Multiphase fluid flows with mass transfer between different phases are governed by compositional models, in the context of petroleum engineering. These are evolution equations that represent the conservation of mass of each chemical component, supplemented by equations of state and thermodynamic relationships. Analytical solutions for this type of problems are very poor, then accurate numerical methods to simulate these class of systems are a very important and powerfull tool to get insight about the qualitative behavior of the structure of the solution. In this paper we concerned of a class of 2 by 2 system of balance laws with phase change. Here we introduce new mathematical theory for such systems and a fractional time-step method is presented and used to address the problem at hand.Key words: Balance Laws, Operator Splitting, Central Differencing Scheme, Thermal Porous Media Flow.
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