Pore structure

File:Porosity thin section GP.jpg shown as purple color(Thin section under gypsum plate of microscopic carbonate grains). Scale bar 500 micrometres. ]]

The proportion of empty space in a porous media is called porosity.{{cite journal |last1=Xiong |first1=Yunwu |last2=Long |first2=Xiaoxu |last3=Huang |first3=Guanhua |last4=Furman |first4=Alex |title=Impact of pore structure and morphology on flow and transport characteristics in randomly repacked grains with different angularities |journal=Soils and Foundations |date=1 December 2019 |volume=59 |issue=6 |pages=1992–2006 |doi=10.1016/j.sandf.2019.10.002|s2cid=214526290 |doi-access=free |bibcode=2019SoFou..59.1992X }} It is determined by dividing the volume of the pores or voids by the overall volume. It is expressed as a percentage or as a decimal fraction between 0 and 1. Porosity for the majority of rocks ranges from less than 1% to 40%.

Porosity influences fluid storage in geothermal systems, oil and gas fields, and aquifers, making it evident that it plays a significant role in geology. Fluid movement and transport across geological formations, as well as the link between the bulk properties of the rock and the characteristics of particular minerals, are controlled by the size and connectivity of the porous structure.{{cite journal |last1=Anovitz |first1=Lawrence M. |last2=Cole |first2=David R. |title=Characterization and Analysis of Porosity and Pore Structures |journal=Reviews in Mineralogy and Geochemistry |date=1 January 2015 |volume=80 |issue=1 |pages=61–164 |doi=10.2138/rmg.2015.80.04 |bibcode=2015RvMG...80...61A |issn=1529-6466|doi-access=free }}

The samples' total volume and pore space volume were measured in order to calculate the porosities.

Measuring pore space volume

A helium pyrometer was used to calculate the volume of the pores and relied on Boyle's law. (P₁V₁=P₂V₂) and helium gas, which easily passes through tiny holes and is inert, to identify the solid fraction of a sample. A sample chamber with a known volume is where the core is put. Pressure is applied to a reference chamber with a known volume. The helium gas may now go from the reference chamber to the sample chamber thanks to the connection between the two rooms. The volume of the sample solid is calculated using the ratio between the starting and final pressures. The pore volume, as calculated by the helium pycnometer, is the difference between the total volume and the solid volume.{{cite web |title=Wisconsin Geological & Natural History Survey » Understanding porosity and density |url=https://wgnhs.wisc.edu/maps-data/data/rock-properties/understanding-porosity-density/ |website=wgnhs.wisc.edu}}

Typically, the effective radius of the pore body or neck is used to define the size of pores. The position, shape, and connection of pores in solids are only a few of their numerous attributes and the most straightforward aspect of a pore to visualize is likely its size, or its extent in a single spatial dimension.

In comparison to other factors like pore shape, it is arguable that pore size has the biggest or broadest impact on the characteristics of solids. Therefore, using pore size or pore size distribution to describe and contrast various porous substances is definitely convenient and valuable.{{cite journal |last1=Mays |first1=T.J. |title=A new classification of pore sizes |journal=Studies in Surface Science and Catalysis |date=2007 |volume=160 |pages=57–62 |doi=10.1016/s0167-2991(07)80009-7|isbn=9780444520227 }}

The three main pore size ranges (The current classification of pore size recommended by the International Union of Pure and Applied Chemistry) are as following:

The relative abundance of each pore size in a typical volume of soil is represented by the pore size distribution. It is represented by the function f(r), whose value is proportional to the total volume of all pores whose effective radius is within an infinitesimal range centered on r. And f(r) can be thought to have textural and structural components.

Mercury intrusion porosimetry{{cite journal |last1=Pawelec |first1=Kendell M. |last2=White |first2=Ashley A. |last3=Best |first3=Serena M. |title=4 - Properties and characterization of bone repair materials |journal=Bone Repair Biomaterials (Second Edition) |date=1 January 2019 |pages=65–102 |doi=10.1016/b978-0-08-102451-5.00004-4 |url=https://doi.org/10.1016/B978-0-08-102451-5.00004-4 |publisher=Woodhead Publishing |isbn=9780081024515 |language=en}} and gas adsorption{{cite book |last1=Wypych |first1=George |title=Handbook of Foaming and Blowing Agents |date=1 January 2017 |publisher=ChemTec Publishing |isbn=978-1-895198-99-7 |pages=219–225 |url=https://doi.org/10.1016/B978-1-895198-99-7.50015-5 |language=en |chapter=13 - ANALYTICAL TECHNIQUES USEFUL IN FOAMING|doi=10.1016/B978-1-895198-99-7.50015-5 }} are common techniques for determining the pore size distribution of materials and power sources.

When studying the pore size distribution using the gas adsorption technique utilizing the nitrogen or argon adsorption isotherm at their boiling temperatures, it is possible to determine the pore size from the molecular level to a few hundred nm. The pressure sensor's precise constraints and the coolant's temperature stability result in a maximum observed pore size of just a little bit more than 100 nm in a realistic environment.{{cite web |title=Methods for Pore Size Distribution measurement :: Microtrac |url=https://www.microtrac.com/applications/knowledge-base/method-of-pore-size-distribution-measurement/ |website=www.microtrac.com}}

Mercury porosimetry determines the pore size distribution and quantifies the associated incursion amount by applying pressure to the non-wetting mercury. The pore size may be readily estimated using this method and ranges from a few nm to 1000 m. The material must be robust enough to withstand the pressure since mercury intrusion requires 140 MPa of pressure for pores smaller than 10 nm. Additionally, it utilizes the idea to determine the pore size of the inkbottle neck.

The relationship between pore size and pore size distribution in a randomly constructed porous system, is expected to be monotone: bigger pores are connected to larger particles. The relationship between pore size and particle size is complicated by the nonrandom nature of most soils. Big pores may be found in both large and tiny particles, including clays, which promote aggregation and therefore the development of large interaggregate pores. Subdivisions of a pore size distribution in randomly structured media can express more specific characteristics of soils with more complex conceptualizations, such as the hysteresis of soil water retention.

The pore morphology is the shape, surface roughness, and tortuosity of pore channels representing the liquid and gaseous phases.{{cite book |last1=Pagliai |first1=Marcello |chapter=Pore Morphology and Soil Functions |title=Encyclopedia of Agrophysics |series=Encyclopedia of Earth Sciences Series |date=2011 |pages=640–645 |doi=10.1007/978-90-481-3585-1_123 |chapter-url=https://doi.org/10.1007/978-90-481-3585-1_123 |publisher=Springer Netherlands |isbn=978-90-481-3584-4 |language=en}}

File:Tortuosity via geodesic distance calculation.tif, imaged by x-ray microtomography. ]]

Tortuosity of pore channels is a unique geometric quantity that is utilized not only to measure the transport characteristics of porous system, but also to express the sinuosity and complexity of internal percolation routes.{{cite journal |last1=Clennell |first1=M. Ben |title=Tortuosity: a guide through the maze |journal=Geological Society, London, Special Publications |date=1997 |volume=122 |issue=1 |pages=299–344 |doi=10.1144/gsl.sp.1997.122.01.18 |bibcode=1997GSLSP.122..299C |s2cid=130626761 |url=https://doi.org/10.1144/GSL.SP.1997.122.01.18 |issn=0305-8719}}{{cite journal |last1=Fu |first1=Jinlong |last2=Thomas |first2=Hywel R. |last3=Li |first3=Chenfeng |title=Tortuosity of porous media: Image analysis and physical simulation |journal=Earth-Science Reviews |date=1 January 2021 |volume=212 |pages=103439 |doi=10.1016/j.earscirev.2020.103439 |bibcode=2021ESRv..21203439F |s2cid=229386129 |url=https://doi.org/10.1016/j.earscirev.2020.103439 |language=en |issn=0012-8252}}{{cite journal |last1=Ghanbarian |first1=Behzad |last2=Hunt |first2=Allen G. |last3=Ewing |first3=Robert P. |last4=Sahimi |first4=Muhammad |title=Tortuosity in Porous Media: A Critical Review |journal=Soil Science Society of America Journal |date=September 2013 |volume=77 |issue=5 |pages=1461–1477 |doi=10.2136/sssaj2012.0435 |bibcode=2013SSASJ..77.1461G |url=https://doi.org/10.2136/sssaj2012.0435 |language=en}}

Toruosity is intimately connected to the transport behavior of electrical conductivity, fluid permeation,{{cite journal |last1=Fu |first1=Jinlong |last2=Cui |first2=Shaoqing |last3=Cen |first3=Song |last4=Li |first4=Chenfeng |title=Statistical characterization and reconstruction of heterogeneous microstructures using deep neural network |journal=Computer Methods in Applied Mechanics and Engineering |date=1 January 2021 |volume=373 |pages=113516 |doi=10.1016/j.cma.2020.113516|bibcode=2021CMAME.373k3516F |s2cid=228892100 |url=https://cronfa.swan.ac.uk/Record/cronfa55670/Download/55670__18678__b5c2e882e0cb411da11c8290f3137a4c.pdf }} molecular diffusion, and heat transfer in geoscience, impacting petrophysical parameters such as permeability, effective diffusivity, thermal conductivity, and formation resistivity factor.{{cite journal |last1=Backeberg |first1=Nils R. |last2=Iacoviello |first2=Francesco |last3=Rittner |first3=Martin |last4=Mitchell |first4=Thomas M. |last5=Jones |first5=Adrian P. |last6=Day |first6=Richard |last7=Wheeler |first7=John |last8=Shearing |first8=Paul R. |last9=Vermeesch |first9=Pieter |last10=Striolo |first10=Alberto |title=Quantifying the anisotropy and tortuosity of permeable pathways in clay-rich mudstones using models based on X-ray tomography |journal=Scientific Reports |date=December 2017 |volume=7 |issue=1 |pages=14838 |doi=10.1038/s41598-017-14810-1|pmid=29093572 |pmc=5665904 |bibcode=2017NatSR...714838B }}

The standard definition of surface roughness for porous medium is based on the average measured vertical coordinate value in comparison to a relative surface height, such as root-mean-square roughness or arithmetic roughness. However, the lack of fractal topology consideration led to the relative surface height definition being deemed inadequate in reality.{{cite journal |last1=Ghanbarian |first1=Behzad |last2=Hunt |first2=Allen G. |last3=Daigle |first3=Hugh |title=Fluid flow in porous media with rough pore-solid interface: FLOW IN ROUGH-WALLED POROUS MEDIA |journal=Water Resources Research |date=March 2016 |volume=52 |issue=3 |pages=2045–2058 |doi=10.1002/2015WR017857|s2cid=131002491 |doi-access=free }}{{cite journal |last1=Jiang |first1=Hao |last2=Guo |first2=Bo |last3=Brusseau |first3=Mark L. |title=Characterization of the micro-scale surface roughness effect on immiscible fluids and interfacial areas in porous media using the measurements of interfacial partitioning tracer tests |journal=Advances in Water Resources |date=1 December 2020 |volume=146 |pages=103789 |doi=10.1016/j.advwatres.2020.103789 |pmid=33311835 |pmc=7727783 |bibcode=2020AdWR..14603789J |url=https://doi.org/10.1016/j.advwatres.2020.103789 |language=en |issn=0309-1708}}

The ratio of "real surface area" to "geometric smooth-surface area" was used as the second definition of surface roughness. This definition has been applied in several research to alter flow equations or measure the fluid-fluid interfacial area.{{cite journal |last1=Toledo |first1=Pedro G. |last2=Novy |first2=Robert A. |last3=Davis |first3=H. Ted |last4=Scriven |first4=L. E. |title=Hydraulic Conductivity of Porous Media at Low Water Content |journal=Soil Science Society of America Journal |date=May 1990 |volume=54 |issue=3 |pages=673–679 |doi=10.2136/sssaj1990.03615995005400030007x |bibcode=1990SSASJ..54..673T |language=en}}{{cite journal |last1=Jiang |first1=Hao |last2=Guo |first2=Bo |last3=Brusseau |first3=Mark L. |title=Pore-Scale Modeling of Fluid-Fluid Interfacial Area in Variably Saturated Porous Media Containing Microscale Surface Roughness |journal=Water Resources Research |date=January 2020 |volume=56 |issue=1 |doi=10.1029/2019WR025876 |pmid=33408424 |pmc=7785087 |bibcode=2020WRR....5625876J |language=en |issn=0043-1397}}

The fundamental idea of fractal geometry is where the third definition of surface roughness comes from,{{cite book |last1=Mandelbro |first1=B.B. |title=Mandelbrot The Fractal Geometry of Nature |location=New York}} in which either modifies the pore surfaces (two-dimensional) or the whole porous medium (three-dimensional) using fractal dimension adjustments, resulting in larger surface dimensions or reduced media dimensions.{{cite journal |last1=Toledo |first1=Pedro G. |last2=Novy |first2=Robert A. |last3=Davis |first3=H. Ted |last4=Scriven |first4=L. E. |title=Hydraulic Conductivity of Porous Media at Low Water Content |journal=Soil Science Society of America Journal |date=May 1990 |volume=54 |issue=3 |pages=673–679 |doi=10.2136/sssaj1990.03615995005400030007x |bibcode=1990SSASJ..54..673T |language=en}} The hurst roughness exponent, a similar definition, is occasionally used. This quantity, which spans from 0 to 1, is connected to the fractal dimension.

• Bulk density
• Filtration
• Permeability
• Poromechanics
• Porous medium
• Reactive transport modeling in porous media

{{reflist}}

• J. Bear; (1972) Dynamics of Fluids in Porous Media. (Elsevier, New York)
• Hillel, D.; (2004) Introduction to environmental soil physics. (Sydney : Elsevier/Academic Press: Amsterdam ;)
• Leeper GW (1993) Soil science : an introduction. (Melbourne University Press: Carlton, Victoria.)

• [https://geology.buzz/threads/porosity.104/ Geology Buzz: Porosity]
• [https://careers.slb.com/inside-schlumberger/transformative-technology/defining-permeability Defining Permeability ]
• [https://imechanica.org/files/JCIS-2019-Tailoring%20porous%20media%20for%20controllable%20capillary%20flow_0.pdf Tailoring porous media to control permeability]
• [http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/chapter-2-the-porous-medium/permeability/ Permeability of Porous Media]
• [http://techalive.mtu.edu/meec/module06/Permeability.htm Graphical depiction of different flow rates through materials of differing permeability]
• [http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/ Fundamentals of Fluid Flow in Porous Media]

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Category:Hydrology

Category:Soil mechanics

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Category:Porous media

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