Abstract: The main objective of this paper is to present a number of the new mathematical models of the multiphase flow with phase transitions in porous media. The models were formulated as generalizations of the classical Stefan problem and are based upon fundamental conservation laws and relations of equilibrium thermodynamics. It was shown that phase transition moving boundary can be considered as a jump of saturation functions. This fact allowed apply the theory of discontinuity to obtain the boundary conditions at unknown moving boundaries for a wide class of various processes in porous media. The semi-analytical asymptotic method using both similarity solutions and numerical calculation was developed. This approach was applied to investigate the phase transitions problems in the fields of soil science (freezing, thawing and evaporation in soils), geothermal reservoir modeling and mathematical modeling of gas hydrate decomposition in gas fields and marine sediments.

Brief Biography of the Speaker:
G. Tsypkin is a Senior Researcher in the Institute for Problems in Mechanics of Russian Academy of Sciences. He received the Ph.D and Doctor of Sciences degrees from the Institute in 1982 and 1995 respectively. His research interests include phase transitions in porous media, geothermal reservoir modeling, transport phenomena in soils (evaporation, freezing and thawing), gas hydrates formation and decomposition in gas fields and marine sediments, stability of interface in porous media. He has held several research grants from the Russian Fund for Basic Research, NATO, INTAS, CNR (Italy), Royal Society of London etc. He gave lectures as a full professor at the Moscow State Technical University n.a. N. E. Bauman and Yakutsk State University. G. Tsypkin has over 80 high impact publications and 2 books.