Capillary pressure during immiscible displacement

Experiments performed on the immiscible displacement of heptane and mineral oil by water in capillary tubing showed that capillary pressure during drainage and imbibition were constant over a range of velocities from 10(-4) to 10(-2) m/s. The results obtained were quite different from the equilibrium capillary pressure. The drainage capillary pressure was lower than its equilibrium value by 25% for heptane, and higher by 10% for mineral oil. In the case of imbibition, the capillary pressure for both oils was lower than their respective equilibrium value. Due to the limitation of the apparatus, velocities lower than 10(-4) m/s could not be measured. It is, therefore, not clear if capillary pressure during flow would, in fact, reduce to its equilibrium value at low enough velocities. While it is quite adequate to describe the capillary behaviour of two fluids inside a tubing by a single number, one needs to consider capillary pressure as a function of the wetting fluid saturation in the porous medium. The problem of considering the effect of flow on this function is going to be more complicated than the single capillary tubing case. The present result indicates that it is inconsistent to use capillary pressure determined from equilibrium conditions and apply it to flowing conditions.