51
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Attenuation of an external signal in a thermoelastic material with triple porosity in local thermal non-equilibrium

ORCID Icon
Pages 768-783 | Received 25 Feb 2021, Accepted 26 Mar 2021, Published online: 28 Apr 2021

References

  • M. Bai, D. Elsworth, and J. C. Roegiers, “Modelling of naturally fractured reservoirs using deformation dependent flow mechanism,” Int. J. Rock Mech. Min. Sci., vol. 30, pp. 1185–1191, 1993. DOI: 10.1016/0148-9062(93)90092-R.
  • M. Bai and J. C. Roegiers, “Triple-porosity analysis of solute transport,” J. Contam. Hydrol., vol. 28, pp. 247–266, 1997. DOI: 10.1016/S0169-7722(96)00086-1.
  • R. F. Aguilera and R. Aguilera, “A triple-porosity model for petrophysical analysis of naturally fractured reservoirs,” Petrophysics, vol. 45, pp. 157–166, 2004. DOI: SPWLA-2004-v45n2a4.
  • A. J. Ali, S. Siddiqui, and H. Dehghanpour, “Analysing the production data of fractured horizontal wells by a linear triple porosity model: Development of analysis equations,” J. Pet. Sci. Eng., vol. 112, pp. 117–128, 2013. DOI: 10.1016/j.petrol.2013.10.016.
  • H. Wang, L. Zhang, and J. Guo, “A new rod source model for pressure transient analysis of horizontal wells with positive/negative skin in triple porosity reservoirs,” J. Pet. Sci. Eng., vol. 108, pp. 52–63, 2013. DOI: 10.1016/j.petrol.2013.03.005.
  • B. K. Olusola, G. Yu, and R. Aguilera, “The use of electromagnetic mixing rules for petrophysical evaluation of dual- and triple-porosity reservoirs,” SPE Reservoir Eval. Eng., vol. 16, pp. 378–389, 2013. DOI: 10.2118/162772-PA.
  • Z. Wei and D. Zhang, “Coupled fluid-flow and geomechanics for triple-porosity/dual-permeability modelling of coalbed methane recovery,” Int. J. Rock Mech. Min. Sci., vol. 47, pp. 1242–1253, 2010. DOI: 10.1016/j.ijrmms.2010.08.020.
  • J. H. Deng, J. A. Leguizamon, and R. Aguilera, “Petrophysics of triple-porosity tight gas reservoirs with a link to gas productivity,” SPE Reservoir Eval. Eng., vol. 14, pp. 566–577, 2011. DOI: 10.2118/144590-PA.
  • M. Zou, C. Wei, H. Yu, and L. Song, “Modelling and application of coalbed methane recovery performance based on a triple porosity/dual permeability model,” J. Nat. Gas Sci. Eng., vol. 22, pp. 679–688, 2015. DOI: 10.1016/j.jngse.2015.01.019.
  • M. Svanadze and A. Scalia, “Mathematical problems in the theory of bone poroelasticity,” Biomath, vol. 1, no. 2, pp. 1–4, 2012. DOI: 10.11145/j.biomath.2012.11.225.
  • M. Svanadze and A. Scalia, “Mathematical problems in the coupled linear theory of bone poroelasticity,” Comput. Math. Appl., vol. 66, pp. 1554–1566, 2013. DOI: 10.1016/j.camwa.2013.01.046.
  • M. Sakamoto and T. Matsumoto, “Development and evaluation of superporous ceramics bone tissue scaffold materials with triple pore structure a) Hydroxyapatite b) Betatricalcium phosphate,” in Bone Regeneration, Haim Tal, Ed. Rijeka, Croatia, InTech, 2012. www.cdn.intechopen.com/pdfs-wm/34836.pdf.
  • D. Zhou, Y. Gao, M. Lai, H. Li, B. Yuan, and M. Zhu, “Fabrication of NiTi shape memory alloys with graded porosity to imitate human long-bone structure,” J. Bionic Eng., vol. 12, pp. 575–582, 2015. DOI: 10.1016/S1672-6529(14)60147-5.
  • A. Zuber and J. Motyka, “Hydraulic parameters and solute velocities in triple-porosity karstic-fissured-porous carbonate aquifers: Case studies in southern Poland,” Environ. Geol., vol. 34, pp. 243–250, 1998. DOI: 10.1007/s002540050276.
  • R. Ghasemizadeh, et al., “Review: Groundwater flow and transport modelling of karst aquifers, with particular reference to the North Coast Limestone aquifer system of Puerto Rico,” Hydrogeol. J., vol. 20, pp. 1441–1461, 2012. DOI: 10.1007/s10040-012-0897-4.
  • T. M. Müller, B. Gurevich, and M. Lebedev, “Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks – a review,” Geophysics, vol. 75, pp. 75A147–75A164, 2010. DOI: 10.1190/1.3463417.
  • S. R. Pride, “Relationships between seismic and hydrological properties,” in Hydrogeophysics. Water Science and Technology Library, Y. Rubin, S.S. Hubbard, Eds., vol. 50, pp. 253–290. Dordrecht: Springer, 2005. DOI: 10.1007/1-4020-3102-5-9.
  • D. A. Nield, “A note on modelling of local thermal non-equilibrium in a structured porous medium,” Int. J. Heat Mass Transfer, vol. 45, pp. 4367–4368, 2002. DOI: 10.1016/S0017-9310(02)00138-2.
  • D. A. S. Rees, A. P. Bassom, and P. G. Siddheshwar, “Local thermal non-equilibrium effects arising from the injection of a hot fluid into a porous medium,” J. Fluid Mech., vol. 594, pp. 379–398, 2008. DOI: 10.1017/S0022112007008890.
  • B. Straughan, Convection with Local Thermal Non-equilibrium and Microfluidic Effects, Advances in Mechanics and Mathematics, vol. 32, Chapters 2–7, pp. 49–103. New York, NY: Springer, 2015.
  • F. Franchi, B. Lazzari, R. Nibbi and B. Straughan, “Uniqueness and decay in local thermal non-equilibrium double porosity thermoelasticity,” Math. Methods Appl. Sci., vol. 41, pp. 6763–6771, 2018. DOI: 10.1002/mma.5190.
  • M. Svanadze, “On the linear theory of double porosity thermoelasticity under local thermal nonequilibrium,” J. Therm. Stresses, vol. 42, pp. 890–913, 2019. DOI: 10.1080/01495739.2019.1571973.
  • S. Chiriţă, “Modeling triple porosity under local thermal nonequilibrium,” J. Therm. Stresses, vol. 43, pp. 210–224, 2020. DOI: 10.1080/01495739.2019.1679057.
  • B. Straughan, Mathematical Aspects of Multi-Porosity Continua, Advances Mechanics Mathematics, vol. 38, pp. 191–204. New York: Springer, 2017.
  • M. Svanadze, Potential Method in Mathematical Theories of Multi-Porosity Media, Interdisciplinary Applied Mathematics, vol. 51, pp. 283–298. Cham, Switzerland: Springer International Publishing AG, 2019.
  • C. O. Horgan and J. Knowles, “Recent developments concerning Saint-Venant’s principle,” Adv. Appl. Mech., vol. 23, pp. 179–269, 1983. DOI: 10.1016/S0065-2156(08)70244-8.
  • J. N. Flavin and R. J. Knops, “Some spatial decay estimates in continuum dynamics,” J. Elast., vol. 17, pp. 249–264, 1987. DOI: 10.1007/BF00049455.
  • C. O. Horgan, “Recent developments concerning Saint-Venant’s principle: An update,” Appl. Mech. Rev., vol. 42, pp. 295–303, 1989. DOI: 10.1115/1.3152414.
  • C. O. Horgan, “Recent developments concerning Saint-Venant’s principle: A second update,” Appl. Mech. Rev., vol. 49, pp. S101–S111, 1996. DOI: 10.1115/1.3101961.
  • S. Chiriţă, “Saint-Venant’s principle in linear thermoelasticity,” J. Therm. Stresses, vol. 18, pp. 485–496, 1995. DOI: 10.1080/01495739508946316.
  • S. Chiriţă, “On the spatial decay estimates in certain time-dependent problems of continuum mechanics,” Arch. Mech., vol. 47, pp. 755–771, 1995.
  • S. Chiriţă, “A Phragmèn-Lindelöf principle in dynamic linear thermoelasticity,” J. Therm. Stresses, vol. 20, pp. 505–516, 1997. DOI: 10.1080/01495739708956116.
  • S. Chiriţă and M. Ciarletta, “Time-weighted surface power function method for the study of spatial behaviour in dynamics of continua,” Eur. J. Mech. A/Solids, vol. 18, pp. 915–933, 1999. DOI: 10.1016/S0997-7538(99)00121-7.
  • M. Gurtin, “The linear theory of elasticity,” in Encyclopedia of Physics, vol. VIa/2, C. Truesdell, Ed. Berlin, Heidelberg, New York: Springer, 1972, pp. 1–293.
  • M. M. Mehrabadi, S. C. Cowin, and C. O. Horgan, “Strain energy density bounds for linear anisotropic elastic materials,” J. Elast., vol. 30, pp. 191–196, 1993. DOI: 10.1007/BF00041853.
  • S. Chiriţă and C. Galeş, “Wave propagation and attenuation in time in local thermal non-equilibrium triple porosity thermoelastic medium,” Acta Mechanica, submitted.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.