Ch. 32] 



RELATIVE PERMEABILITY 



591 



relative permeability of the rock to fluid B may be defined in a similar 

 manner. 



Botset (1940) measured the relative permeabilities of both uncon- 

 solidated and consolidated sand to gas and to liquid. His experimental 

 curves are shown in Fig. 4. The solid lines refer to the consolidated 

 Nichols Buff sandstone, and the dotted lines refer to unconsolidated 

 sand (permeability 17.8 darcys). For both of these porous media 

 the saturation of gas at which gas first starts to flow is at 10 percent. 



100 



£80 



60 



•40 



20 



20 40 60 80 



Percent liquid saturation 



100 



Fig. 4. Permeability-saturation curves. (After Botset, 1940, p. 94.) 



This is defined as the equilibrium gas saturation. From 90 to 100 

 percent liquid saturation, the gas phase is probably present as bubbles 

 which are certainly not continuous. Flow of gas does not occur until 

 the gas phase assumes a continuity. When this occurs and a pressure 

 gradient develops in the gas phase, flow occurs. In this experiment, it 

 is very probable that the liquid or the wetting phase occupies first and 

 then flows through the smallest pores, whereas the gas tends to seek 

 first the larger pores. 



When three phases, gas, oil, and water, occupy the pores in a rock, 

 the situation with regard to relative permeability is still more com- 

 plicated. This was experimentally treated by Leverett and Lewis 

 (1941) for unconsolidated sand. These investigators conclude that, 

 for this system, the relative permeability to water is determined by the 

 water saturation alone and is not affected by the introduction of an 

 additional non-aqueous phase. The relative permeability to gas in 

 three-phase flow is slightly less than would correspond to the same gas 

 saturation in two-phase flow. The relative permeability to oil varies 

 in a more complex manner, being in some regions less and in others 



