The darcy (or darcy unit) and millidarcy (md or mD) are

units Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation Music * Unit (album), ...

of permeability, named after

Henry Darcy Henry Philibert Gaspard Darcy (, 10 June 1803 – 3 January 1858) was a French engineer who made several important contributions to hydraulics, including Darcy’s law for flow in porous media. Early life Darcy was born in Dijon, France, on J ...

. They are not

SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...

, but they are widely used in petroleum engineering and

geology Geology () is a branch of natural science concerned with Earth and other astronomical objects, the features or rocks of which it is composed, and the processes by which they change over time. Modern geology significantly overlaps all other Ear ...

. 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

dimensional units In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantity, base quantities (such as length, mass, time, and electric current) and units of measur ...

length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Interna ...

².

Definition

Permeability measures the ability of

fluids In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...

to flow through rock (or other porous media). The darcy is defined using

Darcy's law Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of e ...

, which can be written as: :

Q = \frac

where: : 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 The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

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

Origin

The darcy is named after

. 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 Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...

has a viscosity of 1.0019 cP at about room temperature. The unit abbreviation "d" is not capitalized (contrary to industry use). The American Association of Petroleum Geologists 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 or 0.9869233 µm². This conversion is usually approximated as 1 µm². 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 Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...

of water under

hydrostatic pressure Fluid statics or hydrostatics is the branch of fluid mechanics that studies the condition of the equilibrium of a floating body and submerged body "fluids at hydrostatic equilibrium and the pressure in a fluid, or exerted by a fluid, on an imme ...

(~ 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

{{reflist * Richard Selley's "Elements of Petroleum Geology (2nd edition)," page 250. Units of measurement Hydraulics Hydraulic engineering Hydrology Hydrogeology Soil mechanics Soil physics