Darcy
Encyclopedia
A darcy and millidarcy (mD) are units
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...

of permeability, named after Henry Darcy
Henry Darcy
Henry Philibert Gaspard Darcy was a French engineer who made several important contributions to hydraulics.-Biography:...

. They are not SI units
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

, but they are widely used in petroleum engineering
Petroleum engineering
Petroleum engineering is an engineering discipline concerned with the activities related to the production of hydrocarbons, which can be either crude oil or natural gas. Subsurface activities are deemed to fall within the upstream sector of the oil and gas industry, which are the activities of...

and geology
Geology
Geology is the science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which it evolves. Geology gives insight into the history of the Earth, as it provides the primary evidence for plate tectonics, the evolutionary history of life, and past climates...

. Like other measures of permeability, a darcy has the same units as area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

.

## Definition

Permeability measures the ability of fluids to flow through rock (or other porous media). The darcy is defined using Darcy's law
Darcy's law
Darcy's law is a phenomenologically derived constitutive equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments on the flow of water through beds of sand...

, which can be written as:

where:
 is the superficial (or bulk) fluid flow rate through the medium is the permeability of a medium is the dynamic viscosityViscosityViscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity... of the fluid is the applied pressurePressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :... difference 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
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

1 cP (1 mPa·s) under a pressure gradient of 1 atm/cm acting across an area of 1 cm². A millidarcy (md) is equal to 0.001 darcy and a microdarcy (µd) equals 0.000001 darcy.

## Origin

The darcy is named after Henry Darcy
Henry Darcy
Henry Philibert Gaspard Darcy was a French engineer who made several important contributions to hydraulics.-Biography:...

. Rock permeability is usually expressed in millidarcies (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
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

has a viscosity of 1.0019 cP at about room temperature.

Although the unit is named after Henry Darcy, it should be noted that the unit abbreviation is not capitalized (contrary to industry use). The American Association of Petroleum Geologistsuse 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
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

units, 1 darcy is equivalent to 9.869233×10−13
Square metre
The square metre or square meter is the SI derived unit of area, with symbol m2 . It is defined as the area of a square whose sides measure exactly one metre...

or 0.9869233 (µm
Micrometre
A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...

)². This conversion is usually approximated as 1 (µm)². Note that this is the reciprocal of 1.013250—the conversion factor from atmospheres to bars
Bar (unit)
The bar is a unit of pressure equal to 100 kilopascals, and roughly equal to the atmospheric pressure on Earth at sea level. Other units derived from the bar are the megabar , kilobar , decibar , centibar , and millibar...

.