IntroductionThe recently presented modified RAND framework [1] is extended from the isothermal flash specification to a number of other state function based flash specifications, including (P,H), (P,S), (T,V), (U,V) and (S,V).... [ view full abstract ]
Introduction
The recently presented modified RAND framework [1] is extended from the isothermal flash specification to a number of other state function based flash specifications, including (P,H), (P,S), (T,V), (U,V) and (S,V). Among them, the isenthalpic (P,H) flash and the isoenergetic-isochoric (U,V) flash are of renewed interest to a number of industrial applications involving simulation of non-isothermal processes, including heavy oil recovery. We will also demonstrate a consistent method to modify the RAND matrix in a consistent way to guarantee the convergence of the isothermal flash specification without significantly increasing the complexity of the problem.
Methods
The modified RAND framework was initially derived for solving isothermal multiphase flash problems, in the presence or absence of chemical reactions. It consists of E+F equations for E elemental potentials and F phase molar amounts, where E is the number of elements and F the number of phases. In the absence of chemical reactions, the E elements are replaced by the C components and the total number of equations becomes C+F. The method treats all components in all phases in the same manner leading to a simple structure which can be easily extended to include any number of phases. To extend the isothermal framework to other flash specifications, the general case where the temperature and pressure are unknown is considered. The constraints are then introduced based on the flash problem being considered.
The modified RAND method is not restricted to a certain equation of state. In many cases the equation of state used causes the flash problem to be highly nonlinear in the phase compositions. If one of the phases is unstable then it is possible for the direction generated by the modified RAND method to be ascending in the Gibbs energy. We consider this and demonstrate a simple and robust correction which can be added to the unstable phase matrix to ensure the direction is descending, which when combined with a line search, guarantees local convergence.
Conclusion
The presented formulation is an extension of the isothermal modified RAND method to a number of other state function based flash specifications. The formulation is radically different from the existing formulations for non-isothermal flash. In most cases the method can be used directly with a suitable implementation, though a backup nested isothermal flash is sometimes necessary to guarantee convergence for non-isothermal flash specifications.
The correction method presented for the unstable phase makes the modified RAND a robust method for solving the isothermal flash problem. The update is simple to calculate and maintains the excellent convergence properties of the method when far from the solution.
References
[1] Paterson, D., Michelsen, M. L., Stenby, E. H., & Yan, W. (2017, February 20). New formulations for isothermal multiphase flash. SPE-182706-MS. Society of Petroleum Engineers. doi:10.2118/182706-MS
[2] Michelsen, M. L. (1999). State function based flash specifications. Fluid Phase Equilibria, 158–160(0), 617–626, doi.org/10.1016/S0378-3812(99)00092-8
Carbon capture and other industrial applications , Challenges and advances in fluid phase equilibria
