A rigorous formulation of streamline approach in reservoir simulation for compressible compositional case

For the system of equations of multi-component, multi-phase filtration the calculation procedure, which is based on the notion of ‘streamline’, is considered. This notion as well as the methodology has in mind the presence in real flows of the effect of specific directions when the main flow of the mixture in the reservoir takes place along some curves that are similar to streamlines in ordinary hydrodynamics. It is shown that conventional application of this notion, as a rule, contains implicit assumptions. These assumptions make difficult the assessment of the accuracy of the method. New geometric interpretation of ‘streamline’ concept is shown. Such interpretation can be considered as in a sense rigorous. It is also demonstrated how one can approach the accuracy assessment problem for ‘streamline’ methodology with the help of geometric formulation.