Geodesic
Thermomechanical model for impermeable porous medium with chemically active filler
Matematičeskoe modelirovanie, Tome 29 (2017) no. 12, pp. 117-133.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider self-consistent mathematical model for thermomechanical behavior of a linear elastic medium which contains voids filled with chemically active substance. The medium is described by linear thermomechanics equations. Substance in voids is described by lumped model which accounts for energy balance, chemical reactions and phase equilibrium conditions. The model allows to consider an arbitrary number of components which can be presented in solid and three fluid phases (liquid and gaseous hydrocarbon phases and water phase). Distribution of components between phases is obtained in thermodynamically consistent way and each component can be present in each phase. To describe thermodynamical behavior of phases in a presence of phase transitions, equation of state (EoS) approach is used based on cubic EoS widely used in engineering practice. For numerical solution of the complete coupled system of equations we propose an algorithm based on combination of domain decomposition method and physical splitting approach.
Keywords: thermomechanics, chemical kinetics, chemical reactions.
Mots-clés : phase equlibrium 
@article{MM_2017_29_12_a8,
     author = {M. V. Alekseev and A. A. Kuleshov and E. B. Savenkov},
     title = {Thermomechanical model for impermeable porous medium with chemically active filler},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {117--133},
     publisher = {mathdoc},
     volume = {29},
     number = {12},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_12_a8/}
}
TY  - JOUR
AU  - M. V. Alekseev
AU  - A. A. Kuleshov
AU  - E. B. Savenkov
TI  - Thermomechanical model for impermeable porous medium with chemically active filler
JO  - Matematičeskoe modelirovanie
PY  - 2017
SP  - 117
EP  - 133
VL  - 29
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2017_29_12_a8/
LA  - ru
ID  - MM_2017_29_12_a8
ER  - 
%0 Journal Article
%A M. V. Alekseev
%A A. A. Kuleshov
%A E. B. Savenkov
%T Thermomechanical model for impermeable porous medium with chemically active filler
%J Matematičeskoe modelirovanie
%D 2017
%P 117-133
%V 29
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2017_29_12_a8/
%G ru
%F MM_2017_29_12_a8
M. V. Alekseev; A. A. Kuleshov; E. B. Savenkov. Thermomechanical model for impermeable porous medium with chemically active filler. Matematičeskoe modelirovanie, Tome 29 (2017) no. 12, pp. 117-133. http://geodesic.mathdoc.fr/item/MM_2017_29_12_a8/

[1] L.W. Lake, Enhanced Oil Recovery, Society of Petroleum Engineers, 2010, 550 pp.

[2] L.W. Lake, R. Johns, B. Rossen, G. Pope, Fundamentals Enhanced Oil Recovery, Digital Edition, Society of Petroleum Engineers, 2014, 498 pp.

[3] E. Catalano, B. Chareyre, A. Cortis, E. Barthelemy, “A pore-scale hydro-mechanical coupled model for geomaterials”, II International Conference on Particle-based Methods – Fundamentals and Applications (PARTICLES 2011), 2011

[4] E.H. Saenger, F. Enzmann, Y. Keehm, H. Steeb, “Digital rock physics: Effect of fluid viscosity on effective elastic properties”, Journal of Applied Geophysics, 74 (2011), 236–241 | DOI

[5] H. Cao, A. Boyd, V. Da Silva Simoes, “Numerical simulation of the elastic properties of porous carbonate rocks”, 14th International Congress of the Brazilian Geophysical Society, 2013, SBGF-4064 http://sys2.sbgf.org.br/congresso/abstracts/trabalhos/sbgf_4064.pdf

[6] R. Sain, Numerical simulation of pore-scale heterogeneity and its effects on elastic, electrical and transport properties, PhD Thesis, Stanford University, 2010

[7] H. Lan, C.D. Martin, B. Hu, “Effect of heterogeneity of brittle rock on micromechanical extensile behavior during compression loading”, J. Geophys. Res., 115 (2010), B01202 | DOI

[8] V.S. Zarubin, G.N. Kuvyrkin, Matematicheskie modeli termomekhaniki, Fizmatlit, M., 2002, 168 pp.

[9] O. Iu. Batalin, A. I. Brusilovskii, M. Iu. Zakharov, Fazovye ravnovesiia v sistemakh prirodnykh uglevodorodov, Nedra, M., 1992, 272 pp.

[10] R.C. Reid, J.M. Prausnitz, T.K. Sherwood, The properties of gases and liquids, 3rd Ed., McGraw-Hill, New York, 1977

[11] J.M. Prausnitz, R.N. Lichtenthaler, E.G. de Azevedo, Molecular thermodynamics of fluid-phase equilibria, 3rd Ed., Prentice Hall, 1998, 864 pp.

[12] M.L. Michelsen, J. Mollerup, M.P. Breil, Thermodynamic models: fundamental and computational aspects, Tie-Line Publications, 2008

[13] K.S. Krasnov (red.), Fizicheskaia khimiia, v. 1, 2, Vyshaya shkola, M., 1995, 831 pp.

[14] L. Formaggia, J.F. Gerbeau, F. Nobile, A. Quarteroni, “Numerical treatment of defective boundary conditions for the Navier-Stokes equations”, SIAM J. Numer. Anal., 40:1 (2002), 376–401 | DOI | MR | Zbl

[15] L. Formaggia, J.F. Gerbeau, F. Nobile, A. Quarteroni, “On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels”, Computer Methods in Applied Mechanics and Engineering, 191:6–7 (2001), 561–582 | DOI | MR | Zbl

[16] M. Tayachi, A. Rousseau, E. Blayo, N. Goutal, V. Martin, Design and analysis of a Schwarz coupling method for a dimensionally heterogeneous problem, Project-Teams MOISE, Research Report, No 8182, INIRIA, 2012

[17] J.G. Heywood, R. Rannacher, S. Turek, “Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations”, International Journal for Numerical Methods in Fluids, 22 (1996), 325–352 | 3.0.CO;2-Y class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl