Darcy (unit)

Template:Short description Template:Infobox unit The 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. The unit has also been used in biophysics and biomechanics, where the flow of fluids such as blood through capillary beds and cerebrospinal fluid through the brain interstitial space is being examined.<ref name="drs" /> A darcy has dimensions of 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:

<math>Q = \frac{A k\,\Delta P}{\mu\,\Delta x}</math>

where:

<math>Q\,</math>	is the volumetric fluid flow rate through the medium
<math>A\,</math>	is the area of the medium
<math>k\,</math>	is the permeability of the medium
<math>\mu\,</math>	is the dynamic viscosity of the fluid
<math>\Delta P\,</math>	is the applied pressure difference
<math>\Delta x\,</math>	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.

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.<ref>Peter C. Lichtner, Carl I. Steefel, Eric H. Oelkers, Reactive Transport in Porous Media, Mineralogical Society of America, 1996, Template:ISBN, p. 5.</ref>

Tissue permeability, whose measurement {{#invoke:Lang|lang}} is still in its infancy, is somewhere in the range of 0.01 to 100 darcy.<ref name="drs" />

Origin

The darcy is named after Henry Darcy.<ref name="drs" /> 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.

The unit abbreviation "d" is not capitalized (contrary to industry use).Template:Clarify The American Association of Petroleum Geologists<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> uses 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 Template:Val or 0.9869233 μm².<ref name=spe>Template:Cite book</ref> This conversion is usually approximated as 1 μm². This is the reciprocal of 1.013250—the conversion factor from atmospheres to bars.<ref name=drs>Template:Cite journal</ref>

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. <ref>K. N. Duggal, J. P. Soni: Elements of Water Resources Engineering. Publisher New Age International, 1996, p. 270</ref>

References

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