Flow Through Porous Media

Darcy’s law for permeable media and the Ergun equation for packed beds and granular filters.

Cross-section input

Diameter

Bed / Medium Length (L)

Fluid Density (ρ)

kg/m³

Dynamic Viscosity (μ)

Pa·s

Computed area: 176.715 cm²

Particle Diameter (dₚ)

Void Fraction (ε)

Superficial Velocity (u₀)

m/s

ε = 0.35–0.45 for random sphere packing. Superficial velocity = Q/A (not interstitial).

Results

Total Pressure Drop

2031.2Pa

ΔP per Metre

4062.5Pa/m

Flow Rate

0.3534L/s

Modified Re

100.00

Pressure drop breakdown

Viscous (Blake-Kozeny)

937.5Pa

Inertial (Burke-Plummer)

1093.7Pa

Viscous 46.2%Inertial 53.8%

Transitional — Ergun equation applies

Darcy’s Law

Q = k · A · ΔP / (μ · L)

Ergun Equation

ΔP/L = 150μ(1−ε)²u/(d²ₚε³)
+ 1.75ρ(1−ε)u²/(dₚε³)

Common permeabilities: Gravel 10⁵–10⁷ mD · Sand 1–10⁴ mD · Sandstone 0.1–500 mD · Limestone 0.01–10 mD