Capillary Transition Zone Profile

Compute water saturation as a function of height above the free water level using Brooks-Corey capillary pressure. Essential for initializing reservoir simulation models and estimating OOIP in the transition zone.

Hydrostatic equilibrium. At any height h above the FWL, the capillary pressure equals the hydrostatic pressure difference between water and oil columns: Pc = 0.433 × (ρw − ρo) × h [psi]. The 0.433 factor converts from [ft × g/cc] to [psi]. This assumes static conditions (no flow) and immiscible fluids.

Entry height. Below the entry height (h < Pd/gradient), capillary pressure is insufficient to displace water from the largest pores. The rock remains 100% water-saturated. Above the entry height, water saturation decreases continuously following the Brooks-Corey relationship until reaching Swi at very large heights.

Brooks-Corey parameters. λ controls the shape of the transition: higher λ (more uniform pore size) gives a sharper transition; lower λ (heterogeneous pores) gives a more gradual transition. Pd depends on permeability and pore throat size — higher-k rock has lower Pd and thinner transition zones.

OOIP in transition zone. Oil in place within the transition zone can be significant, especially in low-permeability or thick formations. Integrate So(h) × φ over the zone thickness to estimate transition-zone OOIP. This oil is partially mobile depending on where Sw sits relative to Swi + Sor.

Reference: Brooks, R.H. and Corey, A.T. (1966). "Properties of Porous Media Affecting Fluid Flow." J. Irrigation and Drainage Div., ASCE, 92(IR2): 61–88.

• Rock & Fluid Properties (rows 3–8): Brooks-Corey Pc parameters (Swi, Pd, λ) and fluid densities (ρw, ρo) at reservoir conditions. Default parameters represent a moderate-permeability sandstone with light oil.
• Computed Parameters (rows 10–12): Capillary pressure gradient = 0.433×(ρw−ρo) [psi/ft], entry height = Pd/gradient (height above FWL where desaturation begins), and Leverett scaling factor for reference.
• Saturation-Height Profile (rows 14–26): Height above FWL from 0 to 200 ft with emphasis on the transition zone region. Columns: height, Pc from hydrostatic equilibrium, Sw from Brooks-Corey inverse, and oil saturation So = 1−Sw. Below the entry height, Sw = 1 (fully water-saturated). Above, Sw decreases following the Brooks-Corey model toward Swi.