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A rigorous method to evaluate the consistency of experimental data in phase equilibria. Application to VLE and VLLE
AIChE Journal ( IF 3.7 ) Pub Date : 2017-08-09 22:11:04 , DOI: 10.1002/aic.15876 Luís J. Fernández 1 , Juan Ortega 1 , Jaime Wisniak 2
AIChE Journal ( IF 3.7 ) Pub Date : 2017-08-09 22:11:04 , DOI: 10.1002/aic.15876 Luís J. Fernández 1 , Juan Ortega 1 , Jaime Wisniak 2
Affiliation
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 [
,
], and the standard deviations [
,
]. 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:
,
,
, and
. In systems with VLLE, in addition to the previous criteria, must occur that:
and
. 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
中文翻译：
一种评估相平衡中实验数据一致性的严格方法。适用于VLE和VLLE
这项工作构成了更广泛研究的一部分，该研究描述了一种从热力学数学角度验证多组分系统相平衡实验数据的方法。本文的目的是介绍和证明这种方法，并研究其在等压/等温条件下获得的汽-液平衡（VLE）和汽-液-液平衡（VLLE）中的应用。建立了一个基于Gibbs-Duhem方程的程序，该程序提供了两个独立的解决方案：（a）积分法和（b）微分法。对于这两种建立数据验证或一致性的情况，都会生成函数，积分测试的δψ和微分方法的δζ，均通过相应的平均值进行统计评估[，
]和标准偏差[
，
]。使用一组假设系统（人工生成的数据）对这些参数进行评估，以应用于实际案例，对其值进行适当更改以确定它们对方法的影响。以这种方式，评估了所提出的方法对数据的要求，并响应规范变量（p，T，相组成）的任何破坏，评估了它们的行为。用于数据的热力学一致性的条件是：
，
，
，和
。在具有VLLE的系统中，除了先前的标准外，还必须发生以下情况：
和
。该新方法已经过300套从公开书目中获得的双相和三相实验二元系统的测试，并将结果与通常用于测试热力学一致性的其他测试的结果进行了比较。结果表明，提出的方法更加严格的主要原因是同时验证了各个自变量。结果，与使用文献中提到的其他测试（即Fredenslund测试和Van Ness的直接测试）相比，使用更少的系统对新测试的条件进行了验证。其独特的应用程序足以确保实验数据的一致性，而无需使用其他测试。©2017美国化学工程师学会AIChE J ，2017
更新日期：2017-08-10
,
], and the standard deviations [
,
]. 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:
,
,
, and
. In systems with VLLE, in addition to the previous criteria, must occur that:
and
. 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
中文翻译：
一种评估相平衡中实验数据一致性的严格方法。适用于VLE和VLLE
这项工作构成了更广泛研究的一部分，该研究描述了一种从热力学数学角度验证多组分系统相平衡实验数据的方法。本文的目的是介绍和证明这种方法，并研究其在等压/等温条件下获得的汽-液平衡（VLE）和汽-液-液平衡（VLLE）中的应用。建立了一个基于Gibbs-Duhem方程的程序，该程序提供了两个独立的解决方案：（a）积分法和（b）微分法。对于这两种建立数据验证或一致性的情况，都会生成函数，积分测试的δψ和微分方法的δζ，均通过相应的平均值进行统计评估[
，
]和标准偏差[
，
]。使用一组假设系统（人工生成的数据）对这些参数进行评估，以应用于实际案例，对其值进行适当更改以确定它们对方法的影响。以这种方式，评估了所提出的方法对数据的要求，并响应规范变量（p，T，相组成）的任何破坏，评估了它们的行为。用于数据的热力学一致性的条件是：
，
，
，和
。在具有VLLE的系统中，除了先前的标准外，还必须发生以下情况：
和
。该新方法已经过300套从公开书目中获得的双相和三相实验二元系统的测试，并将结果与通常用于测试热力学一致性的其他测试的结果进行了比较。结果表明，提出的方法更加严格的主要原因是同时验证了各个自变量。结果，与使用文献中提到的其他测试（即Fredenslund测试和Van Ness的直接测试）相比，使用更少的系统对新测试的条件进行了验证。其独特的应用程序足以确保实验数据的一致性，而无需使用其他测试。©2017美国化学工程师学会AIChE J ，2017
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