LiquidâVapor Equilibrium Data Correlation - American Chemical Society

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Liquid-Vapor Equilibrium Data Correlation: Part I. Pitfalls and Some Ideas to Overcome Them A. Marcilla,* M. M. Olaya, and M. D. Serrano Chemical Engineering Department, University of Alicante, Apdo. 99, Alicante 03080, Spain. ABSTRACT: Accurate description of VLE (and VLLE) plays an essential role in many industrial separation processes. Local composition models for the activity coefficient description, such as NRTL and UNIQUAC, have contributed significantly over the past four decades toward the fitting of experimental VLE data, for example, to the design of distillation towers. However, a critical examination of this field reveals that important deficiencies still exist due to the complex nature of the topic. In the present paper, these pitfalls are classified and discussed in detail, and some examples are selected to conveniently illustrate every one of them. We also comment on some aspects that could improve the distribution, evaluation and correlation of these VLE (and VLLE) data that, in turn, could lead to better results and avoid misinterpretations.

1. INTRODUCTION Vapor-liquid equilibrium (VLE) data for mixtures are among the most important physicochemical properties required by industry. Accurate description of VLE plays a crucial role in many industrial separation processes. Efficient design, development, and rational operation of distillation and rectification processes are based on these equilibrium data. Because of this important practical application, a vast number of papers have been published on the experimental determination of VLE data for many binary and multicomponent systems. Some authors have patiently organized all this scattered information in very useful monographs, data compilation books, and data banks, which provide an overall picture of the whole field. A useful compilation of experimental phase-equilibrium data is provided by the multivolume DECHEMA series.1 Dortmund Data Bank (DDB) contains VLE and LLE data for nearly all the phase equilibrium data available worldwide, which includes more than 64 000 references.2 NIST SOURCE Data Archival System3 provides access to VLE and LLE data for over 33 000 mixtures. Moreover, the VLE data have to be reduced to a suitable mathematical form before being used in, for example, design calculations. Through the correlation of these equilibrium data using an empirical or physically grounded equation, VLE data can be systematically interpolated and, with caution, extrapolated to new conditions of temperature and pressure. The thermodynamic equations used to correlate and predict VLE data are classified as excess Gibbs energy (GE) or activity coefficient models, and equations of state (EOS). The development and use of models based on binary parameters have always aroused great interest. The convenience of this type of model is obvious: the variety of mixtures in chemical technology is extremely large. In addition, the process development and preliminary design require evaluation of different alternatives in a short time. The experimental measurement of VLE data is not too difficult to perform, but it can be very timeconsuming to carry out, especially for multicomponent systems which require that the number of data points cover the whole range of compositions, temperature, and pressure conditions. r 2011 American Chemical Society

The development of equations that represent multicomponent VLE using exclusively binary parameters is attractive, because it can reduce the amount of experimental work drastically. Lack of experimental VLE data for multicomponent systems could be compensated for by their prediction with, for instance, activity coefficient models like NRTL and UNIQUAC, or group contribution models like UNIFAC, with parameters based on the correlation of binary VLE data. There is no doubt about the significant contribution of equations like NRTL and UNIQUAC to the modeling of vaporliquid equilibria over the past four decades. However, the limited number of parameters in these models may not be sufficient to reproduce binary data with the required accuracy. Besides, the predictive ability of these models is too restricted, frequently yielding poor or unreliable results when extrapolated from binary to ternary or multicomponent systems. Therefore, the key potential value of these binary parameter based models is not entirely fulfilled in practice. Another deficiency of the currently most widely used GE models is that the simultaneous description of VLE and LLE data is too frequently not possible.4,5 All the above-mentioned limitations are well-known and discussed in a number of papers. For example, Chen and Mathias4 state that the main unsolved problems are primarily related to the necessity of more experimental data and model parameters and, in a number of cases, better models are clearly needed. Rarey5 argues that the limited number of parameters in current GE models is often not sufficient to reproduce binary data within, or sometimes even close to, the experimental uncertainty. He proposes a method to increase the flexibility of the composition dependence of GE models and then applies it to the UNIQUAC (FlexQUAC) and NRTL (FlexNRTL) models. However, we have noticed that these and other similar papers seem to not have influenced in depth the subsequent work on phase equilibrium calculations. The procedures and models used Received: September 16, 2010 Revised: December 21, 2010 Accepted: February 3, 2011 Published: February 24, 2011 4077

dx.doi.org/10.1021/ie101909d | Ind. Eng. Chem. Res. 2011, 50, 4077–4085

Industrial & Engineering Chemistry Research nowadays to regress VLE (and VLLE) data are exactly the same as those of thirty years ago, and obviously the same limitations still apply. As an example, the ThermoData Engine (TDE) is an expert program designed to generate recommended data and model parameters based on the raw experimental data available from NIST SOURCE.3 The activity coefficient models supported in TDE are the common ones: Margules, van Laar, Wilson, NRTL, and UNIQUAC. Because databanks of validated experimental data and model parameters of known accuracy for binary and multicomponent VLE play key roles in engineering calculations, we believe that a step in the right direction is necessary. Chen et al.4 stated that “only after proper validation of models and parameters against real experimental data can scientists and engineers reliably use process models to simulate, analyze, design, construct, start-up, control, and optimize industrial processes”. Part II of this paper will deal with a systematic analysis of the capabilities and limitations of the NRTL model for VLE data correlation. Besides, more flexible equations should be proposed for the correlation of VLE data for systems that cannot be suitably fitted using common models, as for example those that require simultaneous representation of VLE and VLLE. The present paper classifies and discusses in detail several problems that are encountered when experimental VLE data or correlation results, which are usually organized in data banks or compilation books, are used. Thus, we will reflect on a number of aspects that could improve the distribution, evaluation and correlation of these VLE (and VLLE) data, with a view to obtaining better results and avoiding inconsistencies. Several pertinent examples have been selected to illustrate the ideas that will be discussed here. The DECHEMA Data Series Collection1 is used as a convenient source of information for the examples discussed in this paper, because in this compilation not only experimental data are presented, but also correlations using different models for the activity coefficient are applied for data reduction. We focus on binary systems because they constitute the basis of the VLE framework.

2. DISCUSSION 2.1. Pitfalls in VLE Correlations. The problems that affect the quality of binary VLE (and VLLE) data correlations using an activity coefficient based model have been grouped into three categories: • Very poor VLE correlations for too many binary systems irrespective of the common activity coefficient model used. • Difficulties in the simultaneous description of VLE and VLLE data. • Inconsistent VLE correlation results that incorrectly reproduce VLLE splitting. 2.1.1. Very Poor VLE Correlations for Too Many Binary Systems Irrespective of the Common Activity Coefficient Model Used. It is true in general that the quality of the results obtained for the VLE data correlation using for example an activity coefficient based model is generally better than for LLE data. Nevertheless, this idea can wrongly lead one to believe that the fit of the VLE data is much better than it actually is. For example, in the DECHEMA Data Series the following equations are tested based on their ability to reduce the VLE data of all the compiled binary systems: Margules, van Laar, Wilson, NRTL, and UNIQUAC. These include all the existing representative models for activity coefficients employed in this kind of data fitting. Local

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Figure 1. VLE data (mole fractions) for the binary system methyl vinyl ketone (1) þ water (2) at 743 mmHg (ref 6, p 355). Experimental data points and equilibrium lines obtained by correlating data using NRTL and Wilson equations.

composition models such as Wilson, NRTL and UNIQUAC ought to provide the best results. The last two also have the advantage, unlike Wilson, of being able to represent LL splitting. The UNIQUAC equation is based upon a solution model that is significantly more detailed and sophisticated than the other types of equations, and it is also the foundation for the UNIFAC method of estimation of liquid phase activity coefficients for systems without measured data. In this compilation, the y versus x diagram of experimental data points, and the equilibrium line calculated by the activity coefficient equation yielding the lowest mean deviation are represented on the same graph. An inspection of these experimental and calculated binary VLE data reveals two very important aspects that we would like to underscore: a. For Many Systems No Common Model Provides an Adequate Data Fit. The inspection of any VLE compilation book that includes data regression results reveals that for many systems no common model can reproduce the VLE behavior at the required precision, for example, for design calculations. Unfortunately, it is possible to find many systems that illustrate this problem. For example, Figure 1 is an x-y representation of the experimental and regressed VLE data for the system methyl vinyl ketone (1) þ water (2) at 743 mmHg (ref 6, p 355) and shows the magnitude of the deviations that we are trying to call attention to. All the common activity coefficient models produce similar results; Wilson yields the lowest mean deviation in the vapor mole fraction. These are poor, but qualitatively correct, correlation results in the sense that the model reproduces the type of system, nonazeotropic or with a homogeneous or heterogeneous azeotropic point, but the calculated compositions are very far from the experimental ones. Qualitatively incorrect results are discussed further on. b. Better Results Are Not Achieved with the Supposedly Superior Models. For example, if the number of times a given model produces the best correlation (i.e., yields the lowest mean deviation in the DECHEMA Chemistry Data Series6) for binary systems, is counted, the results obtained are: van Laar 7.2%, Margules 14.3%, UNIQUAC 14.3%, Wilson 23.7%, and NRTL 40.6%. The aqueous-organic systems in this data compilation 4078

dx.doi.org/10.1021/ie101909d |Ind. Eng. Chem. Res. 2011, 50, 4077–4085

Industrial & Engineering Chemistry Research include mixtures of widely differing behavior, from close to ideal to highly nonideal solutions. Better results with the UNIQUAC equation should be expected since it is based on a more complex theory of liquid mixtures that takes into account the sizes and shapes of the molecules. UNIQUAC was developed to retain the advantages of the Wilson equation but without the restriction of being limited to only totally miscible mixtures. However, the results obtained from the VLE data fitting are significantly better when using Wilson and comparable to those obtained using the empirical Margules equation. These results are in agreement with those obtained by Novak et al.7 that measure the relative usefulness of these same equations on the basis of the first eight books of the work by Gmehling and Onken.8 They conclude that for slight and medium deviations from ideality the differences between the individual equations are quite small, but for strongly nonideal systems, with positive deviations from Raoult’s law, the best results are obtained using the Wilson and NRTL equations. The semiempirical formalisms included in the UNIQUAC model, such as the nonrandom distribution of molecules (local composition concept) and the molecular parameters, while providing the equation with a more realistic picture of liquid mixtures, are not able to give better results than other simpler models, when these are used to fit binary VLE data. Therefore, in many cases the models are unavoidably incapable of representing the experimental results, which is not because of the lack of accuracy of the experimental data, the calculation algorithm or the expertise of the researcher; the solution is just impossible since it does not exist in the space defined by the models. Excessive confidence in the capability of existing models, a deviation from meeting practical and engineering needs as well as doubts about the calculation algorithms and data reduction procedures (in the case of multicomponent mixtures) are key factors that could obstruct the development of newer and more capable models. Obviously, the most difficult task is to deduce what the characteristics of the new equations should look like if present results are to be improved upon. The following are usually considered as desirable features for a model: simplicity, two parameters (or only a few more) per binary pair, only binary parameters, and a theoretical basis for its derivation. But, above all, if the model is to represent experimental data at the required precision, it seems that these are very severe demands that impose serious restrictions on the models to better represent all the possible VLE behaviors that exist in nature, and a change in the strategy to develop new models must be devised. Chen and Mathias4 state, “Practicing engineers prefer simple and intuitive thermodynamic models that can be applied easily: Models that are constantly being revised, sophisticated theories requiring expert users, models with excessive computational load, or models requiring extensive parameterization (e.g., ternary parameters) have limited industrial applications”. But they also claim in the same paper that “Highly parameterized models are accepted and useful if they represent available data within experimental accuracy”. We believe that it would be convenient to open or relax some of these common requirements in favor of practical and engineering oriented results, while trying to retain the unquestionable advantages of the insight provided by molecular thermodynamics. Prausnitz and Tavares9 discuss the advantages of proceeding from “blind” empiricism to “thermodynamicallygrounded” empiricism to “phenomenological or molecular” thermodynamics. For example, equations such as NRTL and UNIQUAC

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could be extended with some adequate additional parameter that provides some more of the required flexibility, for example, FlexNRTL and FlexUNIQUAC.5 However, a great reluctance exists about the use of models with more than two parameters. To remove existing prejudices about the number of parameters for an activity coefficient model, we should take into account the fitting of other physical properties, for example, the vaporpressure data of pure components as a function of temperature. In this case, the logarithm of the vapor pressure is expressed as a function of the reciprocal of absolute temperature, using at least three parameters. In this example only two variables, T and P, are related to each other. VLE data requires relating the liquid composition to the vapor composition and also to the bubble temperature for a variety of system behaviors, ranging from nonazeotropic near ideal systems to heterogeneous azeotropic systems, which additionally need to reproduce the experimental LL splitting for the VLLE azeotropic point. However, it is insisted upon that the binary VLE data of all these systems be fitted using exclusively two parameters. From this point of view, we deduce that unfortunately but necessarily the results obtained for too many systems are poor. An additional effort will have to be made to improve this situation in view of the relevance of the accuracy of VLE data correlation in distillation and rectification process design. 2.1.2. Difficulties in the Simultaneous Description of VLE and VLLE Data. One of the major goals in dealing with the phase equilibrium problem is the simultaneous representation, using a unique set of model parameters, of all the existing phase equilibrium regions of a system, including VL, LL, VLL, LS, or any other type of phase equilibrium present in the system, over the whole range of T and P conditions. The advantages of global versus local fitting are evident. Some papers refer to concepts such as universal parameter values or quantitative global phase diagram.10 Unfortunately, the present state of phase equilibrium modeling is still far from achieving this important goal. However, a very different issue is the correlation of the VLE data for systems that exhibit liquid splitting and therefore one VLLE data point. For these systems, the VLE data correlation should include a realistic representation of the VLLE composition, because this point not only belongs to the VLE region, but it is a singular or characteristic point of that region. However, the currently most widely used GE models are frequently not able to simultaneously describe, at the required precision, the VLE and VLLE data for binary systems with liquid-liquid splitting.4 To illustrate this problem, Figure 2 shows the experimental VLE and VLLE data for the water (1) þ 1-butanol (2) binary system at 760 mmHg together with the correlation results obtained using NRTL (ref 6, p 410). The experimental VLLE composition is compared with the one obtained using the NRTL model. A very high composition deviation is obtained for one of the liquid phases: x1(exp) = 0.67011 and x1(calc) = 0.444 (mole fractions). This fact is discussed in a previous paper5 that also demonstrates that the additional parameter used in the nonlinear transformation of the composition space, as proposed by this author, considerably improves the ability of the model to cope with a simultaneous VLE and VLLE regression. We do not consider the difficulty to provide a simultaneous description of VLE and VLLE to be a minor limitation of the common models but in fact a very serious problem. Therefore, the transformation proposed by Rarey5 or other alternative equations that provide the GE models with the required flexibility 4079


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Figure 2. VLE data (mole fractions) for the binary system water (1) þ 1-butanol (2) at 760 mmHg (ref 6, p 410). Experimental data points and NRTL correlation results showing a large deviation in the LL compositions.

to solve this and other limitations discussed further on, is absolutely necessary, at least for practical purposes. 2.1.3. Inconsistent VLE Correlation Results That Incorrectly Reproduce VLLE Splitting. This is the case of binary systems without liquid phase splitting, for which the models produce a VLLE region during the VLE correlation, or even a heterogeneous instead of homogeneous azeotrope, that actually does not exist. Even though this problem is known, we think that it has not been sufficiently discussed and it continues to be an obscure subject. The reason for this problem seems to be the difficulty or impossibility of the common activity coefficient models to reproduce VLE data that are nearly horizontal in some part of the y versus x curve. If the system exhibits a homogeneous azeotropic point in this part of the x-y curve, a heterogeneous instead of homogeneous azeotrope would be calculated by the model from the equilibrium data regression. Two situations can be distinguished based on the distribution of the experimental VLE data published for systems that experience the problem discussed here: a. Data are located exclusively close to the pure components; an indeterminate region exists in the middle part of the x composition range. b. Data are distributed uniformly throughout the x composition space. In the first case (a), it is not possible, from the shape of the experimental VLE curve, to deduce whether or not the system shows VLL splitting. If these incomplete data sets are fitted without using any extra information about the system, the parameter set obtained is prone to be inconsistent with the real behavior of the system. These parameters would only be valid in the very limited region of existence of the data used for the correlation. However, these parameters will generally end up being used for any composition region, for example, when they are included in software packages for separation process design. The results obtained using parameters in this way could be complete nonsense. Many incomplete sets of correlated VLE data have this problem, for example the system 1-propanol (1) þ water (2) at 323.15 K (ref 12, p 414) shown in Figure 3. The experimental

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Figure 3. VLE data (mole fractions) for the binary system 1-propanol (1) þ water (2) at 323.15 K (ref 12, p 414). Experimental data points and NRTL correlation results showing a false VLL splitting.

data are very limited and located very close to both pure components. The results published include not only this experimental data set but also the VLE data correlation using NRTL, which produces better results than all the common models tested but generates a false VLLE splitting, since at 323.15 K this system has a homogeneous azeotrope.13 The false liquid compositions that correspond to a heterogeneous, instead of homogeneous, azeotrope are marked in a similar way in the published figure as in Figure 3 without providing any warning, explanation or discussion of this inconsistency, which can lead to misinterpretations. In the second case (b), we refer to examples for which the experimental VLE data are homogeneously distributed over the entire composition range of the system while it is evident that LL splitting actually does not occur, yet the x-y diagram shows a very flat, almost horizontal, curve in some part of the composition range, very similar in shape to the curves that produce VLLE. For these types of systems many correlation results are published that generate false VLL splitting, without any warning in this regard. For example, the system acetone (1) þ water (2) at P = 2570 mmHg (ref 14, p 197) shows a homogeneous liquid phase (Figure 4). The experimental points do not suggest the presence of VLL splitting, and nevertheless, the published results using the NRTL model are not only very poor but reproduce a nonexisting VLLE point, that appears in the published figure, again without any explanation. In Figure 5, the T-x,y diagrams for this system are represented using (a) the experimental data and (b) the published NRTL parameters, showing the serious consequences of the utilization of these calculated parameters that generate a nonexistent LL region and prevent correct VLE calculations in the region around T = 373.15 K. On the other hand, the nonideality of the vapor phase, which has not been considered in ref 14, should be conveniently formulated by an EOS. All the parameter sets obtained having the problems that are being discussed in this section, are consequently inconsistent and could lead to serious mistakes if they were used, for example, in chemical process simulation software. In our opinion, it would be desirable to clearly indicate whether or not the system shows VLL splitting and to impose this real behavior on the model during the VLE data correlation. However, this is not common practice. Usually, when VLE data for this type of binary systems collected in compilations are inspected, the real behavior of the system on 4080



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Figure 4. VLE data (mole fractions) for the binary system acetone (1) þ water (2) at 2570 mmHg (ref 14, p 197). Experimental data points and NRTL correlation results showing a false VLL splitting.

the possibility of VLL splitting, is not indicated. However, if the model produces VLLE, the two theoretical liquid compositions are still represented on the x-y diagram, even when the real behavior of the system does not produce liquid splitting, as evidenced by the examples we cited earlier. Because this inconsistency is not suitably indicated, the user of these data is wrongly led to believe in the existence of a real VLL split. On the other hand, the difficulty common models have in reproducing almost horizontal y versus x curves, without generating VLLE phases, necessitates modification of the common models, or the development of more flexible GE functions, with an ability to cope with this kind of VLE behavior that occurs rather frequently in nature. In the meanwhile, we suggest that an advice should be clearly given if correlation results inconsistent with the qualitative behavior of systems are published, such as those shown in Figures 3 and 4. 2.2. Some Ideas to Improve the VLE (VLLE) Data Correlations. The deficiencies in the reduction of VLE data using activity coefficient models, discussed in the previous section, could at least be partially sorted out by acting on the following aspects: • Improving the experimental VLE data distribution and defining “key points”. • Improving the quality of the VLE data, e.g., by inspection of the GM curve for the liquid phase. • Assuring the highest level of purity for the substances for VLE data and vapor pressure determination. • Modifying the existing models or developing new ones to gain the required flexibility for a correct description of the x, y, and P or T equilibrium data. All these aspects are discussed in detail below. 2.2.1. VLE Data Distribution and Definition of “Key Points”. The influence of data distribution on the correlation results of any property is well-known. In the particular case of VLE data, the following example eloquently illustrates this fact. Three data sets, obtained by different authors, are compiled in the DECHEMA Data Series (ref 14, p 278; ref 6, pp 364 and 366) for the system 2-butanone (1) þ water (2) at 760 mmHg. Obviously, the distribution of data among the three experimental data sets (Figure 6) is different. At the P and T conditions of the data, this system has one homogeneous azeotropic point, x1 = y1 = 0.652

Figure 5. Temperature (K) versus x, y (mole fractions) for the VLE in the binary system acetone (1) þ water (2) at 2570 mmHg (ref 14, p 197): (a) experimental and (b) calculated using the published NRTL parameters.

(mole fraction) and T = 346.55 K15 and also a region where VLL splitting occurs, at T = 352.75 K, with the following LL compositions (mole fractions), xI1 = 0.047 and xII1 = 0.585.11 These liquid compositions are not included in any of the three data sets, nor taken into account in the published correlation results. As a consequence, the results obtained in the correlation of each data set, fore example, using the NRTL model, are quantitatively very different and even differ in the type of azeotrope reproduced. The liquid compositions (mole fractions) and temperatures for the VLLE data, obtained using the NRTL model parameters that come from the correlation of each data set, are as follows: Set 1 (ref 14, p 278): xI1 = 0.056 and xII1 = 0.694; T = 346.65 K Set 2 (ref 6, p 364): xI1 = 0.048 and xII1 = 0.599; T = 346.55 K Set 3 (ref 6, p 366): xI1 = 0.019 and xII1 = 0.350; T = 349.05 K If these results are compared with the experimental ones, we find that the best results are obtained using the second data set (Figure 6b), even though a deviation of six degrees in the temperature is obtained. For the first data set (Figure 6a), the high deviation in the liquid compositions produces a heterogeneous azeotropic point. Nevertheless, the azeotropic data compilations13 clearly indicate that, for this system, the azeotrope is homogeneous as opposed to heterogeneous. The NRTL correlation of the third data set (Figure 6c) produces the highest deviations in the LL compositions (more than 20% molar for one of the components in one of the phases) and also in the calculated azeotrope (x1 = y1 = 0.714, T = 347.53 K). All these results are usually published without any indication as to the real nature of the azeotrope, the true liquid compositions of the VLLE 4081



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quality of the data fitting. But if all the experimental points are considered equally important, lower standard deviations could even be obtained with parameter sets that are inconsistent with the behavior of the system, that is, that produce false or highly deviated LL compositions for the VLLE. If these problems are not clearly pointed out, the user will use the correlation results in the belief that they are consistent with the behavior of the system. Moreover, it does not make sense that the results can differ so much, even qualitatively, depending on the page from which the correlation parameters are taken. The consequences can be disastrous when the parameters are used for the design of VL separation equipment. The success of the data correlation is contingent upon, among other things, homogeneous distribution of the VLE experimental data as well as inclusion of all the singular points of the system, for example, the two conjugated liquid compositions in systems with LL splitting. Every system, depending on its T-x,y or P-x,y behavior contains several, though generally very few, singular or “key points”, which are necessary and sufficient to correctly specify the behavior of the system, at least qualitatively, and therefore must be included in the data correlation. For systems with VLLE splitting, this point must be considered a “key point” and, as a consequence, the two conjugated liquid compositions are essential to the data fitting and have to be correctly reproduced by the model. Other “key points” are the equilibrium data for the pure components. These points together with the azeotropes must be reproduced for the given system. 2.2.2. Evaluation of the Quality of the Experimental VLE Data. With reference to the validation of the experimental VLE data, the first step obviously involves visual inspection of the x-y and the T or P versus x, y diagrams, to ensure that a smooth trend is obtained. Next, thermodynamic consistency tests are generally employed to check whether or not the experimental data obey thermodynamic relations. These tests are devised based on various manipulations of the Gibbs-Duhem equation and are traditionally classified into two groups: Area Tests (Redlich et al., 1948;16 Herington, 1947;17 Wisniak 199418) and Point to Point Tests (van Ness et al. 1973;19 Fredenslund et al, 1977;20 Wisniak, 199321). The Differential and Infinite Dilution Tests, proposed by Kojima and co-workers,22,23 are also used to evaluate the consistency of VLE data. In this paper, we propose a further evaluation of the quality of the experimental data by inspecting the Gibbs energy function for the liquid mixture (GM,L exp ), which is derived from the experimental values for the liquid and vapor compositions (x and y) and the temperature and pressure. These data are used to calculate the experimental activity coefficient for each component in the mixture (γi,exp). Obviously, although activity coefficients are referred to as “experimental”, they are not measured but indirectly calculated through experimental boiling points and liquid and vapor compositions:

Figure 6. VLE data (mole fractions) for the binary system water (1) þ 2-butanone (2) at 760 mmHg (compiled in DECHEMA: (a) ref 14, p 278; (b) ref 6, p 364; and (c) ref 6, p 366). Three experimental data sets and NRTL correlation results showing the experimental and calculated LL splitting.

data, or a discussion or warning anywhere in the compilation information. Only the standard deviation between experimental and calculated data is presented as a measure of the

γi, exp ¼

P 3 yi p0i 3 xi

ð1Þ

∑

M, L Gexp ¼ RT 3 xi lnðxi γi, exp Þ ð2Þ i We have calculated the experimental Gibbs energy of mixing curves for some of the experimental VLE data sets compiled in DECHEMA. The results show that for some systems that have passed at least one of the thermodynamic consistency tests mentioned earlier,16-21 the GM,L exp curve exhibits an evident

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Figure 7. Gibbs energy of mixing (dimensionless) for the binary system 2-butanone (1) þ water (2) at P = 500 mmHg (ref 6, p 362).

dispersion of the corresponding points. For example, the data set for the system 2-butanone (1) þ water (2) at 500 mmHg (ref 6, p 362) passes possitively the two consistency tests, however the GM,L exp curve represented in Figure 7 shows some clearly deviated points. For example, the deviation of one of the binary points (x1 ≈ 0.75) in this figure, a consequence of some experimental error, is not detected by the consistency tests because they are necessary but not sufficient conditions to validate VLE data. Although the T versus x, y diagram shows a deviation for this inconsistent point, it is magnified and, therefore, more easily detected by using the GM,L exp representation. The GM,L exp curve that we suggest be inspected can be also used to verify this type of consistency. When the Antoine coefficients are consistent with the VLE data for the pure components, the GM,L exp values of the pure components must be located on the = 0). A deviation from zero of the GM,L x-axis (Gpure,L exp exp function for the two pure components gives an estimation of the magnitude of the inconsistency between the two sources of data. For example, in Figure 7 there is much better agreement between the vapor pressure data and the VLE data set for water than there is for the 2-butanone component. Many binary VLE data sets can be encountered where this kind of inconsistency exists for either one or both of the components. The mistake can be in the VLE data set, the vapor pressure data used to obtain the Antoine constants or both. Otherwise, it may be caused by an incorrect analytical measurement. However, an alternative explanation could be that it is due to the presence of an impurity in some of the chemicals used to determine the VLE or vapor pressure data. This problem can be present in many experimental data and might explain many inconsistencies, as will be discussed in detail in the next section. For all these cases that exhibit deviated or inconsistent points, the difficulties in the experimental data correlation might be due not to the lack of capability of the model used, but rather to the poor quality of the experimental data, which is revealed neither by the graphs that are usually inspected, y versus x and P or T versus x, y, nor by consistency tests. Therefore, the Gibbs energy of mixing curve may provide additional and valuable information about the quality of experimental VLE data that would be convenient to consider in future in addition to the consistency tests. 2.2.3. Purity of the Substances for VLE Data and Vapor Pressure Determination. Opposite to separations in extraction

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that only depend on liquid phase non idealities, separations in distillation also depend on differences in vapor pressure.24 Therefore, highly accurate measurements of the vapor pressures of pure components are required for the determination and regression of VLE data. The vapor pressure is usually determined by either ebulliometric or static methods.25 Both these methods are very reliable if the conditions of the experimental runs are carefully controlled. However, we believe that special attention should be paid to the purity of the substances used in these measurements. It is accepted that 99% purity is enough for performing experimental vapor pressure determinations, which is the minimum value recommended by the Standard Test Method for Vapor Pressures of Liquids by Ebulliometry (E 1719-05, ASTM26). Depending on the vapor pressure differences between the impurities and the compound of interest, this level of purity may be too low. One percent of foreign substances can considerably modify the vapor pressure of the pure compound, and the effect could be very significant even for lower quantities of highly nonideal impurities. For example, 1% of water in 1-butanol decreases the bubble temperature of 1-butanol at 760 mmHg by 4 degrees. This value is much higher in various other mixtures, for example, 1% of ethanol in toluene reduces its normal boiling temperature by 7 degrees. Besides, for VLE data regressions, these data are combined with vapor pressure data from a different source to obtain the required Antoine constants. If a different criterion is used to select the purity of the reagents, it might be impossible to simultaneously regress the values of these two data series, regardless of model, because they are incompatible. This type of problem is easily spotted using the GM,L exp representation when the VLE data set includes the pure components, because GM,L exp 6¼ 0 is obtained for either one or both of the pure components, as was shown for the example represented in Figure 7. Fortunately, most researchers employ higher purity chemicals, 99.95-99.99% and thus obtain very accurate results. However, we think that clear restrictions regarding this matter must be established to avoid the inconsistencies discussed here. Besides, it must be pointed out that parameters for the Antoine equation are frequently used in VLE data correlations outside their range of validity. The larger the difference between the boiling points of the two pure compounds, the larger the extrapolation and the possibility of making a substantial error in the calculation of the activity coefficient. 2.2.4. Improving the Ability of Activity Coefficient Models in Fitting VLE Data. It was mentioned earlier that there is a need for more capable models able to correlate the VLE data of many binary systems, which can only be fitted very poorly using the existing activity coefficient models. The development of a universal theoretically grounded model for phase equilibria that delivers accurate results for all the various types of equilibria (VLE, VLLE, LLE, LSE, etc.) and for all the various kinds of mixtures possible is a complicated matter that unfortunately will demand much time and dedication from researchers. However, far from discouraging us, the difficulties should instead spur us to devote more efforts to this endeavor. In the meanwhile, engineers need immediate but practical solutions, for example, a significant improvement of the VLE data reduction of many systems of industrial interest, and therefore, we must provide them with some “provisional” but efficient response to the problem. 4083


Industrial & Engineering Chemistry Research In a previous paper,27 we showed how a slight but adequate modification of the NRTL equation achieved important improvements in the LLE data correlation of some systems. In a subsequent part of the present paper, we will apply this same modified NRTL equation to the VLE data reduction of some systems that exhibit poor results using the common models. The strategies to develop more capable models will be presented and the results delivered by these equations discussed.

3. CONCLUSIONS A survey of the published results for VLE data correlations of binary systems has revealed that limitations and pitfalls exist, in a field that seemed to be very well established because of the importance of the distillation processes which require such data. In the present paper, these problems have been classified and discussed in detail, and some examples have been chosen to conveniently illustrate every one of them. For example, correlation results are published that reproduce VLLE for systems that do not exhibit liquid splitting. Conversely, VLLE data are not generated or deviate significantly for systems that do actually present VLLE. Another inconsistency is encountered when VLE data are correlated using incompatible vapor pressure data, which leads to erroneous conclusions regarding model capabilities. A number of ways to overcome these problems are suggested, for example: correlation of the defined “key points” for each system, inspection of the Gibbs energy of mixing curve as an additional criterion to inspect the quality of the experimental VLE data, checking the consistency between the VLE and the vapor pressure data and assuring the highest level of purity for the substances. Another conclusion reached is that there exists a need for more flexible models capable of fitting the VLE data of many systems, particularly those that require simultaneous VLE and VLLE regression. ’ AUTHOR INFORMATION Corresponding Author

*Phone: (34) 965 903789. Fax: (34) 965 903826. E-mail: [email protected].

’ ACKNOWLEDGMENT The authors gratefully acknowledge financial support from the Vice-presidency of Research (University of Alicante). ’ NOMENCLATURE xIi = mole fraction of component i in liquid phase I xIIi = mole fraction of component i in liquid phase II yi = mole fraction of component i in the vapor phase γi = activity coefficient of component i T = temperature (K) P = pressure (Pa) R = gas constant (J K-1 mol-1) GM = Gibbs energy of mixing (J mol-1) GE = excess Gibbs energy (J mol-1) VLE = vapor-liquid equilibrium LLE = liquid-liquid equilibrium LSE = liquid-solid equilibrium VLLE = vapor-liquid-liquid equilibrium Superscripts

I, II = liquid phases I and II, respectively L = liquid phase

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Subscripts

exp = experimental calc = calculated i = component i

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