Ch. 32] CAPILLARY PROPERTIES 593 



the proportions of the fluids present. There is a difference in pressure 

 between the fluids across this interface; it is usually termed the capil- 

 lary pressure at a particular saturation of the wetting phase. The pres- 

 sure is sustained by the tension in the surfaces and therefore depends on 

 both the interfacial tension and the curvature. It can be expressed 

 mathematically as 



Pc = y 



(hk) 



where P c is the capillary pressure, y the interfacial tension, and Ri 

 and R 2 the principal radii of curvature of the surface. When Ri and 

 R 2 are very nearly equal, the equation for capillary pressure can be 

 written 



r -* 



c R 3 



where R3 is the average of Ri and R 2 . It should be noted that these 

 equations do not assume the porous medium to be a bundle of capillary 

 tubes. For a capillary tube, 



27 cos 6 



P c = 



Ra 



where R± is the radius of the tube and is the contact angle in the wetting 

 phase. In this case the average radius of' curvature would be 



R± 



cos 6 



Capillary pressure is a function of saturation of the fluid phases 

 occupying the interstices of a porous medium. To demonstrate this 

 fact, an experiment may be performed: A porous sample of rock is 

 first completely saturated with brine (the wetting phase) and placed 

 in a cell in contact with a porcelain or cellophane barrier which is 

 permeable to brine but not to gas or oil (non-wetting phases) . Such 

 a cell is shown in Fig. 5. The space surrounding the core is then filled 

 with oil or gas. When pressure is applied to the oil or gas, it is forced 

 into the porous sample, and brine is forced out through the semi- 

 permeable barrier. The difference in pressure across this barrier, which 

 is the same as that across the interface between the two fluid phases 

 in the sample, is the capillary pressure. When plotted against the 

 saturation of the wetting phase, it normally provides a curve similar to 

 that shown in Fig. 6. 



