Darcy (unit)

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| name = darcy

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| quantity = Permeability

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| namedafter = Henry Darcy

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| extralabel = Derivation

| extradata = cP⋅cm{{sup|2}}/(s⋅atm)

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| units1 = SI

| inunits1 = {{val|9.869233e-13|u=m2}}

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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. 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:

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

where:

$Q\,$	is the volumetric fluid flow rate through the medium
$A\,$	is the area of the medium
$k\,$	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.

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.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.

Tissue permeability, whose measurement {{lang|la|in vivo}} is still in its infancy, is somewhere in the range of 0.01 to 100 darcy.

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.

The unit abbreviation "d" is not capitalized (contrary to industry use).{{clarify|date=November 2021}} The American Association of Petroleum Geologists{{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}} 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 {{val|9.869233|e=-13|ul=m2}} or 0.9869233 μm².{{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 }} This conversion is usually approximated as 1 μm². This is the reciprocal of 1.013250—the conversion factor from atmospheres to bars.{{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 }}

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. K. N. Duggal, J. P. Soni: Elements of Water Resources Engineering.

Publisher New Age International, 1996, p. 270

References

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