The difference between phase pressures due to difference in fluids interaction with rock matrix:
 

Capillary pressure is a function of reservoir saturation, permeability and wettability.
One of the strong assumptions in reservoir fluid dynamic modelling is that 3phase capillary pressure is a function of one saturation only:

 


Mathematical model of capillary pressure is given by interpolation of laboratory data and also by a number of physical and empirical capillary pressure correlations
See also
Physics / Fluid Dynamics / Percolation
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Field Study & Modelling