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



ing a pressure difference between two points in the same non-wetting phase, 

 involves the difference in curvature between two phase boundaries (opposed 

 meniscuses) and only two wherever, as with real materials, a droplet or bubble 

 of one fluid cannot stop by complete plugging the tendency of a second fluid 

 to relieve pressure differences caused by the plug [Hassler, 1943]. 



Welge (1948) took cores from a petroleum reservoir, restored them 

 to their natural state by the above drainage-displacement technique, 

 and then attempted to produce the oil from these cores by displacing 

 the oil by brine from below or gas from above. The semi-permeable- 

 barrier technique is again used in the displacement of the oil from the 

 restored cores, but in this instance the porcelain plate is made oil- 

 wet by treating it with silicones. 



The Capillary Retention Function 



Leverett (1941) found that when the dimensionless function 



Apgh [R 



7 V/ 



is plotted vs. the saturation S w of the wetting phase in four clean sands, 

 the data fall satisfactorily near two curves, one for the imbibition of 

 water and the other for drainage. K is the permeability of the sand 

 to a homogeneous fluid, / the porosity, y the interfacial tension, g the 

 gravitational constant, h the height above a free-water surface, A P 

 the difference in density between the two fluid phases. Rose and Bruce 

 (1949) treat the subject in greater detail and develop the capillary 

 pressure or j function, which is 



P c [k 



j(S w ) = - 



7 cos \ / 



where 9 is the contact angle which the wetting fluid makes with the 

 rock surface. With gas-liquid systems of the usual type, the liquid 

 almost completely wets the rock interstitial surface; hence cos 6 is very 

 nearly 1. 



The term j{S w ) denotes a dimensionless function that varies with the 

 water saturation. P c is the capillary pressure at the same water satura- 

 tion. It is found experimentally that the plot of j(S w ) vs. S w is very 

 nearly the same for two samples of the same kind of rock, even though 

 the porosity and permeability may differ. The curves shown in Fig. 

 8 each apply to several samples of different permeability and porosity. 

 Thus the "Hawkins" curve applies to several different samples of 



