Page 176 - gas transport in porous media

Persoff
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do not actually have pores in the same sense as a porous medium such as sandstone,
but the term “pore size” will refer to the aperture at any location in the fracture.
Similarly as for porous media, hysteresis in the capillary pressure curve may also
cause water to be “trapped” in pores larger than r given by Eq. (9.1) when the water
table is falling. Water, being the wetting fluid, occupies the smallest pores. Given a
pore-size distribution, one can calculate the saturation of the fracture at any distance
above the water table. Because the smallest pores contribute the least to the fracture
conductivity, if the fracture liquid saturation is low, (e.g., 10%), gas flow is scarcely
impeded by the presence of water, and the permeability to gas is almost as great in
the partially saturated fracture as in the dry fracture (i.e., relative permeability to gas
is close to 1). At low liquid saturation, gas flow will normally be stable. Because flow
velocities in fractures may be much greater than in porous media, inertial effects may
be significant (i.e., non-darcy flow).
At smaller values of d (closer to the water table), larger pores are saturated and gas
permeability is reduced significantly; that is, gas relative permeability is less than 1.
Experiments to measure gas and liquid relative permeabilities in fractures at a range of
moisture tension and water saturation were conducted by Persoff and Pruess (1995).
Those experiments were conducted in horizontally-mounted transparent replicas of
natural fractures, to permit flow visualization and avoid gravitational effects. Gas
flow was unstable at low capillary pressures (at high water saturations) and this was
attributed to intermittent blocking of gas flow paths by water, as discussed below.

9.2 UNSTABLE GAS FLOW IN AN UNSATURATED FRACTURE
Persoff and Pruess (1995) conducted experiments to measure relative permeabilities
to gas and liquid flow in 7.6-cm square, horizontally mounted, transparent replicas of
natural rock fractures and in a natural rock fracture sample. The hydraulic apertures
(aperture of a parallel plate fracture with the same absolute permeability) of these
samples ranged from 9 to 22 µm. An aperture map was produced by comparing
digitized images of a fracture replica filled with either plain water or dyed water. Light
attenuation by Beer’s law was used to calculate the aperture, a technique similar to
that used by Detwiler et al. (1999), calibrated with measurements on a “stair-step”
fracture of known apertures.
In these experiments gas and liquid were injected simultaneously at one edge of
the sample and removed from the opposite edge. Gas was injected directly to the edge
of the fracture and liquid through a porous plate; this allowed gas to be injected at a
greater pressure than liquid without invading the liquid injection line (an adaptation
of the Hassler method for measuring relative permeability). Liquid was injected at
constant rate, and gas was injected at either constant mass flow rate or constant
pressure. Inlet and outlet pressures were measured, and boundary conditions were
adjusted to achieve equal capillary pressures (defined as p cap = p g − p l ) at the inlet
and outlet.
All experiments started with the fracture saturated with liquid, and liquid flowing.
When gas was introduced at constant pressure at the inlet, gas fingers penetrated into