poroelasticity

Poroelasticity is a field in materials science and mechanics that studies the interaction between fluid flow, pressure and bulk solid deformation within a linear porous medium and it is an extension of elasticity and porous medium flow (diffusion equation). [https://hal.science/hal-02344039 M.Liu et al. Multiscale modeling of effective elastic properties of fluid-filled porous materials] International Journal of Solids and Structures (2019) 162, 36-44 The deformation of the medium influences the flow of the fluid and vice versa. The theory was proposed by Maurice Anthony Biot (1935, 1941){{Cite journal|last=Biot|first=Maurice A. | name-list-style = vanc |date=1941-02-01|title=General Theory of Three‐Dimensional Consolidation|journal=Journal of Applied Physics|volume=12|issue=2|pages=155–164|doi=10.1063/1.1712886|bibcode=1941JAP....12..155B |issn=0021-8979|url=https://hal.archives-ouvertes.fr/hal-01368635/document }} as a theoretical extension of soil consolidation models developed to calculate the settlement of structures placed on fluid-saturated porous soils.

The theory of poroelasticity has been widely applied in geomechanics,{{cite book | title = Poroelasticity | volume = 27 | publisher = Springer | last = Cheng | first = Alexander H.-D.| name-list-style = vanc | doi = 10.1007/978-3-319-25202-5 | year = 2016| series = Theory and Applications of Transport in Porous Media | isbn = 978-3-319-25200-1 | s2cid = 240649873 }} hydrology,{{cite book | title = Theory of linear poroelasticity with applications to geomechanics and hydrogeology | last = Wang | first = Herbert F. | name-list-style = vanc |publisher=Princeton University Press|year=2000}} biomechanics,{{cite journal | vauthors = Cowin SC | title = Bone poroelasticity | journal = Journal of Biomechanics | volume = 32 | issue = 3 | pages = 217–38 | year = 1999 | pmid = 10093022 | doi = 10.1016/s0021-9290(98)00161-4 }} tissue mechanics,{{Citation|last1=Malandrino|first1=Andrea|title=Poroelasticity of Living Tissues|url=https://www.sciencedirect.com/science/article/pii/B978012801238399932X|encyclopedia=Encyclopedia of Biomedical Engineering|pages=238–245|editor-last=Narayan|editor-first=Roger|place=Oxford|publisher=Elsevier|language=en|isbn=978-0-12-805144-3|access-date=|last2=Moeendarbary|first2=Emad|year=2019|doi=10.1016/B978-0-12-801238-3.99932-X|s2cid=186300583|url-access=subscription}} https://www.researchgate.net/publication/321986395_Poroelasticity_of_Living_Tissues cell mechanics,{{cite journal | vauthors = Moeendarbary E, Valon L, Fritzsche M, Harris AR, Moulding DA, Thrasher AJ, Stride E, Mahadevan L, Charras GT | title = The cytoplasm of living cells behaves as a poroelastic material | journal = Nature Materials | volume = 12 | issue = 3 | pages = 253–61 | date = March 2013 | pmc = 3925878 | doi = 10.1038/nmat3517 | pmid = 23291707 | bibcode = 2013NatMa..12..253M | url = https://dash.harvard.edu/bitstream/handle/1/11879812/3925878.pdf?sequence=1 }} and micromechanics.{{cite book | title = Microporomechanics | publisher = Wiley | last1 = Dormieux | first1 = Luc | last2 = Kondo | first2 = Djimédo | last3 = Ulm | first3 = Franz-Josef | name-list-style = vanc | doi = 10.1002/0470032006 | year = 2006 | isbn = 9780470032008 }}

An intuitive sense of the response of a saturated elastic porous medium to mechanical loading can be developed by thinking about, or experimenting with, a fluid-saturated sponge. If a fluid-saturated sponge is compressed, fluid will flow from the sponge. If the sponge is in a fluid reservoir and compressive pressure is subsequently removed, the sponge will reimbibe the fluid and expand. The volume of the sponge will also increase if its exterior openings are sealed and the pore fluid pressure is increased. The basic ideas underlying the theory of poroelastic materials are that the pore fluid pressure contributes to the total stress in the porous matrix medium and that the pore fluid pressure alone can strain the porous matrix medium. There is fluid movement in a porous medium due to differences in pore fluid pressure created by different pore volume strains associated with mechanical loading of the porous medium.{{cite book|title=Tissue Mechanics|publisher=Springer|year=2007|isbn=978-0-387-36825-2|editor-last1=Cowin|editor-first1=Stephen C.|doi=10.1007/978-0-387-49985-7|editor-last2=Doty|editor-first2=Stephen B.|name-list-style=vanc}} In unconventional reservoir and source rocks for natural gas like coal and shales, there can be strain due to sorption of gases like methane and carbon dioxide on the porous rock surfaces.{{Cite book|last1=Zoback|first1=Mark D.|url=https://www.cambridge.org/core/books/unconventional-reservoir-geomechanics/39665444034A2EF143D749DF48A5E5DC|title=Unconventional Reservoir Geomechanics: Shale Gas, Tight Oil, and Induced Seismicity|last2=Kohli|first2=Arjun H.|date=2019|publisher=Cambridge University Press|isbn=978-1-107-08707-1|location=Cambridge|doi=10.1017/9781316091869|s2cid=197568886}} Depending on the gas pressure the induced sorption-based strain can be poroelastic or poroinelastic in nature.{{Cite journal|last1=Saurabh|first1=Suman|last2=Harpalani|first2=Satya|date=2018-01-01|title=The effective stress law for stress-sensitive transversely isotropic rocks|url=https://www.sciencedirect.com/science/article/pii/S1365160917303738|journal=International Journal of Rock Mechanics and Mining Sciences|language=en|volume=101|pages=69–77|doi=10.1016/j.ijrmms.2017.11.015|issn=1365-1609|url-access=subscription}}