Streamline concept for compositional reservoir simulation: HT-splitting and asymptotic solutions

@inproceedings{OladyshkinRM2006,
 abstract = { The streamline simulators, based on calculating a set of one-dimensional hydrodynamic problems along each flow streamline, are considered as a powerful and extremely fast tool which allows keeping simultaneously the true geometry and heterogeneity of petroleum reservoirs and ensuring an adequate reproduction of all the hydrodynamic singularities. The method efficiency is however seriously reduced in the case of multiphase compositional flow, when even the one-dimensional problems require a lot of time to simulate numerically the high order system of partial differential equations with coupled hydrodynamic and thermodynamic effects. We propose a new method based on splitting the thermodynamics and hydrodynamics (HTsplitting) for general compositional model, which enables us to obtain an effective semi-analytical solution to the two-phase compositional problem along streamlines. Such a splitting is based on the mathematical result obtained by the authors when studying the limit behaviour of the compositional model at high difference between the phase mobilities (gas-liquid systems). We have shown that the subsystem of the concentration transport equations formulated along a streamline can be transformed into limit thermodynamic differential equations, independent of space and time. Due to this the total compositional model can be split into a thermodynamic independent subsystem and a hydrodynamic subsystem which consists of two equations determining the pressure and the saturation fields. The new independent thermodynamic model, which describes the phase equilibrium in a thermodynamically open system, consists of nonlinear algebraic equations (equivalence between chemical potentials, equations of state) and nonlinear ordinary differential equations. To obtain the analytical solutions for the hydrodynamic part, we have developed a special singular perturbation method based on matching the asymptotic expansions obtained within different space sub-domains. To calculate compositional flow along each streamline it is then sufficient to simulate once the thermodynamic part and to insert the obtained thermodynamic functions into the analytical hydrodynamic solution. },
 author = { Oladyshkin, Sergey AND Panfilov, Mikhail },
 booktitle = { 26th gOcad Meeting },
 month = { "june" },
 publisher = { ASGA },
 title = { Streamline concept for compositional reservoir simulation: HT-splitting and asymptotic solutions },
 year = { 2006 }
}