Geodesic
Thermodynamically consistent approach for numerical simulation of oil displacement processes
Matematičeskoe modelirovanie, Tome 21 (2009) no. 10, pp. 7-18

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In the present paper we deal with some problems of calculations related to the filtration of multicomponent mixtures with complicate thermodynamic behavior. As a rule corresponding calculations, taking into account complicated thermodynamics especially with phase transitions and separate treating of each component, consume much of computational time. Moreover, thermodynamically consistent models are necessary for proper calculations. We propose in the paper the simple and robust methodology that resolves both these issues in case of compressible fluids that experience phase transitions. Namely, we propose some analytic approximations of Gibbs potentials separately for multi-component gas and liquid phases and obtain analytically the equations of phase equilibrium surfaces. This allows reaching the consistent thermodynamic model and reduces computational time consumption because of analyticity. The exemplary calculations demonstrate satisfactory accuracy for practical purposes. 
@article{MM_2009_21_10_a1,
     author = {Elena Koldoba and Alexander Koldoba and Artyom Myasnikov and Olga Podgornova and Yuri Rykov},
     title = {Thermodynamically consistent approach for numerical simulation of oil displacement processes},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {7--18},
     publisher = {mathdoc},
     volume = {21},
     number = {10},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2009_21_10_a1/}
}
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Elena Koldoba; Alexander Koldoba; Artyom Myasnikov; Olga Podgornova; Yuri Rykov. Thermodynamically consistent approach for numerical simulation of oil displacement processes. Matematičeskoe modelirovanie, Tome 21 (2009) no. 10, pp. 7-18. http://geodesic.mathdoc.fr/item/MM_2009_21_10_a1/