Page 277 - gas transport in porous media

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the sample producing a steady flow of gas, Q. For a compressible, ideal gas the perme-
ability, k, is determined from the solution of the one-dimensional gas flow equation
2µQp 1 L
k = 2 (15.1)
2
A(p − p )
1 o
where µ is the gas viscosity, L the length of the sample, A the cross-sectional area
of the sample, p 1 the pressure at the inlet, and p o the pressure at the outlet. Note that
the gradient is predicated on the squared pressure owing to the compressibility of the
gas (e.g., Bear, 1972).
When performing permeability measurements with gas, attention must be paid
to gas slippage and inertial effects. Permeabilities measured with gas tend to be
larger than equivalent measurements made with liquid. The disparity results from the
“slippage” of gas along pore walls that stands in contrast to the no flow boundary
layer behavior of liquids. Klinkenberg (1941) provides a thorough explanation of this
phenomenon and suggests corrections for its effect. Gas-slippage is most pronounced
at low mean pore pressures and for low permeability materials. Alternatively, inertial
effects occur when the gas flow is no longer viscous dominated. Such effects can be
encountered at relatively low flow rates given the low density to viscosity ratio of
gases. Asimple check for these effects involves measuring the permeability at several
different pressures to verify that the gas flux increases linearly with the gradient.
One disadvantage of the permeameter is that testing requires the destructive sam-
pling of the porous medium. Another disadvantage of the conventional permeameter
method is that it is performed on a specific volume of rock or soil, thus aggre-
gating structural detail occurring at smaller scales. These limitations prompted the
development of the gas minipermeameter to provide a rapid, inexpensive, and often
non-destructive means of sampling permeability (Dykstra and Parsons, 1950; Eijpe
and Weber, 1971). Operation involves compressing a tip seal against a flat, fresh
rock/outcrop or core surface while injecting gas at a constant pressure. The steady
gas flow is directed through the center of the tip seal, discharging through the open
faces of the sample beyond the seal (Figure 15.1). Using information on the seal
geometry, gas flow rate, gas injection pressure, and ambient (atmospheric) pressure,
the permeability is calculated. The solution takes a form similar to that given in
Eq. (15.1); however, because of the divergent nature of the flow field L is not known
explicitly. Rather, it is replaced by a geometric factor that depends on the ratio of
the inner to outer tip seal radii and the shape/size of the test medium. Goggin et al.
(1988) provides estimates of the geometric factor as a function of these dimensionless
parameters. The active sampling range of the gas minipermeameter is generally from
a few milli-Darcys to several hundred Darcys.
Davis and others (1994) modified the gas minipermeameter to facilitate out-
crop sampling. The lightweight syringe-based air-minipermeameter (LSAMP) uses a
hand-operated syringe to inject gas into the formation whereas the classical miniper-
meameter depends on a source of compressed gas. The low gas injection pressures
used by the LSAMP allow sampling of poorly lithified sediments without damaging