Ch. 32] SURFACE AREA 601 



Through the use of this ; function, it is easy to study the effect of 

 variations in interfacial tension, contact angle, permeability, and poros- 

 ity on the capillary pressure-saturation curve, as shown in Fig. 9. In 

 making this diagram, these authors have kept all the parameters in the 

 j function constant, except one which was allowed to vary. 



Surface Area 



In any review of porosity, permeability, and capillarity, it is neces- 

 sary to treat the subject of interstitial surface area, or, in other words, 

 the exposed surface of the void space in the porous medium. Accord- 

 ing to Carman (1937, 1948) and Kozeny (1927), this interstitial surface 

 area is related to porosity and permeability by the equation 



/ 3 

 K = 



k A< 



where K is permeability, / the fractional porosity, A the specific inter- 

 stitial surface area (that is, the interstitial surface area per unit of 

 bulk volume), and k is a constant depending on the packing of the 

 material and the tortuosity of the pores. For unconsolidated sand 

 beds of very nearly spherical particles, k is about 5. For a bundle of 

 uniform-sized capillary tubes, k is equal to 2. The Kozeny-Carman 

 equation has been tested experimentally for unconsolidated media. 

 Carman (1941) gives the conditions under which this law is valid. 

 In summary, they are: (a) no pores are sealed off; (b) pores are dis- 

 tributed at random; (c) pores are reasonably uniform in size; (d) 

 porosity is not too high; (e) diffusion and surface effects are absent. 



Some discussion of these conditions is warranted. Condition (a) 

 is obvious as sealed-off pores do not contribute surface area for fluid 

 flow but are part of the total porosity of the medium. In this case, 

 however, an approximation to the above law can be written as 



(/ - /o) 3 

 K. = 



k (A - A y 



where / is the porosity associated with the sealed-off pores and A is 

 the specific surface area associated with the sealed-off pore space. 

 With regard to condition (6) it is quite possible that the law may be 

 inapplicable to stratified materials such as sandstone, which exhibits 

 a permeability anisotropy ; that is, it has a greater permeability parallel 

 to the bedding plane than across it. As a practical example, many 



