Parameterization of models of the equation of state type based on the exact reproduction of experimental key point information of binary systems (Poster)

J. I. RAMELLO; MARTÍN CISMONDI; MARCELO S. ZABALOY

Puerto Varas

Conferencia; IX Iberoamerican Conference on Phase Equilibria and Fluid Properties for Process Design; 2012

Universidad de Concepción

In two-parameter equations of state (EOSs) of the van der Waals type the pure compound critical point (PCCP) is usually considered a “key point” for defining the values of the pure compound attractive and covolume parameters. The most easily measurable variables at the PCCP are the temperature (Tc), the pressure (Pc) and the molar volume (Vc). Typically, the experimental Tc and Pc are the variables chosen to be exactly reproduced by the EOS. The critical values for the attractive and covolume parameters result from solving a system of equations where the experimental Tc and Pc appear as input parameters. The third variable of such system of equations is the EOS pure compound critical volume. This is a value for Vc predicted by the two-parameter EOS from the experimental Tc and Pc. Such predicted Vc value usually differs from the experimental Vc value to an extent well beyond the experimental uncertainty. The experimental coordinates of a key point, whose reproduction by the model is imposed, are named “key coordinates” in this work. Thus, in the above described customary use of two-parameter EOSs, Tc and Pc are key coordinates of the PCCP while Vc is not. When dealing with the modeling of the phase behavior of binary systems, it is also possible to use binary key coordinates to obtain values for the interaction parameters (IPs) that exactly reproduce the experimental key coordinates, with the ultimate goal of achieving a proper quantitative performance by the model, in ranges of conditions as wide as possible. Binary key coordinates are, e.g. the minimum temperature (Tm) at which the main critical line of a type III binary system (in the classification of van Konyneburg and Scott) exists. In other words, Tm is the temperature value at the local minimum temperature point of the mentioned critical line. Another example of “key coordinate” is the pressure value (CPM) at the local maximum pressure point of a critical line of a type I binary system. This last key point is described by a system of equations that consists of the critical conditions for a binary system coupled to the condition of local maximum pressure. In this work, we first obtain the characteristic systems of equations (CSEs) of a number of types of binary key points. Next, for a chosen binary system, we set a proper number of experimental values of key coordinates as known parameters of the CSEs. Then, we solve the CSEs for the IPs. Finally, we evaluate the model performance over wide ranges of conditions by comparing the model predictions with experimental data on the phase behavior of binary systems. For highly non-ideal systems, the number of IPs available to the model has to be large enough, if a good quantitative performance is to be achieved. Classical quadratic mixing rules do not provide a large enough number of independent interaction parameters, as opposite to cubic mixing rules (CMRs). In this work, we use CMRs for describing binary systems with a complex phase behavior, e.g. type III systems. In the best case, the values of the IPs resulting from solving the CSEs are satisfactory enough. In such situation, the model parameterization does not correspond to a typical parameter fitting process, where the IP values come from minimizing an objective function which usually depends on a relatively large number of experimental data. In the worst case, i.e. when the values of the IPs resulting from solving the CSEs are not satisfactory enough, they can be used as excellent initial values for a conventional parameter fitting calculation. Alternatively, a different choice of key points can be set to obtain a more balanced model performance.