# 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)