Abstract
A simple, unsteady-state apparatus and appropriate theory have been developed for measuring the Klinkenberg permeability, Klinkenberg slip factor, and Forchheimer turbulence factor of core plugs. The technique is last and accurate and bas replaced nearly all steady-state gas permeability determinations made in our laboratory. The theory of operation, capabilities and limitations of the apparatus are discussed. New data are presented for more than 100 cores, correlating slip and turbulence factor vs permeability.
Introduction
Permeability is usually measured with air at mean pressures just above 1 atm. This steady-state determination is rapid, but it can lead to serious errors. For example, the low-pressure air permeability of tight core often differs from its permeability of tight core often differs from its permeability to liquid or high-pressure gas by 30 permeability to liquid or high-pressure gas by 30 to 100 percent or more. Correction factors (Klinkenberg slip factors) from correlations are available, but still, the corrected, low-pressure measurement can exhibit considerable error.
These errors are avoided by determining gas permeabilities at two or three mean pressures such permeabilities at two or three mean pressures such as 25, 50 and 100 psi, and then extrapolating to infinite pressure to obtain the equivalent liquid or Klinkenberg permeability. This method is generally reliable, but has two drawbacks it requires tedious rate measurements with a soap bubbler or other device, and the back-pressured flow system requires several minutes to reach steady state. Typical throughputs are 8 to 12 cores per day.
The desire to estimate accurately the injectivity into secondary and tertiary oil recovery prospects and to find the deliverability of very tight gas reservoirs has created a growing demand for reliable Klinkenberg permeability determinations in our laboratory. This demand made clear the need for a more rapid, yet accurate permeameter. On the premise that pressure measurements are made more premise that pressure measurements are made more conveniently and accurately than rate determinations, we developed a permeameter in which both rate and pressure drop across a core can be derived from pressure drop across a core can be derived from pressure measurements alone. The resulting pressure measurements alone. The resulting unsteady-state instrument is fast and accurate.
Transient permeability techniques have been discussed and other unsteady-state permeameters have been built and reported, but to our knowledge the instrument described herein is the only practical one for routine measurement of Klinkenberg permeability that does not require an empirical permeability that does not require an empirical correlation using cores of known permeability to construct calibration curves. It is also the only one from which Klinkenberg permeability, Klinkenberg slip factor and Forchheimer turbulence factor can be determined from a single run.
THEORY OF OPERATION
Fig. 1 shows the essentials of the unsteady-state permeameter. It consists of a tank and pressure permeameter. It consists of a tank and pressure transducer that can be pressurized with nitrogen. A core holder is attached to the tank, separated by a quick opening valve. To perform a run, the tank is charged with nitrogen to an initial pressure of about 100 psig. If the valve at the bottom of the tank is opened, nitrogen will flow through the core and the pressure in the tank will decline as illustrated in the inset of Fig. 1 rapidly at first, then more and more slowly. The volumetric rate of nitrogen flow at the inlet face of be core, qo(t) can be derived (see Appendix A) from the ideal gas law, since the compressibility factor (deviation factor) is unity for nitrogen at low pressure and room temperature. The volumetric flow rate at any position, x, downstream from the inlet face of the position, x, downstream from the inlet face of the core, at time t, is (Eq. A-30):
.............................(1)
where delta and f(c, g) axe correction factors that account for variable mass flow rate with position at any instant in time. The constant delta is given by:(2)
from Eq. 2, delta is equal to two-thirds of the ratio of the pore volume of the core to the volume of the tank. Normally it is a small correction.
SPEJ
P. 383
Particularities of Membrane Gas Separation Under Unsteady State Conditions
