Improving the Predictability of Chemical Equilibrium Software

Subscriber access provided by University of Otago Library

Thermodynamics, Transport, and Fluid Mechanics

Improving the Predictability of Chemical Equilibrium Software Qi LIU, Christophe Proust, Francois Gomez, Denis Luart, and Christophe Len Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b03571 • Publication Date (Web): 10 Dec 2018 Downloaded from http://pubs.acs.org on December 13, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

1

Improving the Predictability of Chemical

2

Equilibrium Software

3

Qi Liua, Christophe Prousta,d,*, François Gomeza, Denis Luartb, Christophe Lena,c

4

a Sorbonne Universités, Universite de Technologie de Compiegne, Centre de Recherche

5

Royallieu, CS60319, F-60203 Compiegne, France

6

b Ecole Superieure de Chimie Organique et Minerale, 1, rue du reseau Jean-Marie

7

Buckmaster, F-60200 Compiègne, France

8

c PSL University, UMR 8247 CNRS Chimie ParisTech, Institut de Recherche de Chimie, 11

9

rue Pierre et Marie Curie, F-75005 Paris, France

10

d INERIS, dept DRA, parc Technologique Alata P.O box. 2, F-60550 Verneuil-en-Halatte,

11

France

12

Abstract:

13

Over the past few decades, researchers have been developing tools to predict chemical

14

reactions to aid the growing field of industrial chemistry. Currently, a large variety of

15

numerical tools are used to predict the final chemical equilibrium based on the minimization

16

of the Gibbs free energy. Due to the mathematical complexity of the problem, numerical

17

methods were developed to solve this problem. These methods were reviewed in another

18

study1, 2 exhibiting their limitations and proposing an alternative. In this study, the sensitivity

19

of the prediction as function of the thermochemical (input) parameters is discussed showing

1 ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 27

20

that significant deviations are possible when the relative uncertainty between the enthalpies

21

of formation is larger than a few kJ/mole. Often the scatter between various data sources is

22

much larger than this. To solve this difficulty, it is attempted to derive all the required

23

thermodynamical parameters from a base of molecular descriptors common to the chemistry

24

targeted in this work (organic). The group contribution theory is implemented and in

25

particular the UNIFAC descriptors and is shown to give very satisfactory results.

26 27 28

Keywords

29

Gibbs free energy minimization, thermodynamic equilibrium calculations, group contribution

30

theory.

31 32

Introduction

33

The development of computers made it possible to predict the final equilibrium

34

composition of a multiphase and reactive mixture by minimizing the total Gibbs energy of the

35

products. The method is potentially powerful but suffers from some practical limitations. The

36

first limitation is to be able to find the absolute minimum of the Gibbs energy while

37

preserving the conservation of the atoms. Very innovative step by step mathematical

38

techniques were proposed which may not converge to the absolute minimum (may converge

39

at some local “constrained” minimum) depending on the choice of the starting point. These

40

aspects were reviewed in another paper,1, 2 and an alternative minimization technique was

41

proposed to avoid this. The second limitation is undoubtedly the accuracy of the

42

thermochemical data incorporated in the database of the software and is addressed below.

43

Lastly, the third limitation is the choice of the product list, which strongly orientate towards

44

the final result. The method of selection of the product will be addressed in a forthcoming 2 ACS Paragon Plus Environment

Page 3 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

45


paper.

46

The following work deals with the influence of the uncertainties of the thermochemical

47

data on the prediction of thermodynamic equilibria. This influence is first quantified, which

48

was not openly done in the literature before. Second, it is shown that the group contribution

49

theory can be used to calculate all the required thermodynamical parameters in order to bring

50

more coherence and reduce the influence of scattering of the thermodynamical data sources.

51

These developments were implemented in CIRCE code, a homemade software prepared by

52

the present authors, and the performances of this technique are illustrated by comparison to

53

tricky experimental configurations.

54 55

Influence on the accuracy of the thermochemical data on the chemical equilibrium

56

Fundamentals of chemical equilibrium

57

Only the leading aspects of the underlying thermochemistry are recalled below.1, 2 It is

58

assumed that a chemical reaction occurs between nSp molecules (They are indexed by

59

i=1…nSp) composed of nEl atoms (They are indexed by j=1…nEl). If aij is the number of

60

atom j in the molecule i (available in ni moles in the mixture), then the conservation of mass

61

can be expressed as (bj is the total number of atoms j in the initial mixture):

62

𝜖𝑗 =

𝑁 𝑖=1 𝑎𝑖𝑗

∙ 𝑛𝑖 − 𝑏𝑗 = 0 𝑓𝑜𝑟 1 < 𝑗 < 𝑛𝐸𝑙

(1)

63

In the most general situation, the chemical potential μi of the molecule i in a mixture is μi(P,

64

T)= μio(T)+RT.lnai where μio(T) is the standard Gibbs energy of formation of the species and

65

ai stands for its “activity” in the mixture. For ideal mixtures, ai is simply the molecular

66

fraction xi. Often ai is expressed as a function of the molar fraction xi, such as, ai=γi.xi where

67

γi is the coefficient of activity. This represents the intermolecular interactions which may

68

favor or limit the mobility of the species as compared to an ideal mixture where the

69

intermolecular forces are zero. Note that for solids, it is often assumed that the chemical 3 ACS Paragon Plus Environment


70

Page 4 of 27

potential mostly depends on the temperature and does not depend on other compounds.

71

At constant temperature and pressure, the chemical equilibrium is reached when the Gibbs

72

energy of the mixture is minimum. The Gibbs energy of the mixture is most often expressed

73

as the sum of the contributions of the Gibbs energies of formation of each pure species G0, of

74

the mixing of the species Gmix (the increase of the entropy) and of the non-ideality GE

75

(“excess Gibbs energy”) caused by the intermolecular forces in the real mixture:

76

𝐺0 =

77

𝐺𝑚𝑖𝑥 =

78

𝐺𝐸 =

79

𝐺 = 𝐺 0 + 𝐺𝑚𝑖𝑥 + 𝐺 𝐸

𝑁𝑆 𝑖=1 𝑛𝑖

∙ 𝜇𝑖0 +

𝑁𝐿 𝑖=1 𝑛𝑖 𝑁𝐿 𝑖=1 𝑛𝑖

𝑁𝐿 𝑖=1 𝑛𝑖

∙ 𝑅 ∙ 𝑇 ∙ 𝑙𝑛

∙ 𝜇𝑖0 + 𝑛𝑖 𝑁𝐿 𝑛 𝑖 𝑖

∙ 𝑅 ∙ 𝑇 ∙ 𝑙𝑛 𝛾𝑖 +

𝑁𝐺 𝑖=1 𝑛𝑖

+


(2)

∙ 𝜇𝑖0


∙ 𝑅 ∙ 𝑇 ∙ 𝑙𝑛

𝑛𝑖 𝑁𝐺 𝑛 𝑖 𝑖

∙ 𝑅 ∙ 𝑇 ∙ 𝑙𝑛 𝛾𝑖

(3) (4) (5)

80

Where μi0(T) is the Gibbs energy of formation of component i (considered pure) at

81

temperature T and pressure P of the reaction, γi the activity coefficient of component i in the

82

real mixture at T and P, NS, NL and NG stand respectively for the number of solid, liquid and

83

gaseous species.

84

Uncertainties related to the accuracy of the thermochemical data

85 86

The required thermochemical data are the chemical potentials of the pure components and the activity coefficients.

87

Considering a three components mixture (n1, n2, and n3) with one product (n3) being

88

diluents (no variations of its number of moles). The atom balance (1) between n1 and n2,

89

imposes a relationship which can be written as below:

90

𝑛2 = 𝐶 − 𝐴 ∙ 𝑛1

(6)

91

Where C and A are constants. In the present context where n1 turns into n2, typically for a

92

phase change which is considered here, A is unity. Equation (6) can be inserted into (2) to

93

(5),and the only dependent variable is n1 since n3 is a constant. The minimum of G is 4 ACS Paragon Plus Environment

Page 5 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


94

obtained when 𝑑𝐺 𝑑𝑛1 = 0. If we consider that n1 is a liquid and n2 and n3 are gases, after

95

some straightforward calculations (Appendix S1), the final expression can be expressed as: 𝑑𝛾

1−𝑥 2 ∙𝑥 2

𝑑𝛾

0 = 𝜇10 − 𝐴 ∙ 𝜇20 − 𝐴 ∙ 𝑅 ∙ 𝑇 ∙ 𝑙𝑛 𝑥2 − 𝐴 ∙ 𝑅 ∙ 𝑇 ∙ 𝑙𝑛𝛾2 − 𝑑𝑥2 ∙

97

Where x2 is the molar fraction of component 2 in the gaseous phase (containing only

98

components 2 and 3) and is the eigenvalue parameter of this problem. The contribution of the

99

formation energies of the components and the molecular interactions are now rather explicit.

100

2

𝐴∙𝛾2

+ 𝑑𝑥3 ∙

1−𝑥 2 2

96

2

𝛾3

(7)

The influence of the chemical potential of the pure components is illustrated first setting the

101

fugacity coefficients equal to 1 and constant (ideal mixtures). Then (7) reduces to:

102

ln 𝑥2 =

𝜇 10 −𝐴∙𝜇 20

(8)

𝐴∙𝑅∙𝑇

103

This equation suggests that the accuracy of the determination of the chemical potentials

104

should be smaller than R.T or, more accurately that the method used to determine the

105

chemical potentials should not generate deviations from one component to another

106

component comparable to R.T, and thus it should typically be smaller than 1 kJ/mole.

107

A more practical illustration is proposed for a 5 components chemical reaction consisting

108

of a water-gas shift simulation (C, CO, CO2, H2O, H2). In this kind of reactions, the amount

109

of produced CO can be seen as a sensitive indicator of the global reaction since it is produced

110

by the C/H2O reaction and consumed by the CO/H2O reaction. The evolution of the CO

111

molar fraction is shown in Figure 1 as a function of pressure and temperature of the reactions.

112

All components except C are gases obeying the perfect gas law. In this simulation, the

113

standard enthalpy of formation for CO is 110 kJ/mole.



0.6

0.5

XCO

0.4

0.3

0.2

0.1

0.0 0

200

400

600

800

1000

1200

1400

1600

1800

2000

T/K

114 115

Figure 1. CO volumetric fraction in a 5 components water shift reaction as a function of

116

pressure and temperature of the reaction under the assumption of perfect gas reference cases

117

(CIRCE code).10kPa, ■; 100kPa, ●; 1MPa, ▲.

118 119

In Figure 2, the changes in the CO volumetric fraction is shown when the standard enthalpy

120

of formation of CO is changed by ±1%, ±5%, and ±10%, respectively.

0.6

a)

0.5

0.4

xCO

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 27

0.3

0.2

0.1

0.0 0

121

200

400

600

800

1000 1200 1400 1600 1800 2000 T/K


Page 7 of 27

0.6

b) 0.5

xCO

0.4

0.3

0.2

0.1

0.0 0

200

400

600

800

1000 1200 1400 1600 1800 2000 T/K

122

0.6

c) 0.5

0.4

xCO

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.3

0.2

0.1

0.0 0

200

400

600

800

1000 1200 1400 1600 1800 2000 T/K

123 124

Figure 2. CO volumetric fraction in a 5 components water shift reaction as a function of

125

different pressure a) 100kPa, b) 10kPa and c) 1MPa and temperature of the reaction under the

126

assumption of a perfect gas influence of the accuracy of thermochemical data (variation of

127

the standard enthalpy of formation of CO). Reference case at 100kPa, ■; HfCO+0.01HfCO, ●;

128

HfCO+0.05HfCO, ▲; HfCO+0.1HfCO, ▼; HfCO-0.01HfCO, ◆; HfCO-0.05HfCO, ◄; HfCO-

129

0.1HfCO, ►.

130

This example shows an evident influence on the values of the thermochemical data 7 ACS Paragon Plus Environment


Page 8 of 27

131

particularly concerning the Gibbs energy of formation of the components (in which the

132

standard enthalpy of formation is the main aspect). The pressure influences the evolution of

133

the entropy. It can be observed that a 10% change in the standard enthalpy of formation of

134

CO (i.e., ±10 kJ/mole) produces a variation into the CO concentration within a factor of two

135

at 1 MPa and 1000 K for instance. A ±1% variations (±1 kJ/mole), would produce, in the

136

same configuration, only a relative scatter of 10% of the CO concentration which might be

137

judged acceptable in chemical engineering.

138

This example should be considered as an illustration. But together with the simple

139

theoretical approach proposed in Equation (8), it shows that even if the minimization

140

technique is robust enough and the product list is well selected, erroneous results can be

141

obtained if the relative accuracy of the thermochemical data is lower than, typically 1kJ/mole.

142

This last point questions the used of the published database where the uncertainties about the

143

energies of formations may amount ±10kJ/mole.3

144

Now, the question of the accuracy of the activity coefficients is addressed. From equation

145

(7), the deviation of the molar fraction of component 2 from the ideal mixture case (given by

146

equation (8)) reads: 𝑥2

𝑑𝛾

= − 𝑙𝑛𝛾2 − 𝑑𝑥2 ∙

1−𝑥 2 ∙𝑥 2 𝐴∙𝛾2

𝑑𝛾

+ 𝑑𝑥3 ∙

1−𝑥 2 2

(9)

147

𝑙𝑛

148

A graphical representation is proposed on Figure 3 in which the ideal mixture case is

149

compared to a constant (γ2=2) and also to a variable activity coefficient (γ2=2 and

150

1/γ2∙dγ2/dx2=1), which is more realistic. Note that both the chosen values of coefficient of

151

activity and their variations are typically in the orders of magnitude encountered in real

152

systems.4

𝑥 2_𝑖𝑑

2

2

𝛾3


Page 9 of 27

2.0

1.5

x2/x2id

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.0

0.5

0.0 0.0

0.2

0.4

0.6

0.8

1.0

x2

153 154

Figure 3. ideal mixture approximation as compared a constant (γ2=2) and to a variable of the

155

coefficient of activity (γ2=2 and 1/γ2∙dγ2/dx2=1). The latter case is labeled “real mixture”.

156

ideal mixture,■; constant activity coefficient,●; real mixture,▲.

157 158

It appears that a significant deviation is possible, within the ratios of 2 to 4, when the

159

details of the variations of the coefficient of activity are ignored. Even a quasi-constant

160

approximation (with dγ2/dx2=0) may not be satisfactory.

161

An illustration is presented below about the distillation of ethanol-water mixtures at 100

162

kPa pressure (Figure 4). Assuming ideal mixtures (Figure 4-b) provides results rather far

163

from reality. In textbooks, the activity coefficients of ethanol and water are respectively on

164

the order of two so that the real concentrations in the gaseous phase should be about half of

165

the concentration of the ideal mixture (see Figure 3). However, even after this correction (not

166

shown in Figure 4), the agreement would remain poor. The variations of the activity

167

coefficient with the compositions should be included. This is partly done in the RAND

168

method5 for instance (Figure 4-a)but it can be realized that the simulated values deviate by a

169

few % from the experiments. This is presumably due to the quadratic Taylor approximation 9 ACS Paragon Plus Environment


170

of G which is done in the RAND method to run the step by step algorithm.

375

370

T/K

365

360

355

350 0.0

0.2

0.4

0.6

0.8

1.0

xEthanol

171 (a)

172

375

370

365

T/K

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 27

360

355

350 0.0

0.2

0.4

0.6

0.8

1.0

xEthanol

173 174

(b)

175

Figure 4. Simulation of vapor-liquid equilibria of the water-ethanol mixture at 100kPa

176

pressure using the RAND method (ASPEN Plus®-RGIBBS code) (a) and the ideal mixture

177

model approximation (CIRCE code) (b). Simulations -vapor, ○; experiments -vapor, ●;

178

simulations-liquid,□; experiments-liquid, ■. 10 ACS Paragon Plus Environment

Page 11 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


179 180

So there is a need to find a way to estimate all the thermochemical properties for the pure

181

components and the intermolecular forces in a “coherent” way. A systematic bias may not be

182

so problematic since the absolute value of G is not looked for but only its minimum, but

183

scattering/inconsistencies between the data sources for the components would easily produce

184

large uncertainties. A common route/model for estimating the chemical potentials should be

185

looked for, or in other words, based on the same physical principles. Possibilities are

186

presented hereafter.

187 188

Thermochemical properties and interaction parameters

189

Group contribution theory

190

Equation (5) contains both a historical and conceptual vision of thermodynamics.

191

Historically, pure and ideal mixtures where considered at first (G0 and Gmix) and conceptually

192

since real fluids and mixtures (GE) are approached as deviations from the ideal cases, which

193

can be calculated via some virtual transformation.

194

So what is needed is a common set of descriptors enabling the estimation of the enthalpy of

195

formation of the pure ideal components, of the real fluid “transformation” (using the equation

196

of state of the fluid) and of the activity coefficients.

197

As explained in textbooks, many attempts were made over the last century to connect

198

molecular descriptors to the thermodynamic properties. The simplest and perhaps the first

199

attempt is to use the property and number of each atom and to add up each atomic

200

contribution to the searched property for the molecule (additivity rule), just as what is done to

201

calculate the molar mass of a molecule. But even for this simple property, careful verification

202

shows that the contribution of a given type of atom depends on the neighboring atoms. The

203

extent to this effect depends upon the importance of outer valence electrons. A refinement is 11 ACS Paragon Plus Environment


Page 12 of 27

204

to consider on contributions in which specific differences between various types of bonds (ex

205

for carbon: carbon-carbon, carbon-oxygen, carbon-nitrogen...) could be integrated. But this

206

adds many complications. A medium way is to consider groups of atoms from which most

207

molecules are made of and apply the additivity to these groups. To some extent, such groups

208

have built-in information on the valence structure associated with a significant proportion of

209

the atoms present. The “group contribution” theory is hence widely and successfully used at

210

least in organic chemistry.

211

Perhaps the most developed side of the group contribution theory appears in the

212

determination of the activity coefficient via the well-known UNIFAC method.6 Today, in

213

organic chemistry, UNIFAC incorporates about 54 main groups and about 113 subgroups

214

from the DDBST7 database. It is recalled that “main groups” are groups of atoms

215

(“subgroups”) sharing the same interaction effects with the other groups of atoms. The

216

“subgroups” describe the interactions of the molecule into the mixture. Using UNIFAC the

217

activity coefficients in the standard conditions can be calculated. But the group contribution

218

theory can also be used very satisfactorily to derive most of the important thermodynamic

219

parameters like those for the equation of state of each component from which the real fluid

220

behavior can be calculated.6 The latter method provides the critical parameters, temperature

221

Tc, pressure Pc and volume Vc from the group contribution theory enabling the derivation of

222

the “co-volume” and “energy” parameters of the equation of state. An extension was

223

proposed by Gani-Constantinou8 about the “acentric factor” of the equation of state.

224

Joback’s9 method also uses the group contribution theory to derive the standard enthalpy,

225

entropy of formation,… of the ideal gas form of the components. Further refinements were

226

proposed by Klincewicz,10 Ambrose…11

227

Thus, the group contribution theory was implemented (in CIRCE). The molecular

228

descriptors are those from UNIFAC. The ideal gas thermodynamical data (standard enthalpy 12 ACS Paragon Plus Environment

Page 13 of 27

229

and entropy of formation, heat capacity,…) and real fluid parameters (acentric factor, critical

230

parameters,…) were extracted from the works of Joback.9 The activity coefficient is derived

231

from the UNIFAC theory.

232

A “cubic” equation of state was chosen to account for the real fluid “transformation”

233

because of its ease of implementation in numerical codes. However, since the activity

234

coefficients in a mixture can also be extracted from the equation of state of the mixture

235

(according to the mixing rule associated with the equation of state), precautions were taken so

236

that the activity coefficients, appearing in GE, obtained through the equation of state (EoS)

237

were identical to those obtained using the UNIFAC theory for the standard conditions. This

238

important aspect is clarified later.

239 240

The final organization of the thermodynamical properties generator of CIRCE software is represented schematically in Figure 5.

Molecular descriptors from UNIFAC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Ideal fluid properties

Real fluid properties (EoS parameters & mixing rules)

Fitting Activity coefficients

241 242

Figure 5. Organization of the thermodynamical properties generator of CIRCE software.

243 244

When running a simulation, the properties of each component considered as an ideal gas at 13 ACS Paragon Plus Environment


Page 14 of 27

245

the temperature and the pressure of the reaction are first calculated. The non-ideality of the

246

component is added under the form of the “departure function” detailed later (integration of

247

the equation of state from the ideal gas state to the real fluid state – liquid or gaseous). This

248

calculation provides G0. Then the activity coefficients are calculated using UNIFAC (thus in

249

the standard conditions) and incorporated in the EoS. Using the EoS, the activity coefficients

250

are computed at T and P of the reaction. Note that if liquids, gases, and even supercritical

251

fluids can be handled this way, provided the EoS is well chosen, this does not hold for solids,

252

for which a classical method is used.

253 254

The details are presented in the next paragraphs. Ideal (and some real) fluid properties

255

The following parameters are needed to run a calculation: standard formation enthalpy and

256

entropy, heat capacities at specific temperatures for extrapolation purposes (typically at 290K,

257

1000K, 2500K, 3500K, and 5000K), the critical parameters (Vc, Tc, Pc) and the acentric

258

factor.

259

The Joback method uses the group contribution theory as an extension of the pioneering

260

work of Parks and Huffman.12 Note that Joback assumed no interactions between the groups

261

so that only linear combinations are considered. These data used in the development of all the

262

methods were obtained from the literature. The experimental value of Critical property values:

263

Tc, Pc, and Vc from Ambrose13 and Reid et al.14 have been used. The data from Reid et al.14

264

0 0 and Stull et al15 has been used for the thermodynamic properties(∆𝐻𝑓,298 , ∆𝐺𝑓,298 and 𝐶𝑝0 ).

265

Multiple linear regression techniques were employed to determine the group contributions for

266

each structurally-dependent parameter.7 The acentric factor is given by Lydersen’s work.16

267 268

Note however that the “groups” considered by Joback are not those from UNIFAC but,

269

fortunately, the latter can be globally deduced from the former by additions which enables a 14 ACS Paragon Plus Environment

Page 15 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


270

unique type of “groups” (those from UNIFAC) to be considered. After having redefined the

271

“groups” in the Joback technique identical to those from UNIFAC a verification was

272

performed on typical molecules (Table 1). The analysis was carried out using methanol,

273

ethanol, formic acid acetaldehyde molecules which are simple and common in the chemistry.

274

The results are in agreement with those obtained by Joback, except may be a better accuracy

275

on the enthalpy of formation.

276 277

Table 1. Comparison of the modified JOBACK method with experimental data.9

Simulated C2H5OH Measured C2H5OH Simulated CH3COOH Measured CH3COOH Simulated CH3OH Measured CH3OH Simulated CH3CHO Measured CH3CHO Standard deviation

0 Tb(K) Tc(K) Pc(100kPa) Vc(cm3/mole) ∆𝐻𝑓,298 (kJ/mole) ΔHv,b(kJ/mole) 337.34 499.11 57.57 166.50 -236.84 36.64

351.5

514

63

168

-234

42.3

390.67 587.25

57.31

171.50

-434.88

40.67

391.2

57.81

170.34

-433

50.3

66.97

110.50

-216.20

33.91

81

117

-205

35.21

293.82 465.29

56.03

164.50

-170.19

26.92

293.9

466.0

55.7

151.38

-170.7

26.12

20

20

8

5

2

6

593

314.46 475.49 337.8

513

278

a

Tb is boiling temperature. bTc is the critical temperature. c Pc is the critical pressure. dVc is the

279

critical volume. eΔH0f,298 is the enthalpy of formation at 298K. fΔH0v,b is the enthalpy of

280

formation at 298K.

281 282 283 284 285

Equation of state

The ideal gas equation of state was established empirically and theoretically mainly during the 18th and 19th century. It is assumed that molecules are infinitely small and do not interact. In 1893, Van der Waals concluded that in real gases the volume occupied by the molecules 15 ACS Paragon Plus Environment


Page 16 of 27

286

is not zero and should be subtracted from the total volume to retrieve the real free volume and

287

that molecules interact with various forces which change their velocities, and thus the

288

pressure and a correction term should be added.17

289

The ideal gas can be considered as a limiting case of the van der Waals equation of state

290

when P tends to zero since in such conditions Vm tends to infinity in such a way that the

291

correction terms are negligible. This remark is used to calculate the “departure function”.

292

It was recognized that although being significant progress, the van der Waals equation is

293

deficient on many aspects and alternative EoS, based on a very similar equation, were

294

proposed later like the RK equation,18 the SRK19 EoS, and the well-known Peng-Robinson

295

EoS.20 The latter, detailed below, is particularly efficient in predicting liquid densities and

296

vapor pressures even on the saturation line.

297

As it stands, however, the Peng Robinson EoS has deficiencies mostly when mixtures are

298

concerned for which the “binary interaction” parameters are to be fitted from experimental

299

data.

300

To overcome this deficiency, Vidal in 197820 coupled the Peng-Robinson equation to the

301

GE parameter, incorporating this correction into the energy parameter (α). The criterion is that

302

GE derived from the EoS should be equal to that obtained from an explicit formulation (like

303

UNIFAC…) of the activity coefficients at some reference pressure.

304

As a reminder, the activity coefficients are associated with the fugacities (or more precisely

305

to the fugacity coefficients) which can be derived from the EoS (Appendix S1). If 𝜑𝑖 is the

306

fugacity coefficient of component i in the mixture, and 𝜑𝑖 is the pure compound i, the excess

307

Gibbs energy, GE is calculated as:

308 309 310

𝐺𝐸 𝑅𝑇

=

𝑖 𝑥𝑖

𝜑

ln 𝜑 𝑖 = 𝑖

𝑖

(10)

𝑥𝑖 ln 𝛾𝑖

Since the fugacities can be derived from the EoS so that the following relationship is found between the activity coefficients obtained from UNIFAC and those derived from the EoS: 16 ACS Paragon Plus Environment

Page 17 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

311 312 313 314


𝜑

ln 𝛾𝑖 = ln 𝜑 𝑖 =

𝜕𝐺 𝐸

(11)

𝜕𝑛 𝑖 𝑇,𝑃,𝑛 𝑗 ≠𝑖

𝑖

In Huron-Vidal, Wong-Sandler approaches the reference pressure to which this equality is applied in infinity whereas for PSRK model the reference pressure is zero. In the present case, the LCVM method21 is selected which does not specify a specific

315

pressure.22 For this the Peng-Robinson EoS is used as:

316

𝑃 = 𝑉−𝑏 − 𝑉

317

𝑅𝑇

𝑎

The pure component parameters a and b are:

318

𝑎 = 0.45724

319

𝑏=

320 321 322 323 324

(12)

𝑉+𝑏 +𝑏 𝑉−𝑏

𝑖

𝑅 2 𝑇𝑐2 𝑃𝑐

(13)

∙ 𝑓 𝑇𝑟

(14)

𝑥𝑖 𝑏𝑖

If (𝑇𝑟 ≤ 1): 𝑓 𝑇𝑟 = 1 + 𝑐1 1 − 𝑇𝑟 + 𝑐2 1 − 𝑇𝑟

2

+ 𝑐3 1 − 𝑇𝑟

3 3

(15)

If (𝑇𝑟 ≥ 1): 𝑓 𝑇𝑟 = 1 + 𝑐1 1 − 𝑇𝑟

2

(16)

Coquelet et al.23 proposed a method to generate the parameter of c1, c2, and c3 automatically:

325

𝑐1 = 0.1316𝜔2 + 1.4031𝜔 + 0.3906

(17)

326

𝑐2 = −1.3127𝜔2 + 0.3015𝜔 ± 0.1213

(18)

327

𝑐3 = 0.7661𝜔 + 0.3041

(19)

328

A linear combination of the mixing rules of Huron and Vidal24 and Michelsen25 is

329

implemented, which does need a reference pressure.21 And it has been proved26,

27

330

superior to the other EOS/GE models. Clearly, other categories of EoS existed, using the

331

group contribution theory23 and based on the Statistical Associating Fluid Theory24, but a

332

“cubic” EoS was preferred in this work. The pressure/temperature domain of the LCVM EoS

333

is also well adapted to the practical applications targeted by our research group.

to be



334 335 336

Page 18 of 27

The co-volume parameter is unmodified as compared to the standard Peng Robinson EoS (12). But the innovation is in the formulation of the energy parameter a. 𝑎 𝑏∙𝑅∙𝑇

=𝜆∙

1 𝐴𝑉

𝐺𝐸

∙ 𝑅𝑇 +

𝑎

𝑖 𝑥𝑖 𝑏 ∙𝑅∙𝑇 + 1−𝜆 ∙ 𝑖

1 𝐴𝑀

∙

𝐺𝐸 𝑅𝑇

×

𝑥𝑖 ln

𝑏 𝑏𝑖

+

𝑎

(20)

𝑖 𝑥𝑖 𝑏 ∙𝑅∙𝑇 𝑖

𝑏

337

Where the terms 𝐺 𝐸 𝑅𝑇 is calculated using the UNIFAC model, the terms

338

𝑖 𝑥𝑖 𝑏 ∙𝑅∙𝑇 come from the Peng Robinson Equation of state, and AM, AV are constant

339

coefficients proposed respectively by Michelsen25 and Vidal24 ( 𝐴𝑀 = −0.52 , and 𝐴𝑉 =

340

−0.623 ). Coefficient λ is a sort of relaxation parameter, and its value was selected

341

empirically at 0.36.

342

The “departure function”

𝑥𝑖 ln

𝑏𝑖

and

𝑎

𝑖

343

By definition, the “departure functions” are used to calculate the difference between a real

344

fluid and the ideal fluid. The principle of the “virtual” transformation of an ideal gas to a real

345

fluid is outlined in the appendix S2. The resolution uses the expression of the thermodynamic

346

function as a function of the state variables (P, V, and T). For the Gibbs energy:

347

G 𝑇, 𝑃

348

𝑟𝑒𝑎𝑙

− G 𝑇, 𝑃

𝑖𝑑𝑒𝑎𝑙

=

𝑟𝑒𝑎𝑙 𝑖𝑑𝑒𝑎𝑙

𝑉 𝑑𝑃 =

𝑟𝑒𝑎𝑙 𝑖𝑑𝑒𝑎𝑙

𝑑 𝑃𝑉 −

𝑉 𝑃 𝑑𝑣 𝑉=∞

= 𝑃𝑉 − 𝑅𝑇 −

𝑉 𝑃𝑑𝑉 𝑉=∞

(21)

The departure function is used to calculate the chemical potentials of the pure components

349

(to calculate G0) for which the LCVM EoS reduces to the (modified) Peng Robinson EoS.

350

Performances

351

Some simulations using the above methods (Joback, UNIFAC, LCVM, departure

352

functions...) are presented below for some critical systems. Note that the minimization

353

technique is the MGCE method presented elsewhere1. All these are implemented in CIRCE

354

software. The first is the vapor-liquid equilibria of the ethanol-water mixture which was

355

shown to exhibit specific difficulties and illustrates the influence of significant molecular

356

interactions. The second and third systems involve the investigation of the impact of the

357

pressure on the prediction of a vapor/liquid multicomponent equilibrium and the last one deal 18 ACS Paragon Plus Environment

Page 19 of 27

358

with a supercritical dissolution case traditionally challenging to handle.

359

Vapor-liquid equilibrium of a significantly polar system

360

The distillation at ambient pressure as the function of the temperature of an equimolar

361

ethanol-water mixture is considered identical to that presented in Figure 4. The results are

362

shown in Figure 6. The simulation results are entirely consistent with the experimental data,

363

suggesting first that the thermodynamical data are calculated relevantly and that the

364

minimization techniques can conveniently follow the variations of the activity coefficients.

375

370

365

T/K

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


360

355

350 0.0

0.2

0.4

0.6

0.8

1.0

XEthanol

365 366

Figure 6. Simulation of vapor-liquid equilibria of the water-ethanol mixture (100kPa

367

pressure) using the LCVM/departure function/MGCE methods (CIRCE code). Simulations:

368

vapor, ○; experiments: vapor,●; simulations: liquid,□; experiments: liquid,■.

369 370 371 372

High-pressure distillation cases

The distillation of n-pentane in propane at 344 K and various pressures (non-polar system) is shown in Figure 7. The simulation result agrees well with available experimental data.



100

80

P/100kPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 27

60

40

20

0 0.0

0.2

xC3H8

373 374

Figure 7. Prediction of the P-x-y diagram for the distillation propane/n-pentane at 344.26 K

375

using the LCVM/departure function/MGCE methods (CIRCE code), Experimental data from

376

Knapp et al. (1982).28Simulations: vapor, ○; experiments: vapor, ●; simulations: liquid,□;

377

experiments: liquid,■.

378 379 380

The distillation of methanol in water at 423 K and various pressures (polar system) is shown in Figure 8 again showing a satisfactory agreement with available experimental data.


Page 21 of 27

14

12

P/100kPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

8

6

4 0

20

40

60

80

100

xmethanol

381 382

Figure 8. Prediction of the P-x-y diagram for the distillation methanol-water at 423 K using

383

the LCVM/departure function/MGCE methods (CIRCE code), Experimental data from

384

Griswold and Wong.29 Simulations: vapor, ○; experiments: vapor, ●; simulations: liquid,□;

385

experiments: liquid,■.

386 387

Solubility of supercritical CO2 in methanol

388

Solubility is the property of gases for instance (CO2 here) to dissolve in liquids (methanol).

389

The solvent is assumed to have negligible vapor pressure and to remain entirely in the liquid

390

phase. The specific difficulty is linked to the possibility of the mixture to become

391

supercritical. But the general character of the LCVM EoS offers in principle the options to

392

deal with the supercritical state since no reference pressure is used to couple the EoS with GE.

393

Some example of the solubility of CO2 have been inverstigated.30, 31A typical example of

394

the solubility of methanol in CO2 is shown in Figure 9. In this particular example, CO2

395

reaches supercritical state above 7 MPa whereas methanol is not. The mixture is neither

396

liquid nor gas.32 The simulation strategy enables to mimic this behavior although with a

397

reduced accuracy than in the example above. A possible reason for this may lie in the fact 21 ACS Paragon Plus Environment


398

that the parameters of the EoS are only approximate using the Constantinou approaches 7 and

399

that the deviations become more influenced when P and T are not far from the critical points.

80

60

P/100kPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 27

40

20

0

0

20

40

60

80

100

xCO2

400 401

Figure 9. Prediction of the solubility of methanol in CO2 at 313K using the LCVM/departure

402

function/MGCE methods (CIRCE code), Experimental data by Suzuki et al.32 at

403

313K.simulations: vapor, ○; experiments: vapor, ●; simulations: liquid, □; experiments:

404

liquid, ■.

405 406

Conclusions

407

This work is a contribution to the simulation of the thermodynamic equilibrium of reactive

408

multiphase mixtures. Besides the specific difficulties in minimizing the very complex Gibbs

409

energy of the mixture, addressed in another article, the attention is focused in the present

410

work on the incidence of the inputted thermodynamical data on the final result. It is shown

411

that inaccuracies more significant than 1 kJ/mole on the Gibbs formation energy of the

412

component have a visible impact. Similarly, the evolution of the coefficient of activities as a

413

function of the composition of the mixture is important. Thus using data from different

414

sources and (too) rough models for activity coefficients may lead to uncontrolled deviations 22 ACS Paragon Plus Environment

Page 23 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


415

in the final results. To limit such occurrence, it is proposed to use the same molecular

416

descriptors to calculate the thermodynamical data and activity coefficients. The group

417

contribution theory is implemented not only to calculate the activity coefficients (UNIFAC)

418

but also to estimate the standard energies of formation of the species (Joback’s approach) and

419

to introduce the effect of pressure and temperature via the LCVM equation of state.

420

Some examples suggest that this approach can give very satisfactory results.

421 422

NOTATION A,C aij ai AV,AM ai,aj a,b bi bj C1,C2,C3 Cp0 fi G0 Gmix GE

Constant number of atoms of element j in compound i activity of compound i constant coefficients proposed respectively by Michelsen and Vidal interaction parameter the parameter of PENG Robinson volume parameter total number moles of atoms j in the mixture the parameter for the LCVM Heat capacity (J/K) fugacity of component i (Pa) standard Gibbs energy (J) Gibbs energy of mixture (J) Excess Gibbs energy (J)

ΔG0f,298 Hf ∆Hv,b ni nSp nEl NG,NL,NS P R Tr Tf Tb T Vm Vc, Tc, Pc

Gibbs formation energy (J) enthalpie of formation (J) enthalpie of evaporation (J) mole number of i number of species number of elements number of Gas, liquid and solid Pressure (Pa) gas constant (J mol−1K−1) relative temperature temperature of fusion (K) boiling point (K) Temperature (K) molar volume (m3) the critical parameter 23 ACS Paragon Plus Environment


Z

Page 24 of 27

compressibility factor

423 424

Greek Symbols: 𝜖𝑖 μio(T) μi γi Φi δij 𝜑𝑖 𝜑𝑖 Λ Ω Κ

function of the conservation of mass chemical potential (J) chemical potential of component I (J) Activity coeffiient of component i fugacity coefficient i empirically determined binary interaction coefficient Fugacity coefficient of component i in the mixture Fugacity coefficient of pure component i a sort of relaxation parameter acentric factor constant characteristic of each substance

425 426 427

Supporting Information

428

Supporting Information Available: Appendix S1: analytical derivation of equation (7).

429

Appendix S2: Estimate the departure function.

430 431

Corresponding author:

432

Christophe Proust,

433

*E-mail: [email protected]

434

ORCID

435

Christophe. PROUST: 0000-0002-9097-4292

436 437

Funding Sources

438

None.

439


Page 25 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


440

References:

441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488

1. Liu, Q.; Proust, C.; Gomez, F.; Luart, D.; Len, C., Predicting multi-phase chemical equilibria using a Monte Carlo technique. Comput. Chem. Eng. submitted in 2018. 2. Liu, Q. CIRCE a new software to predict the steady state equilibrium of chemical reactions Universite de Technologie de Compiegne, 2018. 3. Yaws, C. L., Physical properties. In Handbook of Chemical Compound Data for Process Safety, Elsevier: 1997; pp 1-26. 4. Hino, T.; Song, Y.; Prausnitz, J. M., Liquid‐liquid equilibria and theta temperatures in homopolymer‐solvent solutions from a perturbed hard‐sphere‐chain equation of state. J. Polym. Sci., Part B: Polym. Phys. 2015, 34, (12), 1961-1976. 5. Gautam, R.; Seider, W. D., Computation of phase and chemical equilibrium: Part I. Local and constrained minima in Gibbs free energy. AlChE J. 1979, 25, (6), 991-999. 6. Fredenslund, A.; Jones, R. L.; Prausnitz, J. M., Group‐contribution estimation of activity coefficients in nonideal liquid mixtures. AlChE J. 1975, 21, (6), 1086-1099. 7. Gmehling, J.; Rarey, J.; Menke, J., Dortmund Data Bank. Oldenburg (29/08/2013) http://www.ddbst.com 2008. 8. Constantinou, L.; Gani, R., New group contribution method for estimating properties of pure compounds. AlChE J. 1994, 40, (10), 1697-1710. 9. Joback, K. G.; Reid, R. C., Estimation of pure-component properties from groupcontributions. Chem. Eng. Commun. 1987, 57, (1-6), 233-243. 10. Klincewicz, K.; Reid, R., Estimation of critical properties with group contribution methods. AlChE J. 1984, 30, (1), 137-142. Ambrose, D., Correlation and Estimation of Vapour-liquid Critical Properties: I, 11. Critical Temperatures of Organic Compounds. National Physical Laboratory: 1978. 12. Parks, G. S.; Huffman, H. M., Free energies of some organic compounds. 1932. 13. Ambrose, D., Correlation and estimation of vapour-liquid critical properties. Part 1: Critical temperatures of organic compounds. 1978. Poling, B. E.; Prausnitz, J. M.; John Paul, O. C.; Reid, R. C., The properties of gases 14. and liquids. Mcgraw-hill New York: 2001; Vol. 5. 15. Stull, D. R.; Westrum, E. F.; Sinke, G. C., The chemical thermodynamics of organic compounds. 1969. 16. Lydersen, A. L.; Station, M. E. E., Estimation of critical properties of organic compounds by the method of group contributions. University of Wisconsin: 1955. 17. van der Waals, J. D., The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. J. Stat. Phys. 1979, 20, (2), 200-244. 18. Redlich, O.; Kwong, J. N., On the thermodynamics of solutions. V. An equation of state. Fugacities of gaseous solutions. Chem. Rev. 1949, 44, (1), 233-244. 19. Soave, G., Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 1972, 27, (6), 1197-1203. 20. Peng, D.-Y.; Robinson, D. B., A new two-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15, (1), 59-64. 21. Boukouvalas, C.; Spiliotis, N.; Coutsikos, P.; Tzouvaras, N.; Tassios, D., Prediction of vapor-liquid equilibrium with the LCVM model: a linear combination of the Vidal and Michelsen mixing rules coupled with the original UNIF. Fluid Phase Equilib. 1994, 92, 75106. 22. Kontogeorgis, G. M.; Coutsikos, P., Thirty Years with EoS/GE Models-What Have We Learned? Ind. Eng. Chem. Res. 2012, 51, (11), 4119-4142. 23. Coquelet, C.; Chapoy, A.; Richon, D., Development of a new alpha function for the Peng–Robinson equation of state: comparative study of alpha function models for pure gases 25 ACS Paragon Plus Environment


489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518

Page 26 of 27

(natural gas components) and water-gas systems. Int. J. Thermophys. 2004, 25, (1), 133-158. 24. Huron, M.-J.; Vidal, J., New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures. Fluid Phase Equilib. 1979, 3, (4), 255-271. 25. Michelsen, M. L., A method for incorporating excess Gibbs energy models in equations of state. Fluid Phase Equilib. 1990, 60, (1-2), 47-58. 26. Spiliotis, N.; Boukouvalas, C.; Tzouvaras, N.; Tassios, D., Application of the LCVM model to multicomponent systems: Extension of the UNIFAC interaction parameter table and prediction of the phase behavior of synthetic gas condensate and oil systems. Fluid Phase Equilib. 1994, 101, 187-210. 27. Voutsas, E. C.; Spiliotis, N.; Kalospiros, N. S.; Tassios, D., Prediction of vapor-liquid equilibria at low and high pressures using UNIFAC-based models. Ind. Eng. Chem. Res. 1995, 34, (2), 681-687. 28. Knapp, H., " Vapor-Liguid Equilibria for Mixtures of Low Boiling Substances" Part14. DECHEMA Chemistry Data Series 1982. 29. Griswold, J.; Wong, S. In Phase-equilibria of the acetone-methanol-water system from 100 degrees C into the critical region, Chemical Engineering Progress Symposium Series, 1952; 1952; pp 18-34. 30. Zirrahi, M.; Azinfar, B.; Hassanzadeh, H.; Abedi, J., Measuring and modeling the solubility and density for CO2–toluene and C2H6–toluene systems. J. Chem. Eng. Data 2015, 60, (6), 1592-1599. 31. Chen, S.; Chen, S.; Fei, X.; Zhang, Y.; Qin, L., Solubility and characterization of CO2 in 40 mass% N-ethylmonoethanolamine solutions: explorations for an efficient nonaqueous solution. Ind. Eng. Chem. Res. 2015, 54, (29), 7212-7218. 32. Suzuki, K.; Sue, H.; Itou, M.; Smith, R. L.; Inomata, H.; Arai, K.; Saito, S., Isothermal vapor-liquid equilibrium data for binary systems at high pressures: carbon dioxide-methanol, carbon dioxide-ethanol, carbon dioxide-1-propanol, methane-ethanol, methane-1-propanol, ethane-ethanol, and ethane-1-propanol systems. J. Chem. Eng. Data 1990, 35, (1), 63-66.


Page 27 of 27

519

Molecular descriptors from UNIFAC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Ideal fluid properties

Real fluid properties (EoS parameters & mixing rules)

Activity coefficients

520 521

The Software architecture.

522

ACS Paragon Plus Environment

27

Improving the Predictability of Chemical Equilibrium Software

Recommend Documents