Ch. 32] GRAIN SIZE 605 



high vertical permeability. Among these are the Smackover pools of 

 Arkansas, where water is being injected at a point lower than the 

 lowest oil saturation. The water is apparently advancing upward from 

 under the oil in the center of the pool, as well as laterally from the 

 margins (Horner and Snow, 1943). 



Permeability may also vary in different directions in a horizontal 

 plane parallel to the bedding. When gas is injected into a well in order 

 to maintain pressure in a reservoir, it usually appears in greater quan- 

 tity in one offset well than in the others. Often it may skip the off- 

 set wells and appear at a well two or three locations distant. Even 

 small core samples may exhibit perferential permeability in one direc- 

 tion (Johnson and Hughes, 1948) . 



Geain Size 



Slichter showed that porosity is independent of the actual size of the 

 grains but dependent on the uniformity of grain size and the manner 

 of packing. Tickell, Mechem, and McCurdy (1933) investigated the 

 effect of uniformity of grain size on porosity. The porosity decreased 

 as the number of different sizes of particles increased. These authors 

 also investigated the effect of angularity of the particles. 



Slichter believed, on theoretical grounds, that the permeability should 

 increase with the square of the grain diameter. Muskat (1937) and 

 later Hubbert (1940) showed that the constant of proportionality in 

 Darcy's law includes a size factor d 2 that expresses the pore diameter, 

 which should be related to the grain diameter for unconsolidated sands. 

 Natural sandstones, however, contain a wide range of grain sizes, and 

 some mathematical method of expressing the distribution of grain sizes 

 must be employed. 



Krumbein (1938) suggested that the diameter of the particles be ex- 

 pressed logarithmically in "phi" units, where </> = — log 2 |, and | is the 

 diameter of the particle in millimeters. When the grain diameter is 

 expressed in phi units, the grain-size distribution of natural sands can 

 be plotted as a frequency curve which has the attributes of the normal 

 Gaussian curve of mathematical statistics. From such curves the 

 "mean" or center of gravity of the distribution, and the "standard 

 deviation," which expresses the range of particle sizes, can be deter- 

 mined. The standard deviation is the spread in diameters, expressed 

 by Krumbein in phi units, within which 68.2 percent of the particles 

 fall. Otto (1939) adapted logarithmic probability paper for plotting 

 grain-size distribution curves and developed graphical methods of ob- 

 taining the statistical parameters. 



Krumbein and Monk (1942) investigated the effect of grain size and 



