The Saturation-Height Model

Part 11, Chapter 11: Capillary Pressure and Saturation-Height

Learning objectives

Write the Brooks-Corey saturation-height function Sw(h)
Explain how rock quality sets the transition-zone height
Read the oil-water contact as the entry-pressure height per rock
Use Sw(h) to fill water saturation away from well control

From a Curve to a Field Model

The J-function gave one master curve; combined with each rock's permeability and porosity it predicts a different saturation-height curve per rock. That curve is the deliverable of the whole chapter: a function that fills water saturation into every cell of a reservoir model, far from any well, from the height above the free-water level alone, with capillary pressure standing in for that height,

S_w(h) = S_{wi} + (1-S_{wi})\left(\frac{P_c}{P_e}\right)^{-\lambda}, \quad P_c = 0.433\,(\rho_w - \rho_{hc})\,h.

Rock Quality Sets the Height

The same three rocks draw three very different profiles. The good rock's oil-water contact sits just above the free-water level, and it drains to irreducible within tens of feet. The poor rock's contact is over a hundred feet up, because its high entry pressure must be beaten before oil enters at all, and from there it bleeds down a long ramp that holds high water saturation for hundreds of feet. At the same height above the free-water level, the poor rock can be nearly all water while the good rock is already dry. Rock quality, not just height, sets the saturation.

Why It Matters

Between wells the model has no resistivity to run Archie on, only structure and rock type. The saturation-height function is how the chapter's laboratory and log work reaches those cells: one $S_w(h)$ per rock type, applied by height. It also resolves a classic field puzzle, two wells at the same depth with very different water cuts, when one sits in clean rock and the other in tight rock. The next section calibrates this model against the Ogbon-1 well and lays it beside the Archie saturation the logs give directly.

References

Worthington, P. F. (2002). Application of saturation-height functions in integrated reservoir description. Geological Society Special Publication, 215.
Harrison, B. and Jing, X. D. (2001). Saturation height methods and their impact on volumetric hydrocarbon in place estimates. SPE Annual Technical Conference, SPE 71326.