petrophysics · rock physics
Leverett J-Function
J = (Pc / (σ·cosθ)) × √(k/φ) [SI: Pc in Pa, σ in N/m, k in m²; dimensionless output]
click formula to derive ↑
Inputs
psi
mD
fraction
mN/m
°
Description
Computes the Leverett J-function — a dimensionless capillary pressure that normalizes Pc data across samples with different permeability and porosity. The J-function removes the pore-size dependence of Pc, allowing capillary pressure curves from different core plugs (or different fields with similar rock type) to be averaged onto a single J vs. Sw curve for use in reservoir modeling.
Variables
| Symbol | Unit | Description |
|---|---|---|
| J | — | J-function |
| Pc | psi | Capillary pressure at the saturation of interest, measured or converted to reservoir fluid conditions. For mercury-injection data, apply the mercury-to-reservoir fluid correction (σ·cosθ ratio) before entry. |
| k | mD | Air or Klinkenberg-corrected permeability measured on the same core plug as the Pc curve. Must come from the same sample as the Pc data for the normalization to be valid. |
| φ | fraction | Total or effective porosity of the same core plug used for the Pc measurement. Using a porosity from a different sample introduces error in the normalization. |
| σ | mN/m | Interfacial tension between the wetting and non-wetting phases at reservoir conditions. Typical values: water/oil 20–30 mN/m; water/gas 50–72 mN/m at surface; decreases with temperature and pressure. |
| θ | ° | Contact angle of the wetting phase against the rock surface. 0° = strongly water-wet (most laboratory drainage measurements); 30–60° = mixed-wet; use 0° as the default when wettability is unknown. |
Assumptions
- All samples being normalized belong to the same rock type (similar pore geometry and wettability); J-function normalization does not work across fundamentally different lithofacies.
- Interfacial tension σ and contact angle θ are representative of the wetting state of the samples (water-wet by default for most Pc measurements).
- Permeability k and porosity φ are measured on the same sample as the Pc curve, or are representative of the interval being described.
- The Kozeny-Carman pore-geometry analogy underlying Leverett's normalization holds for the rock type being analyzed; it works best in clean, granular sandstones.
Limitations
- J-function normalization fails for heterogeneous carbonates with multi-modal pore systems (vuggy + interparticle porosity); different pore types produce different J-Sw trends even at similar k and φ.
- Contact angle θ for reservoir rock under reservoir conditions is difficult to measure; typically assumed 0° (strongly water-wet) for primary drainage but may be 30–60° in mixed-wet or oil-wet systems, introducing uncertainty.
- For mercury-injection Pc data, σ = 480 mN/m and θ = 140° (mercury-air on rock) must be used — not reservoir fluid values. Convert to reservoir conditions using (σ_res·cosθ_res)/(σ_Hg·cosθ_Hg) after computing J.
- The square-root normalization assumes a single characteristic pore throat controls both k and Pc; dual-permeability or vuggy systems require alternative approaches.
Use Cases
- → Averaging Pc curves across plugs: Average Pc curves from multiple core plugs in the same facies onto a single representative J-Sw curve by normalizing for k and φ — the standard input for reservoir model Sw initialization.
- → Pc extrapolation to uncored wells: Extrapolate Pc behavior from cored wells to uncored wells using log-derived k and φ, enabling Sw-height modeling across the reservoir without requiring Pc measurements from every well.
- → Wettability comparison: Detect wettability changes between reservoir sections: a systematic upward or downward shift in J-Sw at the same Sw indicates a change in σ·cosθ (wettability alteration by oil contact).
- → FWL and Swirr determination: Define the free water level (J ≈ 0) and irreducible water saturation (J at plateau) from the J-Sw curve, providing the fluid contact depth and Swirr for reserve volumetrics.
Related Calculations
Region Notes
Global
Typical reservoir-condition σ values: water/oil ≈ 20–30 mN/m; water/gas ≈ 50–72 mN/m (depends on pressure, temperature, composition). Use σ = 72 mN/m (pure water/gas, surface conditions) only if no reservoir-condition measurement is available. Contact angle 0° is a common default for primary drainage in water-wet systems.
Middle East (carbonates)
Arab Formation and Mishrif carbonates: J-function normalization often fails across vuggy and interparticle pore types. Standard practice is to split the Pc dataset by rock type (using FZI or RQI) before computing J for each sub-population.
North Sea (Brent Group)
Tarbert and Etive sandstones: well-sorted, water-wet quartzose sands respond well to J-function normalization. Published J-Sw curves from Dake (1978) and Archer & Wall (1986) provide baseline values for k = 10–1000 mD.
Permian Basin
Wolfcamp and Bone Spring: micro-porosity dominates in tight intervals (< 1 mD). J-function at low k overestimates reservoir-scale capillary behavior due to sample-scale heterogeneity; thin-section petrography and MICP integration are recommended before applying J to volumetrics.
References
Primary source
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