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Permeability (fluid)

 

 
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Permeability (fluid)
 
 
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Permeability in the earth science
Earth science

Earth science , 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....
s (commonly symbolized as ?, or k) is a measure of the ability of a material (typically, a rock
Rock (geology)

In geology, rock is a naturally occurring solid aggregate of minerals and/or mineraloids.The Earth's outer solid layer, the lithosphere, is made of rock....
 or unconsolidated material) to transmit fluids. It is of great importance in determining the flow characteristics of hydrocarbons in oil
Petroleum

Petroleum or crude oil is a naturally occurring, flammable liquid found in rock formations in the Earth consisting of a complex mixture of hydrocarbons of various molecular weights, plus other organic compounds....
 and gas
Gas

In physics, a gas is a state of matter, consisting of a collection of particles without a definite shape or volume that are in more or less random motion....
 reservoirs, and of groundwater
Groundwater

Groundwater is water located beneath the ground surface in soil porosity 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....
 in aquifer
Aquifer

An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials from which groundwater can be usefully extracted using a water well....
s. It is typically measured in the lab by application of Darcy's law
Darcy's law

In fluid dynamics and hydrology, Darcy's law is a Phenomenology derived constitutive equation that describes the flow of a fluid through a porous medium....
 under steady state conditions or, more generally, by application of various solutions to the diffusion equation
Diffusion equation

The diffusion equation is a partial differential equation which describes density fluctuations in a material undergoing diffusion. It is also used to describe processes exhibiting diffusive-like behaviour, for instance the 'diffusion' of alleles in a population in population genetics....
 for unsteady flow conditions.
intrinsic
Intensive and extensive properties

In the physical sciences, an intensive property , is a physical property of a system that does not depend on the system size or the amount of material in the system....
 permeability of any porous
Porosity

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 is used in multiple fields including ceramics, metallurgy, materials, manufacturing, earth sciences and construction....
 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
Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle....
 [L]

Permeability needs to be measured, either directly (using Darcy's law
Darcy's law

In fluid dynamics and hydrology, Darcy's law is a Phenomenology derived constitutive equation that describes the flow of a fluid through a porous medium....
) or through estimation
Estimation

Estimation is the calculation approximation of a result which is usable even if input data may be incomplete or uncertainty.In statistics, see estimation theory, estimator....
 using empirically
Empirical method

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 Experiment....
 derived formulas.

A common unit for permeability is the darcy
Darcy

A darcy is a Units of measurement of Permeability , named after Henry Darcy. It is not an SI, but it is widely used in petroleum engineering and geology....
 (D), or more commonly the millidarcy (mD) (1 darcy 10−12m2).






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Encyclopedia


Permeability in the earth science
Earth science

Earth science , 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....
s (commonly symbolized as ?, or k) is a measure of the ability of a material (typically, a rock
Rock (geology)

In geology, rock is a naturally occurring solid aggregate of minerals and/or mineraloids.The Earth's outer solid layer, the lithosphere, is made of rock....
 or unconsolidated material) to transmit fluids. It is of great importance in determining the flow characteristics of hydrocarbons in oil
Petroleum

Petroleum or crude oil is a naturally occurring, flammable liquid found in rock formations in the Earth consisting of a complex mixture of hydrocarbons of various molecular weights, plus other organic compounds....
 and gas
Gas

In physics, a gas is a state of matter, consisting of a collection of particles without a definite shape or volume that are in more or less random motion....
 reservoirs, and of groundwater
Groundwater

Groundwater is water located beneath the ground surface in soil porosity 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....
 in aquifer
Aquifer

An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials from which groundwater can be usefully extracted using a water well....
s. It is typically measured in the lab by application of Darcy's law
Darcy's law

In fluid dynamics and hydrology, Darcy's law is a Phenomenology derived constitutive equation that describes the flow of a fluid through a porous medium....
 under steady state conditions or, more generally, by application of various solutions to the diffusion equation
Diffusion equation

The diffusion equation is a partial differential equation which describes density fluctuations in a material undergoing diffusion. It is also used to describe processes exhibiting diffusive-like behaviour, for instance the 'diffusion' of alleles in a population in population genetics....
 for unsteady flow conditions.

Formula

The intrinsic
Intensive and extensive properties

In the physical sciences, an intensive property , is a physical property of a system that does not depend on the system size or the amount of material in the system....
 permeability of any porous
Porosity

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 is used in multiple fields including ceramics, metallurgy, materials, manufacturing, earth sciences and construction....
 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
Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle....
 [L]

Permeability needs to be measured, either directly (using Darcy's law
Darcy's law

In fluid dynamics and hydrology, Darcy's law is a Phenomenology derived constitutive equation that describes the flow of a fluid through a porous medium....
) or through estimation
Estimation

Estimation is the calculation approximation of a result which is usable even if input data may be incomplete or uncertainty.In statistics, see estimation theory, estimator....
 using empirically
Empirical method

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 Experiment....
 derived formulas.

A common unit for permeability is the darcy
Darcy

A darcy is a Units of measurement of Permeability , named after Henry Darcy. It is not an SI, but it is widely used in petroleum engineering and geology....
 (D), or more commonly the millidarcy (mD) (1 darcy 10−12m2). Other units are cm2 and the SI
International System of Units

The International System of Units is the modern form of the metric system and is generally a system devised around the convenience of the number ten....
 m2.

Permeability is part of the proportionality constant in Darcy's law
Darcy's law

In fluid dynamics and hydrology, Darcy's law is a Phenomenology derived constitutive equation that describes the flow of a fluid through a porous medium....
 which relates discharge (flow rate) and fluid physical properties (e.g. viscosity
Viscosity

Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
), 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
Hydraulic conductivity

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....
; 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
Viscosity

Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
 of gas with respect to oil). Rocks with permeabilities significantly lower than 100 mD can form efficient seals (see petroleum geology
Petroleum geology

Petroleum geology refers to the specific set of geological disciplines that are applied to the search for hydrocarbons ....
). Unconsolidated sands may have permeabilities of over 5000 mD.

Tensor permeability


To model permeability in anisotropic media, a permeability tensor
Tensor

A tensor is an object which extends the notion of Scalar , Vector , and Matrix . The term has slightly different meanings in mathematics and physics....
 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
Matrix (mathematics)

In mathematics, a matrix is a rectangular array of numbers, as shown at the right. In addition to a number of elementary, entrywise operations such as matrix addition a key notion is matrix multiplication....
 being both symmetric
Symmetric matrix

In linear algebra, a symmetric matrix is a square matrix, A, that is equal to its transposeThe entries of a symmetric matrix are symmetric with respect to the main diagonal ....
 and positive definite
Positive-definite matrix

In linear algebra, a positive-definite matrix is a Hermitian matrix matrix which in many ways is analogous to a positive real number. The notion is closely related to a Definite bilinear form symmetric bilinear form ....
 (SPD matrix):
  • The tensor is symmetric by the Onsager reciprocal relations
    Onsager reciprocal relations

    In thermodynamics, the Onsager reciprocal relations express the equality of certain relations between fluxs and forces in thermodynamic systems out of equilibrium , but where a notion of local thermodynamic equilibrium exists....
    .
  • The tensor is positive definite as the component of the flow parallel
    Parallel (geometry)

    Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more line s or plane , or a combination of these....
     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 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
Hydraulic conductivity

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....
, which are specific to the material through which the fluid is flowing.
Permeability Pervious Semi-Pervious Impervious
Unconsolidated Sand
Sand

Sand is a naturally occurring granular material composed of finely divided rock and mineral particles.As the term is used by geologists, sand particles range in diameter from 0.0625 to 2 millimeters....
 & Gravel
Gravel

Gravel is rock that is of a specific particle size range. Specifically, it is is any loose rock that is larger than two millimeters in its largest dimension and no more than 64 millimeters ....
 Well Sorted Gravel Well Sorted Sand or Sand & Gravel Very Fine Sand, Silt, Loess
Loess

Loess is a homogeneous, typically nonstratified, porous, friable,slightly coherent, often calcareous, fine-grained, silty, pale yellow or buff, windblown sediment....
, Loam
Loam

Loam is soil composed of sand, silt, and clay in relatively even concentration , considered ideal for gardening and agricultural uses. Loam soils generally contain more nutrients and humus than sandy soils, have better infiltration and drainage than silty soils, and are easier to tillage than clay soils....
 
Unconsolidated Clay & Organic  Peat
Peat

Peat is an accumulation of partially decayed vegetation biological tissue. Peat forms in wetlands or peatlands, variously called bogs, Moorland, muskegs, pocosins, mires, and peat swamp forests....
 Layered Clay
Clay

Clay is a naturally occurring material composed primarily of fine-grained minerals, which show plasticity through a variable range of water content, and which can be hardened when dried and/or fired....
 Fat / Unweathered Clay
Consolidated Rocks Highly Fractured Rocks Oil Reservoir
Petroleum geology

Petroleum geology refers to the specific set of geological disciplines that are applied to the search for hydrocarbons ....
 Rocks		 Fresh Sandstone
Sandstone

Sandstone is a sedimentary rock composed mainly of sand-size mineral or rock Particle size . Most sandstone is composed of quartz and/or feldspar because these are the most common minerals in the Earth's crust ....
 Fresh Limestone
Limestone

File:Limestone Formation In Waitomo.jpgLimestone is a sedimentary rock composed largely of the mineral calcite . The deposition of limestone strata is often a by-product and indicator of biological activity in the geology record....
, Dolomite
Dolomite

Dolomite is the name of a sedimentary carbonate rock and a mineral, both composed of calcium magnesium carbonate calciummagnesium2 found in crystals....
 Fresh Granite
Granite

Granite is a common and widely occurring type of Intrusion , felsic, igneous rock rock . Granite has a medium to coarse texture, occasionally with some individual crystals larger than the groundmass forming a rock known as Porphyry ....
? (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
? (millidarcy) 10+8 10+7 10+6 10+5 10,000 1,000 100 10 1 0.1 0.01 0.001 0.0001
Source: modified from Bear, 1972

See also

  • Hydraulic conductivity
    Hydraulic conductivity

    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....
  • Hydrogeology
    Hydrogeology

    Hydrogeology is the area of geology that deals with the distribution and movement of groundwater in the soil and rock of the Earth's crust , ....
  • Permeation
    Permeation

    Permeation, in physics and engineering, is the penetration of a permeate through a solid, and is related to a material's intrinsic permeability....
  • Petroleum geology
    Petroleum geology

    Petroleum geology refers to the specific set of geological disciplines that are applied to the search for hydrocarbons ....
  • Relative permeability
    Relative permeability

    In multiphase flow in porous media, relative permeability is a dimensionless measure of the effective Permeability of each phase. It can be viewed as an adaptation of Darcy's law to multiphase flow....
  • Klinkenberg correction
    Klinkenberg correction

    In petroleum engineering, a Klinkenberg correction is a procedure for calibration of permeability data obtained from a minipermeameter device. When using nitrogen gas for core plug measurements, the Klinkenberg correction is usually necessary due to the so called Klinkenberg gas slippage effect....


Footnotes


External links