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Poroelasticity

Summary

Poroelasticity is a field in materials science and mechanics that studies the interaction between fluid flow and solids deformation within a linear porous medium and it is an extension of elasticity and porous medium flow (diffusion equation). The deformation of the medium influences the flow of the fluid and vice versa. The theory was proposed by Maurice Anthony Biot (1935, 1941)[1] 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,[2] hydrology,[3] biomechanics,[4] tissue mechanics,[5] cell mechanics,[6] and micromechanics.[7]

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.[8] 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.[9] Depending on the gas pressure the induced sorption-based strain can be poroelastic or poroinelastic in nature.[10]

Types of Poroelasticity

The theories of poroelasticity can be divided into two categories: static (or quasi-static) and dynamic theories,[11] just like mechanics can be divided into statics and dynamics. The static poroelasticity considers processes in which the fluid movement and solid skeleton deformation occur simultaneously and affect each other. The static poroelasticity is predominant in the literature for poroelasticity; as a result, this term is used interchangeably with poroelasticity in many publications. This static poroelasticity theory is a generalization of the one-dimensional consolidation theory in soil mechanics. This theory was developed from Biot's work in 1941.[1] The dynamic poroelasticity is proposed for understanding the wave propagation in both the liquid and solid phases of saturated porous materials. The inertial and associated kinetic energy, which are not considered in static poroelasticity, are included. This is especially necessary when the speed of the movement of the phases in the porous material is considerable, e.g., when vibration or stress waves is present.[12] The dynamic poroelasticity was developed attributed to Biot's work on the propagation of elastic waves in fluid-saturated media.[13][14]

Literature

References for the theory of poroelasticity:

• Detournay E, Cheng AH (1993). "Fundamentals of poroelasticity" (PDF). In Fairhurst C (ed.). Comprehensive Rock Engineering: Principles, Practice and Projects. Vol. II, Analysis and Design Method. Pergamon Press. pp. 113–171.
• Cheng AH (2016). Poroelasticity. Theory and Applications of Transport in Porous Media. Vol. 27. Springer. doi:10.1007/978-3-319-25202-5. ISBN 978-3-319-25200-1.
• Wang HF (2000). Theory of linear poroelasticity with applications to geomechanics and hydrogeology. Princeton University Press.
• Zhen (Leo) Liu (2018). Multiphysics in Porous Materials. Springer. ISBN 9783319930275.
• Reint de Boer (2000). Theory of Porous Media - Highlights in Historical Development and Current State. Springer. ISBN 9783642640629.
• Coussy, Olivier (2003-12-09). Poromechanics. doi:10.1002/0470092718. ISBN 9780470092712.

References

1. ^ a b Biot MA (1941-02-01). "General Theory of Three‐Dimensional Consolidation". Journal of Applied Physics. 12 (2): 155–164. Bibcode:1941JAP....12..155B. doi:10.1063/1.1712886. ISSN 0021-8979.
2. ^ Cheng AH (2016). Poroelasticity. Theory and Applications of Transport in Porous Media. Vol. 27. Springer. doi:10.1007/978-3-319-25202-5. ISBN 978-3-319-25200-1.
3. ^ Wang HF (2000). Theory of linear poroelasticity with applications to geomechanics and hydrogeology. Princeton University Press.
4. ^ Cowin SC (1999). "Bone poroelasticity". Journal of Biomechanics. 32 (3): 217–38. doi:10.1016/s0021-9290(98)00161-4. PMID 10093022.
5. ^ Malandrino, Andrea; Moeendarbary, Emad (2019), "Poroelasticity of Living Tissues", in Narayan, Roger (ed.), Encyclopedia of Biomedical Engineering, Oxford: Elsevier, pp. 238–245, doi:10.1016/B978-0-12-801238-3.99932-X, ISBN 978-0-12-805144-3, S2CID 186300583 https://www.researchgate.net/publication/321986395_Poroelasticity_of_Living_Tissues
6. ^ Moeendarbary E, Valon L, Fritzsche M, Harris AR, Moulding DA, Thrasher AJ, Stride E, Mahadevan L, Charras GT (March 2013). "The cytoplasm of living cells behaves as a poroelastic material" (PDF). Nature Materials. 12 (3): 253–61. Bibcode:2013NatMa..12..253M. doi:10.1038/nmat3517. PMC 3925878. PMID 23291707.
7. ^ Dormieux L, Kondo D, Ulm F (2006). Microporomechanics. Wiley. doi:10.1002/0470032006. ISBN 9780470032008.
8. ^ Cowin SC, Doty SB, eds. (2007). Tissue Mechanics. Springer. doi:10.1007/978-0-387-49985-7. ISBN 978-0-387-36825-2.
9. ^ Zoback, Mark D.; Kohli, Arjun H. (2019). Unconventional Reservoir Geomechanics: Shale Gas, Tight Oil, and Induced Seismicity. Cambridge: Cambridge University Press. doi:10.1017/9781316091869. ISBN 978-1-107-08707-1. S2CID 197568886.
10. ^ Saurabh, Suman; Harpalani, Satya (2018-01-01). "The effective stress law for stress-sensitive transversely isotropic rocks". International Journal of Rock Mechanics and Mining Sciences. 101: 69–77. doi:10.1016/j.ijrmms.2017.11.015. ISSN 1365-1609.
11. ^ Liu, Zhen (Leo). "Multiphysics - Poroelasticity and Poromechanics". www.multiphysics.us. Retrieved 2018-10-03.
12. ^ Zhen (Leo) Liu (2018). Multiphysics in Porous Materials. Springer. ISBN 9783319930275.
13. ^ Biot, M. A. (April 1962). "Mechanics of Deformation and Acoustic Propagation in Porous Media" (PDF). Journal of Applied Physics. 33 (4): 1482–1498. Bibcode:1962JAP....33.1482B. doi:10.1063/1.1728759. ISSN 0021-8979.
14. ^ Biot, M. A. (March 1956). "Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. II. Higher Frequency Range" (PDF). The Journal of the Acoustical Society of America. 28 (2): 179–191. Bibcode:1956ASAJ...28..179B. doi:10.1121/1.1908241. ISSN 0001-4966.