Permeability (materials science): Difference between revisions
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'''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 in the lab by application of [[Darcy's law]] under steady state conditions or, more generally, by application of various solutions to the [[diffusion equation]] for unsteady flow conditions.<ref> |
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{{cite web |
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|url=http://www.calctool.org/CALC/eng/fluid/darcy |
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|title=CalcTool: Porosity and permeability calculator |
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|publisher=www.calctool.org |
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|accessdate=2008-05-30}}</ref> |
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==Formula== |
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The '''[[Intensive and extensive properties|intrinsic]] permeability''' of any [[Porosity|porous]] material is: |
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:<math>{\kappa}_{I}=C \cdot d^2</math> |
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where |
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:<math>{\kappa}_{I}</math> is the intrinsic permeability [L<sup>2</sup>] |
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:<math>C</math> is a dimensionless constant that is related to the configuration of the flow-paths |
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:<math>d</math> is the average, or effective pore [[diameter]] [L] |
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Permeability needs to be measured, either directly (using [[Darcy's law]]) or through [[estimation]] using [[Empirical method|empirically]] derived formulas. |
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A common unit for permeability is the ''[[darcy]]'' (D), or more commonly the ''millidarcy'' (mD) (1 darcy <math>\approx</math>10<sup>−12</sup>m<sup>2</sup>). Other units are cm<sup>2</sup> and the [[International System of Units|SI]] m<sup>2</sup>. |
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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). |
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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. |
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== Tensor permeability == |
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<!-- Note: This section is linked to from Darcy's law, also fix there if you change the name if this section --> |
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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): |
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* The tensor is symmetric by the [[Onsager reciprocal relations]]. |
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* 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. |
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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. |
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==Ranges of common intrinsic permeabilities== |
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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. |
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{| border="1" width="600" |
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| bgcolor="#FAEBD7" | Permeability |
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| bgcolor="#FAEBD7" colspan="4" align="center" | Pervious |
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| bgcolor="#FAEBD7" colspan="4" align="center" | Semi-Pervious |
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| bgcolor="#FAEBD7" colspan="5" align="center" | Impervious |
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|- |
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| bgcolor="#FAEBD7" | Unconsolidated [[Sand]] & [[Gravel]] |
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| colspan="2" align="center" | Well Sorted Gravel |
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| colspan="3" align="center" | Well Sorted Sand or Sand & Gravel |
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| colspan="4" align="center" | Very Fine Sand, Silt, [[Loess]], [[Loam]] |
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| colspan="4" | |
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|- |
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| bgcolor="#FAEBD7" | Unconsolidated Clay & Organic |
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| colspan="4" | |
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| colspan="2" align="center" | [[Peat]] |
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| colspan="3" align="center" | Layered [[Clay]] |
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| colspan="4" align="center" | Fat / Unweathered Clay |
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|- |
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| bgcolor="#FAEBD7" | Consolidated Rocks |
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| colspan="4" align="center" | Highly Fractured Rocks |
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| colspan="3" align="center" | [[Petroleum geology|Oil Reservoir]] Rocks |
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| colspan="2" align="center" | Fresh [[Sandstone]] |
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| colspan="2" align="center" | Fresh [[Limestone]], [[Dolomite]] |
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| colspan="2" align="center" | Fresh [[Granite]] |
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|- |
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| bgcolor="#FAEBD7" | ''κ'' (cm<sup>2</sup>) |
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| 0.001 |
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| 0.0001 |
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| 10<sup>−5</sup> |
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| 10<sup>−6</sup> |
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| 10<sup>−7</sup> |
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| 10<sup>−8</sup> |
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| 10<sup>−9</sup> |
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| 10<sup>−10</sup> |
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| 10<sup>−11</sup> |
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| 10<sup>−12</sup> |
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| 10<sup>−13</sup> |
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| 10<sup>−14</sup> |
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| 10<sup>−15</sup> |
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|- |
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| bgcolor="#FAEBD7" | ''κ'' (millidarcy) |
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| 10<sup>+8</sup> |
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| 10<sup>+7</sup> |
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| 10<sup>+6</sup> |
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| 10<sup>+5</sup> |
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| 10,000 |
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| 1,000 |
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| 100 |
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| 10 |
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| 1 |
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| 0.1 |
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| 0.01 |
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| 0.001 |
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| 0.0001 |
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|} |
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Source: modified from Bear, 1972 |
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==See also== |
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*[[Hydraulic conductivity]] |
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*[[Hydrogeology]] |
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* [[Permeation]] |
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*[[Petroleum geology]] |
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*[[Relative permeability]] |
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*[[Klinkenberg correction]] |
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==Footnotes== |
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{{reflist}} |
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==References== |
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*Bear, Jacob, 1972. Dynamics of Fluids in Porous Media, Dover. — ISBN 0-486-65675-6 |
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*Wang, H. F., 2000. Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology, Princeton University Press. ISBN 0691037469 |
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==External links== |
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*[http://techalive.mtu.edu/meec/module06/Permeability.htm Graphical depiction of different flow rates through materials of differing permeability] |
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*[http://www.calctool.org/CALC/eng/fluid/darcy Web-based porosity and permeability calculator given flow characteristics] |
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{{Geotechnical engineering|state=collapsed}} |
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[[Category:Aquifers]] |
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[[Category:Hydrology]] |
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[[Category:Soil mechanics]] |
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[[Category:Petroleum]] |
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[[ar:نفاذية التربة]] |
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[[de:Permeabilität (Geowissenschaften)]] |
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[[es:Permeabilidad]] |
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[[fr:Perméabilité (fluide)]] |
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[[it:Permeabilità]] |
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[[nl:Permeabiliteit (geologie)]] |
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[[ja:透水性]] |
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[[no:Permeabilitet (geologi)]] |
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[[pl:Przepuszczalność hydrauliczna]] |
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[[pt:Permeabilidade (geologia)]] |
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