petrophysics · rock physics
Height Above Free Water Level
h = Pc / (Δρ × 9.80665) where Δρ = ρ_w − ρ_HC [Pc in kPa, ρ in g/cc, h in m]
click formula to derive ↑
Inputs
psi
g/cc
g/cc
Description
Converts capillary pressure (Pc) measured on a core sample to the equivalent height above the free water level (FWL) in the reservoir, using the buoyancy pressure balance between formation water and the hydrocarbon phase. Used to translate laboratory Pc data into a fluid-contact depth scale for reservoir characterization.
Variables
| Symbol | Unit | Description |
|---|---|---|
| h | ft | Height above free water level |
| Pc | psi | Capillary pressure from a Pc measurement at the saturation of interest — typically from a mercury-injection or porous-plate experiment, converted to reservoir fluid conditions before entry. |
| ρ_water | g/cc | Density of the formation water at reservoir conditions. Typical range: 1.00 g/cc (fresh water) to 1.20 g/cc (saturated NaCl brine). Use reservoir-condition density, not surface density. |
| ρ_HC | g/cc | Density of the hydrocarbon phase at reservoir temperature and pressure. Light oil: 0.60–0.80 g/cc; heavy oil: 0.85–0.95 g/cc; gas condensate: 0.30–0.55 g/cc; dry gas at depth: 0.10–0.35 g/cc. |
Assumptions
- The capillary pressure curve was measured under reservoir-equivalent wettability and fluid-pair conditions, or has been converted from mercury-air measurements using appropriate conversion factors (σ·cosθ ratios).
- Fluid densities are representative of reservoir conditions (in-situ temperature and pressure), not surface conditions.
- The reservoir is in capillary-gravity equilibrium; transient effects (e.g., during filling or depletion) are not captured.
- Gravity is taken as the standard value 9.80665 m/s²; variations with latitude are negligible for petroleum engineering purposes.
Limitations
- The free water level (FWL) is not the same as the oil-water contact (OWC) or gas-water contact (GWC) observed on logs; the contact is where hydrocarbon saturation first exceeds the detection threshold, which is above the FWL by the capillary entry pressure height.
- Laboratory Pc data must be converted to reservoir conditions using the ratio (σ_res × cosθ_res) / (σ_lab × cosθ_lab) before applying this equation; omitting this correction introduces systematic error.
- Gas density at reservoir conditions is significantly pressure- and temperature-dependent; use PVT-derived in-situ gas density, not surface gas density.
- Does not account for hysteresis between drainage and imbibition Pc curves; drainage curve is appropriate for primary migration, imbibition for waterflooding.
Use Cases
- → Height-saturation from Pc curves: Convert a mercury-injection or porous-plate Pc curve to a water-HC height-saturation function for a reservoir interval, for input to volumetric Sw modeling.
- → FWL from OWC and entry pressure: Establish free water level (FWL) depth: OWC depth + height at capillary entry pressure. The FWL is always deeper than the log-observed OWC by the entry height.
- → Seal capacity analysis: Estimate maximum hydrocarbon column height that a top seal can support from its Pc breakthrough pressure — used in trap risk assessment and migration modeling.
- → Sw-height functions for volumetrics: Build Sw-height functions for reserve volumetrics in uncored wells when no formation tester (RFT/MDT) data are available to constrain the fluid contact depth.
Related Calculations
Region Notes
Global
The capillary-height equation is universal. The primary regional variable is the hydrocarbon density at reservoir conditions: gas condensate ρ ≈ 0.2–0.5 g/cc; light oil 0.5–0.75 g/cc; heavy oil 0.85–0.95 g/cc. Using the wrong phase density is the most common source of error.
North Sea (chalk)
Ekofisk chalk: very high Pc due to micro-pore throat size; Pc > 1000 kPa at Sw = 0.20, giving height columns of 500–800 m for brine/oil Δρ ≈ 0.20 g/cc. FWL can be 100+ m below the OWC in the same chalk unit.
Gulf of Mexico (deepwater)
GOM turbidite sands: high permeability, low Pc (< 20 kPa at Sw = 0.25). FWL is close to the observed OWC (within 5–15 m). Use in-situ gas density for gas reservoirs — at 70 MPa / 140°C, gas density is 0.35–0.50 g/cc.
Middle East (carbonates)
Arab Formation carbonates: complex pore systems with vuggy, interparticle, and microporosity. Pc curves from plugs may not represent reservoir-scale behavior. Regional Pc averaging using J-function normalization is standard practice.
References
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