Porosity

In gas-liquid two-phase flow, the void fraction is defined as the fraction of the flow-channel volume that is occupied by the gas phase or, alternatively, as the fraction of the cross-sectional area of the channel that is occupied by the gas phase.[1]

Void fraction usually varies from location to location in the flow channel (depending on the two-phase flow pattern). It fluctuates with time and its value is usually time averaged. In separated (i.e., non-homogeneous) flow, it is related to volumetric flow rates of the gas and the liquid phase, and to the ratio of the velocity of the two phases (called slip ratio).

Used in geology, hydrogeology, soil science, and building science, the porosity of a porous medium (such as rock or sediment) describes the fraction of void space in the material, where the void may contain, for example, air or water. It is defined by the ratio:

${\displaystyle \phi ={\frac {V_{\mathrm {V} }}{V_{\mathrm {T} }}}}$

where V_V is the volume of void-space (such as fluids) and V_T is the total or bulk volume of material, including the solid and void components. Both the mathematical symbols ${\displaystyle \phi }$ and ${\displaystyle n}$ are used to denote porosity.

Porosity is a fraction between 0 and 1, typically ranging from less than 0.005 for solid granite to more than 0.5 for peat and clay.

The porosity of a rock, or sedimentary layer, is an important consideration when attempting to evaluate the potential volume of water or hydrocarbons it may contain. Sedimentary porosity is a complicated function of many factors, including but not limited to: rate of burial, depth of burial, the nature of the connate fluids, the nature of overlying sediments (which may impede fluid expulsion). One commonly used relationship between porosity and depth is given by the Athy (1930) equation:[2]

${\displaystyle \phi (z)=\phi _{0}e^{-kz}\,}$

where ${\displaystyle \phi _{0}}$ is the surface porosity, ${\displaystyle k}$ is the compaction coefficient (m⁻¹) and ${\displaystyle z}$ is depth (m).

A value for porosity can alternatively be calculated from the bulk density ${\displaystyle \rho _{\text{bulk}}}$, saturating fluid density ${\displaystyle \rho _{\text{fluid}}}$ and particle density ${\displaystyle \rho _{\text{particle}}}$:

${\displaystyle \phi ={\frac {\rho _{\text{particle}}-\rho _{\text{bulk}}}{\rho _{\text{particle}}-\rho _{\text{fluid}}}}}$

If the void space is filled with air, the following simpler form may be used:

${\displaystyle \phi =1-{\frac {\rho _{\text{bulk}}}{\rho _{\text{particle}}}}}$

Normal particle density is assumed to be approximately 2.65 g/cm³ (silica), although a better estimation can be obtained by examining the lithology of the particles.

Sorting and porosity

Effects of sorting on alluvial porosity. Black represents solids, blue represents pore space.

Well sorted (grains of approximately all one size) materials have higher porosity than similarly sized poorly sorted materials (where smaller particles fill the gaps between larger particles). The graphic illustrates how some smaller grains can effectively fill the pores (where all water flow takes place), drastically reducing porosity and hydraulic conductivity, while only being a small fraction of the total volume of the material. For tables of common porosity values for earth materials, see the "further reading" section in the Hydrogeology article.

The ratio of holes to solid that the wind "sees". Aerodynamic porosity is less than visual porosity, by an amount that depends on the constriction of holes.

Casting porosity is a consequence of one or more of the following: gasification of contaminants at molten-metal temperatures; shrinkage that takes place as molten metal solidifies; and unexpected or uncontrolled changes in temperature or humidity.

While porosity is inherent in die casting manufacturing, its presence may lead to component failure where pressure integrity is a critical characteristic. Porosity may take on several forms from interconnected micro-porosity, folds, and inclusions to macro porosity visible on the part surface. The end result of porosity is the creation of a leak path through the walls of a casting that prevents the part from holding pressure. Porosity may also lead to out-gassing during the painting process, leaching of plating acids and tool chatter in machining pressed metal components.[4]

Optical method of measuring porosity: thin section under gypsum plate shows porosity as purple color, contrasted with carbonate grains of other colors. Pleistocene eolianite from San Salvador Island, Bahamas. Scale bar 500 μm.

Several methods can be employed to measure porosity:

• Direct methods (determining the bulk volume of the porous sample, and then determining the volume of the skeletal material with no pores (pore volume = total volume − material volume).
• Optical methods (e.g., determining the area of the material versus the area of the pores visible under the microscope). The "areal" and "volumetric" porosities are equal for porous media with random structure.[5]
• Computed tomography method (using industrial CT scanning to create a 3D rendering of external and internal geometry, including voids. Then implementing a defect analysis utilizing computer software)
• Imbibition methods,[5] i.e., immersion of the porous sample, under vacuum, in a fluid that preferentially wets the pores.
  • Water saturation method (pore volume = total volume of water − volume of water left after soaking).
• Water evaporation method (pore volume = (weight of saturated sample − weight of dried sample)/density of water)
• Mercury intrusion porosimetry (several non-mercury intrusion techniques have been developed due to toxicological concerns, and the fact that mercury tends to form amalgams with several metals and alloys).
• Gas expansion method.[5] A sample of known bulk volume is enclosed in a container of known volume. It is connected to another container with a known volume which is evacuated (i.e., near vacuum pressure). When a valve connecting the two containers is opened, gas passes from the first container to the second until a uniform pressure distribution is attained. Using ideal gas law, the volume of the pores is calculated as

${\displaystyle V_{V}=V_{T}-V_{a}-V_{b}{P_{2} \over {P_{2}-P_{1}}}}$,

where

V_V is the effective volume of the pores,

V_T is the bulk volume of the sample,

V_a is the volume of the container containing the sample,

V_b is the volume of the evacuated container,

P₁ is the initial pressure in the initial pressure in volume V_a and V_V, and

P₂ is final pressure present in the entire system.

The porosity follows straightforwardly by its proper definition

${\displaystyle \phi ={\frac {V_{V}}{V_{T}}}}$.

Note that this method assumes that gas communicates between the pores and the surrounding volume. In practice, this means that the pores must not be closed cavities.

• Thermoporosimetry and cryoporometry. A small crystal of a liquid melts at a lower temperature than the bulk liquid, as given by the Gibbs-Thomson equation. Thus if a liquid is imbibed into a porous material, and frozen, the melting temperature will provide information on the pore-size distribution. The detection of the melting can be done by sensing the transient heat flows during phase-changes using differential scanning calorimetry – (DSC thermoporometry),[6] measuring the quantity of mobile liquid using nuclear magnetic resonance – (NMR cryoporometry)[7] or measuring the amplitude of neutron scattering from the imbibed crystalline or liquid phases – (ND cryoporometry).[8]

• Void ratio
• Petroleum geology
• Poromechanics
• Bulk density
• Particle density (packed density)
• Packing density
• Void (composites)
• Coherent diffraction imaging

• Glasbey, C. A.; G. W. Horgan; J. F. Darbyshire (September 1991). "Image analysis and three-dimensional modelling of pores in soil aggregates". Journal of Soil Science. 42 (3): 479–86. doi:10.1111/j.1365-2389.1991.tb00424.x.
• Horgan, G. W.; B. C. Ball (1994). "Simulating diffusion in a Boolean model of soil pores". European Journal of Soil Science. 45 (4): 483–91. doi:10.1111/j.1365-2389.1994.tb00534.x.
• Horgan, Graham W. (1996-10-01). "A review of soil pore models" (PDF). Retrieved 2006-04-16. {{cite journal}}: Cite journal requires |journal= (help)
• Horgan, G. W. (June 1998). "Mathematical morphology for soil image analysis". European Journal of Soil Science. 49 (2): 161–73. doi:10.1046/j.1365-2389.1998.00160.x. S2CID 97042651.
• Horgan, G. W. (February 1999). "An investigation of the geometric influences on pore space diffusion". Geoderma. 88 (1–2): 55–71. Bibcode:1999Geode..88...55H. doi:10.1016/S0016-7061(98)00075-5.
• Nelson, J. Roy (January 2000). "Physics of impregnation" (PDF). Microscopy Today. 8 (1): 24. doi:10.1017/S1551929500057114. Archived from the original (PDF) on 2009-02-27.
• Rouquerol, Jean (December 2011). "Liquid intrusion and alternative methods for the characterization of macroporous materials (IUPAC Technical Report)*" (PDF). Pure Appl. Chem. 84 (1): 107–36. doi:10.1351/pac-rep-10-11-19. S2CID 10472849.

• Absolute Porosity & Effective Porosity Calculations
• Geology Buzz: Porosity