a critical value which depends on the mobility ratio M, the density difference
between the displacing and displaced fluids, the flow velocity, and the effective
permeability of the porous medium. Finally, one may have shielding during fingering,
which is when one finger spreads out and grows much faster than other fingers and,
therefore, shields them. Figure 8.2 shows the phenomena of tip splitting and finger
shielding.
Generally speaking, the fingers’ patterns are influenced by the fluids’ character-
istics, including the possible non-monotonicity in their viscosity profile (Manickam
and Homsy, 1993), and the heterogeneity of the porous medium manifested by the
variance and the correlation structure of the permeability field (Waggoner et al., 1992;
Araktingi and Orr, 1993; Sorbie et al., 1994). Fingering is mitigated by small scale
dispersion (at the pore and laboratory scales) and by large-scale heterogeneity effects