A rigorous method to evaluate the consistency of experimental data in phase equilibria. Application to VLE and VLLE

Abstract

This work forms part of a broader study that describes a methodology to validate experimental data of phase equilibria for multicomponent systems from a thermodynamic‐mathematical perspective. The goal of this article is to present and justify this method and to study its application to vapor–liquid equilibria (VLE) and vapor–liquid–liquid equilibria (VLLE), obtained under isobaric/isothermal conditions. A procedure based on the Gibbs‐Duhem equation is established which presents two independent calculation paths for its resolution: (a) an integral method and (b) a differential method. Functions are generated for both cases that establish the verification or consistency of data, δψ for the integral test and δζ for the differential approach, which are statistically evaluated by their corresponding average values [ δtrueψ¯, δtrueζ¯], and the standard deviations [ strue(δψtrue), strue(δζtrue)]. The evaluation of these parameters for application to real cases is carried out using a set of hypothetical systems (with data generated artificially), for which the values are adequately changed to determine their influence on the method. In this way, the requirements of the proposed method for the data are evaluated and their behavior in response to any disruption in the canonical variables (p,T, phase compositions). The conditions for thermodynamic consistency of data are: δtrueψ¯<2, strue(δψtrue)<0.2, δtrueζ¯<5, and s(δξ)<0.2. In systems with VLLE, in addition to the previous criteria, must occur that: δxLLE<0.05 and δTLLE<0.5 K. The new proposed method has been tested with a set of 300 experimental binary systems, biphasic and triphasic, obtained from published bibliography, and the results are compared with those of other tests commonly used for testing thermodynamic consistency. The results show that the greater rigor of the proposed method is mainly due to the simultaneous verification of various independent variables. As a result, the conditions for the new test are verified for fewer systems than using other tests mentioned in the literature (i.e., Fredenslund‐test and direct of Van Ness). Its unique application is sufficient to ensure the consistency of experimental data, without using other tests. © 2017 American Institute of Chemical Engineers AIChE J, 2017

Extension of the validation method for vapor–liquid equilibrium data to systems with nonvolatile components

“…The problem lies in confirming whether the experimental information obtained is coherent/consistent with the theoretical formalism established by thermodynamics . As explained in previous articles, phase equilibria experimentation usually leads to measuring a number of variables larger than those established by the degrees of freedom of the system studied; clearly oversized as determined by the phase rule. Therefore, a mathematical‐thermodynamic tool must be found that checks the “degree of correlation” between the variables found experimentally and scientific formalism.…”

“…To carry out some applications that show the practical utility of the previous mathematical formalism, binary solutions are chosen (with a volatile and a nonvolatile component), as the extension to multicomponent solutions is immediate as described previously . Likewise, the application to VLLE is similar to the cases already presented . The particularization of Equation for binary solutions produces: …”

“…The resolution of this differential equation is not possible because the term in square brackets cannot be evaluated from experimental data, as the relation between the compositions in the two phases is constant, fulfilling the condition: ∀ x 1 : y nv = 0 → ( ∂y 1 / ∂x 1 ) = 0. However, the resolution of Equation , using the integral‐procedure , allows evaluating the consistency of the {data+model} set. In this case, the assessment of the data quality is done by checking that the difference between the experimental values of ψ , ψ i,exp , and those calculated by the test, ψ i,cal , are lower than the maximum admissible degree of inconsistency which, in turn, depends upon the quality level required. …”

“…The principles described previously are applied here to different VLE of solutions containing a nonvolatile species (nv‐VLE). The irruption of ionic compounds, solids and/or liquids, in multiple applications, especially in the field of chemical engineering, has led to the development of a unique line of work in the area of phase equilibria.…”

“…Based on the above considerations, the structure proposed for this manuscript is as follows: A mathematical approach that allows formalizing a consistency test/procedure for the phase equilibria of nv‐VLE systems. Description of the model used and the procedure followed to optimize its parameters. This step a crucial given the repercussions of the model on the consistency, as described previously Graduation step (quantitative and qualitative) of the designed methodology, with application to artificial data sets of dissolutions, containing induced errors in the variables, where the influence of errors on the definition of the test is analyzed. The last part presents the results obtained by applying the proposed method to real data sets, choosing the most significant cases from the literature to obtain a more in‐depth analysis, which can be of value to other researchers in the field.…”