Porosity and Permeability Calculator - Darcy's Law k and Porosity from Core Flood Data

A porosity and permeability calculator takes the volumetric discharge through a porous sample, its length and cross-sectional area, the pressure drop, and the dynamic viscosity, and returns permeability plus porosity from a tracer residence time.

• • Core-flood homework: Solve Darcy's law for k on a sandstone or limestone plug from a teaching lab.
• • Sand permeability check: Back out the permeability of a sandy soil sample after measuring discharge under a known head difference.
• • Aquifer estimate: Estimate the hydraulic conductivity of a coarse sand or gravel layer from a slug test.
• • Petroleum-engineering cross-check: Convert a laboratory k from m^2 to millidarcy so a core plug result can be entered into reservoir simulation software.

Permeability tells you how easily a fluid moves through the connected pore space, while porosity tells you how much of the rock is open to that fluid. Both numbers are required before you can translate a measured discharge into an in-situ flow speed.

Darcy's law k = Q mu L / (A delta-p) is the textbook rearrangement used to back out k from a steady-state flow experiment. Once k is known, porosity from residence time phi = Q t / (A L) gives the void fraction.

For tanks and reactors rather than porous rock, the hydraulic retention time calculator uses the same volume-over-flow ratio to estimate how long a fluid actually spends in a vessel.

The calculator applies Darcy's law to your inputs and reports permeability in SI units, in darcy, and in millidarcy, plus porosity from the residence time. All conversions use the SPE standard 1 darcy = 9.869233 x 10^-13 m^2.

• Q: Volumetric discharge through the sample, m^3/s.
• mu: Dynamic viscosity of the flowing fluid, Pa*s. Water at 20 C is 1.002 x 10^-3 Pa*s.
• L: Length of the sample along the flow direction, m.
• A: Cross-sectional area of the sample perpendicular to flow, m^2.
• delta-p: Pressure drop across the sample, Pa. Must be greater than 0.
• t: Residence time of a tracer pulse, s. Set to 0 to skip the porosity result.

Permeability is reported in three unit families because geologists, hydrogeologists, and petroleum engineers all use the field they grew up in. According to the SPE Petroleum Engineering Handbook, 1 darcy equals 9.869233 x 10^-13 m^2, so the calculator multiplies your m^2 result to get darcy and millidarcy.

Porosity is a dimensionless fraction between 0 and 1. Values around 0.05 correspond to tight shales; values around 0.4 correspond to unconsolidated sands.

According to SPE Petroleum Engineering Handbook, 1 darcy equals 9.869233 x 10^-13 m^2, which the calculator uses to convert between SI permeability and the oil and gas industry darcy unit.

When you are working with a pipe rather than a porous medium, the Poiseuille's law calculator solves the analogous laminar-flow problem for a circular conduit.

Four concepts come up every time you read a permeability result. These cards give you the working definitions so the rest of the page reads like a refresher.

Permeability and porosity are not the same thing and they do not correlate strongly. A clay-rich sandstone can have phi around 0.25 and k below 0.1 mD; a pumice can have phi around 0.5 with k around 1000 mD.

Before trusting a Darcy-law result, confirm the flow regime with the Reynolds number calculator so you know your Reynolds number is still inside the linear Darcy range.

Enter the measured lab or field values below and the calculator returns k in m^2, darcy, and millidarcy plus phi and the two velocities.

1. 1 Pick the fluid preset: Choose water at 20 C, water at 25 C, or air at 20 C to auto-fill mu. Pick Custom to type your own mu for crude oil, brine, or a gas mixture.
2. 2 Enter the pressure drop: Either type delta-p directly, or switch to upstream/downstream and enter both gauges so the calculator computes the difference.
3. 3 Type the sample geometry: Enter L (length, m) and A (area, m^2). For a cylindrical core plug, A = pi d^2 / 4 from the diameter.
4. 4 Enter discharge and residence time: Type Q in m^3/s. If you also measured a tracer residence time t, type that in seconds; otherwise leave t at 0.
5. 5 Read the results: The result panel updates as you type and shows k in m^2, D, and mD, plus phi, q, and v.
6. 6 Sanity-check the numbers: Compare k to the published range for your rock type and confirm that v > q.

For a sandstone core plug with L = 0.1 m, A = 1 cm^2, water at 20 C flowing at Q = 1 mL/min under delta-p = 1 atm, the calculator returns k around 1.65 x 10^-16 m^2.

If you are converting electrical or thermal properties in the same lab session, the conductivity to resistivity calculator follows the same single-equation pattern.

The point of a Darcy worksheet is to turn measurements into defensible k and phi values. These are the practical wins you get from using this one.

• • Three unit families at once: Reads m^2 for physics, darcy for geology, and millidarcy for petroleum engineering from the same inputs.
• • Pressure-pair input mode: Lets you paste upstream and downstream gauge readings when the lab record does not have the delta-p already worked out.
• • Built-in fluid presets: Auto-fills mu for water at 20 C, water at 25 C, and air at 20 C, and lets you override mu for crude oil, brine, or gas mixtures.
• • Catches bad inputs: Returns a friendly warning when delta-p, mu, L, or A is zero, instead of letting the result blow up to Infinity.
• • Authoritative citations: Every formula links back to a primary source - Bear for Darcy's law, Freeze and Cherry for porosity, SPE for the darcy conversion - so the result can be defended in a homework report.

Used in physics, hydrogeology, and petroleum-engineering courses, the worksheet doubles as a teaching tool and a sanity check. If your measured k is two orders of magnitude off the published range for the rock type, the warning line finds the typo fast.

For soil-science and irrigation follow-ups after the permeability step, the vapor pressure deficit calculator works with the same moisture and temperature inputs in a different way.

Five factors move the k and phi numbers the calculator returns. Knowing which is which tells you when to trust a measurement.

• • The calculator assumes a single-phase, isothermal, incompressible fluid, so it does not handle gas slippage or relative-permeability corrections for multiphase flow.
• • The residence-time phi depends on a tracer that follows the bulk fluid, so reactive tracers will under-report the true connected porosity.
• • The calculator uses 1 darcy = 9.869233 x 10^-13 m^2 at 20 C; check your textbook for the alternate conversion at other temperatures.

According to Wikipedia, Hydraulic conductivity, Freeze and Cherry define porosity from residence time as phi = Q t / (A L) and the Darcy velocity as q = Q / A, the two reference values the calculator uses for those outputs.

According to Wikipedia, Darcy's law, the linear relationship Q = k A (Δp) / (μ L) is the standard rearranged form used in core-flood and aquifer experiments to back out permeability from measured Q, mu, L, A, and pressure drop.

To compare laminar pipe flow against the porous-medium case, the Poiseuille's law calculator returns the analogous flow rate from a pressure drop across a circular tube.