Published: November 22, 2011

r2011 American Chemical Society 260 dx.doi.org/10.1021/ci200456w |J. Chem. Inf. Model. 2012, 52, 260–276 ARTICLE

pubs.acs.org/jcim

ThermoData Engine (TDE) Software Implementation of the Dynamic

Data Evaluation Concept. 7. Ternary Mixtures

Vladimir Diky,† Robert D. Chirico,† Chris D. Muzny,† Andrei F. Kazakov,† Kenneth Kroenlein,†

Joseph W. Magee,† Ilmutdin Abdulagatov,† Jeong Won Kang,‡,§ and Michael Frenkel*,†

†

Thermophysical Properties Division, National Institute of Standards and Technology, Boulder, Colorado 80305-3337, United States

‡

Department of Chemical and Biological Engineering, Korea University, 5-1 Anam-Dong, Sungbuk-Ku, Seoul 136-701, South Korea

’INTRODUCTION

As discussed in the first six papers of this series,16 the NIST

ThermoData Engine (TDE) software represents the first fullscale implementation of the concept of dynamic data evaluation

for thermophysical properties.7,8 This concept requires large

electronic databases capable of storing essentially all relevant

experimental data known to date with detailed descriptions of

metadata and uncertainties. The combination of these electronic

databases with expert system software, designed to automatically

generate recommended property values based on available experimental and predicted data, leads to the ability to produce

critically evaluated data dynamically or ‘to order’.

TDE has evolved from a first release, limited to thermophysical properties of pure compounds,9 to on-demand generation

of equations of state (EOS),10 dynamic web-based updates of

local data resources10 through the TRC-SOURCE data storage

system,11 support for binary mixtures, including phase equilibria,12 properties of chemical reactions,13 and experiment planning

and product design tools14 as well as dynamic web-based dissemination of properties of pure components through the NIST Web

Thermo Tables.15 Currently, TDE is used in a multitude of applications varying from data quality assurance16 and validation of new

experimental data17 to chemical process and product design.18,19 It

is also a core component in implementation of the concept of

Global Information Systems in Science with application to the field

of thermodynamics.20

The present paper describes an extension of TDE (version 6

released in 2011)21 to critical evaluation of thermophysical properties of ternary mixtures through on-demand dynamic evaluation of the properties of the binary subsystems. Other additions

described here are a vaporliquid equilibrium (VLE) data modeling test that complements consistency tests implemented previously for low-pressure/subcritical VLE data14,22 as well as

addition of the NIST-KT-UNIFAC prediction method23 for VLE

data, which was developed based on data quality factors (i.e., data

set weighting factors) described previously22 and automatic decomposition of molecular structures into KT-UNIFAC groups and

subgroups.24

’SCOPE

The types of compounds within the scope of TDE are unchanged since the first release of the program.1 The focus of the

program is organic compounds composed of the elements C, H,

N, O, F, Cl, Br, I, S, and P, plus industrially important inorganic compounds, such as ammonia and water, are included. In

analogy to the approach used for binary mixtures in TDE

(version 3),3 the expansion into property evaluations for ternary

mixtures (version 6) has progressed along two paths: one for properties modeled individually (volumetric properties, transport

Received: September 26, 2011

ABSTRACT: ThermoData Engine (TDE) is the first full-scale software

implementation of the dynamic data evaluation concept, as reported in this

journal. The present paper describes the first application of this concept to the

evaluation of thermophysical properties for ternary chemical systems. The

method involves construction of RedlichKister type equations for individual

properties (excess volume, thermal conductivity, viscosity, surface tension,

and excess enthalpy) and activity coefficient models for phase equilibrium

properties (vaporliquid and liquidliquid equilibrium). Constructed ternary models are based on those for the three pure component and three binary

subsystems evaluated on demand through the TDE software algorithms. All

models are described in detail, and extensions to the class structure of the

program are provided. Reliable evaluation of properties for the binary

subsystems is essential for successful property evaluations for ternary systems,

and algorithms are described to aid appropriate parameter selection and fitting for the implemented activity coefficient models

(NRTL, Wilson, Van Laar, RedlichKister, and UNIQUAC). Two activity coefficient models based on group contributions

(original UNIFAC and NIST-KT-UNIFAC) are also implemented. Novel features of the user interface are shown, and directions for

future enhancements are outlined.
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properties, etc.) and one for properties modeled collectively with

activity coefficient (AC) models for phase equilibrium properties.

The Gibbs phase rule specifies the maximum number of phases

present and the number of independent variables required to fully

define a property for a system with a given number of components

(chemical compounds). In the case of a ternary chemical system,

the maximum number of phases is five (an invariant state with no

independent variables), and the maximum number of independent

variables is four (for a single-phase system). These restrictions limit

the number of possible system types, but the number of potential

phase and variable combinations is very large for ternary mixtures.

The extensions to the TDE software described here target systems

with a maximum of two phases: vaporliquid equilibrium (VLE)

and liquidliquid equilibrium (LLE). Solidliquid equilibrium

(SLE) is not included for ternary mixtures at this time. Singlephase properties (excess volume, thermal conductivity, viscosity,

surface tension, and enthalpy of mixing) at low pressures (<10 bar)

are considered for the liquid phase.

Figure 1. Algorithm for property evaluations for ternary chemical systems with TDE.
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’ALGORITHM

To model properties for a binary mixture, the properties of the

two pure components are required.3 Similarly, to model properties for a ternary mixture, the properties of the three binary subsystems must be available and modeled. The program algorithm

involves three major steps: (1) evaluation of the properties for

the three pure components, as described in the first two papers of

this series;1,2 (2) evaluation of the properties for the three binary

subsystems (described in the third paper of this series,3 with

additions described here); and (3) calculation of the properties

of the ternary system at specified conditions with uncertainty assessment. Experimental property data for the ternary system

may be compared with the values derived from the combined

binary models, but the ternary experimental data are not used in

model fitting.

The general algorithm for property evaluations for ternary

chemical systems with TDE is shown in Figure 1. The major steps

are numbered in the figure and are described in the paragraphs

that follow.

Step 1: Compound Selection by User. The user initiates the

evaluation process by selecting the three components for the

mixture. Special features of this selection process, such as selection of components with known availability of experimental data,

are analogous to those described previously for binary systems.3

The only other required user action is selection of the AC model

and gas-phase model to be used for representation of the phase

equilibrium properties (VLE and LLE). (If application of an AC

model is not of interest to the user, this action can be skipped.)

A variety of common AC models are available for selection:

NRTL, RedlichKister, UNIQUAC, Van Laar, Wilson, and the

UNIFAC group contribution method. Gas-phase models are the

ideal gas, virial, RedlichKwong, PengRobinson, and Hayden

O’Connell models. The AC and gas-phase models implemented

in TDE for binary systems were described previously.3

Recently, this research group reported development of a

method for generation of UNIFAC-type group parameters

based on data quality factors (i.e., data set weighting factors)22

and automatic parsing of molecular structures into KTUNIFAC groups and subgroups.23 The resulting new parametrization for the KT-UNIFAC framework was labeled NIST-KTUNIFAC,23 and this method is now implemented in TDE. New

group parameters for NIST-KT-UNIFAC will be included in

future releases of TDE, as newly published experimental data

allow their determination.

Step 2: Experimental Data Are Retrieved From TDESOURCE by TDE. Following compound selection by the user,

the TDE software retrieves (loads) all experimental data for the

ternary mixture, its components, and the binary subsystems from

the local database, TDE-SOURCE. TDE-SOURCE is an archive

of experimental data and is a subset of the TRC SOURCE

archive,11 which is a relational data archival system for experimental thermophysical and thermochemical properties reported in the scientific literature. Presently (August, 2011), TDESOURCE contains 4.3 million experimental property values,

including those for 37 000 binary mixtures and 10 000 ternary

mixtures. In addition, proprietary or other experimental data can

be added by the user. As described previously,1,2 property values

can be modified (corrected) or selected for forced rejection by

the user. Added or modified data are not transferred to the TDESOURCE database but are maintained separately to ensure

traceability and database integrity. Property data are normalized

at the data-loading step, where mixture compositions are converted to mole fractions, phases and variables are sorted, and

equivalent representations of the same property (e.g., density and

molar volume) are converted to a single property (density, in this

example).

Step 3: Pure-Component Properties Are Evaluated by

TDE. Following retrieval and basic processing of the available experimental data, the properties of the pure components are

evaluated automatically. The dynamic evaluation of pure component properties was described in the first two articles of this

series.1,2 This step is bypassed if evaluated properties for the

compounds are available from the NIST REFPROP database.25

There are 105 such compounds included in TDE version 6, and

these include water, many simple hydrocarbons (e.g., methane,

ethane, etc.), light alcohols (methanol, ethanol), and other

common chemicals. On-demand property evaluations for these

compounds with TDE may be slow due to the large amount of

available data, and the REFPROP database provides high-quality

models; plus, there is little expectation of significant changes in

the evaluated properties due to new measurements for these

compounds.

Step 4: Single-Property Models for Binary Subsystems Are

Evaluated by TDE. Application of the concept of dynamic data

evaluation to properties for binary chemical systems was first described in the third article of this series.3 For properties represented by single equations, RedlichKister type equations are

used to represent the properties of of the binary subsystems. The

equations used and the fitting procedures were described fully in

the earlier article,3 and those procedures were used here, except

for viscosities, where a revised equation is given in Appendix A.

Step 5: Creation of Ternary Single-Property Models. The

portions of the algorithm that are specifically related to formulation of the ternary models are shown within the dotted rectangles

in Figure 1. The general program flow for single-property models

is shown in steps 5a through 5f. Because a model for a ternary

system can be created only if models were successfully created for

all three binary subsystems, the process involves checking for the

existence of the requisite binary models and formulating the

composite ternary model, once all are determined to exist. The

mathematical details of the composite ternary models are provided in Appendix A. The ranges (temperature and pressure) of

validity of the various binary models are not considered at this

juncture. The ranges are considered only when properties are

calculated at the request of the user. Values for conditions outside

the region of mutual overlap of the binary systems are labeled

extrapolated by the software, and users can decide whether the

extrapolated values meet their purposes.

Step 6: AC Models for Binary Subsystems Are Evaluated

by TDE. In the initial development of the TDE software for

application of AC models (i.e., multiproperty models), substantial user interaction with the software was necessary to optimize

fitting of the models to experimental phase equilibrium data. Procedures for automatic evaluation (i.e., without user intervention)

have been improved to increase their reliability. The improvements are described in the following paragraphs.

Successful creation of an AC model requires many considerations, including the extent of the available experimental data,

selection of an appropriate mathematical function to represent

temperature dependence of the activity coefficients, chemical

nature of the components (hydrogen bonding, reactivity, etc.),

availability of required auxiliary data (virial coefficients for some

gas-phase models, densities for Poynting corrections, etc.), data
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gaps, and others. Figure 2 shows the algorithm used in TDE for

creation of an AC model for a binary system. After selection of

the pure components, the user is required to select an AC model

and a gas-phase model (step 1, Figure 2 or step 1, Figure 1). Steps

27 of the algorithm (Figure 2) involve selection and initialization of the gas-phase model. In step 2, the program provides a

warning if a binary pair is suspected of being reactive and cannot

be correctly represented by an AC model. Presently, this includes

any mixtures containing methanal and mixtures of amines with

acids. If the selected gas-phase model seems inappropriate for a

binary pair, an alternative model (an “upgrade”) is suggested to

the user before fitting. For example, the program may suggest

an upgrade from the ideal gas to virial model for a mixture

containing alcohols or to the HaydenO’Connell gas-phase

model for mixtures containing formic or acetic acid (steps 25,

Figure 2.)

The TDE software includes many stored molecular structures

(presently, ∼20 000) that can be parsed for application in various

Figure 2. Algorithm for creation of an AC model for a binary chemical system with TDE.
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group contribution methods1 as well as a structure drawing tool

to add new compounds. This structural information is the key

component in provision of guidance by the software in the

selection of models. Guidance provided in the present version

of TDE (version 6) represents only the initial application of

TDE technology to model selection. At present, guidance for

the selection of an appropriate AC model based on the chemical

nature of the pure components is outside the scope of TDE but

is an active area of research by this group.

The initialization of gas-phase models (step 6, Figure 2), plus

enumeration of any required auxiliary data for those models, was

described previously.3 If the gas-phase model can be created

(step 7, Figure 2), formulation of the AC model (steps 819,

Figure 2) begins. If a gas-phase model cannot be created (step 20,

Figure 2), the algorithm is terminated, and the user is informed.

Steps 812 of the algorithm (Figure 2) involve the UNIFAC,

UNIQUAC, and NIST-KT-UNIFAC models, which use group

parameters for structural fragments determined from connectivity

Figure 3. Algorithm for determination of the appropriate number of parameters for creation of an AC model for a binary system with TDE.
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tables for the mixture components. Absence of required group

parameters causes the algorithm to terminate for the UNIFAC

and NIST-KT-UNIFAC models (steps 10 and 11b, Figure 2).

At step 13 (Figure 2), program links are made to auxiliary pure

component property models that may be necessary for the

particular AC model. Details of the AC model and auxiliary data

were described earlier.3 Step 14 (Figure 2) involves linking

(accessing) of the experimental data (VLE, LLE, SLE, activity coefficients, and excess enthalpies) needed for the model fit. Steps

1518 (Figure 2) involve setting the number and type of parameters to be fit for a particular AC model. Figure 3 shows details

of step 16 (Figure 2). Since the group contribution methods

(UNIFAC and NIST-KT-UNIFAC) involve no fitting to experimental data, steps 16 and 17 (Figure 2) are bypassed for those

methods. In steps 18 and 19, all parameters are initialized, and the

model is created.

Key steps in achieving a successful fit of an AC model to

experimental phase equilibrium data are selection of an AC (and

gas phase) model that is appropriate for the chemical system and

selection of an appropriate form for the temperature dependence

of the activity coefficient that will neither under fit the experimental data, resulting in a crude representation, nor overfit the

data, resulting in unphysical property predictions. This is an area

of continuous research in our development of dynamic data evaluation in TDE, and the sophistication and reliability of the

algorithm will continue to be enhanced. The present status is

described here to demonstrate how some of the major considerations are implemented. AC models with parameters fitted to

experimental data in TDE are UNIQUAC, NRTL, Redlich

Kister, Wilson, and Van Laar. Features of each of these models are

considered in determination of an appropriate number and type

of fitted parameters, as described in the following paragraphs.

The algorithm for determination of the appropriate number of

parameters for creation of an AC model for a binary system with

TDE is shown in Figure 3. The Wilson model is an inappropriate

choice for systems involving LLE, and steps 1 and 2 of the

algorithm address this. In steps 3 and 4, the choices for AC model

are reduced to only the NRTL or UNIQUAC models when

additional experimental data are not available. Steps 57 establish the form of the temperature dependence for any AC model

parameter Θ, as represented in steps 8a8c. The formulation for

Θ = f(T) ranges from a two-parameter fit (step 8a), when the

temperature range exceeds 30 K or excess enthalpy or LLE are

available, to a simple constant (step 8c), when few data are available. In steps 9 and 10, the number of terms in the polynomial for

Θ within the RedlichKister model is set based on the distribution of the available data, as described earlier.3 Finally, in steps

1115, the total number of parameters to be determined is compared with the amount of available experimental data. If sufficient

data are not available, no model can be created, and the user is

notified.

Another key aspect in the fitting of AC models to experimental

phase equilibrium data is appropriate weighting of data sets when

multiple sets are available for a given binary system. Recently, this

research group described a quality assessment algorithm for

binary VLE data that combines four widely used tests of data consistency based on the requirements of the GibbsDuhem equation with a check of consistency between the VLE data and the

vapor pressures of the pure components.22 Results of the five

tests were given numerical scores that were combined algebraically to yield an overall data quality factor QVLE, which then could

be used to weight diverse experimental data sets in the fitting of

AC models. Though valuable for many systems, application was

limited to low-pressure (<1 MPa) subcritical systems.

A sixth test for binary VLE is added here specifically for highpressure (p > 1 MPa) data sets, including those for which the

conditions are supercritical for one component. The background

and mathematical formulation of this test is given in Appendix B.

Calculation of the quality factor QVLE is now modified relative to

the original description22 to ease addition of new tests. Previously,

all tests were included in the calculation ofQVLE, including default

contributions for tests that were not applicable to the particular

data scenario. As different consistency tests have different requirements, their applicability is now considered individually. Data requirements for each test are summarized in Table 1. The overall

quality factor QVLE is now calculated only from the results of

applicable consistency tests through the following equation:

QVLE 1⁄4 qpure

1

N ∑

N

i1⁄41

qi ð1Þ

where qpure represents consistency with pure component vapor

pressures (value: 0.11), N is the number of applicable tests, and

qi are the numerical results of the applicable individual tests. Full

descriptions of all tests and calculation of qi values have been

published.22

Table 1. Requirements for Application of Data Quality Tests Used in TDEa

requirement Herrington van Ness point infinite dilution end point EOS

complete pTxy set b bb b O b

subcritical b bb b b O

composition span 0.5 0.5 0.5 0.5 0.5 or end points 0.3

composition gaps b bb b O O

less than 0.8

isovariable typeb T or p T or p T only T or p T or p T or p

p < 0.5 pc

c b bb b O O

more than 5 points b bb b or end points b

pure component data b bb b b b

end point gaps <0.3 d O OO O b b

a b indicates the requirement is necessary for the test; O indicates that the requirement is not necessary. b T indicates that the test can be applied to

isothermal data set, and p indicates that the test can be applied to isobaric data sets. c

pc is the critical pressure for the component with the lower value of

pc.

d An end point gap is defined as the range in mole fraction between an end point (i.e., mole fraction x = 0 or 1) and the first experimental binary data

value. This implies that some experimental binary data must exist for x < 0.3 and x > 0.7.
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Step 7: Creation of ternary AC models. Creation of a ternary

AC model requires successful model creation for all of the binary

subsystems (step 6, Figure 1). Steps 7a and 7b (Figure 1) indicate

this requirement in Figure 1. The mathematical formulations for

the ternary AC models available in TDE (version 6) are given in

Appendix A.

Step 8: Update the User Interface and Return User Control.At

this step the user can review all results, including those for the pure

Figure 4. Basis of initial approximations for calculation of phase compositions with liquidliquid phase splitting based on AC models. The example

shows phase splitting for one binary subsystem.
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components and binary subsystems. Features of the TDE interface

for display of experimental data, deviation plots, fitted models, etc.,

have been described in earlier articles of this series.13 An alternative

AC model can be chosen, but this model (and the gas-phase model)

must be applied to all of the binary systems. A mixture of models cannot be used inthe calculation ofthe properties fortheternary mixture.

Step 9: Properties Are Calculated at User-Specified Conditions. Ternary properties are calculated in accordance with the

Figure 5. Basis of initial approximations for calculation of phase compositions with liquidliquid phase splitting based on AC models. The example

shows phase splitting for two binary subsystems.
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equations given in the Appendix A. The equations for representation of single properties (eqs A1A4) are analogous to those for

the binary properties. The equations for AC models (eqs A5

A20) involve calculation of activity coefficients of the components

within a multicomponent (ternary) mixture. Calculation of LLE

compositions is a special case. These compositions are calculated

explicitly when specified by the user and also as part of the calculation for other properties supported by AC models in order to get

the compositions of the coexisting liquid phases.

Calculation of phase compositions for two coexisting liquid

phases is now supported by TDE. The calculation consists of an

initial approximation for the phase compositions, followed by a

series of refining steps. The initial approximations to the two

liquid-phase compositions are built based on the evaluated binary

LLE compositions and the overall composition of the ternary

mixture. If only one binary pair shows LLE splitting at a given

temperature, it is assumed that the same proportion of the split

components exists in the ternary LLE, as represented by the

sector ABC in Figure 4 (upper figure). If the overall composition

lies outside of this two-phase region, the initial composition of

one phase is modified, as shown in Figure 4 (lower figure).

Figure 5 shows the analogous constructs for the initial estimates

of the phase compositions for the case involving the presence of

LLE in two binary subsystems. Here, the initial approximation for

the two-phase region is represented by area ABCD in the figure.

The possibility of LLE occurring in all three subsystems is not

addressed in this release. Such systems are rare, and the user is

notified that no model can be created by the software.

Refining iterations are applied to one mole of the ternary

mixture with preservation of the overall composition. At each

step, an amount of each component is transferred between the

liquid phases. The amount transferred Δn from liquid phase 1 to

liquid phase 2 is determined as

ΔnL1 f L2 1⁄4  γL2xL2  γL1xL1

γL1NL1 þ γL2NL2

ð2Þ

where γL1 and γL2 are its activity coefficients in liquids 1 and 2, xL1

and xL2 are its mole fractions in phases 1 and 2, and NL1 and NL2

are amounts of liquid phases 1 and 2. Refinement is complete

when activities of all components are equal in both liquid phases

within a narrow tolerance: 1  106

. If the liquid compositions are equal within the tolerance or the amount of one liquid is

less than the tolerance level, it is concluded that one liquid phase

exists at the considered overall composition.

’SOFTWARE ARCHITECTURE

Previous articles in this series described pure compound,2

binary mixture,3 and chemical reaction4 objects. In the present

work, a fourth object is added: ternary mixture. The new ternary

mixture class (Figure 6) includes objects representing the three

pure components, the three binary mixture subsystems, and the

ternary properties. Pure components are represented by compound classes containing all relevant information (identification,

molecular structure, property data, and models: equations and

covariance matrix). Binary subsystems are represented by binary

mixture objects containing links to the components, property

data, and models. Models for the calculation of properties for

ternary mixtures are divided into two groups: those used for

representation of single properties (e.g., viscosity, excess volume,

etc.) and those used to represent multiple properties simultaneously (i.e., AC models used to represent VLE and LLE). This is

analogous to the approach described previously for binary

mixtures.3 The class structure was designed to allow application

to mixtures with an unlimited number of components n with

specification of n component classes and (n2  n)/2 binary pair

classes. It is planned that models for all multicomponent mixtures

will be based on those for the binary subsystems. In the figures

showing class structures (Figures 68), connecting arrows indicate links to external objects, and lines indicate objects

belonging to the parent object.

In analogy to the class structure for binary mixture properties

(Figure 11 of ref 3), the ternary mixture property class (Figure 7)

Figure 6. Structure of the ternary mixture class in TDE. Numerical values below the substructure elements indicate the possible indices for the element.
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contains data sets (sets of property data from a given literature

source), as seen in the center of Figure 7. Data sets contain a

collection of property values, each with values of independent

variables and phases that define the state. The number of possible

independent variables and phases is related through the Gibbs

phase rule with maximum values of four and five, respectively.

Models in TDE for ternary systems are presently restricted to

those involving a maximum of two phases, with the further

restriction that models involving solid phases are not considered.

Structures of the ternary multiproperty and single property

model classes are shown in Figure 8. Ternary mixture property

models are synthesized from, and linked to, binary and pure component models. Auxiliary models are included as needed, and at

present, the only such models used are for liquid densities of pure

components needed for calculation of Poynting corrections26

required for modeling of VLE. Consequently, auxiliary models

appear only in the upper section of Figure 8. Similarly, a model

for the gas phase is required for representation of VLE with an

AC model. Such a model is not needed for the single property

models (lower section of Figure 8).

’INTERFACE FEATURES FOR TERNARY MIXTURES

Progress Monitor. The first release of TDE involved evaluation of the properties for single pure components only.1 Processing for calculation of properties for ternary mixtures involves

evaluations for three pure components and the three binary

subsystems, plus creation of the ternary models. This large

number of evaluations can take several minutes to complete on

modern computers, so it is important that the user be kept

informed of progress. The TDE progress monitor form is shown

in Figure 9. The check boxes are marked as each major step in the

evaluation process is completed. The form also serves as a reminder

to the user concerning the overall complexity of the process and the

availability of access to the experimental data and evaluated results at

all steps. Full traceability for all results, including the underlying

experimental data, remains a core feature of TDE.

Graphical Representation of pTx1x2y1y2 Data.

Representation of ternary VLE compositions in the liquid and

gas phase (“tie-line” data) is displayed in triangular plots. A typical graph is shown in Figure 10, where the lines connect the compositions of the phases in equilibrium (i.e, those that are “tied”).

The experimental data plotted in Figure 10 are isobaric (p = 101.3

kPa) results for temperatures T in the range {330 < (T/K) < 350}

reported by Amer et al.27 Reported pTx1x2 (“bubble

point”) or pTy1y2 (“dew point”) data can also be shown

on such a plot as single points without ties. Access to numerical

values and literature data sources is available through interactive

features of the plot, as described in the first article of this series.1

Graphical Comparison of Experimental and Calculated

Gas-Phase Compositions. Gas-phase compositions calculated

with TDE (based on the combined results for the binary subsystems) may be compared readily with available experimental

data from the literature. Display in TDE of calculated and experimental gas-phase compositions for the system (acetone +

methanol + ethanol) is shown in Figure 11. Green lines connect

the experimental liquid and gas compositions, and blue lines connect the experimental and calculated gas compositions.

Graphical Representation of Ternary LLE (Binodal Curve

and Tie-Line Data). Binodal curve and tie-line data are clearly

distinguished in graphical representation of ternary LLE in TDE.

An example is shown in Figure 12, where experimental binodal

and tie-line compositions are shown. The lines connect compositions for the tie-line data for liquid phases in mutual equilibrium.

Graphical Comparison of Experimental and Calculated

LLE Compositions. Graphical comparison of calculated and

experimental LLE results for a ternary system is shown in Figure 13.

The experimental tie-line data were reported by Gramajo de Doz

et al.28 and Plackov and Stern.29 Green lines connect compositions

Figure 7. Structure of the ternary property class in TDE. Numerical

values below the substructure elements indicate the possible indices for

the element.

Figure 8. Structure of the ternary property class in TDE. Numerical

values below the substructure elements indicate the possible indices for

the element.
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determined experimentally for the liquid phases in mutual equilibrium (tie lines), and blue lines represent the calculated binodal

curves and tie lines. Consistency of slopes for the calculated and

experimental tie-lines is a useful visual indicator of good model

quality. In this case, two of the binary subsystems show phase

separation, and the method depicted in Figure 5 was used to

provide initial approximations for the phase compositions prior

to refinement.

’OTHER ADDITIONS TO TDE

Beyond implementation of dynamic data evaluation for ternary mixtures, which is the main focus of the new version of TDE

(version 6), there are three other major enhancements incorporated: (1) addition ofthe NIST-KT-UNIFAC prediction method23

for VLE data, which was developed based on data quality factors

described previously22 and automatic decomposition of molecular

structures into KT-UNIFAC groups and subgroups24 (see Algorithm Section, step 1); (2) addition of a data quality test for VLE

data at high pressures (see Algorithm Section, step 4; mathematical

details are provided in Appendix B); and (3) improved representation

of viscosities for mixtures. Indeed, to avoid calculation of unphysical

negative values, the formulation for viscosity of a mixture η fitted by

the RedlichKister equation reported earlier3 is now changed to a

logarithmic representation. Details are provided in Appendix A.

’UNCERTAINTY EVALUATIONS

Uncertainties for ternary properties represented by single property equations are calculated with the covariance matrix method,

as described in the first article of this series.1 Contributions from

pure components and excess property are considered:

uðΨÞ

2 1⁄4 ∑

3

i1⁄41

uðΨiÞ

∂Ψ

∂Ψi

 2

þ fuðΨexÞg2 ð3Þ

where u(Ψi

) is the uncertainty for the pure component property,

∂Ψ/∂Ψi is the partial derivative of the mixture property with

respect to the pure component property, and u(Ψex) is the

uncertainty contribution to the mixture property propagated

from the excess property:

uðΨexÞ

2 1⁄4 DTCD ð4Þ

where C is the covariance matrix consisting of three blocks of

binary-parameter covariance, D is a vector of partial derivatives of

the mixture property with respect to the binary parameters, and

DT is transposed D. There is no covariance between the binary

Figure 9. Screenshot of the TDE progress monitor.
271 dx.doi.org/10.1021/ci200456w |J. Chem. Inf. Model. 2012, 52, 260–276

Journal of Chemical Information and Modeling ARTICLE

pairs, and the method does not consider possible errors caused by

not accounting for higher-order (ternary and greater) interactions.

Figure 10. An example of graphical representation of pTx1

x2y1y2 data in TDE: b, liquid composition; O, gas composition,

and lines connect results for phases in mutual equilibrium. The experimental data shown were reported by Amer et al.27 for the system

(methanol + ethanol + acetone).

Figure 11. Display of calculated and experimental VLE gas-phase compositions in TDE. Results are shown for the system (acetone + methanol +

ethanol). Black filled circles, experimental liquid compositions; white filled

circles, experimental gas compositions; blue filled circles, calculated gas

compositions; green lines connect the experimental liquid and gas compositions; and blue lines connect the experimental and calculated gas compositions. The experimental data were reported by Amer et al.27

Figure 12. Display of binodal and tie-line ternary LLE compositions in

TDE. Results are shown for the system (methanol + water + cyclohexane). Experimental binodal and tie-line data are those of Gramajo

de Doz et al.28 and Plackov and Stern:29 b, binodal compositions; and O,

tie-line data. The lines connect compositions for the liquid phases in

mutual equilibrium (“tied” values).

Figure 13. Graphical comparison of experimental and calculated LLE

compositions for ternary systems in TDE. Results are shown for the

system (methanol + water + cyclohexane), and the experimental binodal

and tie-line data are those of Gramajo de Doz et al.28 and Plackov and

Stern:29 b, binodal compositions; and O, tie-line data. Green lines

connect compositions determined experimentally for the liquid phases

in mutual equilibrium (tie lines), and blue lines represent the calculated

binodal curves and tie lines.
272 dx.doi.org/10.1021/ci200456w |J. Chem. Inf. Model. 2012, 52, 260–276

Journal of Chemical Information and Modeling ARTICLE

Although successful for single property equations, the method

involving the covariance matrix yielded unreasonable uncertainties for properties derived from AC models. While this

problem requires additional research (planned for the next

version of TDE), an alternative approach was developed here.

First, property uncertainties are calculated for binary mixtures

containing the components in the same proportion as in the

ternary mixtures. Then, they are multiplied by fractions of the

corresponding binary pairs in the ternary mixtures and combined to give an uncertainty estimate u(Ψ) for the ternary

property:

uðΨÞ

2 1⁄4 ∑

3

i1⁄41

∑

j61⁄4i

fðxi þ xjÞ3 uðΨijÞg2 ð5Þ

where xi and xj are mole fractions of components i and j in the

ternary mixture, and u(Ψij) is the uncertainty of the property

for the corresponding binary mixture with the components in

the same proportion as in the ternary mixture.

’CONCLUSIONS AND FUTURE DEVELOPMENT

The algorithm for extension of dynamic data evaluation for

ternary mixtures has been developed and implemented in the

newest version of the NIST ThermoData Engine software

(version 6).21 Other important enhancements are the addition

of the NIST-KT-UNIFAC prediction method, the incorporation of a data quality test for VLE data at high pressures, and the

improved representation of viscosities for mixtures.

Future plans include propagation of combined expanded uncertainties from the properties of pure compounds and mixtures

to those of process streams and development of algorithms for

thermodynamic analysis of solubility and extraction options in

chemical process design.

’APPENDIX A: MATHEMATICAL FORMULATION OF

MODELS FOR TERNARY CHEMICAL SYSTEMS

Data evaluation for a ternary mixture includes evaluation for

three pure components and three binary mixtures. Two types of

binary models are used to calculate properties of ternary mixtures. The RedlichKister equation is used to fit excess volume,

excess enthalpy, viscosity, thermal conductivity, surface tension,

and index of refraction for single phase (liquid or gas) systems.

The form Ψex used for excess volume and excess enthalpy is

Ψex 1⁄4 1

2 ∑

3

i1⁄41

∑

3

j1⁄41

∑

nTerms

k1⁄40

aijk 3 xi 3 xj 3ðxi  xjÞ

k ðA1Þ

where aijk are binary parameters for components i and j. Bulk

properties Z (except viscosity and density) are calculated as

Z 1⁄4 ∑

3

i1⁄41

xi 3 Zi þ

1

2 ∑

3

i1⁄41

∑

3

j1⁄41

∑

nTerms

k1⁄40

aijk 3 xi 3 xj 3ðxi  xjÞ

k ðA2Þ

Density F is calculated as

F 1⁄4 ∑

3

i1⁄41

xi 3 Mi=Vm; Vm 1⁄4 ∑

3

i1⁄41

xi 3 Mi=Fi

þ

1

2 ∑

3

i1⁄41

∑

3

j1⁄41

∑

nTerms

k1⁄40

aijk 3 xi 3 xj 3ðxi  xjÞ

k ðA3Þ

where Mi is the molar mass of component i. Viscosity η is

calculated as

lnðη=ηÞ 1⁄4 ∑

3

i1⁄41

xi 3 lnðηi=ηÞ þ 1

2 ∑

3

i1⁄41

∑

3

j1⁄41

∑

nTerms

k1⁄40

aijk 3 xi 3 xj 3ðxi  xjÞ

k

( )

ðA4Þ

where η is 1 Pa3 s.

AC models for ternary mixtures were implemented in accordance with the methods described by Novak.30

NRTL Model.

lnðγiÞ 1⁄4

∑

3

j1⁄41

xj 3 τji 3 Gji

∑

3

k1⁄41

xk 3 Gki

þ ∑

3

j1⁄41

xj 3 Gij

∑

3

k1⁄41

xk 3 Gkj

3 τji 

∑

3

m1⁄41

xm 3 τmj 3 Gmj

∑

3

k1⁄41

xk 3 Gkj

0

BBBB@

1

CCCCA

ðA5Þ

where Gji = exp(αij 3 τij) and αij and τij are binary NRTL parameters at a given temperature. Parameter τ12 is binary parameter

c1, τ21 is binary parameter c2, α12 and α21 are binary parameter k

for a mixture of components 1 and 2, τii = 0, and αii = 0. The

binary parameters c1, c2, and k were defined previously.3

UNIQUAC Model.

lnðγiÞ 1⁄4 ln

Φi

xi

  þ 10qi ln Θi

Φi

   qi ln ti

 qi ∑

3

j1⁄41

Θjτij

tj

þ li þ qi  Φi

xi ∑

3

j1⁄41

xjlj ðA6Þ

where

Θi 1⁄4 xiqi

∑

3

j1⁄41

xjqj

; Φi 1⁄4 xiri

∑

3

j1⁄41

xjrj

; li 1⁄4 5ðri  qiÞ þ 1  ri; ti 1⁄4 ∑

3

j1⁄41

Θjτji

ðA7Þ

and τ12 is binary parameter t12, τ21 is binary parameter t21 for a

mixture of components 1 and 2 at temperature T, ri is parameter r

for component i, qi is parameter q for component i, and τii = 1.

The binary parameters t12 and t21 and the pure component parameters r and q were defined previously.3

Wilson Model.

lnðγiÞ 1⁄4 1  lnð∑

3

j1⁄41

Aij 3 xjÞ  ∑

3

j1⁄41

Aji 3 xj

∑

3

k1⁄41

Ajk 3 xk

ðA8Þ

where A12 is binary parameter a2, A21 is binary parameter a1 for a

mixture of components 1 and 2, and Aii = 1. Definitions of the

binary parameters were given previously.3

Van Laar.

lnðγiÞ 1⁄4 Ai 3ð1  ziÞ

2

3 1 þ 2 3 zi 3 Ai 3 Bi

jAi 3 Bij  1

" # ! ðA9Þ

where

zi 1⁄4 jAij 3 xi

jAij 3 xi þ jBij 3ð1  xiÞ

; Ai 1⁄4

∑

3

j1⁄41

xj 3 Aij

ð1  xiÞ

; Bi 1⁄4

∑

3

j1⁄41

xj 3 Aji

ð1  xiÞ

ðA10Þ
273 dx.doi.org/10.1021/ci200456w |J. Chem. Inf. Model. 2012, 52, 260–276

Journal of Chemical Information and Modeling ARTICLE

where A12 is binary parameter a1, A21 is binary parameter a2 for a

mixture of components 1 and 2, and Aii = 0. The binary parameters were defined previously.3

RedlichKister.

lnðγiÞ 1⁄4 ∑

3

j1⁄41

∑

N

n1⁄41

xjAijnðxi  xjÞ

n  2

ðnxi  xjÞ

"

 1

2 ∑

3

k1⁄41

∑

N

n1⁄41

xjxkAjknðxj  xkÞ

n  2

1⁄2ð2n  1Þxj  xk ðA11Þ

where N is number of terms and Aijk is binary parameter ak for

components (i + j).3

UNIFAC.

ln γi 1⁄4 lnðγi, cÞ þ ∑

N

j1⁄41

ni, jflnðγGroup

j Þ  lnðγi, j

Þg ðA12Þ

where

lnðγi,cÞ 1⁄4 ln φi

xi

  þ 5 3 qi 3 ln θi

φi

 ! þ li  φi

xi

  3 ∑

3

k1⁄41

xklk

ðA13Þ

θi 1⁄4 xiqi

∑

3

j1⁄41

xjqj

; φi 1⁄4 xiri

∑

3

j1⁄41

xjrj

; li 1⁄4 5ðri  qiÞ þ 1  ri ðA14Þ

lnðγj, kÞ 1⁄4 QtypeðkÞ 3 1  ∑

N

i1⁄41

θj, i 3 ψki= ∑

N

m1⁄41

θj,m 3 ψmi  ln ∑

N

i1⁄41

θj, i 3 ψki " #

ðA15Þ

lnðγGroup

k Þ 1⁄4 QtypeðkÞ 3 1  ∑

N

i1⁄41

θM, i 3 ψki= ∑

N

m1⁄41

θM,m 3 ψmi  ln ∑

N

i1⁄41

θM, i 3 ψki " #

ðA16Þ

xi, j 1⁄4 nj, i

∑

N

m1⁄41

nm, i

; θi, j 1⁄4 xi, j 3QtypeðjÞ

∑

N

m1⁄41

xi,m 3QtypeðmÞ

ðA17Þ

xM, i 1⁄4

∑

3

m1⁄41

xmnm, i

∑

N

k1⁄41

∑

3

m1⁄41

xmnm, k

; θM, i 1⁄4 xM, i 3QtypeðiÞ

∑

N

j1⁄41

xM, j 3QtypeðjÞ

ðA18Þ

where ni,j is the number of groups of type j in the molecule of

component i, and N is the number of distinct types of structural

groups in the mixture.

ψij 1⁄4 exp1⁄2  BfMainGroupðiÞ, MainGroupðjÞg=T ðA19Þ

for original UNIFAC,3 and

ψij 1⁄4 exp1⁄2ðAfMainGroupðiÞ, MainGroupðjÞg

þ BfMainGroupðiÞ, MainGroupðjÞg=TÞ ðA20Þ

for NIST-KT-UNIFAC,23 where A(i,j) and B(i,j) are the interaction parameters between groupsiand j.Qtype(k) is the UNIFAC

parameter q for structural group k. The quantities q and r for each

component are calculated as the sum of q and r contributions for

all structural groups.

’APPENDIX B: NEW EOS CONSISTENCY TEST FOR

BINARY HIGH-PRESSURE (P > 1 MPA) VLE DATA SETS

Several methods have been suggested in the literature for a

consistency test of VLE data set at high pressure. Won and

Prausnitz31 proposed an extension of Barker’s method, but an

appropriate equation of state (EOS) model was not available at

that time and an AC model with an unsymmetrical convention

was used. Jackson and Wilsak32 applied a differential test and the

van Ness test and concluded that such tests can be applied only

when data are far from critical conditions. Valderrama and

Alvarez33 and Trejos et al.34 suggested an extension of the

GibbsDuhem equation for the gas phase. However, the calculation involves the ratio of two small numbers (compressibility

factor Z  1 and the logarithm of the fugacity) at low pressure,

which often results in poor test results for VLE of good quality

data at low pressures.

A new high-pressure test for isothermal Tpxy data sets

has been developed for use in the present version of TDE. It is

based on an extension of Barker’s method at high pressure with

the use of the PengRobinsion EOS, the MathiasCopeman

function,35 and the universal mixing rule (UMR) suggested by

Voutsas et al.36

p 1⁄4 RT

V  b

 a

VðV þ bÞ  bðV  bÞ ðB1Þ

The UMR mixing rule can be expressed as

a 1⁄4 1

A

GE, SG

AC þ GE, resAC

RT þ ∑

i

xiai ðB2Þ

where A = 0.53 and ai is based on properties of the pure components:

ai 1⁄4 0:45724 ðRTcÞ

2

pc

fðTÞ ðB3Þ

where R is the gas constant, Tc and pc are the critical temperature

and critical pressure, respectively, and f(T) is the Mathias

Copeman function:

fðTÞ1⁄41⁄21 þ c1ð1  ffiffiffiffiffi

Tr

p Þ þ c2ð1  ffiffiffiffiffi

Tr

p Þ

2

þ c3ð1  ffiffiffiffiffiTr

p Þ

3



2 ðB4Þ

The parameters ci are derived with vapor pressures for the pure

components. The parameter b is also calculated with properties

of the pure components.

b 1⁄4 ∑

i

∑

j

xixjbij; bij 1⁄4 b

1=s

i þ b

1=s

j

2

0

@

1

A

s

ðB5Þ

where

bi 1⁄4 0:0778RTc=pc ðB6Þ

and s = 2. The terms GAC

E,SG and GACE,res represent, respectively,

the StaverrmanGuggenheim term and residual term in the
274 dx.doi.org/10.1021/ci200456w |J. Chem. Inf. Model. 2012, 52, 260–276

Journal of Chemical Information and Modeling ARTICLE

UNIQUAC37 or UNIFAC38 AC model.

GE, SG

AC

RT 1⁄4 z

2 q1x1ln

Φ1

x1

þ q2x2ln

Φ2

x2

  ðB7Þ

where

Φ1 1⁄4 x1r1

x1r1 þ x2r2

; Φ2 1⁄4 x2r2

x1r1 þ x2r2

ðB8Þ

GE, res

AC

RT 1⁄4  q1x1lnðθ1 þ θ2τ21Þ  q2x2lnðθ2 þ θ1τ12Þ

ðB9Þ

where

θ1 1⁄4 x1q1

x1q1 þ x2q2

; θ2 1⁄4 x2q2

x1q1 þ x2q2

ðB10Þ

and

τ12 1⁄4 expð  ε12=RTÞ; τ21 1⁄4 expð  ε21=RTÞ ðB11Þ

Volume parameters (r1 and r2) and surface area parameters (q1

and q2) are required as pure component properties and are

calculated with the method of Bondi.39 Note that the Flory

Huggins terms in the AC expressions are removed due to overlap with the cubic EOS terms, as indicated by Voutas et al.36 For

a given Tpxy data set at isothermal condition, two binary

interaction parameters (ε12 and ε21 in eq B11) are fitted, and

bubble-pressure calculation results are compared with the experimental data.

This test is now added to the previously implemented consistency tests, as described earlier in the text. The test is called

automatically by TDE for all isothermal binary VLE data sets

with pressures p > 1 MPa. The numerical test results are similar to

those for the van Ness test: average percent deviation of vapor

pressure and average absolute deviation of the gas composition.

As it is known that EOS may not be adequate in the critical regions, data in the vicinity of a binary critical point (pressure or

temperature maximum for a supercritical data set) are excluded

from deviation accounting. The pass/fail thresholds are chosen

to be 0.015 3 p for vapor pressure p and 0.01 mol fraction for vapor

composition y. If the test is passed, its contribution to the overall

quality factor is 1, otherwise

qEOS 1⁄4 3=ðΔp þ 100 3 ΔyÞ ðB12Þ

where Δp is the average percent pressure deviation and Δy is the

average gas composition deviation. Numerical and graphical test

results are available to the user. A representative result for the

system (methane + ethane)40 is shown in Figure B1. Due to the

inadequacy of the EOS in the critical region, experimental data

near the mixture critical conditions (shown in gray in Figure B1)

are excluded from calculation of the pressure and gas composition deviations.

’AUTHOR INFORMATION

Corresponding Author

*E-mail: frenkel@boulder.nist.gov.

Notes

§

Guest Researcher at the National Institute of Standards and

Technology 20092011.

’ACKNOWLEDGMENT

The authors express their appreciation to Dr. S. Watanasiri

(AspenTech, Burlington, MA) and Dr. M. Satyro (Virtual

Materials Group, Calgary, Canada) for their valuable advice.

We also thank Dr. A. H. Harvey and Dr. M. L. Huber (both of

NIST, Boulder, CO) for their practical suggestions during testing

of TDE.

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