J-Function Capillary Pressure Scaling

Scale capillary pressure from a reference core plug to a different rock type using the Leverett J-function. Essential for transferring SCAL data between reservoir facies with different porosity and permeability.

Leverett J-function. J = (Pc/σcosθ) × √(k/φ) makes capillary pressure dimensionless by normalizing for rock quality (k, φ) and fluid properties (σ, θ). If two rocks have the same pore geometry (same J-function), their Pc curves differ only by the √(k/φ) factor. This is exact for geometrically similar pore networks and approximate for real rocks.

Scaling factor. Pc_B/Pc_A = √((k_A·φ_B)/(k_B·φ_A)). When Rock B is tighter (lower k, lower φ), the scaling factor > 1 and Pc_B > Pc_A — tighter rock requires higher capillary pressure to achieve the same saturation. Default: k_A=100 mD → k_B=25 mD gives scale factor ≈ 1.73.

Limitations. J-function scaling assumes pore geometry similarity between rocks. It works well within the same depositional facies but poorly across fundamentally different rock types (e.g., sandstone to carbonate, or intergranular to fracture porosity). Always validate with actual SCAL measurements when available.

Reference: Leverett, M.C. (1941). "Capillary Behavior in Porous Solids." Trans. AIME 142: 152–169.

• Reference Rock A (rows 3–7): Lab-measured Brooks-Corey Pc parameters from a core plug — Swi, Pd, λ, k_A, φ_A. This is the rock with actual SCAL data.
• Target Rock B (rows 9–10): Permeability and porosity of the rock to which Pc will be scaled. Typically a different facies or flow unit in the same reservoir.
• Common Properties (rows 12–13): Interfacial tension and contact angle — assumed the same for both rocks (same fluids, similar mineralogy).
• Scaling Results (rows 15–17): J-function scaling factor = √((k_A·φ_B)/(k_B·φ_A)), predicted entry pressure for Rock B = Pd_A × scale factor, and the ratio Pd_B/Pd_A showing how much tighter the target rock is.
• Pc Scaling Table (rows 19–30): Water saturation sweep with Pc_A from Brooks-Corey, dimensionless J-function (same for both rocks), and Pc_B from J-function inverse. The J column should be identical for both rocks at each Sw — this validates the Leverett scaling assumption.