Splitting the Thermodynamlics and Hydrodynamics in Compositional Gas-Liquid Flow through Porous Reservoirs

For two-phase compositional flow with mass transfer in porous media, it is shown that the existing steady-state solutions are unstable for gas-liquid systems, which are characterized by a high relative phase mobility. Instead of them the process model allows stable “semi-stationary” solutions which correspond to a limit model when the liquid-gas mobility ratio tends to zero. In a semi-stationary model the pressure and phase concentration fields are quasi-stationary, while the liquid saturation, in conditions of a continuous condensation/evaporation, is strongly non-stationary and has no a stationary limit in time. Within the framework of the semi-stationary model we have obtained a full splitting between hydrodynamics and thermodynamics, thanks to the fact that N-2 equations describing the phase concentration transport allow an explicit first integration along streamlines. This enables to transform them into differential equations of thermodynamic type (out of space and time) with differentiating over pressure. Being added to the usual equilibrium and EOS equations, such a system constitutes a new closed thermodynamic model which depends on the pressure only. This model describes the thermodynamic behaviour in an open system which corresponds to gas-liquid flow along each streamline. The remaining two flow equations determine the pressure and the saturation fields, with coefficients dependent on thermodynamics. To determine them it is sufficient to calculate the thermodynamic system one time, in contrast to the full compositional model where the thermodynamics is calculated at each space and time point. <br>The obtained hydrodynamic model allows obtaining the analytical solutions along streamlines, by using the singular perturbation method with respect to the relative phase mobility parameter. The irregular character of the asymptotic expansions is determined by the fact that the formal limit solution corresponds to an immobile liquid, which means a full pore plugging by liquid and breaking of gas movement. The full analytical solutions to the non self-similar multicomponent flow problems towards a well were constructed with using the matching asymptotic expansion method. This result was used to propose a new method of gas-condensate well representation in reservoir simulations. The comparison of the solutions obtained for the split thermodynamic and hydrodynamic models with numerical ECLIPSE-based full-compositional simulations has shown a very good agreement. The suggested method was used to develop a new kind of the streamline compositional simulator. We illustrate some examples of its functioning. <br>The research was financed by the Schlumberger Abingdon Technology Center.