Page 279 - gas transport in porous media

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For measuring the permeability of tight formations, non-steady state (transient)
methods are employed. The pressure-decay method was originated by Brace et al.
(1968). With this technique a rock core is confined in a permeameter while vessels
are attached to either end. The upstream vessel is pressurized and then allowed to
equilibrate with the core and the downstream vessel. The pressure decay behavior of
the vessels is measured and used to calculate the permeability. Hsieh et al. (1981)
extended Brace’s analysis to account for the compressive storage effects of the rock
sample, while Haskett et al. (1986) used the pressure-decay method to simultaneously
determine the porosity and permeability of a porous sample. Jones (1992) modified
the gas minipermeameter to operate in a pressure decay mode. The instrument was
modified by removing the flow controller and adding reservoirs of different calibrated
volumes. Solutions to the pressure decay relations were also enhanced to account for
gas-slippage and inertial effects. With these non-steady techniques measurements are
possible in less than a minute and can quantify permeabilities at the micro Darcy
level.

15.3 BOREHOLE TESTS
A variety of techniques are available for field-scale determination of the permeability
of unsaturated and variably saturated media. These techniques are based on both
steady state and transient methods, relying on both natural and induced pressure to
drive the measurement.
Evaluation of reservoir permeability using gas flow methods dates to the 1930s
(Muskat and Botset, 1931; Kirkham, 1946). The traditional single-well pump test
modified for the compressibility effects of gas represents a common means of evalu-
ating permeability of unsaturated formations. Matthews and Russell (1967) adapted
the Theis solution for one-dimensional radial groundwater flow to analyze airflow
data and estimate reservoir permeability. Baehr and Hult (1988) then adapted the
Hantush solution for two-dimensional axisymmetric groundwater flow to a partially
penetrating well in a confined aquifer to evaluate air flow in the unsaturated zone
induced by a vapor extraction well. Later, Baehr and Hult (1991) and Shan et al.
(1992) developed steady-state analytical solutions for a partially penetrating well
in both a leaky confined reservoir and an unconfined reservoir, while Falta (1995)
developed solutions for gas flow through horizontal wells. Analytical and numerical
solutions to multiple well tests have also been developed that are analogous to com-
mon aquifer tests in the saturated zone. These tests are often conducted in less than
a day and require aggressive vacuum and flow rates which may tend to emphasize
the effects of preferential flow paths. As such data from these tests may be more
characteristic of the preferential flow paths than the overall formation.
In addition to solutions involving flow induced by active vapor extraction tech-
niques, Stallman (1967), Weeks (1978), Massman (1989), Shan (1995), and Rossabi
and Falta (2002) have developed analytical solutions for both vertical and lateral per-
meability based on flow through wells caused by atmospheric pressure fluctuations.
These tests generally require long term data logging of pressure and flow. Although