Klinkenberg Effect

LINK LINKEN ENBE BERG RG EF EFFE FECT CT ACKGROUND There is a difference between the flow of a gas and a liquid through a reservoir. This defiantly affecting the measurement of absolute permeability. As gas flow is less impeded by grain surfaces than liquid flow. Thus, this effect of gas flow being less impeded than liquid flow is considered to be a KLINKENBERG KLINKENBERG EFFECT.

NTRODUCTION The difference between gas and water permeabilities is significant not only for solving gas-water two-phase flow problems, but also for quick  measurements of permeability using gas as pore fluid. The observed difference in gas and water permeabilities has been analyzed in view of the KLINKENBERG EFFECT. The flow of gas through porous p orous media was investigated by Klinkenberg (1941).

XPLANATION “When the mean free path of the measuring gas is greater than the diameter of the capillary (pores) through which it is traveling, the rando m kinetic energy of the gas is transferred to movement of the gas molecule through the capillary or slippage of the molecules occur at the pore walls. This slippage causes the molecules of the gas to travel at a higher velocity in the direction of transfer”. This phenomenon, known as the “KLINKENBERG EFFECT,” causes the measured permeability of a gas to be greater than the absolute  permeability of the sample. This effect is due to slip flow of gas at pore walls which enhances gas flow when pore sizes are very small. Experimental results show (1) that gas  permeability is larger than water w ater permeability, (2) that gas permeability increases with increasing pore pressure, and (3) that water permeability slightly increases with increasing pore-pressure gradient across the specimen. The results (1) and (2) can be explained by Klinkenberg effect quantitatively with an empirical power  law for Klinkenberg constant. Thus water wa ter permeability can be estimated from gas  permeability. The Klinkenberg effect is important when permeability is lower  than 10-18 m2 and at low differential pore pressures , and its correction is essential for estimating water permeability from the measurement of gas  permeability.

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Air permeabilities measured in a routine core analysis laboratory on rock  samples from nonfractured reservoirs will give higher values than the actual reservoir   permeability. This difference is dependent upon the magnitude of permeability as well as the pore geometry. The higher laboratory values are thought to be caused by gas slippage (the Klinkenberg effect), relative permeability, reactive fluids, and overburden pressure effects.

The flow of gas through porous media was investigated by Klinkenberg (1941). He found that the permeability of a core sample was not constant, but varied with the gas used to make the measurement, as well as the mean (average) pressure existing in the core at the time of measurement. His investigations indicated that at low mean  pressures-for example, at atmospheric pressure-the gas molecules are so far apart that they slip through the pore spaces with little friction loss, and yield a higher value of   permeability. At higher mean pressures — for example, 1000 psi (6895 kPa) or greater —  the gas molecules are closer together and experience a friction drag at the side of the pore walls. This increases as higher mean pressure increases, with the gas acting more and more like a liquid. This means that the measured value of permeability decreases as reservoir or laboratory mean pressure increases.

XPERIMENTAL VERIFICATION Experiments show that a plot of gas permeability versus the reciprocal mean pressure existing at the time of the gas permeability measurement forms a straight line that can be extrapolated to infinite mean pressure (Figure 5.7). This extrapolated value of permeability, referred to as the Klinkenberg permeability or equivalent liquid   permeability , is lower than the measured gas permeabilities and is comparable to the  permeability that would be obtained if the core were saturated with a nonreactive liquid such as oil. Figure 5.10 (Klinkenberg permeability determination) shows an example of  this relationship for low permeability reservoir.

The Klinkenberg value (kL) can be correlated with the value of   permeability determined with air at the mean pressure normally used in the laboratory measurements. Table 1, below, offers examples of the relationship be tween the air   permeability and Klinkenberg-corrected values for sandstones. The c orrection, on a  percentage basis, is greater in low permeability sand and becomes progressively smaller  as permeability value increases.

Noncorrected permeability (md)

Klinkenberg corrected permeability* (md)

1.0

0.7

10.0

7.8

100.0

88.0

1000.0

950.0

*Air permeability that has been corrected for gas slippage. The Klinkenberg value is the equivalent liquid permeability assuming no reaction between the rock and the fluid. Table 1. A comparison of noncorrected and Klinkenberg-corrected air permeability for some  sandstones.

The table represents the results of laboratory measurements on a suite of  core samples that covered a wide range of air permeabilities. In early core analysis reports, measured air permeability was corrected to the Klinkenberg permeability value, using correlations such as those presented in Table 1. above. In early core analysis the Klinkenberg permeability was estimated by using the following correlation’s;

Where km and kL are the measured- and the absolute (liquid) permeability, respectively. The parameter b depends on the type of gas used and reflects, to some extent, properties of the rock. NOTE: In most laboratory measurements of gas permeability, it is safe to neglect the Klinkenberg effect if the gas pressure is higher than 10 bar. In reservoirs, the  pressure will be much higher and consequently the significance of the Klinkenberg effect of no importance.