What is the difference between porosity and permeability?

Porosity is the fraction of a material's volume that is pore space (voids). Permeability is the material's ability to transmit fluid through those pores. Clay has high porosity (~50%) but very low permeability because pores are tiny and poorly connected. Gravel has moderate porosity (~30%) but extremely high permeability because pores are large and well-connected.

What is the difference between Darcy velocity and pore velocity?

Darcy velocity (q = Q/A) is the volumetric flux spread over the entire cross-section (solid + pores). Pore velocity (v = q/φ) is the actual speed of fluid particles moving through the pore channels. Pore velocity is always higher than Darcy velocity by a factor of 1/φ. Pore velocity is what matters for contaminant transport timing.

When does Darcy's law break down?

Darcy's law assumes laminar (creeping) flow and is valid when the Reynolds number Re < ~10. At higher Re (fast flow through coarse materials), inertial effects become important and the Forchheimer equation should be used instead. Very high porosity materials (e.g., fractured rock with large openings) may also violate Darcy's assumptions.

What is hydraulic conductivity?

Hydraulic conductivity K (m/s) combines the material's permeability with the fluid's properties: K = kρg/µ. For water at standard conditions, K is directly proportional to permeability. Hydrogeologists use K because it directly relates head gradient to flow velocity in aquifer calculations.

How does the Kozeny-Carman equation work?

The Kozeny-Carman equation estimates permeability from porosity and grain size: k = d²φ³/(180(1−φ)²). It works well for uniform granular media (sand, gravel) but poorly for fractured rock, clay (plate-shaped particles), or cemented formations. It shows that permeability is extremely sensitive to porosity — doubling φ increases k by roughly 8×.

What units is permeability measured in?

The SI unit is m², but petroleum engineers use the darcy (D) where 1 D = 9.869×10⁻¹³ m². Most reservoir rocks are measured in millidarcys (mD). Good reservoir rock is 100-1000 mD, tight rock is 0.001-0.1 mD (requiring hydraulic fracturing), and unconventional shale can be nanodarcys.

Porosity & Permeability Calculator

Calculate flow rate, Darcy velocity, pore velocity, and hydraulic conductivity using Darcy's law for porous media. Includes Kozeny-Carman estimation.

Porosity (φ)Volume fraction of pore space (0-70%)

Permeability (k)

Unit

Fluid Type

Pressure Drop (ΔP)

kPa

Flow Length

Cross-Sectional Area

m²

Flow Rate (Q)

852.68 L/day

Darcy\u2019s Law: Q = kA(ΔP)/(µL)

Darcy Velocity

0.99 µm/s

q = Q/A (superficial velocity)

Pore Velocity

4.93 µm/s

v = q/φ (actual fluid speed)

Hydraulic Conductivity

0.0000 m/s

K = kρg/µ

Kozeny-Carman k (est.)

2,814.65 mD

From porosity (d ≈ 0.2mm grain)

Reynolds Number

0.000

✓ Darcy’s law valid (Re < 10)

Porosity Visualization

20%

Solid matrix: 80.0%

Pore space: 20.0%

Specific yield (est.): 16.0%

Darcy Velocity vs Permeability

Permeability (mD)	Classification	Darcy Velocity	Pore Velocity
0.001	Impermeable	0.00 µm/s	0.00 µm/s
0.010	Poor	0.00 µm/s	0.00 µm/s
0.100	Poor	0.00 µm/s	0.00 µm/s
1	Fair	0.00 µm/s	0.02 µm/s
10	Fair	0.05 µm/s	0.25 µm/s
100	Good	0.49 µm/s	2.47 µm/s
1,000	Good	4.93 µm/s	24.67 µm/s
10,000	Excellent	49.34 µm/s	246.72 µm/s
100,000	Excellent	493.45 µm/s	0.2467 cm/s

Rock & Sediment Properties Reference

Material	Porosity (%)	Permeability (mD)	K (m/s)
Gravel	25-40	10⁴–10⁶	10⁻²–1
Coarse sand	30-40	10³–10⁵	10⁻³–10⁻¹
Fine sand	25-50	10–10⁴	10⁻⁵–10⁻³
Silt	35-50	10⁻²–10	10⁻⁸–10⁻⁵
Clay	40-70	10⁻⁶–10⁻²	10⁻¹¹–10⁻⁸
Sandstone	5-30	1–10³	10⁻⁷–10⁻³
Limestone	0-20	10⁻³–10²	10⁻⁸–10⁻⁴
Shale	0-10	10⁻⁷–10⁻³	10⁻¹²–10⁻⁸
Fractured granite	0-5	10⁻²–10²	10⁻⁸–10⁻⁴
Karst limestone	5-50	10²–10⁶	10⁻⁴–1

Planning notes, formulas, and examples

About the Porosity & Permeability Calculator

The **Porosity & Permeability Calculator** applies Darcy's law to compute fluid flow through porous media, from aquifers and reservoirs to filters and concrete. Enter porosity, permeability, fluid viscosity, pressure drop, and geometry to get flow rate, Darcy velocity, pore velocity, and hydraulic conductivity.

It also estimates permeability from porosity with the **Kozeny-Carman equation** and checks whether the Reynolds number still keeps Darcy's law in a valid range. That makes it useful both for quick field estimates and for comparing how different rock or sediment types behave under the same pressure gradient.

The reference table gives you a practical sense of scale, from highly permeable gravel to tight shale, without having to keep every unit conversion in your head.

When This Page Helps

Flow through porous media is easy to underestimate because porosity and permeability do not mean the same thing. A rock can hold a lot of fluid and still pass it very slowly if the pore spaces are poorly connected.

This calculator keeps the geometry, fluid properties, and Darcy outputs together so you can compare materials or test how a change in viscosity or pressure drop alters the result.

How to Use the Inputs

Enter the porosity as a percentage (volume fraction of pore space in the material).
Enter the permeability in millidarcys (mD) or darcys (D).
Select the fluid type (water, light oil, heavy oil) or enter a custom viscosity.
Input the pressure drop across the sample, flow length, and cross-sectional area.
Read the flow rate, Darcy velocity, and actual pore velocity from the outputs.
Check the Reynolds number to verify Darcy's law is valid for your conditions.
Use the reference table to compare your material with typical geological formations.

Formula used

Darcy's Law: Q = (k × A × ΔP) / (µ × L)

Where:
• Q = volumetric flow rate (m³/s)
• k = permeability (m²), 1 mD = 9.869×10⁻¹⁶ m²
• A = cross-sectional area (m²)
• ΔP = pressure drop (Pa)
• µ = dynamic viscosity (Pa·s)
• L = flow length (m)

Darcy velocity: q = Q/A
Pore velocity: v = q/φ
Hydraulic conductivity: K = kρg/µ

Example Calculation

Result: Q = 85.3 m³/day, Darcy velocity = 9.87 µm/s

k = 200 mD = 1.974×10⁻¹³ m². Q = (1.974e-13 × 10 × 500000) / (0.001 × 100) = 9.87e-7 m³/s = 85.3 m³/day. Darcy velocity = 9.87e-7/10 = 9.87×10⁻⁸ m/s. Pore velocity = 9.87e-8/0.2 = 4.94×10⁻⁷ m/s.

Tips & Best Practices

Permeability varies over 15 orders of magnitude — from 10⁻⁶ mD (shale) to 10⁶ mD (gravel). Always check the order of magnitude.
High porosity does NOT guarantee high permeability — clay is the classic example with high φ but very low k.
For oil reservoirs, viscosity matters enormously: heavy oil (100+ cP) flows 100× slower than water (1 cP) through the same rock.
Check the Reynolds number: if Re > 10, Darcy's law overestimates flow rate. Use the Forchheimer equation instead.
Pore velocity governs contaminant transport timing. A contaminant travels 5× faster than Darcy velocity in a 20% porosity material.
The Kozeny-Carman estimate assumes uniform spherical grains — actual permeability in natural formations often differs significantly.

Darcy's Law in Practice

Darcy's law, formulated in 1856 by Henry Darcy, remains the foundation of porous media flow analysis. It states that flow rate is proportional to the pressure gradient and permeability, and inversely proportional to viscosity. This linear relationship holds for most subsurface flows, from slow-moving groundwater to oil migration in reservoirs. The law fails only at very high velocities (turbulent flow in coarse media) or in very tight media where Knudsen diffusion dominates.

Porosity Types and Their Impact

Geologists distinguish between total porosity and effective porosity. Total porosity includes all void space, but some pores are isolated (dead-end or disconnected). Effective porosity — the connected pore space that actually transmits fluid — is what matters for flow calculations. In well-sorted sandstone, effective porosity may be 90% of total porosity, but in fractured granite, it may be less than 1%.

Applications Across Industries

Petroleum engineers use permeability to estimate well productivity and design enhanced oil recovery. Hydrogeologists use hydraulic conductivity to model aquifer behavior and predict contaminant plume migration. Civil engineers use permeability to design earth dams, landfill liners, and foundation drainage. Environmental scientists use these concepts to design soil remediation systems and predict pollution transport in groundwater.

Sources & Methodology

Last updated: January 15, 2025

Frequently Asked Questions

Porosity is the fraction of a material's volume that is pore space (voids). Permeability is the material's ability to transmit fluid through those pores. Clay has high porosity (~50%) but very low permeability because pores are tiny and poorly connected. Gravel has moderate porosity (~30%) but extremely high permeability because pores are large and well-connected.