Capillary pressure

In fluid statics, capillary pressure is the difference in pressure across the interface between two immiscible fluids, and thus defined as

$p_c=p_{\text{non-wetting phase}}-p_{\text{wetting phase}}$

In oil-water systems, water is typically the wetting phase, while for gas-oil systems, oil is typically the wetting phase.

The Young–Laplace equation states that this pressure difference is proportional to the interfacial tension, $\gamma$, and inversely proportional to the effective radius, $r$, of the interface, it also depends on the wetting angle, $\theta$, of the liquid on the surface of the capillary.

$p_c=\frac{2\gamma \cos \theta}{r}$

The equation for capillary pressure is only valid under capillary equilibrium, which means that there can not be any flowing phases.

In porous media

In porous media, capillary pressure is the force necessary to squeeze a hydrocarbon droplet through a pore throat (works against the interfacial tension between oil and water phases) and is higher for smaller pore diameter. The expression for the capillary pressure remains as before, i.e., $p_c=p_{\text{non-wetting phase}}-p_{\text{wetting phase.}}$ However, the quantities $p_c$, $p_{\text{non-wetting phase}}$ and $p_{\text{wetting phase}}$ are quantities that are obtained by averaging these quantities within the pore space of porous media either statistically or using the volume averaging method.^[1]

The Brooks-Corey correlation^[2] for capillary pressure reads

$p_c = cS_w^{-a}$

where $c$ is the entry capillary pressure, $1/a$ is the pore-size distribution index and $S_w$ is the normalized water saturation (see Relative permeability)

See also

• Capillary action
• Capillary number
• Disjoining pressure
• Leverett J-function
• Young–Laplace equation
• Amott test
• Laplace pressure

References

• Kim Kinoshita, Electrochemical Oxygen Technology p139, John Wiley & Sons, Inc. 1992.
• Capillary pressure equations

1. Jacob Bear: “Dynamics of Fluids in Porous Media,” Dover Publications, 1972.
2. Brooks, R.H. and Corey, A.T.: “Hydraulic properties of porous media,” Hydraulic paper no. 3, Colorado State University, 1964.