Page 146 - gas transport in porous media

Chapter 8: Gas Injection and Fingering in Porous Media
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field conditions (Taylor et al., 1987), using the results of tracer tests, were not suc-
cessful. The second approach is theoretical, using various models of heterogeneous
porous media. Numerous attempts have been made in this direction (Sahimi, 1993a,
1995).
It is important to realize that values of the dispersion coefficients measured in
the laboratory are usually smaller than the corresponding field-scale values, which
presumably explains why the empirical relations between the dispersivities and the
hydraulic conductivity, obtained based on laboratory experiments, fail under field
conditions. Thus, onemustdeviseanappropriatemethodforscale-upofthedispersion
coefficients from the laboratory to the field scales (Johns et al., 2000a,b). Mixing by
dispersion in a field-scale porous medium is likely to be much greater than in a
laboratory-scale sample of the same porous medium, since large-scale variations in
the permeability and porosity of the field-scale porous medium strongly increase the
mixing process at that scale.
Mobility ratio and gravity also affect dispersion. If M > 1, viscous instability
develops (see below) in which case the displacement is no longer a simple process.
However, if M < 1, the usual dispersion mechanisms discussed above are operative.
Moreover, since no instability develops for M < 1, the effect of pore space hetero-
geneities is also suppressed. On the other hand, if in a miscible displacement a less
dense fluid displaces a denser fluid, the density difference suppresses the effect of
dispersive mixing.
In some situations, longitudinal dispersion affects a miscible displacement more
strongly than the transverse dispersion, and vice versa. For example, if large fingers
of the displacing fluids develop, which is often the case when M > 1, or when
there are large-scale variations in the permeabilities, there would be a large surface
area on the sides of the fingers which allows for significant transverse dispersion
to occur. This can help join the fingers, stabilize the displacement, and increase its
efficiency. By contrast, longitudinal dispersion can only take place at the tip of the
fingers and, therefore, its effect is much weaker than that of transverse dispersion.
For this reason, models that ignore transverse dispersion are usually not completely
adequate for describing a miscible displacement.

8.2.3 Anisotropy of Porous Media
As mentioned above, dispersion processes are sensitive to the distribution of the het-
erogeneities of a porous medium, including its stratification, which in turn affects the
performance of miscible displacements. This is particularly true when the displacing
agent is a gas. It is clear that the displacing gas preferentially chooses the strata with
higher permeabilities. As a result, large amounts of the fluid (oil) to be displaced can
be left behind in the strata with low permeabilities. If we attempt to displace this
fluid by injecting larger amounts of gas into the low permeability strata, some of the
gas will inevitably enter the high permeability strata and do essentially nothing, as
such strata have already been swept by the previously-injected gas and, therefore,
additional gas injection would not be very efficient. The effect of stratification is