{{Short description|Unit of permeability}} {{Infobox unit | bgcolor = | name = darcy | image = | caption = | standard = | quantity = [[Permeability (materials science)|Permeability]] | symbol = d | symbol2 = | symbol3 = | symbol4 = | nospacebefore = | namedafter = [[Henry Darcy]] | extraheader = | extralabel = Derivation | extradata = [[Centipoise|cP]]⋅cm{{sup|2}}/(s⋅[[Standard atmosphere (unit)|atm]]) | extraheader2 = | extralabel2 = | extradata2 = | convertfromx = | units1 = SI | inunits1 = {{val|9.869233e-13|u=m2}} }} The '''darcy''' (or '''darcy unit''') and '''millidarcy''' (md or mD) are [[Units of measurement|units]] of [[Permeability (earth sciences)|permeability]], named after [[Henry Darcy]]. They are not [[SI|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 [[Dimensional analysis|dimensions]] of [[length]]<sup>2</sup>.

==Definition== Permeability measures the ability of [[fluids]] to [[Fluid flow through porous media|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 (Earth sciences)|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&nbsp;cm<sup>3</sup>/s of a fluid with [[viscosity]] 1&nbsp;[[Poise (unit)|cP]] (1&nbsp;[[pascal second|mPa·s]]) under a pressure gradient of 1&nbsp;atm/cm acting across an area of 1&nbsp;cm<sup>2</sup>.

Typical values of [[Permeability of soils|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, ''[https://books.google.com/books?ei=woosT4DHKYrXmAXjo531Dw&id=nMsPAQAAIAAJ Reactive Transport in Porous Media]'', Mineralogical Society of America, 1996, {{ISBN|0-939950-42-1}}, p. 5.</ref>

Tissue permeability, whose measurement {{lang|la|in vivo}} 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&nbsp;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&nbsp;cP at about room temperature.

The unit abbreviation "d" is not capitalized (contrary to industry use).{{clarify|date=November 2021}} The American Association of Petroleum Geologists<ref>{{cite web|url=http://geoweb.princeton.edu/beijingconference/AAPG_StyleGuidelines.pdf|title=The American Association of Petroleum Geologist Style Guides |archive-url=https://web.archive.org/web/20110809042013/http://geoweb.princeton.edu/beijingconference/AAPG_StyleGuidelines.pdf |archive-date=2011-08-09}}</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&nbsp;darcy is equivalent to {{val|9.869233|e=-13|ul=m2}} or 0.9869233&nbsp;[[micrometre|μm<sup>2</sup>]].<ref name=spe>{{cite book |title=The SI Metric System of Units and SPE Metric Standard |publisher=[[Society of Petroleum Engineers]] |orig-year=First published 1982 |date=June 1984 |edition=2nd |url=http://www.spe.org/authors/docs/metric_standard.pdf }}</ref> This conversion is usually approximated as 1&nbsp;μm<sup>2</sup>. This is the reciprocal of 1.013250&mdash;the conversion factor from atmospheres to [[bar (unit)|bars]].<ref name=drs>{{cite journal |last1=Sowinski |first1=Damian |date=January 2021 |title=Poroelasticity as a Model of Soft Tissue Structure: Hydraulic Permeability Reconstruction for Magnetic Resonance Elastography in Silico |journal=Frontiers in Physics |volume=8 |page=637 |doi=10.3389/fphy.2020.617582|pmid=36340954 |pmc=9635531 |arxiv=2012.03993 |bibcode=2021FrP.....8..637S |doi-access=free }}</ref>

Specifically in the hydrology domain, permeability of soil or rock may also be defined as the [[flux]] of water under [[Hydrostatics#Hydrostatic pressure|hydrostatic pressure]] (≈&nbsp;0.1&nbsp;bar/m) at a temperature of 20&nbsp;°C. In this specific setup, 1 darcy is equivalent to 0.831&nbsp;m/day. <ref>K. N. Duggal, J. P. Soni: Elements of Water Resources Engineering. Publisher New Age International, 1996, p. 270</ref>

==References== {{reflist}} * Richard Selley's "Elements of Petroleum Geology (2nd edition)," page 250.

[[Category:Units of measurement]] [[Category:Hydraulics]] [[Category:Hydraulic engineering]] [[Category:Hydrology]] [[Category:Hydrogeology]] [[Category:Soil mechanics]] [[Category:Soil physics]]