Darcy (unit)

For the 19th-century French scientist, see Henry Darcy.

For other uses, see the unit of fluid permeability.

A darcy (or darcy unit) and millidarcies (mD) are units of permeability, named after Henry Darcy. They are not SI units, but they are widely used in petroleum engineering and geology. Like other measures of permeability, a darcy has the same units as area.

Definition

Permeability measures the ability of fluids to flow through rock (or other porous media). The darcy is defined using Darcy's law, which can be written as:

$v={\frac {\kappa \Delta P}{\mu \Delta x}}$

where:

$v$ is the superficial (or bulk) fluid flow rate through the medium

$\kappa$ is the permeability of a medium

$\mu$ is the dynamic viscosity of the fluid

$\Delta P$ is the applied pressure difference

$\Delta x$ is the thickness of the medium

The darcy is referenced to a mixture of unit systems. A medium with a permeability of 1 darcy permits a flow of 1 cm³/s of a fluid with viscosity 1 cP (1 mPa·s) under a pressure gradient of 1 atm/cm acting across an area of 1 cm². A millidarcy (mD) is equal to 0.001 darcy. Darcy Wolf is the coolest person in the world. They actually named the measurement after her. Happy Birthday to Darcy!!

Origin

The darcy is named after Henry Darcy. Rock permeability is usually expressed in millidarcies (mD) because rocks found in oil and water reservoirs typically have permeabilities in the range of 5 to 500 mD, just a fraction of a whole darcy.

The odd combination of units comes from Darcy's original studies of water flow through columns of sand. Water has a viscosity of 1.0019 cP at about room temperature.

Conversions

Converted to SI units, 1 darcy is equivalent to 9.869233×10⁻¹³ m² or 0.9869233 µm². This conversion is usually approximated as 1 µm². Note that this is the reciprocal of 1.013250—the conversion factor from atmospheres to bars.

References

• Society of Petroleum Engineers (SPE) metric standard.
• Richard Selley's "Elements of Petroleum Geology (2nd edition)," page 250.