Permeability Converter: Darcy, m2, m/s and cm/s

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How to use this tool

Pick a value and two units. The unit list is deliberately split into two groups, because the units above the divider and the units below it do not measure the same physical quantity.

If both your units come from the same group, the temperature setting is ignored and the note under the answer says so. If you cross between the groups, the fluid properties are doing real work and the tool shows you the multiplier it used.

Permeability and conductivity are different quantities

This is the thing worth getting straight, and it is the reason most online converters are quietly incomplete.

Intrinsic permeability, measured in darcy or square metres, is a property of the pore structure alone. Squeeze the same sandstone and the permeability changes. Fill it with a different fluid and it does not.

Hydraulic conductivity, measured in metres per second, is a property of the rock and the fluid together. It is defined as permeability multiplied by fluid density and gravity, divided by dynamic viscosity. The units give it away: metres per second is a velocity, and a velocity has to know what is moving.

So the question what is one darcy in metres per second has no answer on its own. It only has an answer once you say which fluid, at what temperature. For fresh water at 20 degrees the answer is 9.64 times ten to the minus six metres per second, which is where the familiar rule of thumb that a darcy is about ten to the minus five comes from.

Why the temperature is not a detail

Water viscosity falls sharply as it warms. At 5 degrees it is 1.519 milliPascal seconds and at 35 degrees it is 0.719, less than half. Density barely moves over the same range, so viscosity drives almost all of the effect.

The consequence is in the chart above. One darcy of rock gives 6.37 times ten to the minus six metres per second at 5 degrees and 1.34 times ten to the minus five at 35 degrees. That is a factor of 2.1 for a sample that has not changed at all.

This has a practical edge in cold climates. Groundwater across most of Canada sits somewhere between 5 and 10 degrees year round, while a falling head permeameter is usually run at whatever the laboratory happens to be, near 20. Taking the laboratory number straight to the field overstates conductivity by about a third, and nothing in the reported figure will warn you.

A worked check you can repeat on paper

Start from the definition of the darcy itself. One darcy is the permeability that lets one cubic centimetre per second of a one centipoise fluid cross one square centimetre under a pressure gradient of one atmosphere per centimetre. Put those in SI and you get ten to the minus eleven divided by 101325, which is 9.8692 times ten to the minus thirteen square metres. That is the whole definition, and it is exact.

Now convert it. Water at 20 degrees has a density of 998.2 kilograms per cubic metre and a viscosity of 1.002 times ten to the minus three Pascal seconds. Multiply the permeability by density and gravity, then divide by viscosity: 9.8692e-13 times 998.2 times 9.80665, divided by 1.002e-3, gives 9.64 times ten to the minus six metres per second.

Repeat at 5 degrees with a viscosity of 1.519e-3 and the answer drops to 6.37 times ten to the minus six. Nothing about the rock entered the second calculation differently. Only the water did.

Mistakes that catch people out

Calling a conductivity a permeability. A geotechnical report quoting k in centimetres per second is quoting hydraulic conductivity, whatever letter it uses. The letter k is used for both in different disciplines, which is a genuine source of confusion rather than pedantry.

Converting darcy to metres per second without stating a temperature. The answer is only complete with a fluid attached. Most converters assume 20 degree water silently.

Applying a water conversion to oil or gas. A reservoir at 90 degrees with an oil viscosity of 2 centipoise gives a completely different conductivity from the same rock with water in it. Use the custom fluid option rather than the water default.

Reading too much into a single value. Permeability in real ground varies by orders of magnitude over short distances and is usually far higher horizontally than vertically. A converted number is precise, and that is not the same as representative.

Losing track of the scale. These quantities span more than fifteen orders of magnitude from clean gravel to intact clay. Getting an exponent wrong is far more damaging here than getting a factor wrong, which is why the table in the tool is worth glancing at as a sanity check.

Popular permeability conversions

The conversions people look up most. Each opens the tool ready to go with its own address.

How this was checked

The darcy was derived from its own definition rather than copied from a table, giving 9.869233 times ten to the minus thirteen square metres, which matches the published value and the alternative statement of 0.9869233 square microns.

The water properties were the part that needed care. A first attempt used a simple Vogel form for viscosity, which was 2.1 percent out at zero degrees, and near freezing is exactly where Canadian groundwater sits, so it was replaced. The correlation now used is anchored at 20 degrees and sits within 0.14 percent of published values across the whole range from 0 to 80 degrees, tested at thirteen temperatures. Density uses the Kell form and is within 0.003 percent.

The conversions were round tripped, taking a permeability to a conductivity and back at the same temperature and recovering the original figure. The Meinzer unit was derived from its definition as one US gallon per day per square foot, giving 4.7160 times ten to the minus seven metres per second. The typical material ranges in the table were checked in all three unit systems so that a value looked up in one column agrees with the others.

Related Calculators and Reference

• Hazen Permeability Calculator for estimating conductivity from the effective grain size when no test data exists.
• Darcy Flow Calculator for turning a conductivity into a seepage velocity and a travel time.
• Timur and Coates Permeability Calculator for estimating reservoir permeability from porosity and irreducible water saturation.
• Grain Size Curve Plotter for the D10 that feeds the Hazen estimate.
• Viscosity Unit Converter for the fluid property that sits underneath this whole conversion.
• Pressure Unit Converter for the gradient side of Darcy's law.