2. Modeling procedures

compositions, influencing the process performance. Therefore, the accuracy of the selected model is essential and greatly affects the final results of the simulation and

The first one is the selection of the model, built-in with the mathematical relationships that best represent the variables of the system. There is no a priori a procedure to make this choice, so heuristic or experience-based criteria are generally used [2]. The second question refers to get the best parameters that complete the definition of the model for a given data series. For this latter case, there are several numerical procedures [3, 4] that allow to address the problem to optimize

The thermodynamic properties having the greatest influence on the simulation of separation processes are those related to phase equilibria (vapor-liquid equilibrium, VLE, in the scope of this work), as well as other thermodynamic quantities that arise in the mixing process. These properties are associated with the excess

(xi,p,T). As such, the goal of the

. Thus, the VLE fitting process becomes a bi-objective

<sup>E</sup> values can only be

(x,p,T), are

) is

<sup>E</sup> with each one of the vari-

<sup>E</sup> = g E

obtained from VLE, which satisfies a dependency of the type, F(xi,p,T) = 0,

ables. On the other hand, defects in the experimental data could give place to incoherencies between experimental activity coefficients γ<sup>i</sup> = γi(xi,yi,p,T) and the

optimization problem; hence, two error functions are included in the correlation

included in the modeling, since new error functions should also be minimized. However, one of the benefits of this approach is to use a unique thermodynamic model that avoids the issues caused by possible discontinuities or inconsistencies between partial models of some properties. Even more relevant is that this allows the model to describe better the physics of the system under study. This supposes a mean to verify the coherence of the mathematical formalism imposed by thermodynamics, validating the different properties. A drawback of this practice is the increase of the complexity of the procedure, but this is just a numerical issue of relative complexity. Therefore, addressing the global modeling of the thermodynamic behavior of solutions as a problem with multiple objectives is a notable

It is known that the resolution of multi-objective problems does not produce a single result; on the contrary, a set of non-dominated results that constitute the socalled Pareto front [5] is obtained. There is no precise mathematical criterion that allows the selection of a unique result. However, the process simulation requires a single result to define the intended design, having to resort to external criteria

This study evaluates the effect of choosing the different results from the Pareto front in the simulation task. To achieve this, some partial goals are proposed such as (a) to establish a rigorous methodology to carry out the optimization procedure with the suggested modeling and (b) to check the real impact of the chosen model on the simulation, with the purpose of proposing a selection criterion. Thus, the designed methodology should include different stages, like the data selection used in the procedure, obtaining the result front and the election of the final result. Two systems, considered as standard in many studies on thermodynamic behavior of solutions, are selected since the necessary experimental information (VLE and h<sup>E</sup>

available in literature. After checking the data sets [6, 7], making up the

modeling is to achieve a functional type of f = f(θ,xi,p,T) that minimizes the norm

<sup>E</sup> <sup>f</sup> |. The vector <sup>θ</sup> represents a set of parameters in the model, which must be optimized. However, due to the existing relation between phase and mixing prop-

design processes. Two milestones should be considered.

Distillation - Modelling, Simulation and Optimization

the parameter set considering the starting hypothesis.

, which is written as g

preventing us from obtaining individual relations of g

E

contribution in chemical engineering.

different from those used to obtain the front.

erties, former approach may not be enough. In the first place, g

problem. The complexity grows as other properties, such as h<sup>E</sup> = h<sup>E</sup>

Gibbs energy g


48

E

excess Gibbs function g
