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



samples of oil sand contain parallel shale streaks. The permeability- 

 parallel to these streaks is often many times that perpendicular to these 

 streaks. On an experimental or laboratory scale it is often possible 

 to choose the size and boundaries of the system so as to minimize 

 this effect. The sample might be chosen so small as to eliminate the 

 shale streaks or so large that the streaks that cause heterogeneity 

 give rise to a statistical homogeneity. In other words, the sample may 

 be so heterogeneous that it behaves statistically as a homogeneous sys- 

 tem. 



Condition (c), of course, refers also to a statistical average. For a 

 porous medium containing a mixture of large and small pores, more 

 or less equivalent to large and small capillaries in parallel, there exists 

 a higher permeability than if the same porosity is distributed uni- 

 formly. The average pore size obtained from flow calculations is really 

 nearer the size of the larger pores than the true average. Carman 

 states that a very wide range of pore sizes in an unconsolidated bed 

 makes it difficult to avoid segregation into layers of different size dis- 

 tribution. Segregation is merely non-random distribution, and in a 

 consolidated medium it would tend to cause a high permeability in a 

 direction parallel to the stratification. 



The Kozeny-Carman equation breaks down when the porosity / is 

 greater than 0.8. This effect was studied extensively by Sullivan 

 (1941) for fibers. He shows that k ceases to be constant but increases 

 rapidly with / at high porosities. It is thus probable that the law does 

 not hold in a clay containing as much as 75 percent water. Such a 

 system also affects condition (e). In this case it is probable that a 

 portion of the pore water is stationary, that is, chemically bound to 

 the clay surface. In fact, the actual surface over which fluid flow 

 takes place is difficult to ascertain. 



The problem of capillary rise in a porous medium was also treated 

 by Carman (1941) . For a capillary tube, or a bundle of uniform-sized 

 capillaries, the height of capillary rise h is 



2t cos 6 



h = 



rgp 



where y is the surface tension, r the radius of the capillary, $ the contact 

 angle, g the gravitational constant, and p the density of the liquid rising 

 in the capillary system. In non-circular capillaries and in porous 

 media, r is sometimes replaced by 2m, the quantity m being the mean 

 hydraulic radius: 



