Permeability & Darcy's Law Calculator

Hydrogeology, Reservoir Engineering & Porous Media Permeability Metrology

Intrinsic Permeability (k) measures the ability of a porous rock or soil medium to transmit fluids independent of fluid properties:

• **

• Universal Permeability Conversion Formulas (SPE Standards)**:

1 Darcy (D) = 1,000 mD (Millidarcys) = 9.869233 × 10^-13 m^2 ≈ 0.986923 µm^2

1 µm^2 = 10^-12 m^2 = 1.01325 Darcys = 1,013.25 mD

1 mD = 10^-3 D = 1,000 µD (Microdarcys) = 10^6 nD (Nanodarcys)

• **

• Darcy's Law of Porous Media Flow & Hydraulic Conductivity**:

Q = (k × A × Δ P) / (μ × L)

K = (k × ρ × g) / (μ)

• **

• Standard Geotechnical & Reservoir Formation Benchmarks**:

• Coarse Gravel / Clean Sand: 100.0 D 100,000 mD K ≈ 10^-3 m/s (High aquifer flow)

• Sandstone Oil Reservoir: 100.0 mD 0.100 D K = 9.68 × 10^-7 m/s

• Tight Carbonate Gas: 1.0 mD 1,000 µD K = 9.68 × 10^-9 m/s

• Unconventional Shale Rock: 100.0 nD = 10^-4 mD 9.87 × 10^-20 m^2 (Hydraulic fracking required)

How to Use This Calculator

Enter your Intrinsic Permeability (k) (e.g. 100 in permeability), From Permeability Unit — choose from Millidarcys (mD - Petroleum Reservoir Standard), Darcys (D = 1,000 mD - Hydrogeology), Square Micrometers (µm² = 1.01325 D), To Permeability Unit — choose from Darcys (D), Millidarcys (mD), Square Micrometers (µm²), Core Cross-Sectional Area (A in m²) (e.g. 0.0020 in m²), Flow Path Length (L in meters) (e.g. 0.10 in m), Pressure Differential (ΔP in psi) (e.g. 10.0 in psi), Fluid Viscosity (µ in cP, 1.0 for water) (e.g. 1.0 in cP), and Reservoir & Geotechnical Formation Benchmark — choose from Custom Porous Formation, Sandstone Oil Reservoir (100.0 mD = 0.100 D) → 0.0987 µm² | Q = 8.16 mL/min (10 psi @ 1 cP) | K = 9.68 × 10⁻⁷ m/s, Clean Coarse Sand / Gravel Aquifer (100.0 D = 100,000 mD) → 98.69 µm² | K = 9.68 × 10⁻⁴ m/s. Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Multipliers to SI Base Unit m^2 (SPE & Darcy Standards: 1 Darcy = 9.869233e-13 m^2 = 0.9869233 um^2)

Darcy's Law: Q = (k A Delta_P) / (mu * L)

Convert Delta_P from psi to Pascals (1 psi = 6894.757 Pa)

Convert mu from cP to Pas (1 cP = 0.001 Pas)

Hydraulic Conductivity for clean water (rho=1000 kg/m³, g=9.80665, mu=0.001 Pa·s): K = (k rho g) / mu

Worked Example

A petroleum reservoir engineer evaluating a sandstone core sample under a 10 psi pressure differential calculates water (1 cP) flows through at 8.16 mL/min, confirming excellent reservoir pay quality.

Understanding Your Result

Unit conversions are exact by definition within a given measurement system (e.g., 1 km = exactly 1,000 m). Cross-system conversions (metric to imperial) use defined exchange factors: 1 inch = exactly 2.54 cm; 1 pound = 0.45359237 kg. Round your converted result to match the precision of your original measurement — expressing more decimal places than your input justifies implies false accuracy. For regulatory, legal, or safety-critical applications, verify which measurement system is required by the applicable standard.