A parameterization approach for Equation of State models: The case of Water-Hydrocarbon binary systems

Abstract

The water-hydrocarbon systems are highly asymmetric. The reproduction of their experimental fluid phase equilibria over wide ranges of conditions by models of the Equation of State (EOS) type is challenging. The EOS has to be flexible enough with respect to composition and temperature. On the other hand, special equilibrium information (such us binary critical points whose pressure is found to be locally maximum or minimum when looking at the critical line) may be hard to reproduce. This may be due more to the lack of a proper optimization strategy than to an intrinsic limitation of the model. A better optimization strategy can be obtained first by considering the equations that describe special phase equilibrium points. Another example of such points is a binary liquid-liquid-vapor equilibrium point where one of the liquid phases has, locally, a minimum or a maximum component mole fraction value. In this work we use, on one hand, the mathematical conditions of special phase equilibrium points. For deriving some of such conditions, we resort to the method of implicit derivation. On the other hand, we initialize the interaction parameters to be fitted by forcing the exact reproduction of some binary key coordinates of special phase equilibrium points. Next, we fit the parameters through a completely implicit approach, i.e., by setting up the optimization problem without using equality restrictions. In such a case, some experimentally unknown thermodynamic variables, e.g., a phase composition, become optimization variables together with the interaction parameters. Finally, if required, the level of implicitness of the optimization problem is gradually reduced as the estimates of the interaction parameter values become increasingly accurate. A fully explicit approach requires to repeatedly solve, during the optimization course, the systems of equations corresponding to conventional or special critical or phase equilibrium points. Thus, the explicit approach has a higher chance of presenting convergence problems than the semi-implicit or fully implicit approaches. In this work, we use an equation of state coupled to cubic mixing rules and temperature-dependent interaction parameters. This makes the model highly flexible and capable, in principle, of representing the phase behavior of water-hydrocarbon systems. For such systems, there is a considerable amount of information available in the literature regarding binary critical lines. We consider an important number of water-hydrocarbon binary systems. We evaluate the strengths and limitations of both, the modeling approach and the parameterization strategy.