Permeability (earth sciences) 754488 223900664 2008-07-06T12:18:03Z 203.217.85.28 fixed principal permeability text {{Refimprove|date=April 2008}} '''Permeability''' in the [[earth science]]s (commonly symbolized as ''κ'', or ''k'') is a measure of the ability of a material (typically, a [[Rock (geology)|rock]] or unconsolidated material) to transmit fluids. It is of great importance in determining the flow characteristics of [[hydrocarbons]] in [[Petroleum|oil]] and [[gas]] reservoirs, and of [[groundwater]] in [[aquifer]]s. It is typically measured through calculation of [[Darcy's law]].<ref> {{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}}</ref> ==Formula== The '''[[Intensive and extensive properties|intrinsic]] permeability''' of any [[Porosity|porous]] material is: :<math>{\kappa}_{I}=C \cdot d^2</math> where :<math>{\kappa}_{I}</math> is the intrinsic permeability [L<sup>2</sup>] :<math>C</math> is a dimensionless constant that is related to the configuration of the flow-paths :<math>d</math> is the average, or effective pore [[diameter]] [L] Permeability needs to be measured, either directly (using [[Darcy's law]]) or through [[estimation]] using [[Empirical method|empirically]] derived formulas. A common unit for permeability is the ''[[darcy]]'' (D), or more commonly the ''millidarcy'' (mD) (1 darcy <math>\approx</math>10<sup>&minus;12</sup>m<sup>2</sup>). Other units are cm<sup>2</sup> and the [[International System of Units|SI]] m<sup>2</sup>. 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 the [[hydraulic 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'' (see [[petroleum geology]]). Unconsolidated sands may have permeabilities of over 5000 mD. == Tensor permeability == <!-- Note: This section is linked to from Darcy's law, also fix there if you change the name if this section --> To model permeability in [[anisotropic]] media, a permeability [[tensor]] is needed. Pressure can be applied in three directions, and for each direction, permeability can be measured (via [[Darcy'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 (mathematics)|matrix]] being both [[Symmetric matrix|symmetric]] and [[Positive-definite matrix|positive definite]] (SPD matrix): * The tensor is symmetric by the [[Onsager reciprocal relations]]. * The tensor is positive definite as the component of the flow [[Parallel (geometry)|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). The [[eigenvectors]] will yield the principal directions of flow, meaning the directions where flow is parallel to the pressure drop, and the [[eigenvalues]] 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. {| border="1" width="600" | bgcolor="#FAEBD7" | Permeability | bgcolor="#FAEBD7" colspan="4" align="center" | Pervious | bgcolor="#FAEBD7" colspan="4" align="center" | Semi-Pervious | bgcolor="#FAEBD7" colspan="5" align="center" | Impervious |- | bgcolor="#FAEBD7" | Unconsolidated [[Sand]] & [[Gravel]] | colspan="2" align="center" | Well Sorted Gravel | colspan="3" align="center" | Well Sorted Sand or Sand & Gravel | colspan="4" align="center" | Very Fine Sand, Silt, [[Loess]], [[Loam]] | colspan="4" | |- | bgcolor="#FAEBD7" | Unconsolidated Clay & Organic | colspan="4" | | colspan="2" align="center" | [[Peat]] | colspan="3" align="center" | Layered [[Clay]] | colspan="4" align="center" | Fat / Unweathered Clay |- | bgcolor="#FAEBD7" | Consolidated Rocks | colspan="4" align="center" | Highly Fractured Rocks | colspan="3" align="center" | [[Petroleum geology|Oil Reservoir]] Rocks | colspan="2" align="center" | Fresh [[Sandstone]] | colspan="2" align="center" | Fresh [[Limestone]], [[Dolomite]] | colspan="2" align="center" | Fresh [[Granite]] |- | bgcolor="#FAEBD7" | ''κ'' (cm<sup>2</sup>) | 0.001 | 0.0001 | 10<sup>&minus;5</sup> | 10<sup>&minus;6</sup> | 10<sup>&minus;7</sup> | 10<sup>&minus;8</sup> | 10<sup>&minus;9</sup> | 10<sup>&minus;10</sup> | 10<sup>&minus;11</sup> | 10<sup>&minus;12</sup> | 10<sup>&minus;13</sup> | 10<sup>&minus;14</sup> | 10<sup>&minus;15</sup> |- | bgcolor="#FAEBD7" | ''κ'' (millidarcy) | 10<sup>+8</sup> | 10<sup>+7</sup> | 10<sup>+6</sup> | 10<sup>+5</sup> | 10,000 | 1,000 | 100 | 10 | 1 | 0.1 | 0.01 | 0.001 | 0.0001 |} Source: modified from Bear, 1972 ==See also== *[[Hydraulic conductivity]] *[[Hydrogeology]] * [[Permeation]] *[[Petroleum geology]] *[[Relative permeability]] ==Footnotes== {{reflist}} ==References== *Bear, Jacob, 1972. Dynamics of Fluids in Porous Media, Dover. &mdash; 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] {{Geotechnical engineering|state=collapsed}} [[Category:Aquifers]] [[Category:Hydrology]] [[Category:Soil mechanics]] [[Category:Petroleum]] [[de:Permeabilität (Petrophysik)]] [[es:Permeabilidad]] [[fr:Perméabilité (fluide)]] [[it:Permeabilità]] [[nl:Permeabiliteit (geologie)]] [[ja:透水性]] [[no:Permeabilitet (geologi)]] [[pl:Przepuszczalność hydrauliczna]] [[pt:Permeabilidade (geologia)]]