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3A method to compute liquid-gas equilibrium based on the balance of evaporation and condensation rates
M. S. Kulikov, V. P. Bashurin, A. A. Kibkalo, A. S. Myshkin, A. V. Van�kov, A. G. Danilov, M. M. Khabibulin,
L. V. Ktitorov, V. I. Zhigalov
FSUE �Russian Federal Nuclear Center � All-Russian Research Institute of Experimental Physics�, Sarov, Nizhny
Novgorod Region
Email: mikhail.kulikov@sarov-itc.ru
DOI 10.24412/cl-35065-2021-1-00-32
A model is proposed that makes it possible to estimate the rates of evaporation and condensation pro-
cesses in a two-phase medium (liquid-gas). The proposed model provides the preservation of the overall com-
position of the mixture. The method for calculating liquid-gas equilibrium is developed basing on this model
and Peng-Robinson equation is used there as an equation of state for the mixture of the substances. A numeri-
cal method for time evolution calculations of the components concentration in the liquid and gas phases is
proposed. The problem of calculating liquid-gas equilibrium for the mixture of hydrocarbons is considered as
one of the application examples for the proposed model. The computational results for the equilibrium (sta-
tionary) state of hydrocarbons mixtures obtained using the proposed method and the results obtained using
the method of successive substitutions, which is widely used for similar purposes, are compared.
High-order heterogeneous multiscale finite element method for elasticity problems
A. Yu. Kutishcheva1,2, E. P. Shurina1,2
1Trofimuk Institute of Petroleum Geology and Geophysics SB RAS
2Novosibirsk State Technical University
Email: KutischevaAY@ipgg.sbras.ru
DOI 10.24412/cl-35065-2021-1-00-33
Numerical modeling of physical processes in heterogeneous media is an important step of research and
applied problems, for example, modeling of elasticity deformation for the subsequent study of the effective
properties of rock samples or composite materials containing many scattered and randomly located inclusions.
In this case, various modifications of the multiscale finite element method are used, which are adapted to a
specific class of problems. Traditionally, for ease of implementation, algorithms are based on first-order shape
functions on parallelepiped supports (in the three-dimensional case), in which case an increase in the accuracy
of a multiscale solution is possible only by a grid refinement. However, the reduction of the macro-elements is
not always possible, due to the method requirements for the ratio of the sizes of macro-elements and inclu-
sions. In this paper, we investigate the efficiency of increasing the order of basis functions on tetrahedral sup-
ports and shape functions on polyhedral supports for the heterogeneous multiscale finite element method
applied to the problem of elastic deformation of a solid with inclusions.
This work was supported by the Foundation grant No. 0266-2019-0007, grant No. 0331-2019-0015.
Multidimensional computational models of gas combustion in heterogeneous porous medium
Yu. M. Laevsky1,2, T. A. Nosova1
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: laev@labchem.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-34
A two-temperature multidimensional computational model of filtration combustion of gas is proposed
[1, 2]. The model is based on the approximation of a system of conservation laws by the mixed finite element
method in spatial variables and the splitting method in time. Particular attention is paid to improving the per-
formance of the computational model by using parallel computing.
We investigated the process of filtration combustion of gas in inhomogeneous porous media in the case of
a jump in the heat capacity of the frame and a jump in porosity. In the case of a jump in the heat capacity, we
showed that the formula for the instantaneous velocity of the front works adequately away from the media
boundary, i.e. it reflects the real process of what is happening before and after the jump of physical character-
istics, namely, the combustion front slows down when approaching the boundary, and it reaches a new con-
stant value of the velocity after the transition to a new medium. In this case, the process stabilization does not
take place and the speed of the combustion front is not zero. In the case of a jump in porosity, its stabilization
is observed, that is, the front stops abruptly at a certain critical value of the jump in porosity. In the latter case,
the balance relation for the invariance of the process with respect to shear stops working for natural reasons -
the invariance of the problem with respect to shear disappears in the presence of a jump in the parameters of
the problem.
This work was supported by the Russian Science Foundation (grant 19-11-00048).
References
1. Laevsky Yu.M., Nosova T.A. Computational models of filtration gas combustion // Russian J. of Numerical Analysis
and Mathematical Modelling. 2017. V. 32, Is. 2. P. 115-125.
2. Laevsky Yu. M., Nosova T.A. A multidimensional computational model of filtration gas combustion // J. of Applied
and Industrial Mathematics. 2020. V. 14, Is.1. P. 148-161.
Implementation of planar 3D model of hydraulic fracture in rock with layered compressive stress
V. N. Lapin
Kutateladze Institute of Thermophysics SB RAS
Email: v.lapin@nsu.ru
DOI 10.24412/cl-35065-2021-1-00-35
The paper proposes a description of the Planar 3D hydraulic fracture model implemented at the Institute
of Thermophysics SB RAS. Two dimensional fluid flow in the fracture is described using Reynolds equation that
is approximated by finite volume method as in fully 3D model [1]. Fracture opening is connected with fluid
pressure by hypersingular integral equation [2]. Fracture front propagation is described by asymptotic solution
lake in [3]. The system on nonlinear equation (SNE) at each step of fracture propagation is solved by Newton
method. Results obtained by P3D model have been compared with classic 1D model solutions.
The model is planned to be used both for simulation of plane fracture propagation and for test of various
convergence improving technics for SNE.
References
1. Cherny S, Lapin V., Kuranakov D., Alekseenko O. 3D model of transversal fracture propagation from a cavity caused
by Herschel-Bulkley fluid injection // International J. of Fracture. 2018. V. 212, N. 1. P. 15-40.
2. Hills D.A., P. A. Kelly, D.N. Dai, A.M. Korsunsky, Solution of Crack Problems, The Distributed Dislocation Technique,
Solid Mechanics and its Applications. Springer-Science+Business Media, 1996.
3. Peirce A. Modeling multi-scale processes in hydraulic fracture propagation using the implicit level set algorithm
Comput. Methods Appl. Mech. Engrg. 2015. V. 283. P. 881�908.
