Ind. Eng. Chem. Res. 1998, 37, 3485-3489
3485
Vapor-Liquid Equilibrium of Formaldehyde Mixtures Containing Methanol Stefano Brandani, Vincenzo Brandani,* and Ida Tarquini Dipartimento di Chimica, Ingegneria Chimica e Materiali, Universita` de L’Aquila, I-67040 Monteluco di Roio, L’Aquila, Italy
A new description of the vapor phase of formaldehyde solutions containing methanol is presented. In contrast with all previous models for these mixtures, it is recognized that the dimer resulting from the formaldehyde-methanol reaction has a relatively high volatility and should be considered present in the vapor phase. The new model is matched to the experimental vaporliquid equilibrium data for binary and ternary mixtures containing formaldehyde, methanol, and water. The proposed model represents well vapor-liquid equilibrium of these reacting mixtures and does not reveal systematic deviations for the ternary system as observed with previous models. Introduction Formaldehyde is an important commodity of the chemical industry. It is used as a raw material in the production of plastics and adhesives. This versatility is due to the high reactivity of formaldehyde. Formaldehyde is generally stored in the form of aqueous solutions containing methanol, which is added as a stabilizing agent. The description of the vapor-liquid equilibrium for these mixtures is therefore of relevant importance in the chemical industry. The first successful model for the description of binary mixtures of formaldehyde was presented by Brandani et al. (1980). The extension to multicomponent mixtures was not straightforward since physical contributions (activity coefficients) were not considered. The key features of this model were (a) to assume that only the monomer is present in the vapor phase and (b) to describe the liquid-phase reactions using equilibrium constants which were assumed to be equal for the reactions involving the dimer and higher polymers. These simplifying assumptions lead to liquid-phase compositions in closed form. Maurer (1986) presented a new model considering the same assumptions for the vapor phase, but including physical activity coefficients and the first 30 reactions in the liquid phase. Brandani et al. (1991, 1992) include the physical contributions in the original model developed by Brandani et al. (1980). Both models (Maurer, 1986; Brandani et al., 1992) were capable of predicting the ternary system water-methanol-formaldehyde and showed systematic errors in the calculated vapor-phase compositions. In the predictions of Brandani et al. (1992) water compositions were typically underestimated, while methanol compositions were overestimated. The revised model proposed by Maurer (Hasse and Maurer, 1991) showed the opposite behavior, water compositions were overestimated while methanol compositions were underestimated. Both models represented well the formaldehyde compositions in the vapor
phase. More recently, Albert et al. (1996) present a new and revised version of the model originally proposed by Maurer (1986). The key innovation is the calculation of the liquid-phase equilibrium constants from NMR measurements, and acceptance of the equal equilibrium constant values for all reactions involving higher polymers, as suggested by Brandani et al. (1980), but no modification is included for the vapor phase. Even with these improvements, the small systematic deviations in the calculation of the ternary system are still observed. These considerations led us to critically review the basic assumptions used in the formulation of these models. Typically, the model equations were developed for the system water-formaldehyde and then extended to the systems containing methanol. The main difference between the two systems is the relative volatility of the monomers methylene glycol (WF) and hemiformal (MF). Figure 1 shows the comparison of the vapor pressures for these compounds calculated from Hasse and Maurer (1991) and Brandani et al. (1991) using the following relationship:
PSAF )
KAV1H0F,APSA KAL1γ∞AF
(1)
where the active solvent A is either water (W) or methanol (M), KAV1 and KAL1 are the monomer formation equilibrium constants in the vapor and liquid phase, H0F,A is the Henry constant of formaldehyde in the active solvent, and γ∞AF is the infinite dilution activity coefficient. As can be seen from the figure, there is an order of magnitude difference between the two vapor pressures. This may indicate that the vapor phase over mixtures containing methanol may contain appreciable quantities of the dimer (MF2), and this should be reflected in the model describing vapor-liquid equilibrium. Mathematical Modeling of the Vapor Phase
* To whom correspondence should be addressed. Tel.: (+39) 862 434219. Fax: (+39) 862 434203. E-mail: brandani@ ing.univaq.it.
For the systems in which methanol and formaldehyde are present, it is assumed that two reactions need to be
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3486 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998
calculated according to a virial equation of state. For this system the modeling equations are therefore given by Brandani et al. (1991). For the ternary system water-methanol-formaldehyde, considering all the chemical equilibrium relationships and the material balances, the following equations are obtained:
yF uF ) [1 + KW V1uWP + 1 - yF 1 - uF M KM V1uMP(1 + 2KV2uFP)] (11)
uW yW ) (1 + KW V1uFP) 1 - yF 1 - uF
uM yM M ) [1 + KM V1uFP(1 + KV2uFP)] (13) 1 - yF 1 - uF
Figure 1. Calculated vapor pressures of methylene glycol (WF) and hemiformal (MF).
considered:
M + F ) MF
(2)
MF + F ) MF2
(3)
Assuming thermodynamic equilibrium in the vapor phase, the true compositions may be evaluated using the following relationships:
uM )
1 - uF 1+
KM V1uFP(1
+ KM V2uFP)
(4)
uMF ) KM V1uMuFP
(5)
uMF2 ) KM V2uMFuFP
(6)
To simplify the calculations, the gas phase is assumed to be ideal by limiting the application to total pressures lower than 2 bar. Therefore, the following equations relating true mole fractions, of the four species present in the vapor phase, to the apparent mole fractions, yM and yF, need to be solved
uF yF M ) [1 + KM V1uMP(1 + 2KV2uFP)] (7) 1 - y F 1 - uF These mass-balance and equilibrium relationships may be combined to obtain a single equation in uF, which can be readily solved. The two chemical equilibrium constants are temperature-dependent according to M M ln KM V1 ) RV1 + βV1/T
(8)
M M ln KM V2 ) RV2 + βV2/T
(9)
If water is present, it is necessary to consider only the following reaction:
W + F ) WF
(10)
For the binary system water-formaldehyde, the model parameters were reevaluated to consider the vaporphase ideal, since the reported values (Brandani et al., 1991) were obtained using the fugacity coefficients
(12)
uMF ) KM V1uMuFP
(14)
uMF2 ) KM V2uMFuFP
(15)
uWF ) KW V1uWuFP
(16)
These equations allow us to evaluate the true mole fractions of the six species present in the vapor phase. Vapor-Liquid Equilibrium Calculations The liquid-phase compositions are described according to Brandani et al. (1991, 1992). The problem of calculating the equilibrium pressure and compositions, having assigned the liquid-phase apparent mole fractions and the temperature of the system, is fully formulated once the expression for the total pressure is given. Assuming ideal behavior in the vapor phase, and neglecting pressure effects on the liquid-phase fugacity, the following equation applies (Brandani et al., 1992):
yW yM yF + γMzMPsM + γ*FzFHF,MS P ) γWzWPsW uW uM uF
(17)
where
ln HF,MS ) φ*W ln HF,W + φ*M ln HF,M + φ*W
( )
ln
γ∞F,MS γ∞F,W
+
φ*M
( )
ln
γ∞F,MS γ∞F,M
(18)
with
φ*W ) 1 - φ*M )
rWXW rWXW + rMXM
(19)
where the temperature dependence of binary Henry’s constants is given by
ln(HF,A/PC,F) ) RAH + βAH(TC,F/T)
(20)
In the original model of Brandani et al. (1991) the temperature dependence of Henry’s constant included also a quadratic term. For the water-formaldehyde system we have reevaluated Henry’s constant along
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3487
a
b
Figure 3. Comparison between experimental and calculated vapor-phase compositions for the system water-methanolformaldehyde at 80 °C.
a
c b
Figure 2. Comparison between experimental and calculated vapor-liquid equilibrium for the system methanol-formaldehyde: (a) 60 °C; (b) 70 °C; (c) 80 °C.
with the physical parameter necessary for the description of the activity coefficients. These parameters, reported in Table 1, were obtained from the regression of the binary total pressure data of Brandani et al. (1980). The model reproduces this experimental data with an average absolute deviation of 0.92 Torr. The physical interactions in the liquid phase between water (1) and methanol (2) are described according to the UNIQUAC activity coefficient model (Abrahams and
Figure 4. Low-temperature predictions for the system methanolformaldehyde: (a) 20 °C; (b) 40 °C.
Prausnitz, 1975), with the binary parameters given by
a12 ) 19.09 + 0.1297T (K)
(21)
a21 ) -191.37 + 0.5505T (K)
(22)
obtained from the regression of the experimental data
3488 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998
Figure 6. Vapor pressures of methylene glycol (WF), hemiformal (MF), and the dimer of the reaction methanol-formaldehyde (MF2) calculated from the present model.
Figure 5. Comparison between experimental and predicted vapor phase compositions for the system water-methanol-formaldehyde. (a) 60 °C; (b) 70 °C. Table 1. Parameters for the System Water-Formaldehyde RW H
βW H
ξWF
12.152
-9.9974
-0.0308
of Maripuri and Ratcliff (1972) and Othmer and Benenati (1945) in the pressure range 200-760 Torr and temperature range 35-100 °C. The physical parameter which describes the interactions between methanol and formaldehyde, used in the expressions of the activity coefficients, was taken from Brandani et al. (1991). For the binary system methanolformaldehyde a preliminary study indicated that the vapor-phase composition of the dimer is typically of the order of 1%. This information was used to reduce the number of model parameters. The density in the vapor phase is represented, within experimental uncertainty, by the monomer reaction. The equilibrium constant of the monomer reaction was therefore taken from Brandani et al. (1991) who used the experimental density data of Hall and Piret (1949). We decided to obtain the remaining model parameters from the simultaneous regression of the experimental vapor-liquid equilibrium data of the binary system (methanol-formaldehyde) and one isotherm (80 °C) of the ternary system (watermethanol-formaldehyde) reported by Kogan and Ogorodnikov (1980a,b). The values of the parameters needed for the calculation of the vapor-phase dimer formation reaction equilibrium constant, the two liquid-phase reactions equilibrium constants, and Henry’s constant
Table 2. Parameters for the System Methanol-Formaldehyde RM 1L
βM 1L
RM 2L
βM 2L
RM 2V
βM 2V
RM H
βM H
-3.6925
4053.9
-6.8314
4582.4
-21.632
7984.9
8.6090
-7.7240
Table 3. Results of the Model Correlation for the Systems Containing Methanol average absolute deviations authors
T, °C
data points
∆P, Torr
∆yM
∆yW
∆yF
Kogan and Ogorodnikov (1980a) Kogan and Ogorodnikov (1980a) Kogan and Ogorodnikov (1980a) Kogan and Ogorodnikov (1980b)
60 70 80 80
8 10 9 26
6.05 5.41 7.16 7.03
0.0072 0.0074 0.0068 0.0149
0.0128
0.0078
authors
T, °C
data points
∆P, Torr
∆yM
∆yW
∆yF
Hasse and Maurer (1991) Hasse and Maurer (1991) Kogan and Ogorodnikov (1980b) Kogan and Ogorodnikov (1980b)
20 40 60 70
6 6 26 29
3.37 8.04 2.65 4.98
0.0147 0.0077 0.0142 0.0148
0.0138 0.0128
0.0096 0.0093
Table 4. Results of Model Predictions average absolute deviations
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3489
of formaldehyde in methanol are reported in Table 2. The average deviations are reported in Table 3. Figure 2 shows the comparison of model calculations with experimental binary data. An excellent agreement is found even in the region of high formaldehyde compositions where the dimer contribution is greater. Figure 3 shows the comparison of experimental and calculated ternary vapor compositions. Figure 4 shows the comparison of the model extrapolations to low temperatures with the binary experimental data of Hasse and Maurer (1991). These predictions are obtained from the extrapolation of up to 40 °C of the model parameters which were regressed from a data set in a temperature interval of only 20 °C. This is an important check of the validity of the parameters obtained in this study. Figure 5 shows the comparison of experimental and predicted ternary vapor compositions at 60 and 70 °C. The calculated vapor-phase compositions of the ternary system water-methanol-formaldehyde are not subject to systematic deviations. The proposed model represents well both binaries and the ternary system considered. With the parameters obtained in the present study, it is now possible to calculate the vapor pressure of the dimer MF2 according to the following equation:
PSMF2
)
0 ∞ S KM V2HF,MγMFPMF ∞ KM L2γMF2
x: apparent mole fractions in liquid phase y: apparent mole fractions in vapor phase z: true mole fractions in liquid phase Greek Symbols γ: activity coefficient Subscripts and Superscripts A: active solvent C: critical point F: formaldehyde L: liquid M: methanol MF: hemiformal MF2: dimer formed by methanol and two molecules of formaldehyde MS: mixed solvent S: at saturation V: vapor W: water WF: methylene glycol ∞: infinite dilution
Literature Cited
(23)
Figure 6 shows that the vapor pressure of the methanol dimer MF2 is essentially the same as that of the water monomer WF, therefore justifying our initial assumption that this component is present in the vapor phase of formaldehyde mixtures containing methanol. Conclusions It has been shown that the dimer MF2 formed in the reactions between methanol and formaldehyde has a vapor pressure which is of the same order as that of the monomer WF formed by water and formaldehyde. This observation led to a different description of the vapor phase for systems containing methanol and formaldehyde. The model of Brandani et al. (1991, 1992) has been reformulated to take this into account, and the model parameters have been evaluated. Good descriptions of the vapor-liquid equilibrium for the systems methanol-formaldehyde, water-formaldehyde, and water-methanol-formaldehyde have been obtained. Having assumed the gas-phase ideal allows good extrapolation of the model to lower temperatures, for higher temperatures the inclusion of vapor-phase nonidealities should be considered. Furthermore, systematic deviations in the calculated vapor-phase compositions of methanol and water in the ternary system have been eliminated, indicating the relevance of the contribution of the dimer MF2 in the behavior of the vapor phase. Nomenclature a: activity coefficient binary interaction parameters H: Henry’s constant K1: equilibrium constant of monomer formation reaction K2: equilibrium constant of dimer formation reaction P: pressure T: temperature u: true mole fractions in vapor phase
Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems. AIChE J. 1975, 21, 116-128. Albert, M.; Hahnenstein, I.; Hasse, H.; Maurer, G. Vapor-Liquid Equilibrium of Formaldehyde Mixtures: New Data and Model Revision. AIChE J. 1996, 42, 1741-1752. Brandani, V.; Di Giacomo, G.; Foscolo, P. U. Isothermal VaporLiquid Equilibria for the Water-Formaldehyde System. A Predictive Thermodynamic Model. Ind. Eng. Chem. Process Des. Dev. 1980, 19, 179-185. Brandani, S.; Brandani, V.; Di Giacomo, G. A Physical Theory Superimposed onto the Chemical Theory for Describing VaporLiquid Equilibria of Binary Systems of Formaldehyde in Active Solvents. Ind. Eng. Chem. Res. 1991, 30, 414-420. Brandani, S.; Brandani, V.; Di Giacomo, G. The System Formaldehyde-Water-Methanol: Thermodynamics of Solvated and Associated Solutions. Ind. Eng. Chem. Res. 1992, 31, 17921798. Hall, M. W.; Piret, E. L. Distillation Principles of Formaldehyde Solutions. Ind. Eng. Chem. 1949, 41, 1277-1286. Hasse, H.; Maurer, G. Vapor-Liquid Equilibrium of FormaldehydeContaining Mixtures at Temperatures Below 320 K. Fluid Phase Equilibr. 1991, 186-199. Kogan, L. V.; Ogorodnikov, S. K. Liquid-Vapor Equilibrium in the System Formaldehyde-Methanol. J. Appl. Chem. USSR 1980a, 53, 98-101. Kogan, L. V.; Ogorodnikov, S. K. Liquid-Vapor Equilibrium in the System Formaldehyde-Methanol-Water. J. Appl. Chem. USSR 1980b, 53, 102. Maripuri, V. O.; Ratcliff, G. A. Measurement of Isothermal VaporLiquid Equilibriums for Acetone-n-Heptane Mixtures Using Modified Gillespie Still. J. Chem. Eng. Data 1972, 17, 366369. Maurer, G. Vapor-Liquid Equilibrium of Formaldehyde- and Water-Containing Multicomponent Mixtures. AIChE J. 1986, 32, 932-948. Othmer, D. F.; Benenati, R. F. Ind. Eng. Chem. 1945, 37, 299. As reported by Gmehling J.; Onken, U. Vapor-Liquid Equilibrium Data Collection; DECHEMA: Frankfurt, 1977.
Received for review January 12, 1998 Revised manuscript received May 11, 1998 Accepted May 26, 1998 IE980020Y
