Permeability Calculator

Compute absolute permeability (k) of porous materials based on Darcy's law. Interactive visualisation of fluid flow through a core sample.

m³/s
volumetric flow rate (m³/s)
Pa·s
dynamic viscosity (water at 20°C ≈ 0.001 Pa·s)
Pa
pressure differential across sample (Pa)
m
length in flow direction (m)
m²
area perpendicular to flow (m²)
Typical Sandstone (k ~ 1 Darcy)
Low‑Permeability Shale (k ~ 0.0001 mD)
Fractured Limestone (k ~ 10 mD)
Tight Gas Sand (k ~ 0.01 mD)
Water at 20°C, Berea core (~150 mD)
Local computation only: All calculations run in your browser – no data is uploaded. Perfect for confidential core analysis data.

Darcy's Law: Foundation of Permeability Measurement

Darcy's law is the constitutive equation that describes fluid flow through porous media. It was established by Henry Darcy in 1856 during his experiments on water filtration through sand columns. The law states that the volumetric flow rate is proportional to the pressure gradient and inversely proportional to fluid viscosity.

Q = (k · A · ΔP) / (μ · L)

→ k = (Q · μ · L) / (A · ΔP)

where k = absolute permeability (m² or Darcy), Q = flow rate (m³/s), μ = dynamic viscosity (Pa·s), L = length (m), A = cross‑sectional area (m²), ΔP = pressure drop (Pa).

Permeability quantifies the ease with which a fluid can pass through a porous medium. It depends solely on the pore structure (pore size, tortuosity, connectivity) and not on the fluid properties. In petroleum engineering, the unit Darcy (D) is widely used: 1 Darcy = 0.987 × 10⁻¹² m². Typical reservoir rocks range from 0.1 mD (tight gas) to several Darcies (highly permeable sands).

Practical Applications & Relevance

  • Reservoir Engineering: Estimating productivity of oil/gas wells, designing enhanced oil recovery (EOR).
  • Hydrogeology: Assessing groundwater flow rates and aquifer transmissivity.
  • Civil Engineering: Drainage design, dam seepage analysis, landfill liner performance.
  • Chemical Engineering: Catalyst support design, membrane filtration, packed bed reactors.

Step‑by‑Step Calculation Procedure

  1. Measure the sample dimensions: length L (m) and cross‑sectional area A (m²).
  2. Establish a steady‑state flow of a fluid with known viscosity μ (Pa·s) at a constant flow rate Q (m³/s).
  3. Record the differential pressure ΔP (Pa) across the sample.
  4. Apply Darcy's law: k = (Q μ L) / (A ΔP).
  5. Convert to Darcy if needed: 1 Darcy = 9.869233×10⁻¹³ m².

Our calculator automates this process, providing instant results along with permeability classification based on typical industry standards (after Bear, 1972; Tiab & Donaldson, 2015).

Permeability Classification & Typical Values

Material / Rock Type Permeability Range (mD) Classification
Unconsolidated sand & gravel 10⁴ – 10⁶ Very high
Sandstone (good reservoir) 10 – 1000 Moderate to high
Limestone / Dolomite (fractured) 1 – 100 Moderate
Tight gas sandstone 0.01 – 0.1 Low
Shale (unfractured) 0.0001 – 0.001 Very low (nanodarcy)
Concrete (typical) 0.001 – 0.1 Low
Case Study: Core Plug Analysis in Petroleum Exploration

A 3.8 cm diameter, 5 cm long core plug from a sandstone reservoir is tested in a permeameter. Brine (μ = 0.001 Pa·s) is injected at Q = 5 cm³/min. The measured pressure drop ΔP = 35 kPa. Using the calculator: A = π·(0.019)² ≈ 1.134×10⁻³ m², L = 0.05 m, Q = 8.333×10⁻⁸ m³/s → k = 1.05×10⁻¹³ m² ≈ 106 mD. This indicates a moderate to good reservoir quality, suitable for production. The engineer can then estimate expected flow rates under reservoir conditions.

Limitations & Advanced Considerations

Darcy's law assumes laminar flow (low Reynolds number, Re<1–10), incompressible Newtonian fluid, and no fluid–rock chemical interaction. For high flow rates, inertial effects cause non‑Darcy flow described by the Forchheimer equation. In gas flow, the Klinkenberg effect (gas slippage) leads to apparent permeability increase at low pressures. Our calculator provides the absolute (liquid) permeability; for gas permeability correction, additional parameters like mean pressure and Klinkenberg factor are needed.

Frequently Asked Questions

Permeability (k) is a property of the porous medium only, while hydraulic conductivity (K) includes fluid properties: K = k·ρg/μ, where ρ is fluid density and g gravity. K is commonly used in groundwater hydrology.

Yes, but gas permeability measured at low pressure may show higher values due to slippage (Klinkenberg effect). For accurate gas permeability, use high mean pressure or apply correction. This calculator assumes incompressible liquid flow; for gas use as approximation only.

1 Darcy = 0.987×10⁻¹² m² ≈ 1 μm². 1 mD = 0.001 Darcy. To convert from m² to Darcy: multiply by 1.01325×10¹² (approx). Our calculator provides both SI and Darcy units.

In stress‑sensitive formations (e.g., coal, shale), effective stress changes due to pore pressure can alter pore throat dimensions, reducing permeability. Our calculator assumes rigid, non‑deformable porous media.

Scientific rigor & engineering standards – This tool implements Darcy’s law as defined by the classic Darcy experiment. Equations are validated against standard petroleum engineering textbooks (Tiab & Donaldson, "Petrophysics"; Bear, "Dynamics of Fluids in Porous Media"). Permeability classification follows industry conventions. Last updated April 2026.

References: Darcy's Law (Wikipedia); Bear, J. (1972). "Dynamics of Fluids in Porous Media"; Society of Petroleum Engineers – Permeability.