Capillary pressure is the pressure difference across the curved interface between two immiscible fluids in a pore. It controls how water and hydrocarbons are distributed above the free water level, how thick the transition zone is, how tall a column a seal can hold and how fluids are trapped during displacement. Laboratory data must be converted to reservoir fluids before use. This guide covers the physics, the measurement methods and the main applications, with recalculated examples.
Fluid properties, heights and rock properties in the worked examples are a synthetic teaching example.
1. Physics
Pc = Pnw − Pw = 2 σ cos θ / r
Pnw and Pw are the non-wetting and wetting phase pressures, σ the interfacial tension, θ the contact angle measured through the wetting phase and r the pore throat radius. Small throats, high tension and strong wetting give high capillary pressure. In oil-wet rock the roles of the phases are reversed and water must be forced into small pores.
For a related explanation, see our guide to Wettability in Petroleum Engineering.
| Wettability | Contact angle (approximate) | Behavior |
|---|---|---|
| Water-wet | 0 to 75° | Water occupies small pores and coats grains; spontaneous water imbibition |
| Intermediate | 75 to 105° | Little preference; small spontaneous imbibition of either phase |
| Oil-wet | 105 to 180° | Oil occupies small pores; water must be forced in |
Many reservoirs are mixed-wet, with oil-wet surfaces in the larger pores contacted by oil and water-wet surfaces in the smaller ones (Anderson, 1987).
2. Reading the curve
| Process | Reservoir analogy | Use |
|---|---|---|
| Primary drainage | Hydrocarbon migration into a water-filled trap | Initial saturation versus height |
| Spontaneous imbibition | Water entering at zero or positive Pc | Wettability indices (Amott) |
| Forced imbibition | Water forced in at negative Pc | Waterflood residual oil, wettability |
- Entry (displacement) pressure Pd: the pressure at which the non-wetting phase first enters a connected path of the largest throats; it sets the height of the oil-water contact above the free water level and the sealing capacity of cap rock.
- Plateau: a flat section indicates well-sorted, uniform throats; a sloping curve indicates a broad throat size distribution.
- Irreducible wetting phase saturation: the saturation that remains at high capillary pressure, higher in fine-grained and clay-rich rock.
3. Converting laboratory data
Pc,res = Pc,lab × (σ cos θ)res / (σ cos θ)lab
| System | σ (mN/m) | θ | σ cos θ (mN/m) |
|---|---|---|---|
| Mercury-air | 485 | 140° | 372 |
| Brine-air | 72 | 0° | 72 |
| Oil-water (reservoir) | 26 | 30° | 22.5 |
| Gas-water (reservoir) | 50 | 0° | 50 |
With these typical values, mercury-air capillary pressure is multiplied by 22.5 / 372 = 0.061 for oil-water and by 50 / 372 = 0.135 for gas-water; brine-air data are multiplied by 0.31 for oil-water. A mercury pressure of 1,000 psi corresponds to about 61 psi oil-water. The tension and contact angle should be measured or justified for the fluids in question.
4. Measurement methods
| Method | Advantages | Limitations |
|---|---|---|
| Mercury injection (MICP) | Very wide pressure range (to about 60,000 psia), fast, gives throat size distribution | Dry, cleaned samples; mercury-air system needs conversion; sample cannot be reused |
| Centrifuge | Reservoir fluids, drainage and imbibition, days rather than weeks | Saturation and pressure vary along the plug; interpretation methods needed; limited pressure range |
| Porous plate | Direct equilibrium saturations, reservoir fluids and stress possible | Slow (weeks to months), limited by plate entry pressure |
5. Applications
5.1 Saturation above the free water level
Pc (psi) = 0.433 (γw − γo) h (ft)
With specific gravities of 1.05 for water and 0.82 for oil, at 120 ft above the free water level Pc = 0.433 × 0.23 × 120 = 11.95 psi. Reading the converted drainage curve at this pressure gives the initial water saturation, for example 0.35. For a related explanation, see our guide to capillary pressure and saturation-height functions.
5.2 Free water level, contact and transition zone
The free water level is where Pc = 0. The oil-water contact, where oil saturation first appears, lies above it by the entry-pressure height Pd / (0.433 Δγ): for Pd = 2 psi this is 20 ft. The transition zone extends up to the height where saturation reaches its irreducible value: if that occurs at 35 psi, the zone is 35 / (0.433 × 0.23) = 351 ft thick, and wells completed within it can produce water from the start.
5.3 Seal capacity
hmax = Pd,seal,res / (0.433 (γw − γhc))
A shale with a mercury entry pressure of 5,000 psi has a gas-water entry pressure of about 5,000 × 0.135 = 673 psi. With water at 1.05 and gas at 0.25 specific gravity, the maximum gas column is 673 / (0.433 × 0.80) = 1,940 ft before the seal leaks capillarily.
5.4 Leverett J-function
J(Sw) = 0.2166 Pc / (σ cos θ) × √(k / φ) (Pc in psi, σ in dyn/cm, k in md)
For Pc = 11.95 psi, σ cos θ = 22.5 dyn/cm, k = 150 md and φ = 0.22, J = 0.2166 × 11.95 / 22.5 × √(150/0.22) = 3.0. Plugs whose J curves collapse together can share one function; plugs whose curves do not collapse belong to different rock types.
6. Common errors
| Error | Consequence | Prevention |
|---|---|---|
| Mercury data used without conversion | Capillary pressure overstated by more than ten times for oil-water | Convert with justified σ cos θ |
| Wettability altered by cleaning | Curves not representative of the reservoir | Preserved or restored-state samples and wettability tests |
| One curve for all rock types | Wrong saturation distribution and in-place volumes | Rock typing and separate functions |
| Free water level confused with the contact | Contacts misplaced in the model | Distinguish them by the entry-pressure height |
For a related explanation, see our guide to Understanding Capillary Pressure in Petroleum Engineering.
Key points
- Capillary pressure depends on tension, wettability and throat size.
- Convert laboratory capillary pressure to reservoir fluids before use.
- Height above the free water level gives initial saturation; entry pressure separates the contact from the free water level.
- Seal capacity and J-function normalization follow from the same relationships.
References
- M. C. Leverett, Capillary behavior in porous solids, Transactions of the AIME, 142 (1941) 152 to 169.
- W. G. Anderson, Wettability literature survey, Part 4: Effects of wettability on capillary pressure, Journal of Petroleum Technology, 39 (1987) 1283 to 1300.
- D. Tiab and E. C. Donaldson, Petrophysics, 4th ed., Gulf Professional Publishing, 2015.
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