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Permeability in fluid mechanics and the Earth sciences (commonly symbolized as ''k'') is a measure of the ability of a porous material (often, a rock or an unconsolidated material) to allow fluids to pass through it. The permeability of a medium is related to the porosity, but also to the shapes of the pores in the medium and their level of connectedness. Fluid flows can be influenced in different lithological settings by brittle deformation of rocks in fault zones; the mechanisms by which this occurs are the subject of fault zone hydrogeology.

Permeability

Permeability is the property of rocks that is an indication of the ability for fluids (gas or liquid) to flow through rocks. High permeability will allow fluids to move rapidly through rocks. Permeability is affected by the pressure in a rock. The unit of measure is called the darcy, named after Henry Darcy (1803–1858). Sandstones may vary in permeability from less than one to over 50,000 millidarcys (md). Permeabilities are more commonly in the range of tens to hundreds of millidarcies. A rock with 25% porosity and a permeability of 1 md will not yield a significant flow of water. Such “tight” rocks are usually artificially stimulated (fractured or acidized) to create permeability and yield a flow.


Units


The SI unit for permeability is m2. A practical unit for permeability is the ''darcy'' (d), or more commonly the ''millidarcy'' (md) (1 darcy \approx10−12m2). The name honors the French Engineer Henry Darcy who first described the flow of water through sand filters for potable water supply. Permeability values for sandstones range typically from a fraction of a ''darcy'' to several ''darcys''. The unit of cm2 is also sometimes used (1 cm2 = 10−4 m2 \approx 108 d).


Applications


The concept of permeability is of importance in determining the flow characteristics of hydrocarbons in oil and gas reservoirs, and of groundwater in aquifers. 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. The concept also has many practical applications outside of geology, for example in chemical engineering (e.g., filtration), as well as in Civil Engineering when determining whether the ground conditions of a site are suitable for construction.


Description


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: :v = \frac \frac (for linear flow) Therefore: : k = v \frac where: :v is the fluid velocity through the porous medium (i.e., the average flow velocity calculated as if the fluid was the only phase present in the porous medium) (m/s) :k is the permeability of a medium (m2) :\mu is the dynamic viscosity of the fluid (Pa·s) :\Delta P is the applied pressure difference (Pa) :\Delta x is the thickness of the bed of the porous medium (m) In naturally occurring materials, the permeability values range over many orders of magnitude (see table below for an example of this range).


Relation to hydraulic conductivity


The global proportionality constant for the flow of water through a porous medium is called the hydraulic conductivity. Permeability is a part of this, and is a specific property characteristic of the solid skeleton and the microstructure of the porous medium itself, independently of the nature and properties of the fluid flowing through the pores of the medium. This allows to take into account the effect of temperature on the viscosity of the fluid flowing though the porous medium and to address other fluids than pure water, ''e.g.'', concentrated brines, petroleum, or organic solvents. Given the value of hydraulic conductivity for a studied system, the permeability can be calculated as follows: k = K \frac :where * k is the permeability, m2 * K is the hydraulic conductivity, m/s * \mu is the dynamic viscosity of the fluid, Pa·s * \rho is the density of the fluid, kg/m3 * g is the acceleration due to gravity, m/s2.


Determination


Permeability is typically determined 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. Permeability needs to be measured, either directly (using Darcy's law), or through estimation using empirically derived formulas. However, for some simple models of porous media, permeability can be calculated (e.g., random close packing of identical spheres).

Permeability model based on conduit flow

Based on the Hagen–Poiseuille equation for viscous flow in a pipe, permeability can be expressed as: :k_=C \cdot d^2 where: :k_ is the intrinsic permeability ength2:C is a dimensionless constant that is related to the configuration of the flow-paths :d is the average, or effective pore diameter ength

Absolute permeability (aka intrinsic or specific permeability)

''Absolute permeability'' denotes the permeability in a porous medium that is 100% saturated with a single-phase fluid. This may also be called the ''intrinsic permeability'' or ''specific permeability.'' These terms refer to the quality that the permeability value in question is an intensive property of the medium, not a spatial average of a heterogeneous block of material ; and that it is a function of the material structure only (and not of the fluid). They explicitly distinguish the value from that of relative permeability.

Permeability to gases

Sometimes permeability to gases can be somewhat different than those for liquids in the same media. One difference is attributable to "slippage" of gas at the interface with the solid when the gas mean free path is comparable to the pore size (about 0.01 to 0.1 μm at standard temperature and pressure). See also Knudsen diffusion and constrictivity. For example, measurement of permeability through sandstones and shales yielded values from 9.0×10−19 m2 to 2.4×10−12 m2 for water and between 1.7×10−17 m2 to 2.6×10−12 m2 for nitrogen gas. Gas permeability of reservoir rock and source rock is important in petroleum engineering, when considering the optimal extraction of shale gas, tight gas, or coalbed methane.


Permeability tensor


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 realised 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 because the energy being expended (the inner product of fluid flow and negative pressure gradient) is always positive. The permeability tensor is always diagonalizable (being both symmetric and positive definite). The eigenvectors will yield the principal directions of flow where flow is parallel to the pressure gradient, and the eigenvalues represent 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.Bear, Jacob, 1972. ''Dynamics of Fluids in Porous Media,'' Dover.

See also

* Fault zone hydrogeology * Hydraulic conductivity * Hydrogeology * Permeation * Petroleum geology * Relative permeability * Klinkenberg correction * Electrical resistivity measurement of concrete

Footnotes



References

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

External links


Defining Permeability

Tailoring porous media to control permeability

Permeability of Porous Media


* ttp://www.calctool.org/CALC/eng/fluid/darcy Web-based porosity and permeability calculator given flow characteristics
Multiphase fluid flow in porous media

Florida Method of Test For Concrete Resistivity as an Electrical Indicator of its Permeability
{{DEFAULTSORT:Permeability (Earth Sciences) Category:Aquifers Category:Hydrology Category:Soil mechanics Category:Soil physics Category:Porous media Category:In situ geotechnical investigations