Capillary Pressure: The Physics

Water Clings to the Rock

A reservoir is not a bucket with a flat oil-water line. Water clings to the rock by capillarity, and the finer the pore the higher it clings. The force lives in the curved oil-water interface inside a pore throat, and the Young-Laplace law gives the pressure jump across it:

the interfacial tension $\sigma$ and the wettability $\cos\theta$ over the throat radius $r$.

An Inverse Measure of Pore Size

The radius in the denominator is the whole story: capillary pressure is an inverse measure of pore size. Small throats pull hard and lift water high; big throats barely pull and let it drain. The bundle of tubes makes it visible, the thinnest bore raising the tallest column, because each tube lifts water to the height where the capillary pull just balances the buoyancy of the column it holds up.

From Tubes to a Reservoir

A rock is exactly that bundle, a mix of throat sizes side by side. Its fine pores hold water far above the free-water level while its coarse pores drain near it, so the saturation does not jump from oil to water at a line, it grades over a tall transition zone. Weakening the interfacial tension or tilting the contact angle toward 90 degrees, toward a less water-wet rock, drops every column together and shrinks that zone. The next sections turn this physics into the capillary-pressure curve and the saturation-height model that place water in the reservoir.

References

• Leverett, M. C. (1941). Capillary behavior in porous solids. Transactions of the AIME, 142(1).
• Tiab, D. and Donaldson, E. C. (2015). Petrophysics, 4th ed. Gulf Professional Publishing.