- Permeability (earth sciences)
**Permeability**in theearth science s (commonly symbolized as "κ", or "k") is a measure of the ability of a material (typically, a rock or unconsolidated material) to transmit fluids. It is of great importance in determining the flow characteristics ofhydrocarbons in oil andgas reservoirs, and ofgroundwater inaquifer s. It is typically measured in the lab by application ofDarcy's law under steady state conditions or, more generally, by application of various solutions to thediffusion equation for unsteady flow conditions. [*cite web*]

url=http://www.calctool.org/CALC/eng/fluid/darcy

title=CalcTool: Porosity and permeability calculator

publisher=www.calctool.org

accessdate=2008-05-30**Formula**The

**intrinsic permeability**of any porous material is::$\{kappa\}\_\{I\}=C\; cdot\; d^2$where:$\{kappa\}\_\{I\}$ is the intrinsic permeability [L^{2}] :$C$ is a dimensionless constant that is related to the configuration of the flow-paths:$d$ is the average, or effective porediameter [L]Permeability needs to be measured, either directly (using

Darcy's law ) or throughestimation using empirically derived formulas.A common unit for permeability is the "

darcy " (D), or more commonly the "millidarcy" (mD) (1 darcy $approx$10^{−12}m^{2}). Other units are cm^{2}and the SI m^{2}.Permeability is part of the proportionality constant in

Darcy's law which relates discharge (flow rate) and fluid physical properties (e.g.viscosity ), to a pressure gradient applied to the porous media. The proportionality constant specifically for the flow of water through a porous media is thehydraulic conductivity ; permeability is a portion of this, and is a property of the porous media only, not the fluid. In naturally occurring materials, it ranges over many orders of magnitude (see table below for an example of this range).For a rock to be considered as an exploitable hydrocarbon reservoir without stimulation, its permeability must be greater than approximately 100 mD (depending on the nature of the hydrocarbon - gas reservoirs with lower permeabilities are still exploitable because of the lower

viscosity of gas with respect to oil). Rocks with permeabilities significantly lower than 100 mD can form efficient "seals" (seepetroleum geology ). Unconsolidated sands may have permeabilities of over 5000 mD.**Tensor permeability**To model permeability in

anisotropic media, a permeabilitytensor is needed. Pressure can be applied in three directions, and for each direction, permeability can be measured (viaDarcy's law in 3D) in three directions, thus leading to a 3 by 3 tensor. The tensor is realized using a 3 by 3 matrix being both symmetric and positive definite (SPD matrix):

* The tensor is symmetric by theOnsager reciprocal relations .

* The tensor is positive definite as the component of the flow parallel to the pressure drop is always in the same direction as the pressure drop.The permeability tensor is always

diagonalizable (being both symmetric and positive definite). Theeigenvectors will yield the principal directions of flow, meaning the directions where flow is parallel to the pressure drop, and theeigenvalues representing the principal permeabilities.**Ranges of common intrinsic permeabilities**These values do not depend on the fluid properties; see the table derived from the same source for values of

hydraulic conductivity , which are specific to the material through which the fluid is flowing.Source: modified from Bear, 1972**ee also***

Hydraulic conductivity

*Hydrogeology

*Permeation

*Petroleum geology

*Relative permeability

*Klinkenberg correction **Footnotes****References***Bear, Jacob, 1972. Dynamics of Fluids in Porous Media, Dover. — ISBN 0-486-65675-6

*Wang, H. F., 2000. Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology, Princeton University Press. ISBN 0691037469

**External links*** [

*http://techalive.mtu.edu/meec/module06/Permeability.htm Graphical depiction of different flow rates through materials of differing permeability*]

* [*http://www.calctool.org/CALC/eng/fluid/darcy Web-based porosity and permeability calculator given flow characteristics*]

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