Mathematical Modeling of Thermomechanical Behavior of Porous Impermeable Medium with Active Filler

  • M. V. Alekseev
  • E. B. Savenkov
  • N. G. Sudobin
Conference paper
Part of the Springer Geology book series (SPRINGERGEOL)


In this paper we consider a self-consistent mathematical model and numerical simulation techniques which are supposed to be suitable to analyze behavior of the impermeable porous media with isolated pores filled with chemically active multiphase multicomponent substance under thermal loads. The porous matrix is described by linear thermomechanical equations. The substance in pores is described by lumped model which includes chemical (pseudo) components mass conservation equations and energy conservation equation for the mixture. Amount of components can change due to chemical reactions induced by heating of the media. Lumped energy balance equations account for matrix/pores heat transfer and heat produced by chemical reactions. Composition of phases is governed by phase equilibrium conditions with an arbitrary number of components and four phases (solid, liquid hydrocarbon, gas and liquid water phases). The two groups of equations (for the matrix and for the pores) are coupled by suitable interface conditions at the “reservoir”/“pore” interfaces.

The purpose of the model is a validation of the basic mechanisms of the formation of connected porosity and permeability in the initially impermeable heavy hydrocarbon reservoirs treated by the modern thermal recovery techniques such as, e.g., in citu combustion.

Preliminary numerical results are presented for synthetic but realistic test case.


Thermomechanics Chemical reactions Phase equilibrium Pore-scale simulation 



The work was supported by the Russian Foundation for basic research, project No. 16-29-15078 ofi m.


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    Alekseev, M.V., Kuleshov, A.A., Savenkov, E.B.: Thermomechanical model for impermeable porous medium with chemically active filler. In: Mathematical Models and Computer Simulations, vol. 29, No. 12 (2017). AcceptedGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Keldysh Institute of Applied Mathematics of Russian Academy of ScienceMoscowRussian Federation
  2. 2.Autonomous Non-profit Organization Scientific and Technical Association “ITIN”MoscowRussian Federation

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