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Influid mechanics,materials science andEarth sciences, thepermeability ofporous media (often, arock orsoil) is a measure of the ability for fluids (gas or liquid) to flow through the media; it is commonly symbolized ask.Fluids can more easily flow through a material with high permeability than one with low permeability.[1]
The permeability of a medium is related to theporosity, but also to the shapes of the pores in the medium and their level of connectedness.[2] Fluid flows can also be influenced in differentlithological settings by brittle deformation of rocks infault zones; the mechanisms by which this occurs are the subject offault zone hydrogeology.[3] Permeability is also affected by the pressure inside a material.
TheSI unit for permeability is thesquare metre (m2). A practical unit for permeability is thedarcy (d), or more commonly themillidarcy (md)(1 d ≈ 10−12 m2). The name honors the French EngineerHenry Darcy who first described the flow of water through sand filters for potable water supply. Permeability values for most materials commonly range typically from a fraction to several thousand millidarcys. The unit of square centimetre (cm2) is also sometimes used(1 cm2 = 10−4 m2 ≈ 108 d).
The concept of permeability is of importance in determining the flow characteristics ofhydrocarbons inoil andgas reservoirs,[4] and ofgroundwater inaquifers.[5]
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 lowerviscosity of gas in comparison with oil). Rocks with permeabilities significantly lower than 100 md can form efficientseals (seepetroleum geology). Unconsolidated sands may have permeabilities of over 5000 md.
The concept also has many practical applications outside of geology, for example inchemical engineering (e.g.,filtration), as well as in Civil Engineering when determining whether the ground conditions of a site are suitable for construction.
The concept of permeability is also useful in computational fluid dynamics (CFD) for modeling flow through complex geometries such as packed beds, filter papers, or tube banks. When the size of individual components—such as particle diameter in packed beds or tube diameter in tube bundles—are significantly smaller than the overall flow domain, direct modeling becomes computationally intensive due to the fine mesh resolution required. In such cases, the domain can be approximated as a porous medium, with permeability estimated using correlations, experimental data, or separate fluid flow simulations.[6]
Permeability is part of the proportionality constant inDarcy's law which relates discharge (flow rate) and fluid physical properties (e.g.dynamic viscosity), to a pressure gradient applied to the porous media:[7]
Therefore:
where:
In naturally occurring materials, the permeability values range over many orders of magnitude (see table below for an example of this range).
The global proportionality constant for the flow of water through aporous medium is called thehydraulic conductivity (K, unit: m/s). Permeability, or intrinsic permeability, (k, unit: m2) 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., concentratedbrines,petroleum, ororganic solvents. Given the value of hydraulic conductivity for a studied system, the permeability can be calculated as follows:
Tissue such as brain, liver, muscle, etc can be treated as a heterogeneous porous medium. Describing the flow of biofluids (blood, cerebrospinal fluid, etc.) within such a medium requires a full 3-dimensionalanisotropic treatment of the tissue. In this case thescalar hydraulic permeability is replaced with the hydraulic permeabilitytensor so that Darcy's Law reads[8]
Connecting this expression to the isotropic case,, where k is the scalar hydraulic permeability, and 1 is theidentity tensor.
Permeability is typically determined 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.[9]
Permeability needs to be measured, either directly (using Darcy's law), or throughestimation usingempirically derived formulas. However, for some simple models of porous media, permeability can be calculated (e.g.,random close packing of identical spheres).
Based on theHagen–Poiseuille equation for viscous flow in a pipe, permeability can be expressed as:
where:
Absolute permeability denotes the permeability in a porous medium that is 100% saturated with a single-phase fluid. This may also be called theintrinsic permeability orspecific permeability. These terms refer to the quality that the permeability value in question is anintensive property of the medium, not a spatial average of a heterogeneous block of materialequation 2.28[clarification needed][further explanation needed]; and that it is a function of the material structure only (and not of the fluid).[10] They explicitly distinguish the value from that ofrelative permeability.[11]
Sometimes, permeability to gases can be somewhat different than that for liquids in the same media. One difference is attributable to the "slippage" of gas at the interface with the solid[12] when the gasmean free path is comparable to the pore size (about 0.01 to 0.1 μm at standard temperature and pressure). See alsoKnudsen diffusion andconstrictivity. 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.[13] Gas permeability ofreservoir rock andsource rock is important inpetroleum engineering, when considering the optimal extraction of gas fromunconventional sources such asshale gas,tight gas, orcoalbed methane.
To model permeability inanisotropic media, a permeabilitytensor 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 3matrix being bothsymmetric andpositive definite (SPD matrix):
The permeability tensor is alwaysdiagonalizable (being both symmetric and positive definite). Theeigenvectors will yield the principal directions of flow where flow is parallel to the pressure gradient, and theeigenvalues represent the principal permeabilities.
These values do not depend on the fluid properties; see the table derived from the same source for values ofhydraulic conductivity, which are specific to the material through which the fluid is flowing.[14]
| Permeability | Pervious | Semi-pervious | Impervious | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Unconsolidated sand and gravel | Well sortedgravel | Well sortedsand or sand and gravel | Very fine sand, silt,loess,loam | ||||||||||
| Unconsolidated clay and organic | Peat | Layeredclay | Unweathered clay | ||||||||||
| Consolidated rocks | Highly fractured rocks | Oil reservoir rocks | Freshsandstone | Freshlimestone,dolomite | Freshgranite | ||||||||
| k (cm2) | 0.001 | 0.0001 | 10−5 | 10−6 | 10−7 | 10−8 | 10−9 | 10−10 | 10−11 | 10−12 | 10−13 | 10−14 | 10−15 |
| k (m2) | 10−7 | 10−8 | 10−9 | 10−10 | 10−11 | 10−12 | 10−13 | 10−14 | 10−15 | 10−16 | 10−17 | 10−18 | 10−19 |
| k (millidarcy) | 10+8 | 10+7 | 10+6 | 10+5 | 10,000 | 1,000 | 100 | 10 | 1 | 0.1 | 0.01 | 0.001 | 0.0001 |
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