- Permeability (earth sciences)
Permeability in the
earth sciences (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 of hydrocarbonsin oil and gasreservoirs, and of groundwaterin aquifers. It is typically measured in the lab by application of Darcy's lawunder steady state conditions or, more generally, by application of various solutions to the diffusion equationfor unsteady flow conditions. [cite web
title=CalcTool: Porosity and permeability calculator
The intrinsic permeability of any porous material is::where: is the intrinsic permeability [L2] : is a dimensionless constant that is related to the configuration of the flow-paths: is the average, or effective pore
Permeability needs to be measured, either directly (using
Darcy's law) or through estimationusing empirically derived formulas.
A common unit for permeability is the "
darcy" (D), or more commonly the "millidarcy" (mD) (1 darcy 10−12m2). Other units are cm2 and the SI m2.
Permeability is part of the proportionality constant in
Darcy's lawwhich 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
viscosityof 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.
To model permeability in
anisotropicmedia, a permeability tensoris needed. Pressure can be applied in three directions, and for each direction, permeability can be measured (via Darcy's lawin 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 the
Onsager 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). The eigenvectorswill yield the principal directions of flow, meaning the directions where flow is parallel to the pressure drop, and the eigenvaluesrepresenting 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
*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
* [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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