Darcy (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.^[1] A darcy has dimensions of length².

darcy
Unit of	Permeability
Symbol	d
Named after	Henry Darcy
Derivation	cP⋅cm2/(s⋅atm)
Conversions
1 d in ...	... is equal to ...
SI	9.869233×10−13 m2

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:

${\displaystyle Q={\frac {Ak\,\Delta P}{\mu \,\Delta x}}}$

where:

${\displaystyle Q\,}$	is the volumetric fluid flow rate through the medium
${\displaystyle A\,}$	is the area of the medium
${\displaystyle k\,}$	is the permeability of the medium
${\displaystyle \mu \,}$	is the dynamic viscosity of the fluid
${\displaystyle \Delta P\,}$	is the applied pressure difference
${\displaystyle \Delta x\,}$	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.^[2]

Tissue permeability, whose measurement in vivo is still in its infancy, is somewhere in the range of 0.01 to 100 darcy.^[1]

Origin

The darcy is named after Henry Darcy.^[1] 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).^{[clarification needed]} The American Association of Petroleum Geologists^[3] 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 9.869233×10⁻¹³ m² or 0.9869233 μm².^[4] This conversion is usually approximated as 1 μm². This is the reciprocal of 1.013250—the conversion factor from atmospheres to bars.^[1]

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. ^[5]

References

1. Sowinski, Damian (January 2021). "Poroelasticity as a Model of Soft Tissue Structure: Hydraulic Permeability Reconstruction for Magnetic Resonance Elastography in Silico". Frontiers in Physics. 8: 637. arXiv:2012.03993. Bibcode:2021FrP.....8..637S. doi:10.3389/fphy.2020.617582. PMC 9635531. PMID 36340954.
2. 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.
3. "The American Association of Petroleum Geologist Style Guides" (PDF). Archived from the original (PDF) on 2011-08-09.
4. The SI Metric System of Units and SPE Metric Standard (PDF) (2nd ed.). Society of Petroleum Engineers. June 1984 [First published 1982].
5. 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.