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