Simulation of miscible displacement with interphase mass transfer resistance

The modeling of miscible displacement processes in petroleum reservoirs, such as Carbon Dioxide Injection or Enriched Gas Drive, has been traditionally done with compositional simulators in which the distribution of the different components or pseudocomponents among the phases is given by equilibrium constants which are determined with a suitable Equation of State, or given as input to the simulator in the form of tables or correlations as function of pressure, temperature and composition. In other words, the partial differential equations describing the flow of each phase through the reservoir are solved by finite difference techniques assuming thermodynamic equilibrium among the phases in each grid block, every time step. It is shown here that this assumption leads to large errors since at typical conditions interphase mass transfer resistances are large and thermodynamic equilibrium in not nearly reached during the time steps of interest. In this work, a one dimensional compositional simulator is developed where mass transfer kinetics is taken into account by including equations which describe the interfacial molar flow of each component in terms of overall mass transfer coefficients, and the difference between the actual phase concentration and that it would have at equilibrium. Sensitivity studies are carried out to determine mass transfer resistance contributions to process performance. The simulator was validated by modeling CO2 displacement experiments carried out in a laboratory slim tube. In this case, the relative permeability curves were kept constant, and the overall mass transfer coefficient was changed to reproduce the oil production of the experiments. The experimental results were also simulated with a conventional compositional simulator, changing the relative permeability curves to adjust oil production.