Porosity and Permeability Calculator

Porosity (φ) is the fraction of a material's total volume that consists of void (pore) spaces. It is calculated as φ = Vᵥ / Vₜ, where Vᵥ is the void volume and Vₜ is the total bulk volume. It is often expressed as a percentage and ranges from near 0% (very dense rock) to over 50% (loose sand or gravel).

Darcy's law states that the flow rate Q through a porous medium equals k·A·ΔP / (μ·L), where k is permeability, A is cross-sectional area, ΔP is the pressure drop, μ is dynamic viscosity, and L is sample length. Rearranging gives k = Q·μ·L / (A·ΔP), allowing permeability to be determined from measured flow data.

k is the intrinsic permeability of the porous medium, measured in m² or in darcies. It quantifies how easily a fluid flows through the material, independent of the fluid's properties. Higher k values mean the medium allows fluid to pass through more readily.

Porosity describes how much empty space exists within a material (its capacity to store fluid), while permeability describes how easily a fluid can flow through that material (its ability to transmit fluid). A material can have high porosity but low permeability if the pores are not well connected — for example, pumice stone.

Darcy velocity (also called specific discharge) is defined as q = Q / A — the flow rate divided by the total cross-sectional area of the sample. It is not the actual velocity of fluid through the pores (which would be higher), but a useful bulk flux parameter that simplifies porous media flow calculations.

Soil permeability varies widely by type. Gravel can have permeability of 10⁻⁸ to 10⁻⁶ m², sandy soils range from 10⁻¹² to 10⁻⁹ m², silts are around 10⁻¹⁵ to 10⁻¹² m², and clays can be as low as 10⁻²⁰ m². In practical units, reservoir rocks in petroleum engineering are typically measured in millidarcies (1 mD ≈ 9.87×10⁻¹⁶ m²).

Soil porosity depends on grain size, packing, and compaction. Loose sands typically have porosity of 25–50%, clay soils 40–70%, and consolidated sandstone 5–30%. Compact crystalline rocks may have porosity below 1%, while highly fractured rocks or gravel can exceed 30%.

Henry Darcy originally verified his law through experiments on sand-filled columns in Dijon, France in 1856. Since then, it has been extensively confirmed in groundwater aquifer studies, petroleum reservoir testing, and laboratory permeameter experiments worldwide. It remains valid for slow (laminar) flow conditions where the Reynolds number is low, typically Re < 1 for porous media.