iPedia Free Information Center

Information about Permeability (fluid)

In the earth sciences, permeability (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 hydrocarbons in oil and gas reservoirs, and of groundwater in aquifers.

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 diameter [L]


Permeability needs to be measured, either directly (using Darcy's law) or through estimation using 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 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

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 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 eigenvectors will yield the principal directions of flow, meaning the directions where flow is parallel to the pressure drop, and the eigenvalues representing the magnitude of flow along principal directions.

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 water.
PermeabilityPerviousSemi-PerviousImpervious
Unconsolidated Sand & GravelWell Sorted GravelWell Sorted Sand or Sand & GravelVery Fine Sand, Silt, Loess, Loam
Unconsolidated Clay & OrganicPeatLayered ClayFat / Unweathered Clay
Consolidated RocksHighly Fractured RocksOil Reservoir RocksFresh SandstoneFresh Limestone, DolomiteFresh Granite
κ (cm²)0.0010.000110−510−610−710−810−910−1010−1110−1210−1310−1410−15
κ (millidarcy)10+810+710+610+510,0001,0001001010.10.010.0010.0001
Source: modified from Bear, 1972

See also

References

  • Bear, Jacob, 1972. Dynamics of Fluids in Porous Media, Dover. — ISBN 0-486-65675-6

External links

Earth science (also known as geoscience, the geosciences or the Earth Sciences), is an all-embracing term for the sciences related to the planet Earth. It is arguably a special case in planetary science, the Earth being the only known life-bearing planet.
..... Click the link for more information.
Balanced Rock stands in Garden of the Gods park in Colorado Springs, CO]] A rock is a naturally occurring aggregate of minerals and/or mineraloids. The Earth's lithosphere is made of rock. In general rocks are of three types, namely, igneous, sedimentary, and metamorphic.
..... Click the link for more information.
hydrocarbon is an organic compound consisting entirely of hydrogen and carbon. With relation to chemical terminology, aromatic hydrocarbons or arenes, alkanes, alkenes and alkyne-based compounds composed entirely of carbon or hydrogen are referred to as "Pure" hydrocarbons, whereas
..... Click the link for more information.
Petroleum (Latin Petroleum derived from Greek πέτρα (Latin petra) - rock + έλαιον (Latin oleum) - oil) or crude oil
..... Click the link for more information.
Gas is one of the four major states of matter, consisting of freely moving atoms or molecules without a definite shape. Compared to the solid and liquid states of matter a gas has lower density and a lower viscosity.
..... Click the link for more information.
Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of lithologic formations. A unit of rock or an unconsolidated deposit is called an aquifer when it can yield a usable quantity of water.
..... Click the link for more information.
An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well.
..... Click the link for more information.
In physics and chemistry an intensive property (also called a bulk property) of a system is a physical property of the system that does not depend on the system size or the amount of material in the system.
..... Click the link for more information.
Porosity is a measure of the void spaces in a material, and is measured as a fraction, between 0–1, or as a percentage between 0–100%. The term porosity is used in multiple fields including manufacturing, earth sciences and construction.
..... Click the link for more information.
diameter (Greek words diairo = divide and metro = measure) of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle.
..... Click the link for more information.
In fluid dynamics, Darcy's law is a phenomologically derived constitutive equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments[1] on the flow of water through beds of sand.
..... Click the link for more information.
Estimation is the calculated approximation of a result which is usable even if input data may be incomplete, uncertain, or noisy.

In statistics, see estimation theory, estimator.
..... Click the link for more information.
Empirical method is generally taken to mean the collection of data on which to base a theory or derive a conclusion in science. It is part of the scientific method, but is often mistakenly assumed to be synonymous with the experimental method.
..... Click the link for more information.
darcy is a unit of permeability, named after Henry Darcy. It is not an SI unit, but it is widely used in petroleum engineering and geology. Like other measures of permeability, a darcy has the same units as area.
..... Click the link for more information.
International System of Units (abbreviated SI from the French Le Système international d'unités) is the modern form of the metric system.
..... Click the link for more information.
In fluid dynamics, Darcy's law is a phenomologically derived constitutive equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments[1] on the flow of water through beds of sand.
..... Click the link for more information.
Viscosity is a measure of the resistance of a fluid to deform under either shear stress or extensional stress. It is commonly perceived as "thickness", or resistance to flow.
..... Click the link for more information.
Hydraulic conductivity, symbolically represented as , is a property of vascular plants, soil or rock, that describes the ease with which water can move through pore spaces or fractures. It depends on the intrinsic permeability of the material and on the degree of saturation.
..... Click the link for more information.
Viscosity is a measure of the resistance of a fluid to deform under either shear stress or extensional stress. It is commonly perceived as "thickness", or resistance to flow.
..... Click the link for more information.
Petroleum geology refers to the specific set of geological disciplines that are applied to the search for hydrocarbons (oil exploration).

Sedimentary basin analysis


..... Click the link for more information.
Anisotropy (pronounced with stress on the third syllable, IPA: /ˌænaɪˈsɒtrəpi/) is the property of being directionally dependent, as opposed to isotropy, which means homogeneity in all directions.
..... Click the link for more information.
The term tensor has slightly different meanings in mathematics and physics. In the mathematical fields of multilinear algebra and differential geometry, a tensor is a multilinear function.
..... Click the link for more information.
In fluid dynamics, Darcy's law is a phenomologically derived constitutive equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments[1] on the flow of water through beds of sand.
..... Click the link for more information.
matrix (plural matrices) is a rectangular table of elements (or entries), which may be numbers or, more generally, any abstract quantities that can be added and multiplied.
..... Click the link for more information.
In linear algebra, a symmetric matrix is a square matrix, A, that is equal to its transpose



The entries of a symmetric matrix are symmetric with respect to the main diagonal (top left to bottom right).
..... Click the link for more information.
In linear algebra, a positive-definite matrix is a Hermitian matrix which in many ways is analogous to a positive real number. The notion is closely related to a positive-definite symmetric bilinear form (or a sesquilinear form in the complex case).
..... Click the link for more information.
In thermodynamics, the Onsager reciprocal relations express the equality of certain relations between flows and forces in thermodynamic systems out of equilibrium, but where a notion of local equilibrium exists.
..... Click the link for more information.
Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The existence and properties of parallel lines are the basis of Euclid's parallel postulate.
..... Click the link for more information.
In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e. if there exists an invertible matrix P such that P −1AP is a diagonal matrix.
..... Click the link for more information.
eigenvector of the transformation and the blue vector is not. Since the red vector was neither stretched nor compressed, its eigenvalue is 1. All vectors with the same vertical direction - i.e., parallel to this vector - are also eigenvectors, with the same eigenvalue.
..... Click the link for more information.


This article is copied from an article on Wikipedia.org - the free encyclopedia created and edited by online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of the wikipedia encyclopedia articles provide accurate and timely information please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.
Herod_Archelaus


page counter