Mathematical Simulation of Thermomechanics in an Impermeable Porous Medium

Authors: Alekseev M.V., Sudobin N.G., Kuleshov A.A., Savenkov E.B. Published: 07.08.2020
Published in issue: #4(91)/2020  
DOI: 10.18698/1812-3368-2020-4-4-23

Category: Mathematics | Chapter: Computational Mathematics  
Keywords: mathematical simulation, thermomechanics, phase equilibrium, chemical kinetics, thermal decomposition, kerogen, porous medium

The paper reports on mathematically simulating behaviour of a porous medium featuring isolated interstices filled with a chemically active substance by using a mathematical model of thermomechanics in the matrix and thermochemical processes inside the pores. We used three-dimensional thermomechanical equations to describe the behaviour of the medium. A lumped-element model accounting for chemical reactions and phase equilibrium describes the processes in pores. We outline the mathematical model of the medium and the respective computational algorithm. We provide parametric computation results using realistic thermophysical and thermodynamical parameters, composition of the organic substance found inside pores (products of thermal decomposition of kerogen) and chemical reactions, which show that it is necessary to employ complex, interconnected models to simulate the process class under consideration


[1] Lake L.W. Enhanced oil recovery. Society of Petroleum Engineers, 2010.

[2] Lake L.W., Johns R., Rossen B., et al. Fundamentals of enhanced oil recovery. Society of Petroleum Engineers, 2014.

[3] Catalano E., Chareyre B., Cortis A., et al. A pore-scale hydro-mechanical coupled model for geomaterials. II Int. Conf. PARTICLES 2011. Available at: https://pdfs.semanticscholar.org/8f8b/f95bd79030ba0ec0361680e901f3a569d67a.pdf (accessed: 15.09.2020).

[4] Saenger E.H., Enzmann F., Keehm Y., et al. Digital rock physics: effect of fluid viscosity on effective elastic properties. J. Appl. Geophys., 2011, vol. 74, iss. 4, pp. 236--241. DOI: https://doi.org/10.1016/j.jappgeo.2011.06.001

[5] Lan H., Martin C.D., Hu B. Effect of heterogeneity of brittle rock on micro-mechanical extensile behavior during compression loading. J. Geophys. Res., 2010, vol. 115, iss. B1, art. B01202. DOI: https://doi.org/10.1029/2009JB006496

[6] Cao H., Boyd A., Da Silva Simoes V. Numerical simulation of the elastic properties of porous carbonate rocks. 13th Int. Cong. of the Brazilian Geophysical Society, 2013. DOI: https://doi.org/10.1190/sbgf2013-224

[7] Alekseev M.V., Kuleshov A.A., Savenkov E.B. A mathematical model for impermeable porous media under thermomechanical loads. Preprinty IPM im. M.V. Keldysha [Keldysh Institute Preprints], 2017, no. 35, 34 p. (in Russ.). DOI: 10.20948/prepr-2017-35

[8] Alekseev M.V., Kuleshov A.A., Savenkov E.B. Thermomechanical model of an impermeable porous medium with a chemically active filler. Math. Models Comput. Simul., 2018, vol. 10, no. 4, pp. 459--471. DOI: https://doi.org/10.1134/S2070048218040026

[9] Alekseev M.V., Savenkov E.B., Sudobin N.G. Mathematical modeling of thermo-mechanical behavior of porous impermeable medium with active filler. In: Physical and Mathematical Modeling of Earth and Environment Processes 2017. Springer, 2018. DOI: https://doi.org/10.1007/978-3-319-77788-7_22

[10] Zarubin V.S., Kuvyrkin G.N. Matematicheskie modeli termomekhaniki [Mathematical models of thermomechanics]. Moscow, FIZMATLIT Publ., 2002.

[11] Batalin O.Yu., Brusilovskiy A.I., Zakharov M.Yu. Fazovye ravnovesiya v sistemakh prirodnykh uglevodorodov [Phase equilibria in natural hydrocarbon systems]. Moscow, Nedra Publ., 1992.

[12] Reid R.C., Prausnitz J.M., Sherwood T.K. The properties of liquids and gases. McGraw-Hill, 1977.

[13] Bauman J.H., Deo M. Simulation of a conceptualized combined pyrolysis, in situ combustion, and CO2 storage strategy for fuel production from green river oil shale. Energy & Fuels, 2012, vol. 26, no. 3, pp. 1731--1739. DOI: https://doi.org/10.1021/ef2017072

[14] Krasnov K.S., ed. Fizicheskaya khimiya. T. 1, 2 [Physical chemistry. Vol. 1, 2]. Moscow, Vysshaya shkola Publ., 2001.

[15] Mollerup J.M., Michelsen M.L. Calculation of thermodynamic equilibrium properties. Fluid Phase Equilib., 1992, vol. 74, pp. 1--15. DOI: https://doi.org/10.1016/0378-3812(92)85049-E

[16] Behar F., Roy S., Jarvie D. Artificial maturation of a type I kerogen in closed system: mass balance and kinetic modelling. Org. Geochem., 2010, vol. 41, iss. 11, pp. 1235--1247. DOI: https://doi.org/10.1016/j.orggeochem.2010.08.005

[17] Ru X., Cheng Z., Song L., et al. Experimental and computational studies on the average molecular structure of Chinese Huadian oil shale kerogen. J. Mol. Struct., 2012, vol. 1030, pp. 10--18. DOI: https://doi.org/10.1016/j.molstruc.2012.07.027

[18] Kokorev V.I., Sudobin N.G., Polishchuk A.M., et al. [Thermal destruction of bituminous kerogen from Tutleym (Bazhenov) suite of deposits in Krasnoleninsky region]. Mater. II mezhdunar. nauch. simp. "Teoriya i praktika primeneniya metodov uvelicheniya nefteotdachi plastov". T. 1 [Proc. II Int. Sci. Conf. "Theory and practice of enhanced oil recovery methods". Vol. 1]. Moscow, VNIIneft Publ., 2009, pp. 45--49 (in Russ.).