Page 152 - gas transport in porous media

Chapter 8: Gas Injection and Fingering in Porous Media
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The effect of the geometry of a porous medium on fingering phenomena has
received considerable attention (see, e.g., Zimmerman and Homsy, 1991; Waggoner
et al., 1992; Sorbie et al., 1994). Typically, simulations of unstable miscible displace-
ments at field scales are carried out in geometries that have an aspect ratio of about
3 (Christie, 1989). Waggoner et al. (1992) simulated displacements at conditions of
transverse (or vertical) equilibrium. This limit is reached when the generalized aspect
ratio, = (L x /L y )(k v /k h ) 1/2 , is large, where k h and k v are the horizontal and vertical
permeabilities. Sorbie et al. (1994) studied the sensitivity of the displacement patterns
to this parameter in heterogeneous reservoirs, and showed that it significantly affects
the delineation in the parameter space of the various displacement regimes (fingering,
dispersion, and channeling).
In another study,Yang andYortsos (1995, 1996) provided an asymptotic description
of the displacements in porous media, including formation of the fingering, in the
limits that the parameter is large or small. The case of large corresponds to
conditions of transverse equilibrium. This regime is reached in long and narrow
isotropic reservoirs, in those in which the permeability transverse to the applied
pressure gradient exceeds significantly the permeability parallel to it, and in slim
tubes. It is a regime in which intense transverse mixing occurs. Small corresponds
to the opposite regime of zero transverse mixing and is better known as the Dykstra-
Parsons approximation (Dykstra and Parsons, 1950).
In parallel, Yang (1995) reported on the sensitivity of viscous fingering to by
means of high-resolution simulations. He reported that for uncorrelated, weakly het-
erogeneous porous media at conditions near transverse equilibria, most of the viscous
fingering ultimately occurs near the lateral, no-flow boundaries of the system. More
specifically, he found that narrow, single fingers originate at these boundaries and
propagate faster than the fingers in the interior of the domain, until a small perme-
ability value was randomly encountered, at which point the fingers turned inwards.
The intensity of this effect was found to depend on the viscosity ratio, and on the
heterogeneity parameter. Yang and Yortsos (1998, 2002) showed that this effect is
not a numerical artifact, but arises as a consequence of the slip boundary condition
implied by the use of Darcy’s law along no-flow boundaries. They found that the
origin of the boundary effect is the vanishing of the transverse, but not of the stream-
wise, velocity component at the no-flow boundary. When is small (for example,
when k v < k h ), transverse mixing is minimal everywhere (including the boundary),
and so is the boundary effect. By contrast, at large (for example, when k v > k h ),
transverse mixing is intense everywhere, except at the no-flow boundary. Therefore,
the growth of all the fingers, except the one at the boundary, is mitigated.

8.5 GRAVITY SEGREGATION
An important factor that influences vertical sweeps in miscible displacements is the
gravity. Solvents are usually less dense than either oil or brine, and drive gases, such
as hydrocarbons or flue gas, are even less dense. Because of the density differences,
solvents and drive gases may segregate and override the other reservoir fluids, which