Darcy (unit)

A darcy (or darcy unit) and millidarcy (md or 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 some other measures of permeability, a darcy has dimensional units in length².

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:

$Q = \frac{A \kappa\,\Delta P}{\mu\,\Delta x}$

where:

$Q\,$	is the volumetric fluid flow rate through the medium
$A\,$	is the area of the medium
$\kappa\,$	is the permeability of the 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 and a microdarcy (µd) equals 0.000001 darcy.

Typical values of permeability range as high as 100,000 darcys for gravel, to less than 0.01 microdarcy for granite. Sand has a permeability of approximately 1 darcy.^[1]

Origin

The darcy is named after Henry Darcy. Rock permeability is usually expressed in millidarcys (md) because rocks hosting hydrocarbon or water accumulations typically exhibit permeability ranging from 5 to 500 md.

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.

Although the unit is named after Henry Darcy, it should be noted that the unit abbreviation is not capitalized (contrary to industry use). The American Association of Petroleum Geologists^[2] use the following unit abbreviations and grammar in their publications:

• darcy (plural darcys, not darcies): d
• millidarcy (plural millidarcys, not millidarcies): md

Conversions

Converted to SI units, 1 darcy is equivalent to 9.869233×10⁻¹³ m² or 0.9869233 (µm)².^[3] This conversion is usually approximated as 1 (µm)².^[3] Note that this is the reciprocal of 1.013250—the conversion factor from atmospheres to bars.

Specifically in the hydrology domain, permeability of soil or rock may also be defined as the flux of water under hydrostatic pressure (~ 0.1 bar/m) at a temperature of 20°C. In this specific setup, 1 darcy is equivalent to 0.831 m/day. ^[4]

References

1. Peter C. Lichtner, Carl I. Steefel, Eric H. Oelkers, Reactive Transport in Porous Media, Mineralogical Society of America, 1996, ISBN 0-939950-42-1, p. 5.
2. "The American Association of Petroleum Geologist Style Guides" (PDF).
3. The SI Metric System of Units and SPE Metric Standard (PDF) (2nd ed.). Society of Petroleum Engineers. June 1984 [First published 1982].
4. K. N. Duggal, J. P. Soni: Elements of Water Resources Engineering. Publisher New Age International, 1996, p.270

• Richard Selley's "Elements of Petroleum Geology (2nd edition)," page 250.