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Applying Modified Chemical Equilibrium Constants for Improving Equilibrium Species Distribution and Vapor−Liquid Equilibrium (VLE) Prediction of Formaldehyde Aqueous Solutions Guizhen Li,† Yansheng Liu,*,† Yufeng Hu,*,† Jun Wang,‡ Lehuan Wu,† and Chunfeng Shi§ †

College of Chemical Engineering, China University of Petroleum−Beijing, Beijing, 102249, China School of Petrochemical Engineering, Changzhou University, Changzhou, 213164, China § Central Research Institute, Wanhua Chemical Group Co., Ltd., Yantai, 264006, China ‡

S Supporting Information *

ABSTRACT: This paper presented a revised model for calculating the chemical and vapor−liquid equilibria (VLE) of the formaldehyde + water system. Chemical equilibrium constants for the formation of poly(oxymethylene) glycols (HO(CH2O)iH, MGi, i > 1) were reviewed, and selected models were modified to reliably predict the species distribution of formaldehyde aqueous solutions and describe the influence of overall formaldehyde concentration. Besides, the UNIFAC equation for the Gibbs excess energy was combined with the chemical reaction equilibria to represent the experimental VLE data in the literature. In addition, some model parameters were redetermined from the corresponding data fits.

1. INTRODUCTION Formaldehyde (FA) is one of the most important chemical intermediates and is widely used as a reactant in the synthesis of monomers during the production of polymeric materials, such as trioxane and dioxolane.1−3 Synthesis of these monomers is typically based on concentrated formaldehyde aqueous solutions. In aqueous solutions, formaldehyde undergoes hydration, forming methylene glycol (HOCH2OH, MG),4,5 which causes further condensation reactions to form poly(oxymethylene) glycols (HO(CH2O)iH, MGi, i ≥ 2),6−8 as shown in reactions 1 and 2: CH 2O + H 2O ⇌ HOCH 2OH (1)

To our knowledge, chemical equilibrium constant models in previous literature cannot reliably predict the species distribution in formaldehyde aqueous solutions. A comparison of concentration of MG and MGi in chemical equilibrium calculated from the model in ref 15 with their measured results showed that the calculated concentrations of MG and MG2 were systematically above the experimental results at high formaldehyde concentrations. The relative deviations between the experimental and calculated concentrations were typically more than 6% and 10% for MG and MG2, respectively. The maximum deviations were ∼10% and ∼18%, respectively. Furthermore, as for chemical equilibrium constants Ki for the formation of MGi (i ≥ 2), given in eq 3, by comparing the experimental values14,15 with the calculated values from the models in the literature,14,15 it was shown that those constants are dependent on the overall formaldehyde concentration (x̃FA) in the aqueous solution. However, the models in the literature14,15 cannot reliably describe the above-mentioned influence. x MGix W (i ≥ 2) Ki = x MGi−1xMG (3)

HOCH 2OH + HO(CH 2O)i − 1H ⇌ HO(CH 2O)i H + H 2O (i ≥ 2)

(2)

Those monomers are essentially formed from some poly(oxymethylene) glycols in the formaldehyde aqueous solution under the presence of strong acids.9−11 With variation of the reactant concentration, reaction time, and temperature, the concentrations of MGi, as well as the equilibrium concentration and conversion rate of the target production, will change. Therefore, determination of the MGi concentrations plays an important role in the design of a synthesis process. Moreover, chemical equilibrium constants of reactions 1 and 2 exert great influence on properties of formaldehyde aqueous solutions.12 In order to better understand, design, and optimize trioxane and dioxolane production processes involving formaldehyde aqueous solutions, a chemical equilibrium constant model for reliably predicting the species distribution is needed. Besides, chemical equilibria of reactions 1 and 2 are essential for describing phase equilibria of the formaldehyde + water (W) system and shall be taken into account in thermodynamic models for the design of separation processes for formaldehydecontaining mixtures.12−16 © XXXX American Chemical Society

In this study, the Ki terms were modified based on the literature data that were determined by 13C NMR spectroscopy. The influence of the overall formaldehyde concentration on Ki was investigated. Besides, the previous model14 (e.g., combining the UNIFAC equation17 for the Gibbs excess energy with chemical reaction equilibria) was used to describe the vapor− liquid equilibrium (VLE) for the formaldehyde + water system. In addition, some UNIFAC interaction parameters were Received: June 26, 2015 Revised: October 2, 2015 Accepted: October 6, 2015

A

DOI: 10.1021/acs.iecr.5b02340 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research Table 1. Chemical Equilibrium Constants Reported in the Literaturea ln K = A + equilibrium constant

A

B

KV1 KV1 Kn (n ≥ 2) K*2 K*n (n ≥ 3) K2 Kn (n ≥ 3) K*2 Kn* (n ≥ 3)

−22.57 −16.984 1.32708 −7.0265 −7.9316 + (0.32/n) 0.01449 −0.1084 0.00498 0.01908

7368 5233.2

B T (K)

+

C (T (K))2

C

−1.39179 × 106 −1.39179 × 106

6844.1 7132.97 − (238.9/n) 560.9 460.4 869.5 544.5

T (K)

x̃FA (mol/mol)

ref(s)

310−370 310−370

0−0.583 0−0.583

25 21b 10 12

275−357

0.06−0.19

7, 14

275−383

0−0.446

15

= (yMG/(yFAyW))(Pθ/P) (for methylene glycol formation in the vapor phase), Ki = (xMGixW/(xMGi−1xMG)) (i ≥ 2) (expressed in mole fractions, and Ki* = (xMGixW/(xMGi−1xMG))(γMGiγW/(γMGi−1γMG)) (i ≥ 2) (expressed in activities). bUsed for the prediction in this work. a V K1

Figure 1. Chemical equilibrium constants of poly(oxymethylene) glycols (MGi, i ≥ 2) formation in formaldehyde aqueous solutions.

refitted to the VLE data of the formaldehyde + water system in the literature.

Table 2. Numbers for Reaction Enthalpies of Poly(oxymethylene) Glycols (MGi, i ≥ 2) Formation Reactions in Formaldehyde Aqueous Solutions

2. LITERATURE ON CHEMICAL EQUILIBRIUM CONSTANTS The correlations in the literature for chemical equilibrium constants of poly(oxymethylene) glycols formation in formaldehyde aqueous solutions were based on NMR spectroscopy data (Table 1). The equilibrium constants from Albert et al.14,15 decreased as the temperature increased, while the results from Maurer12 showed the opposite trend (Figure 1). In addition, the equilibrium constants from Koberstein et al.10 remained unchanged with temperature. Therefore, according to the temperature dependence of chemical equilibrium constants of Albert et al.,14,15 the poly(oxymethylene) glycols formation should be exothermal, while the results from Maurer12 and Koberstein et al.10 indicated an endothermic reaction or a nonthermal reaction. Hasse18 confirmed that the formation of poly(oxymethylene) glycols was exothermal, according to calorimetric data on the heats of dilution. Rivlin et al.19 achieved the same conclusion using reaction enthalpies that were determined from NMR spectroscopic data on species distribution (Table 2). Based on the above-mentioned analysis, the chemical equilibrium constants proposed by Albert et al.14,15 are more reasonable and will be used for further comparative analysis in this study.

parameter ΔrHm (MG2)

value

ref

method

0.0 kJ/mol −2.76 kJ/mol −0.234 kJ/mol −4.663 kJ/mol

Koberstein et al.10 Kogan24 Hasse18 Hahnenstein et al.7 Rivlin et al.19

NMRa NMRa heat of dilutionb NMRa

Koberstein et al.10 Kogan24 Hasse18 Hahnenstein et al.7

NMRa NMRa heat of dilutionb NMRa

−5.35 kJ/mol ΔrHm (MGn, n ≥ 3)

0.0 kJ/mol −2.76 kJ/mol −0.234 kJ/mol −3.828 kJ/mol

NMRa

a

Determined from NMR spectroscopic measurements. bFitted to data of the heat of dilution.

Literature on NMR spectroscopic data on species distribution of formaldehyde aqueous solutions is relatively rich. Therefore, the current authors decided to use the experimental data published as a basis for the chemical equilibrium constant modification. Chemical equilibrium constants K2 and K3 for the formation of MG2 and MG3 were determined by 13C NMR spectroscopy in that literature at 338.15, 353.15, 368.15, and 383.15 K (ref 15) (see Tables S1 and S2 in the Supporting B


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Figure 2. K2 and K3 terms for the formation of MG2 and MG3 in formaldehyde aqueous solutions with different formaldehyde concentrations: (- - -) calculated by the model proposed by Albert et al.15 and () as determined by NMR spectroscopy in the literature.7,15

Figure 3. Activity coefficients of true components in chemical equilibrium in formaldehyde aqueous solutions calculated by the model proposed by Albert et al.15 versus overall formaldehyde concentration at 338.15 and 383.15 K.

inconsistency in the model, as described in Albert et al.,15 that model was successfully applied to describe the VLE in formaldehyde aqueous solutions, with deviations of 2) are shown in Figure 8. The relative deviations between calculated and measured chemical equilibrium constants15 are typically within ±5%.

Table 5. Average Deviations of Species Distribution in Formaldehyde Aqueous Solutions Using the Present Model and the Previous Model Reported in ref 15a temperature, T (K) 338.15 353.15 368.15 383.15

present model ΔxMG (%) 2.698 1.513 1.011 1.956 ΔxMG2 (%)

model of ref 15 5.191 5.240 5.158 6.429

338.15 353.15 368.15 383.15

2.653 1.472 1.807 2.349 ΔxMG3 (%)

10.521 9.469 10.521 9.144

338.15 353.15 368.15 383.15

1.391 1.365 2.949 7.600 ΔxMG4 (%)

8.976 6.388 5.265 13.733

338.15 353.15 368.15 383.15

5.275 2.662 9.822 15.243

11.403 11.964 11.604 22.434

ΔxMGn = 100 × (1/N)∑Ni=1(|(xMGn,expt − xMGn,calc)/xMGn,expt|)i (N is the number of experimental data points).

a

Figure 8. Deviation map of K2 for the formation of MG2 and Ki for the formation of MGi (i ≥ 3).

present model can be applied to a wider temperature range without larger deviation. Figure 11 shows the distribution of MG, MG2, MG3, and MG4 in chemical equilibria at different temperatures: 338.15, 353.15, 368.15, and 383.15 K. As can be seen from the figure, the present model agrees much better with the experimental data7,15,22 for the concentration of the formaldehyde oligomers than the model reported in ref 15, especially at high concentrations of formaldehyde. 5.3. Vapor−Liquid Equilibrium. Some typical comparisons between experimental data in the literature and calculations from the present model and the model in ref 15 are shown in Table 6 and Figures 12 and 13.

The deviation map of concentrations of MG, MG2, MG3, and MG4 in chemical equilibria at 338.15, 353.15, 368.15, and 383.15 K (from ref 15) are demonstrated in Figure 9, with the relative deviations being within ±5%. The average deviations are shown in Table 5. Figure 10 presents the deviation map for the prediction of the concentration of MG, MG2, MG3, and MG4 at 280−360 K and the relative deviations between calculated and experimental results reported in ref 7 are typically within ±5%. Figures 9 and 10 and Table 5 prove two statements: first, it confirms the very close agreement between calculated and experimental results; second, it shows that the F


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Table 6. Average Deviations of the Vapor-Phase Composition and Average Deviations of the Pressure for the Formaldehyde + Water Systema temperature, T (K) 363 383 413 423 363 383 413 423

UNIFAC of this Study ΔỹFA (%) 4.56 3.67 1.97 1.89 ΔP (%) 2.06 1.72 1.88 1.42

UNIFAC of ref 15 3.99 4.07 3.05 3.21 1.97 1.59 1.47 1.04

ΔỹFA = 100 × (1/N)∑Ni=1(|(ỹFA,expt − ỹFA,calc)/ỹFA,expt|)i and ΔP = 100 × (1/N)∑Ni=1(|(Pexpt − Pcalc)/Pexpt|)i (N is the number of experimental data points). a

Figure 10. Deviation map of concentration of MG, MG2, MG3, and MG4 in chemical equilibria at 280−360 K.7

Figure 12 provides a comparison between the results of the correlation of the present model and the model in ref 15 and the experimental data for the formaldehyde + water system at 363, 383, 413, and 423 K. The calculated results of the present model are in agreement with the experimental results14,15 for both the partition coefficient of formaldehyde and the pressure. Furthermore, Figure 12 confirms that the present model provides a better description of the partition coefficient of

Table 6 compares the average overall deviation of the gasphase composition and average deviation of the pressure for the formaldehyde + water system between experimental data in ref 15 and the two models (the present model and the model in ref 15). The values of the deviations indicate that the model in the present study provides a fairly good description for the VLE of the formaldehyde + water system.

Figure 11. Distribution of MG, MG2, MG3, and MG4 in chemical equilibria at 338.15, 353.15, 368.15, and 383.15 K. [Legend: (■) Hahnenstein et al.,7 (●) Albert et al.,15 (▲) Balashov et al.,22 (- - -) correlated by the model reported in ref 15, and () correlated by the present model.] G


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Figure 12. Pressures and partition coefficients of formaldehyde in VLE in the formaldehyde + water system at 363, 383, 413, and 423 K. [Legend: (■) Maurer,12 (▲) Albert et al.,14 (▼) Albert et al.,15 (- - -) correlated by the model reported in ref 15, and () correlated by the present model.]

MG4 in chemical equilibria. Moreover, the comparison results showed that the present prediction was better than that reported in ref 15, especially at high concentrations of formaldehyde. Besides, some UNIFAC interaction parameters were refitted to the experimental data of the formaldehyde + water system in the literature.12−15 The physicochemical model for VLE of the formaldehyde + water system correlated well with the system without any remarkable difference. The results were at least as accurate as those obtained with the previous model in ref 15. Consequently, the resulting model allowed for quantitative prediction of species distribution in formaldehyde aqueous solutions. In addition, such a model can be used to guide more rational design of trioxane and dioxolane synthesis and separation processes for formaldehyde-containing mixtures.

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ASSOCIATED CONTENT

S Supporting Information *

Figure 13. Pressures in VLE in the formaldehyde + water system at 313.15−353.15 K: (●) Brandani et al.23 and () predicted by the present model.

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b02340. Tables showing the calculated parameter B for K2 and K3 for the formation of MG2 and MG3 from the literature NMR spectroscopic data at 338.15, 353.15, 368.15, and 383.15 K, vapor pressure of pure components used in this study, division of components in UNIFAC groups, the size and surface parameters of the UNIFAC groups, as well as calculation of species distribution in chemical equilibrium of formaldehyde aqueous solutions (PDF)

formaldehyde at higher formaldehyde concentrations by comparison with the model in ref 15. Figure 13 shows the prediction for VLE of the formaldehyde + water system at lower temperatures (313.15, 323.15, 333.15, 343.15, and 353.15 K).23 Good agreement with experimental data for the pressures is obtained with the present model. This figure indicates that the present model provides a good prediction for VLE of the formaldehyde + water system at lower temperatures.

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AUTHOR INFORMATION

Corresponding Authors

*Tel.: +86 10 89733288. E-mail: [email protected] (Y. Liu). *Tel.: +86 10 89733846. E-mail: [email protected] (Y. Hu).

6. CONCLUSIONS The chemical equilibrium constants Ki for the formation of poly(oxymethylene) glycols (MGi, i ≥ 2) in formaldehyde aqueous solutions were modified based on the previous model proposed by Albert et al.14 in this study. Parameter B of the model was correlated to the overall formaldehyde concentration. The modified models were applied to both predict species distribution in chemical equilibrium and to correlate the vapor−liquid equilibrium (VLE) of the formaldehyde + water system. The agreement between the experimental and predicted results from the modified model for Ki was very good, as well as for concentrations of MG, MG2, MG3, and

Funding

This research was funded by the National Natural Science Foundation of China (No. 21176248). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge mathematical support from Yongjun Liu. H


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(23) Brandani, V.; Di Giacomo, G.; Foscolo, P. U. Isothermal vapor liquid equilibria for the water formaldehyde system. Ind. Eng. Chem. Process Des. Dev. 1980, 19, 179−185. (24) Kogan, L. V. NMR-study of the state of aqueous methanol solutions of formaldehyde. Zh. Prikl. Khim. 1979, 52, 2725−2730. (25) Hall, M. W.; Piret, E. L. Distillation principles of formaldehyde solutionsState of formaldehyde in the vapor phase. Ind. Eng. Chem. 1949, 41, 1277−1286.

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