Porosity And Permeability
Calculate permeability k and porosity φ of porous materials using Darcy's law. Free online physics tool for earth sciences, hydrogeology, and petroleum engineering.
About This Calculator
The porosity and permeability calculator uses Darcy's law to compute two fundamental properties of a porous material with a fluid flowing through it. Permeability (k) measures how easily a fluid can flow through a material, while porosity (φ) measures how much void space exists within the material. This calculator is essential for earth scientists, hydrogeologists, petroleum engineers, and civil engineers working with groundwater flow, oil and gas reservoirs, and soil mechanics.
Darcy's law states that the discharge rate Q through a porous medium is proportional to the permeability k, cross-sectional area A, and pressure difference Δp, and inversely proportional to the fluid viscosity μ and distance L: Q = (kA/μL) × Δp. Rearranging gives the permeability formula: k = (Q × μ × L) / (A × Δp). The porosity is calculated from the residence time using: φ = (Q × t) / (A × L), where t is the time taken for fluid to travel the distance L.
Regional Notes
International (SI): Permeability is expressed in square meters (m²), with typical values ranging from 10⁻¹² to 10⁻⁸ m² for natural materials. The SI unit system is used worldwide in scientific research and academic settings.
United States: In the US petroleum industry, permeability is commonly measured in darcys (D) or millidarcys (mD). One darcy (1 D) = 9.87 × 10⁻¹³ m². USGS and environmental agencies also use ft² and ft/day units for hydraulic conductivity calculations.
United Kingdom: UK earth sciences follow the SI convention using m² and darcy units. The British Geological Survey (BGS) uses SI units for hydrogeological assessments, while the oil and gas industry in the North Sea uses darcy and millidarcy units.
Frequently Asked Questions
What is Darcy's law?
Darcy's law is an equation that describes the flow of a fluid through a porous medium. It states that the discharge rate Q is proportional to the permeability k, cross-sectional area A, and pressure difference Δp, and inversely proportional to the fluid viscosity μ and distance L: Q = (kA/μL) × Δp.
How do you calculate permeability?
Permeability is calculated using the rearranged Darcy's law: k = (Q × μ × L) / (A × Δp), where Q is the discharge rate, μ is dynamic viscosity, L is the distance the fluid travels, A is the cross-sectional area, and Δp is the pressure difference across the material.
How do you calculate porosity?
Porosity is calculated as φ = (Q × t) / (A × L), where Q is the discharge rate, t is the residence time of the fluid, A is the cross-sectional area, and L is the distance the fluid travels through the material. The result is a dimensionless value between 0 and 1.
What is the difference between porosity and permeability?
Porosity measures the amount of void space in a material, while permeability measures how easily fluids flow through that material. A material can have high porosity but low permeability if the voids are not connected, preventing fluid flow.
What units is permeability measured in?
Permeability is measured in square meters (m²) in SI units, but the darcy (D) is the most common unit in earth sciences and petroleum engineering. One darcy equals approximately 9.87 × 10⁻¹³ m². Permeability is also commonly expressed in millidarcys (mD), where 1 D = 1000 mD.
What is Darcy velocity?
Darcy velocity (also called specific discharge) is the volumetric flow rate per unit cross-sectional area of a porous material. It is defined as v = Q/A and represents the average fluid velocity if the flow were occurring through the entire cross-section rather than just the pore spaces.
What are typical permeability values for soil?
Soil permeability typically ranges from 1 to 10 darcy depending on soil type. Sandy soils are more permeable at around 10 darcy, while peaty soils with lots of organic material are less permeable at around 1 darcy. Clay soils have much lower permeability, often in the millidarcy range.
What are typical porosity values for soil?
Soil porosity varies by type: sandy soils have porosity between 0.36 and 0.43 (36-43%), while clay-rich soils have higher porosity between 0.51 and 0.58 (51-58%). However, clay soils have lower permeability despite higher porosity because their pores are poorly connected.