590 russell-dickey. POROSITY AND PERMEABILITY [Ch. 32 



Klinkenberg (1941) observed that the permeability of a core to gas 

 is greater than the permeability of the same core to a liquid, and that 

 the gas permeability is a linear function of the reciprocal of the ab- 

 solute pressure of the gas flowing through the core. When this curve 

 is extrapolated to infinite gas pressure, the gas permeability is the 

 same as the liquid permeability. With the above apparatus it is pos- 

 sible to measure this Klinkenberg effect and make the necessary cor- 

 rection to the gas permeability to compute the liquid permeability. 



Calhoun and Yuster (1946) made further studies of this phenomenon. 

 They conclude that gaseous permeability is dependent on the mean 

 pressure during flow but is independent of the pressure differential. 

 Although the permeability for different gases was found to be different, 

 all values have been extrapolated to one common permeability at an 

 infinite mean pressure. This permeability was found to be essentially 

 the same as that for liquid flow. No variation of permeability with 

 temperature and surface tension was noted. 



Calhoun and Yuster also observed an anomaly of liquid flow oc- 

 curring when ordinary salt solutions were employed or when standard 

 buffer solutions were employed. With the ordinary salt solutions, an 

 increase of permeability was noted up to a concentration of 1 N NaCl. 

 With the buffer, an increase of permeability was observed on each 

 side of the neutral point (pH 7) . This ionic effect was also supported 

 by the results of Grunberg and Nissan (1943), but it is still not very 

 well understood. It is, however, believed to be associated with some 

 sort of electrokinetic phenomenon. 



In such limited space, it is not possible to treat porosity and perme- 

 ability very completely. A more comprehensive treatment, together 

 with an analysis of Darcy's law, is given by Muskat (1937) and re- 

 viewed by Hubbert (1940). From the microscopic viewpoint, one of 

 the best studies is by Carman (1937). 



Relative Permeability 



The above discussion of permeability applies when only one fluid 

 occupies the interstices of the porous medium. When two or more 

 fluids are present in the porous medium, the effective permeability of 

 the core to one fluid is a function of the saturation of the fluids in the 

 pores. Relative permeability may be defined as follows: If fluids A 

 and B occupy the pores in a rock, the effective permeability of the 

 rock to fluid A, divided by the total or absolute permeability of the 

 rock when only one fluid fills the pore spaces, is the relative perme- 

 ability of the rock to fluid A at this particular saturation of A. The 



