petrophysics · permeability
Permeability — Kozeny-Carman
k = φ³ × r² / [8 × τ × (1−φ)²] × 1013.25 (mD)
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Inputs
fraction
μm
—
Description
The Kozeny-Carman equation derives permeability from first principles of viscous flow through a bundle of capillary tubes, relating k to the cube of porosity, the square of mean pore throat radius, and the inverse of tortuosity. It provides physical insight into why small changes in pore throat size dominate permeability and is the theoretical foundation for most empirical permeability transforms.
Variables
| Symbol | Unit | Description |
|---|---|---|
| k | mD | Permeability |
| φ | fraction | Effective porosity of the rock framework. The Kozeny-Carman equation is highly sensitive to porosity — a factor-of-2 change in φ changes k by nearly an order of magnitude. |
| r | μm | Mean pore throat radius in microns. Estimate from MICP (mercury injection) at 50th percentile, or from thin-section image analysis. Typical values: tight sands 0.01–0.5 μm, conventional sands 1–50 μm. |
| τ | — | Pore path tortuosity — ratio of actual fluid path length to straight-line distance. Ranges from ~2 for clean sands to 3–5 for cemented or poorly connected pore systems. A value of 2.5 is a common default. |
Assumptions
- Pore geometry can be approximated as a bundle of capillary tubes — valid for inter-granular pore systems; invalid for fracture-dominated or vuggy porosity
- A single representative mean pore throat radius adequately characterizes the pore-size distribution — better suited to well-sorted sands than poorly sorted or heterogeneous carbonates
Limitations
- Highly sensitive to r: doubling r quadruples k; accurate pore-throat radius measurement (from MICP or image analysis) is critical
- Tortuosity τ is not directly measurable from routine logs — use ~2.5 for sandstones as a default but validate against formation factor measurements where possible
Use Cases
- → Physical interpretation of empirical permeability: Use Kozeny-Carman to understand why Timur, Winland, and FZI empirical correlations work — they are all calibrations of the τ and r terms in the theoretical framework.
- → Pore-scale modeling quality check: Compare Kozeny-Carman k against measured core permeability; if they agree, the estimated r and τ are reasonable; large disagreement suggests fractures, vugs, or unusual pore geometry.
- → Predicting permeability in analog rocks without core: Where tight formation cores are unavailable, use MICP data from analog outcrop or nearby wells to estimate r and τ, then project permeability across the field via log-derived porosity.
Related Calculations
Region Notes
Permian Basin
Wolfcamp tight oil: r ≈ 0.05–0.2 μm (50th percentile MICP), τ ≈ 3–5 in cemented siltstones; Kozeny-Carman gives k ≈ 0.001–0.05 mD — consistent with measured plug data.
Gulf of Mexico
Unconsolidated Miocene sands: r ≈ 30–100 μm, τ ≈ 1.5–2.5; Kozeny-Carman gives k ≈ 500–5000 mD — broadly consistent with conventional permeameter measurements.
North Sea
Brent Group: r ≈ 5–30 μm, τ ≈ 2–3; expected k ≈ 50–500 mD at φ 18–25%; good agreement with steady-state core measurements after kaolinite-fines corrections.
Global
The key uncertainty in Kozeny-Carman is always τ — for a quick estimate use τ = 2 (clean sand) to τ = 5 (cemented or tight). Sensitivity to r dominates: a 10× change in r changes k by 100×.
References
Primary source
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