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 porosity is used in multiple fields including manufacturing, earth sciences and construction.

Porosity in earth sciences and construction
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:


 * $$\phi = \frac{V_V}{V_T}$$

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

Porosity is a fraction between 0 and 1, typically ranging from less than 0.01 for solid granite to more than 0.5 for peat and clay, although it may also be represented in percent terms by multiplying the fraction by 100.

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 porosities are a complex 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:


 * $$\phi(z) = \phi_0 e^{-kz}\,$$

where $$\phi_0$$ is the surface porosity, $$k$$ is the compaction coefficient (m&minus;1) and $$z$$ is depth (m).

A value for porosity can alternatively be calculated from the bulk density $$\rho_{\text{bulk}}$$ and particle density $$\rho_{\text{particle}}$$:
 * $$\phi = 1-\frac{\rho_{\text{bulk}}}{\rho_{\text{particle}}}$$

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

Porosity and hydraulic conductivity
Porosity is indirectly related to hydraulic conductivity; for two similar sandy aquifers, the one with a higher porosity will typically have a higher hydraulic conductivity (more open area for the flow of water), but there are many complications to this relationship. Clays, which typically have very low hydraulic conductivity also have very high porosities (due to the structured nature of clay minerals), which means clays can hold a large volume of water per volume of bulk material, but they do not release water very quickly.

Sorting and porosity
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.

Porosity of rocks
Consolidated rocks (e.g. sandstone, shale, granite or limestone) potentially have more complex "dual" porosities, as compared with alluvial sediment. The rock itself may have a certain (low) porosity, and the fractures (cracks and joints), or dissolution features may create a second (higher) porosity. The interaction of these porosities is complex and often makes simple models highly inaccurate.

Porosity of soil
Porosity of surface soil typically decreases as particle size increases. This is due to soil aggregate formation in finer textured surface soils when subject to soil biological processes. Aggregation involves particulate adhesion and higher resistance to compaction. Typical bulk density of sandy soil is between 1.5 and 1.7 g/cm³. This calculates to a porosity between 0.43 and 0.36. Typical bulk density of clay soil is between 1.1 and 1.3 g/cm³. This calculates to a porosity between 0.58 and 0.51. This seems counterintuitive because clay soils are termed heavy, implying lower porosity. Heavy apparently refers to a gravitational moisture content effect in combination with terminology that harkens back to the relative force required to pull a tillage implement through the clayey soil at field moisture content as compared to sand.

Porosity of subsurface soil is lower than in surface soil due to compaction by gravity. Porosity of 0.20 is considered normal for unsorted gravel size material at depths below the biomantle. Porosity in finer material below the aggregating influence of pedogenesis can be expected to approximate this value.

Soil porosity is complex. Traditional models regard porosity as continuous. This fails to account for anomalous features and produces only approximate results. Furthermore it cannot help model the influence of environmental factors which affect pore geometry. A number of more complex models have been proposed, including fractals, bubble theory, cracking theory, Boolean grain process, packed sphere, and numerous other models. See also Characterisation of pore space in soil.

Types of geologic porosities

 * Primary porosity: The main or original porosity system in a rock or unconfined alluvial deposit.
 * Secondary porosity: A subsequent or separate porosity system in a rock, often enhancing overall porosity of a rock. This can be a result of chemical leeching of minerals or the generation of a fracture system. This can replace the primary porosity or coexist with it (see dual porosity below).
 * Fracture porosity: This is porosity associated with a fracture system or faulting. This can create secondary porosity in rocks that otherwise would not be reservoirs for hydrocarbons due to their primary porosity being destroyed (for example due to depth of burial) or of a rock type not normally considered a reservoir (for example igneous intrusions or metasediments).
 * Vuggy porosity: This is secondary porosity generated by dissolution of large features (such as macrofossils) in carbonate rocks leaving large holes, vugs, or even caves.
 * Effective porosity (also called open porosity): Refers to the fraction of the total volume in which fluid flow is effectively taking place (this excludes dead-end pores or non-connected cavities). This is very important for groundwater and petroleum flow, as well as for solute transport.
 * Dual porosity: Refers to the conceptual idea that there are two overlapping reservoirs which interact. In fractured rock aquifers, the rock mass and fractures are often simulated as being two overlapping but distinct bodies. Delayed yield, and leaky aquifer flow solutions are both mathematically similar solutions to that obtained for dual porosity; in all three cases water comes from two mathematically different reservoirs (whether or not they are physically different).
 * Macro porosity: Refers to pores greater than 50 nm in diameter. Flow through macropores is described by bulk diffusion.
 * Meso porosity: Refers to pores greater than 2 nm and less than 50 nm in diameter. Flow through mesopores is described by knudsen diffusion.
 * Micro porosity: Refers to pores smaller than 2 nm in diameter. Movement in micropores is by activiated diffusion.

Porosity in manufacturing
In manufacturing of metal or plastic parts and assemblies, porosity in the raw material is a serious issue affecting the quality of the resulting products. Porosity may be caused by temperature control problems, material impurities, or other causes in the casting of metal or plastic parts. Porosity internal to cast parts may become external or surface pores when material is then removed from the raw part material by machining, grinding or other manufacturing operations. Surface pores, if not detected, may cause leakage to occur between the mating surfaces of parts comprising an assembly or between cavities in an assembly in which substantial pressure differentials are desired. An example is the required pressure differential between the cylinders of an engine or between the region above and below a piston or a valve in a cylinder. The ultimate result of undetected and uncorrected porosity can include loss of performance, leakage of lubricants or fuel, and contamination of various portions of the assembled mechanism or product. Detection of surface porosity requires the use of some form of 3-dimensional high-definition metrology, because pores of concern may be as small as 100 micrometres in diameter (roughly the diameter of an average human hair) and may occur anywhere on the surface of a part. Pores in machined metal or plastic vary significantly in shape, depth, size and the surface characteristics (such as surface roughness ) within the perimeter of the pore. If pores are not detected prior to assembly of mating surfaces during the manufacturing process, then considerable additional manufacturing cost is usually incurred as the resulting assembly has to be disassembled or scrapped after pressure testing or other later performance tests reveal deficiencies.

Measuring porosity
There are several ways to estimate the porosity of a given material or mixture of materials, which is called, material matrix.


 * Volume/density method: This method is fast and surprisingly accurate (normally within 2 % of the actual porosity). To do this method, pour material into a beaker, cylinder or some other container of a known volume. Weigh the container to find its empty weight, then pour the material into the container. Tap the side of the container until it has finished settling and measure the volume in the container. Then weigh the container full of this material, then subtract the weight of the container to know the weight of only the material. Now the volume and the weight of the material is known. The weight of the material divided by the density of the material gives the volume that the material takes up, minus the pore volume. (The assumed density of most rocks, sand, glass, etc. is assumed to be 2.65 g/cm³. If a different material is being used, look up its density) So, the pore volume is simply equal to the total volume minus the material volume, or more directly (pore volume) = (total volume) - (material volume).


 * Water saturation method: This method is slightly harder to do, but is more accurate and more direct. Again, take a known volume of the material and also a known volume of water. (Make sure the beaker or container is large enough to hold the material as well.) Slowly dump the material into the water and let it saturate while pouring. Then seal the beaker (with a piece of parafilm tape or if this isn't available to use, a plastic bag tied around the beaker will do.) and let it sit for a few hours to insure the material is fully saturated. Then remove the unsaturated water from the top of the beaker and measure its volume. The total volume of the water originally in the beaker minus the amount of water not saturated is the volume of the pore space, or again more directly (pore volume) = (total volume of water) - (unsaturated water).


 * Water evaporation method: This method is the hardest to do, but is also the most accurate. Take a fully saturated, known volume of the material with no excess water on top. Weigh the container with the material and water and then place the container into a heater to dry it out. Drying out the sample may take several days depending on the heat applied and the volume of the sample. Then weigh the dried sample. Since the density of water is 1 g/cm³, the difference of the weights of the saturated versus the dried sample is equal to the volume of the water removed from the sample (assuming the measurments are in grams), which is exactly the pore volume. So once again, (pore volume in cubic centimeters) = (weight of saturated sample in grams) - (weight of dried sample in grams).


 * Mercury intrusion porosimetry: Requires the sample to be placed special filling device that allows the sample to be evacuated followed by the introduction of liquid mercury. The size of the mercury envelope is then measured as a function of increased applied pressure.  The greater the applied pressure, the smaller the pore entered by mercury.  Typically this method is used over the range of pores from 300 µm to 0.0035 µm.  This method is used to characterize a variety of porous material from coal to fabrics.  Because of increased concern over use of mercury, several non-mercury intrusion techniques have been developed.


 * Nitrogen gas adsorption: This method is used to determine fine porosity in materials such as charcoal. In very small pores, nitrogen gas condenses on the pore walls less than 0.090 µm.  This condensation is measured either by volume or weight.