Capillary Pressure & Saturation-Height
How the curved interface between oil and water in a pore creates a pressure jump - and a transition zone above the free-water level.
Why does oil float above water in a reservoir, with a fuzzy transition zone between them? The answer is capillary pressure.
Capillary Pressure in a Pore
At a curved oil-water interface inside a pore, the pressure is not the same on both sides. Capillary pressure is that pressure difference, $P_c$, defined as the pressure in the non-wetting phase minus the pressure in the wetting phase. In a water-wet oil-water system oil is the non-wetting phase, so $P_c$ is positive. For an idealized cylindrical pore throat of radius $r$, the Young-Laplace result gives $P_c = 2\sigma\cos\theta / r$, where $\sigma$ is the oil-water interfacial tension and $\theta$ is the contact angle. The key dependence is on $r$: smaller pores have higher capillary pressure, which is why capillary forces dominate in tight rock.
Drainage, Imbibition, and Hysteresis
Saturation changes by two opposite processes. In drainage, the non-wetting phase (oil) displaces the wetting phase (water) - saturation moves toward lower water saturation, and capillary pressure rises. In imbibition, the wetting phase (water) spontaneously displaces oil, and capillary pressure falls. The two paths do not retrace each other: the $P_c$-versus-saturation curve traced during drainage sits above the one traced during imbibition. This path dependence is called hysteresis, and it means a rock's capillary behaviour depends on its saturation history.
Capillary pressure has a height equivalent. Balancing capillary pressure against the density contrast between water and oil gives the saturation-height relation $h = P_c/(\Delta\rho\, g)$, where $\Delta\rho$ is the water-minus-oil density contrast and $g$ is gravity. It says how far above the free-water level a given capillary pressure lifts the oil-water interface - and so it defines the transition zone, the interval over which water saturation grades from 100% toward connate. To compare capillary pressures across rocks of different porosity and permeability, the Leverett J-function normalises $P_c$ into a dimensionless curve - a standard way to average capillary-pressure data across a field.
- (a) Capillary pressure: $P_c = 2\sigma\cos\theta/r = 2 \times 0.025 \times 1 / (5 \times 10^{-6})$.
- Numerator: $2 \times 0.025 \times 1 = 0.05$.
- Divide: $P_c = 0.05 / (5 \times 10^{-6}) = 10000$ Pa $= 10$ kPa.
- (b) Saturation-height: $h = P_c/(\Delta\rho\, g) = 20000/(200 \times 9.81)$.
- Denominator: $200 \times 9.81 = 1962$.
- Divide: $h = 20000/1962 = 10.2$ m above the free-water level.
Check your understanding
- Capillary pressure is the pressure jump across a curved oil-water interface: $P_c = 2\sigma\cos\theta/r$, so smaller pores mean higher $P_c$.
- Drainage (oil entering) and imbibition (water entering) trace a hysteresis loop - the curve depends on saturation history.
- Saturation-height $h = P_c/(\Delta\rho\, g)$ places the transition zone above the free-water level; the Leverett J-function averages $P_c$ across a field.