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Article

Using Two Group-Contribution Methods to Calculate Properties of Liquid Compounds Involved in the Cyclohexanone Production Operations

1
Thermal Engineering & Instrumentation Division (IDeTIC), Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain
2
Chemical Engineering and Materials Department, Universidad Complutense de Madrid, 28040 Madrid, Spain
*
Authors to whom correspondence should be addressed.
Liquids 2022, 2(4), 413-431; https://doi.org/10.3390/liquids2040024
Submission received: 31 October 2022 / Revised: 15 November 2022 / Accepted: 18 November 2022 / Published: 23 November 2022
(This article belongs to the Special Issue Modeling of Liquids Behavior: Experiments, Theory and Simulations)

Abstract

:
A numerical application has been carried out to determine the thermophysical properties of more than fifty pure liquid compounds involved in the production process of cyclohexanone, whose real values are unknown, in many cases. Two group-contribution methods, the Joback and the Marrero–Gani methods, both used in the fields of physicochemistry and engineering, are employed. Both methods were implemented to evaluate critical properties, phase transition properties, and others, which are required for their use in industrial process simulation/design. The quality of the estimates is evaluated by comparing them with those from the literature, where available. In general, both models provide acceptable predictions, although each of them shows improvement for some of the properties considered, recommending their use, when required.

1. Introduction

In a previous work [1], an exhaustive analysis was carried out on the possibilities of the separation of a set of substances generated in the production process of cyclohexanone, the base compound for the manufacture of nylon-6, used in the textile industry. However, the indicated process is not direct, intermediate processes being necessary to obtain ε-caprolactam, a precursor of nylon-6. Therefore, the production of cyclohexanone as a raw material for different industrial processes, including different types of nylon, is high, currently at approximately 6 MTm/year [2]. In addition, the quality requirements of the cyclic ketone are also high, and the purification process from cyclohexane is complex, as shown in Figure 1. This makes it necessary to optimize the different separation stages, both technically and economically, whose performance represents an important area of work in the field of chemical engineering, requiring an appropriate modeling with the support of the mathematics-thermodynamics binomial.
According to Figure 1, cyclohexanone is obtained by the oxidation of cyclohexane, producing, in addition to cyclohexanone, cyclohexanol, cyclohexyl hydroperoxide, and many other compounds, in smaller proportion. The last-mentioned compound is reconverted (after washing with water and alkalis) into the first two, after removing undesirable compounds by decantation. The resulting solution is subjected to distillation, separating the unreacted cyclohexane in the first unit and recycled into the initial process unit, while the cyclohexanol is dehydrogenated to convert it to cyclohexanone. The aforementioned operations, as defined, suggest a simple development of the global process; however, the current development of the process is quite different due to the formation, during the different stages, of many compounds (more than fifty, although they are considered secondary) that are produced from the beginning with the oxidation of cyclohexane, and in varying quantities, some of them unidentified up until now [3,4,5,6,7,8,9,10].
Many of the compounds discovered in various cyclohexanone production plants are shown in Appendix A, indicating the process streams in which they are found. Some of these substances do not pose a problem for the quality of cyclohexanone, either because they are easy to separate, e.g., cyclohexane (streams 1, 3, 5, 7, 9, 11) or cyclohexylidene-cyclohexanone (stream 16), see Figure 1, or because they are only present when the process operates outside its normal conditions, such as 5-hexenal (stream 19 in Figure 1). However, other substances are likely to contaminate cyclohexanone, creating the need to design appropriate separation operations to remove the most undesirable substances. Appendix B shows a list of substances that influence the global process, including some common substances, such as phenol and toluene, as well as many others that are unusual and little studied, whose properties are unknown. In any case, the design of separation processes depends on the availability of the physicochemical information for the substances involved, as well as their solutions. The most important information required, such as boiling temperatures, enthalpies of change of state, thermal capacities, and critical properties, among others, are used to define the corresponding operation units.
The necessary information is obtained through direct experimentation and with appropriate equipment; however, these actions are costly, both in terms of money and time. Without ignoring the importance of experimental work, in the chemical engineering field, the theoretical estimation methods are sometimes used to generate approximate values of the properties involved in the design of operations. In the literature [11,12,13,14,15], there are many methods for estimating the thermophysical properties of pure substances and solutions; of these, the so-called “group contribution methods” (GCM) prove to be useful and easy to use in practical engineering cases. A GCM is generated as a mathematical tool that combines the particular contributions of each of the functional groups present in the molecules of a compound/system to the calculation of a given thermophysical property. In a previous work [1], the Joback method [14] was used to discriminate between positional isomers, but an exhaustive assessment of the reliability of the estimates was not performed.
Once the necessity of certain properties of a large number of substances—more than fifty involved in the global process, shown in Figure 1—is known, the goal of this work is to estimate these requirements to achieve the process design. For this, two GCM procedures were used: the Joback, previously mentioned, and the Marrero–Gani [15], checking the results to determine their reliability given the different levels of theory of both methodologies, which will be quantified by comparing the predicted results with the values available in the literature.

2. Two Group-Contribution Methods for Estimating Properties of Pure Substances

The GCMs are based on the assumption that the properties of a chemical compound can be calculated by combining, by means of certain procedures (differeing according to the method), the contribution to that property of the different “fragments” that make up its molecule. To do this, the molecule is broken down using “standardized” entities or “groups”, varying depending on the method. To each group (see Figure 2 and Figure 3) is assigned a numerical parameter that quantifies its contribution to the studied property. This approach makes it possible to calculate the properties of a substance by determining the number of groups of each type present in the molecule and then applying a simple calculation defined by the corresponding method. In the first-order GCMs, the contribution of each group is assumed to be independent of its environment and of other groups. Therefore, by using experimental data of the compounds containing that group, the contribution of the parameter associated with it can be determined. In this way, the values obtained can be used to estimate the properties of other substances for which experimental information is not available.
One of the best known first-order methods for estimating the properties of pure substances is the Joback [14] method used in this work, since it has been shown to produce estimates with acceptable accuracy and, in addition, it can be applied to a wide variety of groups and properties, characteristics that justify its relevance as a tool in chemical engineering calculations.
The major drawback of the Joback method, and also of others classified as first-order methods, is that they do not differentiate the calculation for the case of molecules constituting the so-called position isomers. These methods are also unsuitable for complex molecules for which the chemical environment significantly influences the thermophysical behavior. These deficiencies are corrected by the higher-order qualified methods, as they include additional groups produced by combinations of lower-order groups, and whose parameters take into account the effect caused by the chemical environment. Marrero and Gani [15] developed a method that includes groups of several levels (specifically three), producing acceptable results. Therefore, this method, along with the Joback method, is used in this work to determine the properties of the selected compounds, as described briefly in the following section, with examples illustrating the specific calculation procedures.

2.1. The Joback Method

In this procedure, the contributions of the groups generate a parameter in a characteristic equation defined for each property with which the estimation is achieved. The authors [14] provide equations for different thermophysical quantities, such as boiling temperatures T b o , melting temperatures T m o , enthalpies of changes of state, vaporization enthalpies Δ h v o , melting enthalpies Δ h m o , enthalpies of formation Δ h f o , Gibbs energy formation Δ g f o , isobaric thermal capacities, cp, and critical properties; pc, vc, Tc. Table A1 of Appendix C compiles the calculation equations for each of these properties, showing the characteristic parameters of the groups of each property in the second column of the table, whose values are quantified [14]. To estimate the molecule’s properties, it is broken down into the groups identified by Joback [14], as shown in Figure 2, with two specific cases taken as examples: cyclohexene and 2-cyclohexen-1-one. Once the groups have been identified and quantified, this method multiplies the parameter of each group by adding the value obtained for all the groups. With these values, the property is estimated using the expressions shown in the third column of Table A1. Table 1 shows the values obtained for the critical properties of the two species chosen in Figure 2, comparing the results with those from the literature, as indicated.

2.2. Marrero–Gani Method

This procedure [15], pointed out in the previous section as of higher order, uses groups in three different orders. The first-order groups correspond to those with a single functional group and divide the molecule into fragments similar to those used in the Joback method, e.g., linear alkanes and monofunctional compounds. Second-order groups are used to improve the estimation of branched and polyfunctional compounds, with a maximum of one aromatic ring; these groups are established by combining two or more functional groups. Lastly, third-order groups are used to represent polycyclic compounds and specific combinations of functional groups, allowing the method to make satisfactory estimates of complex molecules. As in the Joback method, the Marrero–Gani method allows the same properties to be estimated, with the exception of the isobaric thermal capacity. The corresponding mathematical equations of this procedure are presented in Appendix D.
The application of the method to the same compounds chosen as examples in Section 2.1 requires the generation of the groups in the molecules. Figure 3a shows that those with first-order groups corresponding to cyclohexene coincide with those in the Joback method (Figure 2a), with the addition of the second-order groups. However, 2-cyclohexen-1-one is a polyfunctional compound, containing both first- and second-order groups, as shown in Figure 2b. Table 2 shows the results obtained with the application of the Marrero–Gani method to the estimation of the critical properties of the two selected molecules, comparing the results with those from the literature.

3. Evaluation of Estimates for the Selected Substances

The numerical results obtained for the different properties for all the compounds selected, estimated with the Joback and Marrero–Gani methods, are given in Appendix C (Table A2) and Appendix D (Table A5), respectively. A comparison with the values available in the literature is made in this section.

3.1. Evaluation of Temperatures and Enthalpies of Phase Transition

Figure 4a compares the values found [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] for the boiling temperatures, T b o , and the estimates obtained by both methods, showing the existence of a direct correlation. The Joback method produces greater dispersion in the results than does the Marrero–Gani method, which is reflected in a lower R2 coefficient. The residuals yield an average error of 2.2% for the Joback method, and a slightly lower average error of 0.6% for the Marrero–Gani method, the average standard deviation of the former, 12.5 K, being higher than that of the latter, 4.5 K.
Figure 4b shows the comparison of the estimates made using both methods for the melting temperatures, T m o , in relation to the values found in the literature [16,23,24,29,30,31,32,33,34,35,36,37,38,39,40]. In general, both methods present estimates with a lower order than the T b o , the average errors for both methods being close to 9%, with average standard deviations of 32 K for the Joback method and 25 K for the Marrero–Gani method.
Figure 5a compares the estimates of enthalpies of vaporization, Δ h v o with the literature values [16,20,24,41,42,43,44,45,46,47,48]. Both methods yield similar results, with average errors of 15.3%, for the Joback method, and 19.7%, for the Marrero–Gani method. The similarity is greater for the case of melting enthalpies, Δ h m o [16,30,31,46,47,48,49,50], Figure 5b, yielding average error values of 15.9%, with Marrero–Gani method, and 16.9%, with the Joback method. However, in both cases, the determination coefficient for the melting enthalpy is very small.

3.2. Critical Properties

Comparison with literature data [16,17,24,39,51,52,53,54,55,56,57] of the critical temperatures, Tc, is shown in Figure 6a–c, and the estimates are considered acceptable. The two methods show good experimental vs. model correlations; those of the Marrero–Gani method rise to an average error of 3.5%, compared to 2.9% according to the Joback method. In contrast, the critical pressure pc is slightly better represented by the Marrero–Gani method (5.7%) than by the Joback method (6.2%). The results for the critical volume, vc, yield errors of 5.9% (Marrero–Gani) and 4.6% (Joback), although the information for this property is currently scarce. Numerical values of all those properties are shown in Table A2 and Table A5 of the Appendix C and Appendix D.

3.3. Estimation of Enthalpies of Formation and Thermal Capacities

The amount of information available for the enthalpies of formation, Δ h f o [16,24,58,59,60,61,62,63,64,65,66,67], and thermal capacities, cp [16,50,64,68,69,70,71,72,73], is reduced for the set of selected compounds; therefore, the comments made in this work on these properties cannot be assessed generically. The estimation of Δ h f o is acceptable using both models, as shown in Figure 7a. The average errors are around 12% for the Joback method and much higher—21%—for the Marrero–Gani method. The estimation of the cps is only conducted using the Joback method (Figure 7b), with a systematic deviation that underestimates the value of the property with respect to the experimental values, showing an average error of more than 32%.

4. Conclusions

Estimates are presented for different properties of a set of substances involved in the cyclohexanone production process, as obtained using two group-contribution methods: the Joback method [14] and the Marrero–Gani method [15]. The predictions made are evaluated by comparing the results with those available in the experimental research. The latter does not lead to a clear choice of one method over the other, as the comparisons made do not sufficiently clarify the preference.
The Marrero–Gani method has a higher level of theory, since it uses groups of different orders, which allows it to be used for isomeric compounds. In general, it produces better results for most properties, with the exception of the melting enthalpy, critical temperature, and critical volume, which are better represented by the Joback method. The latter can also be used to estimate thermal capacities. Despite these differences and the assessment of the small errors obtained with both methods, at least statistically, it is acceptable to use either of the two procedures. The major advantage of using the Joback method is that it is simpler, where appropriate.
In summary, the use of any of these methods provides a rapid and reasonably reliable approximation of the different properties required to address a given analysis or simulation in order to optimize the cyclohexanone production process. For a practical case, the methods used have served to estimate boiling temperatures and critical properties, which are important for evaluating the distillation process of the towers shown in Figure 1. Likewise, the approximation obtained for the enthalpies of phase change, especially those of vaporization and thermal capacities, facilitates the design of the heat exchangers, such as the reboilers and condensers of the towers mentioned. The properties corresponding to the enthalpies of formation and the Gibbs energies are involved in the prediction of the complex reactions that take place in the different stages of the global process.

Author Contributions

Conceptualization, J.O., L.F. and A.S.; methodology, L.F. and J.O.; software, L.F.; validation, J.O., A.S., A.R. and D.L.; formal analysis, L.D. and J.O.; investigation, J.O. and L.F.; resources, J.O. and L.F.; data curation, L.F.; writing—original draft preparation, L.F. and J.O.; writing—review and editing, J.O., D.L. and L.F.; visualization, L.F., J.O., L.D., A.S., D.L. and A.R.; supervision, J.O.; project administration, J.O.; funding acquisition, J.O. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The data used and presented in this work were calculated according to Appendix C and Appendix D.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A. Compounds Present in the Streams of the Cyclohexanone Production Process

  • Cyclohexane feeding; cyclohexane, hydrocarbons.
  • Oxidant supply; air.
  • Entrance to oxidation; cyclohexane, hydrocarbons, cyclohexanone, cyclohexanol, light oxides.
  • Nitrogen.
  • Oxidation effluent; cyclohexane, cyclohexanone, cyclohexanol, light and heavy oxidized, peroxides, formic acid, acetic acid, other monocarboxylic acids, dicarboxylic acids, esters, butanol, pentanol, cyclopentanone, cyclopentanol, 2-pentanone, 2-cyclo-hexen-1-one, cyclohexene, 2-methylcyclopentanone, methylcyclopentanol, heptanones, 2-methyl-3-heptanone, 1,3-cyclohexanedione, 1,2-cyclohexanediol, methylcyclohexanols, ethers.
  • Washing water; water.
  • Washing emulsion; water, cyclohexane, cyclohexanone, cyclohexanol, light and heavy oxidized, peroxides, formic acid, acetic acid, other monocarboxylic acids, dicarboxylic acids, esters, butanol, pentanol, cyclopentanone, cyclopentanol, 2-pentanone, 2-cyclo hexen-1-one, cyclohexene, 2-methylcyclopentanone, 1-methylcyclopentanol, heptanones, 2-methyl-3-heptanone, 1,3-cyclohexanedione, 1,2-cyclohexanediol, methylcyclohexanols, ethers.
  • Acid water; water, formic acid, acetic acid, other monocarboxylic acids.
  • Oxidized product; cyclohexane, cyclohexanone, cyclohexanol, light and heavy oxidized, peroxides, monocarboxylic acids, dicarboxylic acids, esters, butanol, pentanol, cyclopentanone, cyclopentanol, 2-pentanone, 2-cyclohexen-1-one, cyclohexene, 2-methyl cyclopentanone, 1-methylcyclopentanol, heptanones, 2-methyl-3-heptanone, 1,3-cyclo hexanedione, 1,2-cyclohexanediol, methylcyclohexanols, ethers.
  • Alkali; water, sodium hydroxide.
  • Saponification emulsion; water, sodium hydroxide, cyclohexane, cyclohexanone, cyclohexanol, light and heavy oxidized, peroxides, monocarboxylic acids, dicarboxylic acids, esters, butanol, pentanol, cyclopentanone, cyclopentanol, 2-pentanone, cyclohexenone, cyclohexene, methylcyclopentanone, methylcyclopentanol, heptanones, methylheptanone, cyclohexanedione, cyclohexanediol, methylcyclohexanols, ethers.
  • Sodium salts; sodium hydroxide, sodium salts.
  • Saponified product; sodium hydroxide, cyclohexanone, cyclohexanol, light oxidized.
  • Cx I recycle; cyclohexanone, cyclohexanol, light oxides.
  • KA-Oil; cyclohexanone, cyclohexanol, oxides, alcohols, aldehydes and ketones.
  • Purified cyclohexanone; butanol, pentanol, cyclopentanol, cyclopentanone, 5-hexenal, hexanal, 2-hexanone, cyclohexanone, cyclohexanol, 2-cyclohexen-1-one, heptanones, methylcyclohexanones, butylcyclohexane, cyclohexyl-butyl-ether.
  • Residue from the purification of cyclohexanone; cyclohexanol, 2-cyclohexen-1-one, 2-cyclohexen-1-ol, heptanones, methylcyclohexanones, butylcyclohexane, cyclohexyl-butyl-ether, cyclohexene oxides, cyclohexylidene-cyclohexanone, cyclohexanone oligo mers, pentylcyclohexane, cyclohexyl acetate, other light/heavy condensation products.
  • Heavy-residue; cyclohexylidene-cyclohexanone, cyclohexanone oligomers, heavy condensation products.
  • Cyclohexanol for dehydrogenation; cyclohexanone, cyclohexanol, 2-cyclohexen-1-one, 2-cyclohexen-1-ol, heptanones, methylcyclohexanones, butylcyclohexane, cyclohexyl-butyl-ether, cyclohexene oxides, cyclohexylidene-cyclohexanone, cyclohexa-none oligomers, n-pentylcyclohexane, cyclohexyl acetate, other light/heavy condensation products.
  • Cyclohexanol recycle; cyclopentanol, hexanal, 2-hexanone, cyclohexanone, cyclo-hexanol, cyclohexenone, cyclohexenol, heptanones, methylcyclohexanone, cyclohexyl-butyl ether.
  • Hydrogen.

Appendix B. Compounds Involved in the Production Process of Cyclohexanone

Order number, compound, empirical formula, structure, and CAS number are indicated.
No.CompoundFormulaChemical StructureCAS#
1acetic acidC2H4O2Liquids 02 00024 i00164-19-7
21,1′-bicyclohexylC12H22Liquids 02 00024 i00292-51-3
3[1,1′-bicyclohexyl]-2,3′-dioneC12H18O2Liquids 02 00024 i00355265-34-4
41-butanolC4H10OLiquids 02 00024 i00471-36-3
5butoxycyclohexaneC10H20OLiquids 02 00024 i00524072-44-4
6butylcyclohexaneC10H20Liquids 02 00024 i0061678-93-9
72-butylcyclohexanoneC10H18OLiquids 02 00024 i0071126-18-7
8cycloheptanoneC7H12OLiquids 02 00024 i008502-42-1
91,2-cyclohexanediolC6H12O2Liquids 02 00024 i009931-17-9
101,3-cyclohexanedioneC6H8O2Liquids 02 00024 i010504-02-9
11cyclohexanolC6H12OLiquids 02 00024 i011108-93-0
12cyclohexanoneC6H10OLiquids 02 00024 i012108-94-1
132-cyclohexen-1-olC6H8OLiquids 02 00024 i013822-67-3
142-cyclohexen-1-oneC6H8OLiquids 02 00024 i014930-68-7
151-(1-cyclohexen-1-yl)-2-propanoneC9H14OLiquids 02 00024 i015768-50-3
16cyclohexeneC6H10Liquids 02 00024 i016110-83-8
17cyclohexyl acetoneC9H16OLiquids 02 00024 i017103-78-6
18cyclohexyl butanoateC10H18O2Liquids 02 00024 i0181551-44-6
19cyclohexyl ethanoneC8H14OLiquids 02 00024 i019823-76-7
20cyclohexyl ethanoateC8H14O2Liquids 02 00024 i020622-45-7
21cyclohexyl etherC12H22OLiquids 02 00024 i0214645-15-2
22cyclohexyl hexanoateC12H22O2Liquids 02 00024 i0226243-10-3
23cyclohexyl pentanoateC11H20O2Liquids 02 00024 i0231551-43-5
242-cyclohexylidencyclohexanoneC12H18OLiquids 02 00024 i0241011-12-7
25cyclopentanolC5H10OLiquids 02 00024 i02596-41-3
26cyclopentanoneC7H8OLiquids 02 00024 i026120-92-3
273,3-dimethylhexaneC8H18Liquids 02 00024 i027563-16-6
284-(1,1-dimethylpropyl)cyclohexanoneC11H20OLiquids 02 00024 i02816587-71-6
292-ethylidenecyclohexanoneC8H12OLiquids 02 00024 i0291122-25-4
30formic acidCH2O2Liquids 02 00024 i03064-18-6
312-heptanoneC7H14OLiquids 02 00024 i031110-43-0
323-heptanoneC7H14OLiquids 02 00024 i032106-35-4
33hexanalC6H12OLiquids 02 00024 i03366-25-1
342-hexanoneC6H12OLiquids 02 00024 i034591-78-6
355-hexenalC6H10OLiquids 02 00024 i035764-59-0
361-methoxycyclohexaneC7H14OLiquids 02 00024 i036931-56-6
375-methyl-2-isopropylidenecyclohexanoneC10H16OLiquids 02 00024 i03715932-80-6
382-methyl-3-heptanoneC8H16OLiquids 02 00024 i03813019-20-0
39methylcyclohexaneC7H14Liquids 02 00024 i039108-87-2
402-methylcyclohexanoneC7H12OLiquids 02 00024 i040583-60-8
413-methylcyclohexanoneC7H12OLiquids 02 00024 i041591-24-2
42methylcyclopentaneC6H12Liquids 02 00024 i04296-37-7
431-methylcyclopentanolC6H12OLiquids 02 00024 i0431462-03-9
44(1-methylethyl)cyclohexaneC9H18Liquids 02 00024 i044696-29-7
452-methylcyclopentanoneC6H10OLiquids 02 00024 i0451120-72-5
461-pentanolC5H12OLiquids 02 00024 i04671-41-0
472-pentanoneC5H10OLiquids 02 00024 i047107-87-9
483-pentyl-1-cyclohexeneC11H20Liquids 02 00024 i04815232-92-5
49pentylcyclohexaneC11H22Liquids 02 00024 i0494292-92-6
50phenolC6H6OLiquids 02 00024 i050108-95-2
51p-tert-butylcyclohexanolC10H20OLiquids 02 00024 i05198-52-2
522-tetrahydrofurylmethanolC5H10O2Liquids 02 00024 i05297-99-4
531,2,3,4-tetrahydronaphthaleneC10H12Liquids 02 00024 i053119-64-2
54tolueneC7H8Liquids 02 00024 i054108-88-3

Appendix C. Mathematics of the Joback Method

Equations used to estimate the thermophysical properties of pure substances by the Joback method are compiled in Table A1. The estimated values for the selected compounds in this work are shown in Table A2.
Table A1. Parameters and equations used in the Joback method.
Table A1. Parameters and equations used in the Joback method.
PropertyParameterEquation
Boiling temperature/K τ b , k T b o = 198.2 + k N k τ b , k
Melting temperature/K τ f , k T m o = 122.5 + k N k τ f , k
Critical temperature/K τ c , k T c = T b [ 0.584 + 0.965 k N k τ c , k ( k N k τ c , k ) 2 ] 1
Critical pressure/bar π c , k p c = ( 0.113 + 0.0032 N atoms k N k π c , k ) 2
Critical volume/cm3·mol−1 υ c , k v c = 17.5 + k N k υ c , k
Gibbs energy of formation/kJ·kmol−1 Δ g f , k Δ g f o = 53.88 + k N k Δ g f , k
Enthalpy of formation/kJ·kmol−1 Δ h f , k Δ h f o = 68.29 + k N k Δ h f , k
Enthalpy of vaporization/kJ·kmol−1 Δ h v , k Δ h v o = 15.3 + k N k Δ h v , k
Enthalpy of melting/kJ·kmol−1 Δ h m , k Δ h m o = 0.88 + k N k Δ h m , k
Isobaric thermal capacity/kJ·kmol−1·K−1 c p , k A ; c p , k B
c p , k C ; c p , k D
c p o = k N k c p , k A 37.93 + T ( k N k c p , k B + 0.210 ) + + T 2 ( k N k c p , k C 3.91 · 10 4 ) + T 3 ( k N k c p , k D + 2.06 · 10 7 )
where Nk is the number of groups of type “k” in the molecule whose properties are to be calculated and Natoms is the total number of atoms in it. The parameters τ b , k , τ f , k , τ c , k , and are the group contributions for the boiling, melting, and critical temperatures, respectively; π c , k is the contribution parameter for the critical pressure, υ c , k is that of the critical volume, Δ g f , k is the group contribution parameter for the Gibbs energy of formation, and Δ h f , k , Δ h v , k , Δ h m , k are those corresponding to the enthalpies of formation, vaporization and melting, respectively; c p , k A ; c p , k B ; c p , k C ; c p , k D are the group contributions to calculate the thermal capacities.
Table A2. Properties estimated by the Joback method [14] for the selected compounds in this work.
Table A2. Properties estimated by the Joback method [14] for the selected compounds in this work.
No.Compound T b o
K
T m o
K
Tc
K
pc
bar
vc
m3/kmol
Δ h f o kJ / mol Δ g f o kJ / mol Δ h v o kJ / mol Δ h m o kJ / mol cp
(298 K)
J/(molK)
1acetic acid390.7272.9587.357.310.171−434.8−377.940.6711.0865.7
21,1′-bicyclohexyl544.3262.8782.627.350.587−320.50.847.8516.39275.0
3[1,1′-bicyclohexyl]-2,3′-dione648.7376.2909.127.990.588−457.8−146.163.119.53219.2
41-butanol406.7190.1571.139.760.344−354.6−198.043.2512.87138.0
5butoxycyclohexane470.2232.1665.925.250.547−327.6−47.240.6914.68238.0
6butylcyclohexane447.8209.8644.625.690.529−195.457.838.2813.49223.0
72-butylcyclohexanone515.6278.1729.126.630.536−333.1−64.842.5313.00228.0
8cycloheptanone455.9245689.239.460.361−257.0−94.536.332.06123.0
91,2-cyclohexanediol502.8358.9720.434.80.342−464.9−273.653.7716.55195.0
101,3-cyclohexanedione496.5305.4743.345.290.319−367.9−213.348.191.08114.7
11cyclohexanol431.9264654.649.250.270−278.7−120.941.739.30147.0
12cyclohexanone428.7237.2656.043.230.313−230.2−90.833.941.57105.0
132-cyclohexen-1-ol431.0264.7656.262.890.257−220.9−90.942.0210.53140.0
142-cyclohexen-1-one427.9238654.845.350.299−172.4−60.834.232.7997.5
151-(1-cyclohexen-1-yl)-2-propanone488.6271.8707.434.040.458−180.812.043.4614.40190.0
16cyclohexene360.1169.8566.943.280.292−34.761.829.983.2892.6
17cyclohexylacetone478.7248.5689.030.390.479−287.4−79.642.8012.50201.0
18cyclohexyl butanoate506.0252.2708.425.820.555−512.7−252.645.6917.86239.0
19cyclohexylethanone455.9237.2669.233.880.423−266.7−88.040.589.91178.0
20cyclohexyl ethanoate460.2229.1668.441.520.443−471.4−269.440.9414.44169.0
21cyclohexyl ether544.3262.8782.626.460.587−320.50.847.8516.39275.0
22cyclohexyl hexanoate551.7274.7748.621.430.667−554.0−235.850.1423.04285.0
23cyclohexyl pentanoate528.9263.4728.523.470.611−533.3−244.247.9220.45262.0
242-cyclohexylidencyclohexanone621.1362.1872.027.330.606−235.843.559.4411.56220.1
25cyclopentanol404.7256.2621.054.550.223−251.9−117.239.338.81129.0
26cyclopentanone401.6229.5622.347.560.265−203.4−87.131.541.0887.0
273,3-dimethylhexane379.2182.3553.425.850.473−217.219.334.7714.67184.0
284-(1,1-dimethylpropyl)cyclohexanone535.2291.8758.924.630.581−362.5−53.646.1313.79251.0
292-ethylidenecyclohexanone481.1270.1709.835.260.408−195.5−28.539.627.07142.0
30formic acid363.1203.8534.475.880.127−301.8−278.643.654.7246.1
312-heptanone413.4218.58590.029.960.434−300.4−120.939.0815.49167.3
323-heptanone413.4218.58590.029.960.434−300.4−120.939.0815.49167.3
33hexanal385.3198.9557.836.470.389−252.8−99.935.3715.35148.0
342-hexanone390.6206.8568.135.990.378−279.8−129.335.3014.66144.0
355-hexenal382.0197.1558.135.520.370−127.3−12.034.7014.07137.0
361-Methoxycyclohexane374.4190.5569.633.530.331−238.9−68.831.626.42151.0
375-methyl-2-isopropylidenecyclohexanone522.1274.5755.127.580.520−266.9−27.943.4012.01219.0
382-methyl-3-heptanone435.8214.8615.227.270.483−326.3−114.840.9614.55189.2
39Methylcyclohexane379.1176581.635.220.361−133.532.531.615.72155.0
402-methylcyclohexanone352.0168.28546.938.390.313−106.736.229.405.23112.6
413-methylcyclohexanone352.0168.28546.938.390.313−106.736.229.405.23112.6
421-methylcyclopentanol427.8291.4651.650.660.277−257.3−114.340.415.11121.0
432-methylcyclopentanone419.8236.5637.440.110.320−244.4−86.437.614.74117.5
44(1-methylethyl)cyclohexane424.4183.6628.228.630.467−180.146.935.677.38200.0
45methylcyclopentanone351.9168.2546.938.390.312−106.636.129.405.23111.7
461-pentanol406.0206.9567.638.770.335−298.8−145.643.4012.79131.0
472-pentanone367.6196545.937.410.321−259.1−137.733.9610.30120.7
483-pentyl-1-cyclohexene469.8221.9666.324.190.571−158.396.240.8017.30239.0
49pentylcyclohexane470.6221.1665.223.360.585−216.166.240.5116.08246.0
50phenol439.0283671.059.260.230−96.5−32.943.5811.5195.2
51p-tert-butylcyclohexanol523.6271.8729.825.770.576−270.8−32.750.0418.90214.3
522-tetrahydrofurylmethanol449.3235.8635.248.290.315−399.6−227.748.4514.06125.0
531,2,3,4-tetrahydronaphthalene475.5260.1708.135.690.43862.3192.541.1910.27144.0
54toluene386.2195.1597.841.140.32048.7120.533.457.93102.0

Appendix D. Mathematics of the Marrero–Gani Method

The Marrero–Gani method estimates the same properties as the Joback method, with the exception of the thermal capacity. The combination of groups of different order is performed in the same way for each property, following Equation (A1):
f = i N i A i 1 + j M j A j 2 + k O k A k 3
where Ni, Mj, and Ok are, respectively, the number groups of first, second, or third order for a given type present in the molecule, and A i 1 , A j 2 , and A k 3 are the characteristic parameters of the corresponding group. The function f varies according to the property to be estimated, as shown in Table A3. The constants used for that function are presented in Table A4. Results obtained from the application of the method for the selected compounds are shown in Table A5.
Table A3. Equations used in the Marrero–Gani method [15] for estimating the different thermophysical properties.
Table A3. Equations used in the Marrero–Gani method [15] for estimating the different thermophysical properties.
Property f=Right-Hand Side of Equation (A1)
Melting temperature/K exp ( T m o / T m , 0 o ) i N i T m 1 i o + j M j T m 2 j o + k O k T m 3 k o
Boiling temperature/K exp ( T b o / T b , 0 o ) i N i T b 1 i o + j M j T b 2 j o + k O k T b 3 k o
Critical temperature/K exp ( T c / T c 0 ) i N i T c 1 i + j M j T c 2 j + k O k T c 3 k
Critical pressure/bar ( p c p c 1 ) 0.5 p c 2 i N i p c 1 i + j M j p c 2 j + k O k p c 3 k
Critical volume/cm3·mol−1 v c v c 0 i N i v c 1 i + j M j v c 2 j + k O k v c 3 k
Gibbs energy of formation/kJ·kmol−1 Δ g f o Δ g f , 0 o i N i g f 1 i o + j M j g f 2 j o + k O k g f 3 k o
Enthalpy of formation/kJ·kmol−1 Δ h f o Δ h f , 0 o i N i h f 1 i o + j M j h f 2 j o + k O k h f 3 k o
Enthalpy of vaporization/kJ·kmol−1 Δ h v o Δ h v , 0 o i N i h v 1 i o + j M j h v 2 j o + k O k h v 3 k o
Enthalpy of melting/kJ·kmol−1 Δ h m o Δ h m , 0 o i N i h m 1 i o + j M j h m 2 j o + k O k h m 3 k o
Table A4. Generic constants used in the Marrero–Gani method [15] for equations shown in Table A3.
Table A4. Generic constants used in the Marrero–Gani method [15] for equations shown in Table A3.
Generic Constants
T m , 0 o /K147.450
T b , 0 o /K222.543
Tc0/K231.239
pc1/bar5.9827
pc2/bar−0.50.108998
vc0/cm3·mol−17.95
Δ g f , 0 o /kJ·mol−1−34.967
Δ h f , 0 o /kJ·mol−15.549
Δ h v , 0 o /kJ·mol−111.733
Δ h m , 0 o /kJ·mol−1−2.806
Table A5. Properties estimated by the Marrero–Gani method [15] for the selected compounds used in this work.
Table A5. Properties estimated by the Marrero–Gani method [15] for the selected compounds used in this work.
No.Compound T b o
K
T m o K Tc
K
pc
bar
vc
m3/kmol
Δ g f o kJ / mol Δ h f o kJ / mol Δ h v o kJ / mol Δ h m o kJ / mol
1acetic acid397.3308.4646.2058.880.159−369.2−426.928.959.55
21,1′-bicyclohexyl511.7271.7727.0025.600.59842.6−272.057.9812.91
3[1,1′-bicyclohexyl]-2,3′-dione579.8354.2867.2230.290.599−528.3−229.885.5423.04
41-butanol381.7213.0553.8043.700.276−277.8−151.950.8310.93
5Butoxycyclohexane464.5231.5676.9422.890.610−40.9−357.059.8019.52
6butylcyclohexane454.1199.4650.2025.400.53370.0−200.349.3713.49
72-Butylcyclohexanone493.3286.4762.2727.580.544−105.3−366.363.5819.70
8cycloheptanone451.7278.9734.2041.370.361−111.9−286.148.909.75
91,2-cyclohexanediol504.2349.0714.1444.000.341−263.8−466.590.6316.06
101,3-cyclohexanedione493.4331.6807.2051.560.312−295.2−429.158.7313.74
11cyclohexanol434.0287.8650.0042.600.322−109.5−286.261.209.84
12cyclohexanone431.2265.7715.2645.930.312−125.2−267.545.568.68
132-cyclohexen-1-ol437.2288.9648.3245.390.307−49.6−189.262.298.88
142-cyclohexen-1-one443.2267.8714.0049.120.297−59.2−183.053.0610.23
151-(1-cyclohexen-1-yl)-2-propanone470.7262.3685.8331.520.460−27.4−205.952.3714.73
16cyclohexene356.1183.6558.0043.920.289104.7−8.932.862.66
17cyclohexylacetone473.7266.4679.0129.830.483−75.0−301.254.9615.75
18cyclohexyl butanoate486.2237.2683.4125.830.545−245.5−543.161.0818.83
19cyclohexylethanone453.7278.5662.0533.330.427−83.1−280.449.4313.11
20cyclohexyl ethanoate441.0225.4639.9031.200.448−481.9−267.153.5312.88
21cyclohexyl ether515.7281.6732.5626.160.608−3.9−342.564.8516.71
22cyclohexyl hexanoate515.7257.9727.1320.210.713−221.3−605.575.8126.75
23cyclohexyl pentanoate497.7244.4698.9223.630.601−237.4−563.965.9921.47
242-cyclohexylidencyclohexanone565.4323.2783.2031.560.501−72.1−341.858.9312.95
25cyclopentanol413.4275.3622.2347.410.273−122.8−267.657.8611.73
26cyclopentanone403.8251.1694.6451.440.262−138.5−248.942.227.61
273,3-dimethylhexane385.1187.3555.1425.680.46617.2−217.938.0610.52
284-(1,1-dimethylpropyl)cyclohexanone503.9298.3776.9127.060.575−90.3−392.665.5516.86
292-ethylidenecyclohexanone478.4276.7737.2233.740.448−47.1−211.763.5511.38
30formic acid362.8259.4554.9083.200.102−279.9−303.648.3213.31
312-heptanone426.7223.8611.1329.340.417−300.8−122.046.3817.58
323-heptanone417.1227.2596.9129.440.418−305.0−125.446.2917.26
33hexanal407.6228.8591.0033.100.373−251.1−100.743.9020.10
342-hexanone400.8215.1589.2032.470.373−278.6−127.641.8214.20
355-hexenal405.6232.5594.1034.760.359−128.8−14.942.8017.07
361-Methoxycyclohexane408.2203.4607.2332.330.406−63.2−279.837.5110.73
375-methyl-2-isopropylidenecyclohexanone497.2299.0753.0928.050.558−33.8−255.277.1911.98
382-methyl-3-heptanone431.2233.0613.2026.780.470−122.8−334.249.1616.81
39Methylcyclohexane374.2182.4577.2335.070.37044.6−137.835.176.74
402-methylcyclohexanone448.3266.3723.9938.520.370−299.4−125.348.9511.81
413-methylcyclohexanone448.3266.3723.9938.520.370−299.4−125.348.9511.81
421-methylcyclopentanol409.2283.5580.0544.290.325−142.0−313.457.355.99
432-methylcyclopentanone422.4251.8704.1642.520.321−280.8−138.645.6110.74
44(1-methylethyl)cyclohexane427.9191.4621.0528.420.48157.3−196.443.0011.32
45methylcyclopentanone340.4155.8538.3038.440.31331.3−119.231.835.64
461-pentanol410.9221.5580.3238.120.332−143.9−298.655.8014.20
472-pentanone362.1210.4544.8037.060.306−141.6−263.336.4711.98
483-pentyl-1-cyclohexene473.2180.7652.9925.510.559128.8−109.759.9516.49
49pentylcyclohexane476.9208.7668.0123.270.59078.0−221.254.2816.13
50phenol455.0308.0687.0659.650.271−32.6−94.364.2515.36
51p-tert-butylcyclohexanol494.8240.6694.6024.120.595216.4−43.558.2313.72
522-tetrahydrofurylmethanol451.2258.3641.6948.150.305−239.0−399.264.1714.14
531,2,3,4-tetrahydronaphthalene480.8241.7664.0331.370.521110.1−61.377.1011.86
54toluene383.8202.1604.0542.180.317123.650.638.439.90

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Figure 1. Scheme indicating the different operation units existing in the cyclohexanone production process.
Figure 1. Scheme indicating the different operation units existing in the cyclohexanone production process.
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Figure 2. Decomposition of molecules according to the Joback method [14]. (a) Cyclohexene, (b) 2-cyclohexen-1-one.
Figure 2. Decomposition of molecules according to the Joback method [14]. (a) Cyclohexene, (b) 2-cyclohexen-1-one.
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Figure 3. Decomposition of molecules according to Marrero–Gani method [15]. (a) Cyclohexene, (b) 2-cyclohexen-1-one.
Figure 3. Decomposition of molecules according to Marrero–Gani method [15]. (a) Cyclohexene, (b) 2-cyclohexen-1-one.
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Figure 4. (a) Comparison between the boiling temperatures, T b , lit o , from literature and those estimated, T b , cal o , by the methods of Joback (Liquids 02 00024 i055) and Marrero–Gani (Liquids 02 00024 i056). (b) Analogous comparison for the melting temperatures. Labels correspond to the order of compounds established in Appendix B.
Figure 4. (a) Comparison between the boiling temperatures, T b , lit o , from literature and those estimated, T b , cal o , by the methods of Joback (Liquids 02 00024 i055) and Marrero–Gani (Liquids 02 00024 i056). (b) Analogous comparison for the melting temperatures. Labels correspond to the order of compounds established in Appendix B.
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Figure 5. Comparison between the enthalpies of phase transition obtained by the methods of Joback (Liquids 02 00024 i055) and Marrero–Gani (Liquids 02 00024 i056) and those from the literature: (a) vaporization enthalpies; (b) melting enthalpies. Labels correspond to the order of compounds, as shown in Appendix B.
Figure 5. Comparison between the enthalpies of phase transition obtained by the methods of Joback (Liquids 02 00024 i055) and Marrero–Gani (Liquids 02 00024 i056) and those from the literature: (a) vaporization enthalpies; (b) melting enthalpies. Labels correspond to the order of compounds, as shown in Appendix B.
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Figure 6. Comparison between the critical properties obtained from the literature and those calculated by the methods of Joback (Liquids 02 00024 i056) and Marrero–Gani (Liquids 02 00024 i055): (a) critical temperature; (b) critical pressure; (c) critical volume. Labels correspond to the order of compounds, as shown in Appendix B.
Figure 6. Comparison between the critical properties obtained from the literature and those calculated by the methods of Joback (Liquids 02 00024 i056) and Marrero–Gani (Liquids 02 00024 i055): (a) critical temperature; (b) critical pressure; (c) critical volume. Labels correspond to the order of compounds, as shown in Appendix B.
Liquids 02 00024 g006aLiquids 02 00024 g006b
Figure 7. (a) Comparison between the enthalpies of formation obtained from literature and those calculated by the methods of Joback (Liquids 02 00024 i056) and Marrero–Gani (Liquids 02 00024 i055). (b) Comparison between the thermal capacities obtained from literature and those calculated by the Joback method. Labels correspond to the order of compounds, as shown in Appendix B.
Figure 7. (a) Comparison between the enthalpies of formation obtained from literature and those calculated by the methods of Joback (Liquids 02 00024 i056) and Marrero–Gani (Liquids 02 00024 i055). (b) Comparison between the thermal capacities obtained from literature and those calculated by the Joback method. Labels correspond to the order of compounds, as shown in Appendix B.
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Table 1. Groups for cyclohexene and 2-cyclohexen-1-one, according to Joback method [14], and the contribution terms for critical properties. Nk is the number of groups in the molecules; τ c , k ,   π c , k ,   υ c , k are the contributing parameters corresponding to Tc, pc, and vc, respectively. The calculated values and those estimated by the procedure are shown.
Table 1. Groups for cyclohexene and 2-cyclohexen-1-one, according to Joback method [14], and the contribution terms for critical properties. Nk is the number of groups in the molecules; τ c , k ,   π c , k ,   υ c , k are the contributing parameters corresponding to Tc, pc, and vc, respectively. The calculated values and those estimated by the procedure are shown.
CompoundsGroupsNk τ c , k π c , k υ c , k
Cyclohexene–CH240.01000.002548
=CH–20.00820.001141
total: 0.05640.0122274
estimated→ Tc/K = 567pc/bar = 43.3vc/cm3·mol−1 = 291
from ref. [16] Tc/K = 560.4pc/bar = 48.41vc/cm3·mol−1 = 377.4
2-Cyclohexen-1-one–CH230.01000.002548
=CH–20.00820.001141
>C=O10.02840.002855
total: 0.07840.0125281
estimated→ Tc/K = 655pc/bar = 45.3 vc/cm3·mol−1 = 298
from ref. [17] Tc/K = 685.0pc/bar = 45.30 vc/cm3·mol−1 = 304.9
Table 2. Groups for cyclohexene and 2-cyclohexen-1-one, according to Marrero–Gani method [15], and contribution parameters for critical properties. Nk is the number of groups in the molecules, and j is the group order. Calculated values and those estimated by the procedure are shown.
Table 2. Groups for cyclohexene and 2-cyclohexen-1-one, according to Marrero–Gani method [15], and contribution parameters for critical properties. Nk is the number of groups in the molecules, and j is the group order. Calculated values and those estimated by the procedure are shown.
CompoundsGroupsjNk T c , i , j p c , i , j v c , i , j
CyclohexeneCH2 (cyc)41.88150.00988449.24
CH=CH (cyc)13.64260.01381583.91
total: 11.16860.053351280.87
estimated→ Tc/K = 558pc/bar = 43.9vc/cm3·mol−1 = 289
from ref. [16] Tc/K = 560.4pc/bar = 48.41vc/cm3·mol−1 = 377.4
2-Cyclohexen-1-oneCH2 (cyc)31.88150.00988449.24
CH=CH (cyc)13.64260.01381583.91
CO (cyc)112.6396−0.00020757.38
total: 21.92670.043260289.01
estimated→ Tc/K = 714pc/bar = 49 vc/cm3·mol−1 = 297
from ref. [17] Tc/K = 685.0pc/bar = 45.30 vc/cm3·mol−1 = 304.9
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Fernández, L.; Ortega, J.; Domínguez, L.; Lorenzo, D.; Santos, A.; Romero, A. Using Two Group-Contribution Methods to Calculate Properties of Liquid Compounds Involved in the Cyclohexanone Production Operations. Liquids 2022, 2, 413-431. https://doi.org/10.3390/liquids2040024

AMA Style

Fernández L, Ortega J, Domínguez L, Lorenzo D, Santos A, Romero A. Using Two Group-Contribution Methods to Calculate Properties of Liquid Compounds Involved in the Cyclohexanone Production Operations. Liquids. 2022; 2(4):413-431. https://doi.org/10.3390/liquids2040024

Chicago/Turabian Style

Fernández, Luis, Juan Ortega, Leandro Domínguez, David Lorenzo, Aurora Santos, and Arturo Romero. 2022. "Using Two Group-Contribution Methods to Calculate Properties of Liquid Compounds Involved in the Cyclohexanone Production Operations" Liquids 2, no. 4: 413-431. https://doi.org/10.3390/liquids2040024

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