Experimental results for the vapor–liquid equilibria of(formaldehyde+1,3,5-trioxane+methanol+salt+water) systems and comparison with predictions

Xianming Zhang ,Mengchen Li ,Yufeng Hu,Zhichang Liu,Shuqin Mo

1 State Key Laboratory of Heavy Oil Processing and High Pressure Fluid Phase Behavior &Property Research Laboratory,China University of Petroleum,Beijing 102249,China

2 School of Chemical Engineering,Ordos Institute of Technology,Ordos 017000,China

3 PetroChina Petrochemical Research Institute Science Base PetroChina,Beijing 102206,China

Keywords:Vapor liquid equilibria Reactive distillation Activity coefficient 1,3,5-Trioxane production UNIFAC Salt effect

ABSTRACT The salt effect on the vapor–liquid phase equilibrium(VLE)of solvent mixtures is of significant interest in the industrial production of 1,3,5-trioxane.Experimental data for the VLE of quinary systems(formaldehyde+1,3,5-trioxane+methanol+salt+water) and their ternary subsystems(formaldehyde+salt+water),(1,3,5-trioxane+salt+water),and(methanol+salt+water)were systematic measured under atmospheric pressure.The salts considered included KBr,NaNO3,and CaCl2.The extended UNIFAC model was used to describe the VLE of the salt-containing reactive mixtures.The model parameters were determined from the experimental VLE data of ternary systems or obtained from the literature,and then were used to predict the VLE of systems (1,3,5-trioxane+KBr+water),(methanol+KBr+water),(formaldehyde+KBr+water),and(formaldehyde+1,3,5-trioxane+methanol+salt+water)with salt=KBr,NaNO3,and CaCl2.The predicted results showed good agreements with the measured results.Furthermore,the model was used to uncover the salt effect on the VLE of these multisolvent reactive systems.

1.Introduction

Formaldehyde (CH2O,FA) is an important C1 chemical raw material.However,most reactions with formaldehyde as raw material need to be replaced by 1,3,5-trioxane (C3H6O3,TOX) or polyoxymethylene polymers (POMs),and anhydrous reaction can only use 1,3,5-trioxane [1–3].1,3,5-Trioxane is also an important raw material for the production of POMs and poly(oxymethylene)dimethyl ethers (DMMn,n=2–8).In industrial production,1,3,5-trioxane is produced by reactive distillation under 373.15 K with formaldehyde solution as raw material and sulfuric acid as catalyst[4–6].Formaldehyde is highly reactive,and forms adducts with water and methanol (CH3OH,ME),such as methylene glycol (HO(CH2O)H,MG),poly(oxymethylene) glycols [HO(CH2O)nH (n >1),MGn],hemiformal (HO(CH2O)CH3,HF),and poly(oxymethylene)hemiformals [HO(CH2O)nCH3(n >1),HFn] [5–10]:

The equilibrium distribution of formaldehyde to adducts substantially lowers the concentration of the main reactant HO(CH2-O)3H and thus the concentration of the main product 1,3,5-trioxane in industrial 1,3,5-trioxane synthesis [5].As a result,the energy consumption of 1,3,5-trioxane production is extremely high[3,4,11].The effect of salt on phase equilibrium behavior has widely applications in chemical engineering,such as mutual solubility,the boiling points,and the relative volatility of solvents[12–18].The addition of salt in the liquid phase has significant influence on the vapor–liquid phase equilibrium (VLE) and decreases the energy consumed in 1,3,5-trioxane synthesis [5].Therefore,phase equilibria of (formaldehyde+1,3,5-trioxane+methanol+s alt+water) systems are of significant interest for separation processes in 1,3,5-trioxane production.In our previous work [5],the salt effects on the VLE of systems(formaldehyde+1,3,5-trioxane+methanol+salt+water) were systematically studied,and an extended UNIFAC model combined a Debye–Hückel type was developed to describe the VLE of these systems.The salts evaluated included LiCl,NaCl,KCl,NaBr,MgSO4,MgCl2,and Na2SO4.

In this work,new experimental data for the VLE of quinary systems (formaldehyde+1,3,5-trioxane+methanol+salt+wat er) and their ternary subsystems (1,3,5-trioxane+salt+water),(methanol+salt +water),and (formaldehyde+salt+water) were systematic measured under atmospheric pressure.The salts considered were KBr,NaNO3,and CaCl2.The obtained experimental data were used to verify the reliability of the extended UNIFAC model.The model parameters were determined from the VLE data of the ternary systems or obtained from the literature.Then,the extended UNIFAC model was used to revealed the salt effect of the three salts on the VLE of the chemical reactive system(formaldehyde+1,3,5-trioxane+methanol+water),e.g.,the relative volatility of 1,3,5-trioxane to formaldehyde,of 1,3,5-trioxane to water,of formaldehyde to water,and of methanol to water.

2.Experimental

2.1.Experimental materials

The analytical grade of paraformaldehyde (≥96.0 wt% (weight percent)),1,3,5-trioxane (99.5 wt%),methanol (99.5 wt%),KBr(99.5 wt%),NaNO3(99.0 wt%),and CaCl2﹒2H2O (≥99.0 wt%) were supplied by Aladdin Industrial Corporation (Shanghai,China),without further purification.Deionized water was distilled in a quartz still with conductivity of(0.8–1.2)×10-6S﹒cm-1.Formaldehyde aqueous solutions were prepared by the dissolution of paraformaldehyde in deionized water at 343.15 K [4,5],and then concentrated to required concentrations using vacuum rotary evaporation.A Sartorius CPA225D analytical balance with a precision of 1.0×10-5g was used to prepare the system(formaldehyde+1,3,5-trioxane+methanol+salt+water) and its subsystems from formaldehyde aqueous solutions,1,3,5-trioxane,methanol,water,and each salt [5].All the samples were prepared immediately before use to prevent loss of solvents due to evaporation.

2.2.Experimental procedures

A modified Othmer still was used to measure the VLE data at atmospheric pressure (101.33 kPa),and the experimental procedure have been described previously [5,19,20].Our previous work[5]have fully confirmed its reliability.An oil bath heater was used to provide heat for the boiling of the still,and a DP95 digital RTD thermometer with a standard uncertainty of 0.1 °C was used to monitor the experimental temperatures.

The formaldehyde concentration was determined by sodium sulfite method,and the maximum relative uncertainty of the experimental results was ±1% [3–5].The concentrations of 1,3,5-trioxane and methanol were analyzed by gas chromatography(SP3420A,Beifen-Ruili,China) equipped with a TCD detector.A packed column[length:4 m,diameter:3 mm,packed with Porapak N(50/80 mesh)]was used,and the carrier gas was hydrogen with a flow rate of 15 cm3﹒min-1.The temperature of column was controlled with a temperature rising program:initially injected was set at 408.15 K,and holding for 8 min,then raising the temperature to 453.15 K with a rate of 15 K﹒min-1,and holding at 453.15 K for 10 min.The temperature of the injection port was set at 453.15 K.The temperature of the TCD detector was kept at 493.15 K.n-Propanol was used as the internal standard.

The maximum relative uncertainty of the experimental results for the concentrations of 1,3,5-trioxane and methanol were ±1%and ±2%,respectively [5].The concentration of NaNO3was analyzed by UV–Vis Spectrophotometer (UV-2550,Shimadzu,Japan),and the maximum relative uncertainty of the experimental results was±2%.The concentrations of CaCl2and KBr were determined by titration of Cl-or Br-with AgNO3,and the maximum relative uncertainty of the experimental results was ±0.1% [5].Generally,each sample was analyzed at least three times.

2.3.Experimental results

The VLE of (1,3,5-trioxane+salt+water),(methanol+salt +water),(formaldehyde+salt+water),and (formaldehyde+1,3,5-trioxane+methanol+salt+water) systems are systematic investigated under atmospheric pressure(101.33 kPa).The salts considered are KBr,NaNO3,and CaCl2.The mole fractions of 1,3,5-trioxane,methanol,and formaldehyde in the liquid phase of the corresponding ternary systems are between 1.31%–3.95%(mol),4.38%–13.88%(mol),and 15.65%–46.23%(mol),respectively.The mole fractions of 1,3,5-trioxane,methanol,and formaldehyde in the liquid phase of (formaldehyde+1,3,5-trioxane+methanol +salt+water) systems are between 1.05%–4.61%(mol),2.20%–15.78%(mol),and 9.25%–42.71%(mol),respectively.The maximum molalities of the salt of these ternary and quinary systems are about 1.9 and 1.6 mol﹒(kg solvent mixture)-1,respectively.The experimental results are shown in Tables 1–4.

Table 1 Experimental data and correlation/prediction results for the vapor–liquid equilibrium of the ternary system (1,3,5-trioxane+salt+water) at 101.33 kPa

3.Model

Many efforts have been devoted to develope vapor–liquid and chemical equilibrium models for the chemically reactive system(formaldehyde+1,3,5-trioxane+methanol+salt+water) [5].The model used in the present work to correlate and predict VLE data of the system has been described in detail within our previous work [5],so that only the basic assumptions of the model are briefly presented here.

The schematic of describing the VLE and the chemical equilibria of the system (formaldehyde+1,3,5-trioxane+methanol+salt +water) is shown in Fig.1.It is assumed that the vapor phase consists of monomeric formaldehyde,water (W),methylene glycol,1,3,5-trioxane,methanol,and hemiformal [5,21].The liquid phase is treated as chemical reactive mixture of monomeric formaldehyde,water (W),1,3,5-trioxane,methylene glycol,MGn(n ≥2),methanol,hemiformal,HFn(n ≥2),cation (C),and anion (A) [5].The non-ideality of the liquid phase is described by the extended UNIFAC model [5].

According to the mass balance and chemical reaction equilibria for the system (formaldehyde+1,3,5-trioxane+methanol+salt +water),the relationship between the overall mole fractions of solvents/ionic species and their true mole fractions can be expressed as follows [5,9,22]:

where A and b are Debye–Hückel parameter,Ms,iis the molar mass of the ith solvent,I is the ionic strength of the solution,and diand dmare the density of the ith solvent and the mixed solvent,respectively[14,23,26].

4.Results and Discussion

4.1.Determination of model parameters

Some model parameters are taken from literature report[5,9,21,27,28].The vapor pressures of the pure components are calculated by the Antoine equation,and the parameters are given in Table S1 (Supporting Information) [9,27].The equilibrium constants of formaldehyde oligomerization reactions (Eqs.(1)–(4))are given in Table S2 (Supporting Information) [9,27].The group assignment is given in Table S3 (Supporting Information)[9,21,27].The size(ri)and surface(qi)parameters of components/-groups/ions are also taken from literature report [9,21,27,28],and the results are given in Table S4 (Supporting Information).The densities(di)of pure methanol and water are obtained by interpolation of literature data[29],and those of formaldehyde and 1,3,5-trioxane are estimated by the group contribution method devel-oped by Christian et al.[30].The dielectric constant(ε)of each pure liquid is obtained from the literature [29,31–33].

Table 2 Experimental data and correlation/prediction results for the vapor–liquid equilibrium of the ternary system (methanol+salt+water) at 101.33 kPa

The UNIFAC group interaction parameters ai,j(a is the interaction parameter) between solvent groups are taken from literature report [9,21,27],and are given in Table S5 (Supporting Information).The interaction parameters ai,jbetween solvents/groups and ions(ion=Na+,K+,Cl-and Br-)are obtained from our previous work[5],and are given in Table 5.The residual interaction parameters ai,jbetween solvents/groups and ions(ion=Ca2+and)are determined by fitting the VLE experimental data of systems(formaldehyde+salt+water),(1,3,5-trioxane+salt+water),(methanol+salt+water),and (salt+water).The following assumptions are made for the interaction parameters:(1) The ion–ion interaction parameters conform to aion,ion=0[5,12,23,34];(2) The solvents/groups–ion interaction parameters obey aion,solvent=asolvent,ion[5];(3) aion,CH3O=aion,CH2OH=aion,ME[5].The ai,jof H2O–ion (ion=Ca2+and) are determined by fitting the present model[35–37]to the literature VLE data of binary systems(salt+water),and the comparisons of the correlation results and the literature values are shown in Table S6 (Supporting Information).The ai,jof TOX–ion and ME–ion (ion=Ca2+and) are determined by fitting to the experimental data of ternary systems(1,3,5-trioxane+salt+water)and(methanol+salt+water).The ai,jof FA–ion,MG–ion,CH2–ion,and OH–ion(ion=Ca2+and) are determined by fitting to the experimental data of ternary systems(formaldehyde+salt+water).All interaction parameters are determined by minimization of the following objective function [5,23]:

where M is the number of data types,N is the number of data points for each of the M data types,Q stands for the property yFA,yTOX,yMEand p,and wQis a weighting factor for data type Q.The subscripts exp and cal represent experimental and calculated values,respectively.The correlation quality of the present model is determined using the average absolute relative deviation (AARD) [5]:

The interaction parameters thus obtained are shown in Table 5.

4.2.Comparisons with experimental results

The correlation results for the systems (1,3,5-trioxane+salt +water),(methanol+salt+water),and (formaldehyde+salt+wat er) with salt=NaNO3and CaCl2are shown in Tables 1–3.The model parameters shown in Table 5 and Tables S1–S6 are used to predict the VLE of systems (1,3,5-trioxane+KBr+water),(methanol+KBr+water),(formaldehyde+KBr+water),and(formaldehyde+1,3,5-trioxane+methanol+salt+water) with salt=KBr,NaNO3,and CaCl2.The results are shown in Tables 1–4.The correlation/prediction results for the vapor phase compositions and the total pressure of these systems are compared withthe experimental data in Figs.2–5.The average relative deviations(δ) of these two variables are defined by:

Table 3 Experimental data and correlation/prediction results for the vapor–liquid equilibrium of the ternary system (formaldehyde+salt+water) at 101.33 kPa

Table 4 Experimental data and prediction results for the vapor–liquid equilibrium of the quinary system (formaldehyde+1,3,5-trioxane+methanol+salt+water) at 101.33 kPa

Table 5 Interaction parameters ai,j (K) for the UNIFAC model between structural groups and ions

where N is the number of experimental data.

The correlation/prediction results agree well with the experimental data,with δyTOX≤3.16% and δp ≤1.77% for the systems(1,3,5-trioxane+salt+water),δyME≤1.39% and δp ≤0.98% for the systems (methanol+salt+water),and δy-FA≤3.83% and δp ≤2.24%for the systems(formaldehyde+salt+water).The average relative deviations between the predicted and the experimental results for all these systems are≤2.79%,≤3.85%,≤3.71%,and δp ≤2.79% for the systems (formaldehyde+1,3,5-trioxane+methanol+salt+water).For such complex formaldehyde-containing systems,the agreements between the prediction results and the experimental data are considered to be satisfactory.Hence,once again it is shown that the extended UNIFAC model [5] is applicable and reliable.

4.3.Salt effect

The salt effect on the VLE of systems (formaldehyde+1,3,5-tri oxane+methanol+water) is studied using the extended UNIFAC mode [5].The previously fitted parameters can reliably represent the effect of salt on VLE characteristics [5].The relative volatility of solvent A to solvent B is expressed as:

In order to carry out reliable comparisons of the effects of different salts on the VLE of mixed solvent systems,it is necessary to take similar conditions of commercial production of 1,3,5-trioxane [2,4–7] as the calculation criteria,which the molality(ms) of the salts considered is 0–3.0 mol﹒kg-1with the constant salt-free composition of the liquid phase [formaldehyde (31.31 m ol%)+1,3,5-trioxane (2.08 mol%)+methanol (5.19 mol%)+water(61.42 mol%)] at 373.15 K.The calculation results for ln(αs/α)A,B(αsand α are relative volatilities of solvent A to solvent B with and without salt,respectively)are shown as full symbols and plotted versus the molality of the salt msin Fig.6.The linear regressions of the calculated data of ln(αs/α) as a function of msare performed with the intercept being set as 0,and the regression linear equations are plotted as lines in Fig.6.

Fig.1.The scheme of the VLE and the chemical equilibria of system (formaldehyde+1,3,5-trioxane+methanol+salt+water).

It is apparent from Fig.6A and 6B that ln(αs/α)TOX,Wand ln(αs/α)ME,Wincrease linearly with increasing ms.Therefore,1,3,5-trioxane and methanol are ‘‘salted-out”,whereas water is‘‘salted-in”in(formaldehyde+trimeraldehyde+methanol+salt+water)systems.Such‘‘salting-out”effects on 1,3,5-trioxane follow the order CaCl2>NaNO3>KBr,and those on methanol follow the order KBr >CaCl2>NaNO3.It is remarkable that the addition of CaCl2(2.0 mol﹒kg-1)increases αTOX,Wby 120.15%,and the addition of KBr (3.0 mol﹒kg-1) increases αME,Wby 87.37%.However,due to the solubility limit of the solution,we would not expect a high salt concentration.Fig.6C shows that ln(αs/α)FA,Wincreases or decreases linearly with increasing ms.Accordingly,formaldehyde is ‘‘salted-out”by the addition of CaCl2,and is ‘‘salted-in”by the addition of KBr.The salt molality of NaNO3has weak impact on the ln(αs/α)FA,W.The ‘‘salting-out”effect exhibited by the salt follows the order CaCl2>NaNO3>KBr.It is noticeable that the addition of KBr (3.0 mol﹒kg-1) decreases αFA,Wby 13.32%,and the addition of CaCl2(2.0 mol﹒kg-1) increases αFA,Wby 35.68%.Fig.6D shows that ln(αs/α)TOX,FAincreases linearly with increasing ms,in the order KBr>CaCl2≈NaNO3.The αTOX,FAcan be increased by 86.70% with the addition of KBr (3.0 mol﹒kg-1) to(formaldehyde+1,3,5-trioxane+methanol+water).Additionally,the effects of salts with the same anion or the same cation on the VLE of the systems (formaldehyde+1,3,5-trioxane+methanol +water) are compared,and the salts compared include the three salts studied in this work and the seven salts studied in our previous work[5].For the salts based on Na+,the‘‘salting-out”effect on 1,3,5-trioxane to water conforms to the order NaNO3>Na2SO4>-NaCl >NaBr,and the ‘‘salting-out”effect on 1,3,5-trioxane to formaldehyde follows the order Na2SO4>NaBr >NaNO3>NaCl.For the salts based on Cl-,the ‘‘salting-out”effect on 1,3,5-trioxane to water conforms to the order CaCl2>MgCl2>-LiCl >KCl >NaCl,and the ‘‘salting-out”effect on 1,3,5-trioxane to formaldehyde follows the order CaCl2>KCl >MgCl2>NaCl >LiCl.For the salts based on Br-,the‘‘salting-out”effect on 1,3,5-trioxane to water conforms to the order KCl >KBr,and the ‘‘salting-out”effect on 1,3,5-trioxane to formaldehyde follows the order KBr >KCl.

Fig.2.Comparisons between experimental data (lines) and correlation results(symbols) for the vapor phase composition of the ternary system (1,3,5-trioxane+salt+water) at 101.33 kPa.(■):KBr;(●):NaNO3;(▲):CaCl2.

Fig.3.Comparisons between experimental data (lines) and correlation results(symbols) for the vapor phase composition of the ternary system(methanol+salt+water) at 101.33 kPa.(■):KBr;(●):NaNO3;(▲):CaCl2.

Fig.4.Comparisons between experimental data (lines) and correlation results(symbols) for the vapor phase composition of the ternary system (formaldehyde+salt+water) at 101.33 kPa.(■):KBr;(●):NaNO3;(▲):CaCl2.

In the reactive distillation process of 1,3,5-trioxane,it is expected that the amount of formaldehyde,water and methanol evaporated to the vapor phase is as small as possible,while the amount of 1,3,5-trioxane evaporated to the vapor phase is as great as possible,so as to reduce the loss of formaldehyde and the cost of subsequent distillation operations.In particular,the staying of formaldehyde in the liquid phase is conducive to maintain the high concentration of formaldehyde,which is beneficial for increasing the conversion of formaldehyde to 1,3,5-trioxane.Therefore,an excellent salt additive should perform well in raising the αTOX,Wand αTOX,FAto(formaldehyde+1,3,5-trioxane+methanol+water)simultaneously.This indicates that KBr can act as a potential additive to improve the efficiency of industrial 1,3,5-trioxane production.However,KBr is still not as good as MgSO4,because the addition of MgSO4(3.0 mol﹒kg-1) to (formaldehyde+1,3,5-triox ane+methanol+water) increases αTOX,Wand αTOX,FAby 116.04%and 135.94%,respectively [5].

Fig.5.Comparisons between experimental data (lines) and calculated results(symbols) for the vapor phase compositions of the quinary system (formaldehyde+1,3,5-trioxane+methanol+salt+water)at 101.33 kPa.A:.B:.C:.(■):KBr;(●):NaNO3;(▲):CaCl2.

Fig.6.Plots of ln(αs/α) versus ms for systems (formaldehyde+1,3,5-trioxane+methanol+salt+water) at 373.15 K (A:ln(αs/α)TOX,W;B:ln(αs/α)ME,W;C:ln(αs/α)FA,W;D:ln(αs/α)TOX,FA).Symbols[(■)for KBr,(●)for NaNO3,(▲)for CaCl2]are the calculated data of ln(αs/α).

5.Conclusions

New experimental data for the VLE of the systems(formaldehyde+1,3,5-trioxane+methanol+salt+water) and the related subsystems (1,3,5-trioxane+salt+water),(methanol+salt+water) and (formaldehyde+salt+water) were systematic measured under atmospheric pressure.The salts used were KBr,NaNO3,and CaCl2.An extended UNIFAC model was used to represent the VLE and chemical equilibrium in these saltcontaining reactive mixtures.The newly introduced model parameters were determined from the experimental VLE data of ternary systems (1,3,5-trioxane+salt+water),(methanol+salt+water),and (formaldehyde+salt+water) with salt=NaNO3and CaCl2.These parameters,together with parameters obtained in the literature,can provide good predictions for the phase behavior of the systems (1,3,5-trioxane+KBr+water),(methanol+KBr+water),(formaldehyde+KBr+water),and (formaldehyde+1,3,5-triox ane+methanol+salt+water) with salt=KBr,NaNO3,and CaCl2.Furthermore,the model was used to reveal the effect of considered salts on the VLE of the chemical reactive system (formaldehyde +1,3,5-trioxane+methanol+water).The results show that:(1)1,3,5-trioxane and methanol are ‘‘salted-out”by the salts considered in all the systems,and formaldehyde is ‘‘salted-out”only by CaCl2;(2) KBr has the strongest ability to enhance the relative volatility of 1,3,5-trioxane to formaldehyde among the three salts;(3)CaCl2has the strongest ability to enhance the relative volatility of 1,3,5-trioxane to water among the three salts.However,KBr and CaCl2are still not as good as MgSO4.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (grant numbers 22078355,21890763 and 21776300),Petrochemical Research Institute of PetroChina(grant number HX20200668),and Scientific Research Project of Ordos Institute of Technology (grant numbers KYYB2019006).

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2020.11.019.

Nomenclature

A Debye–Hückel parameter

aithermodynamic activity (normalized according to Raoult’s law)

ai,jUNIFAC parameter for interactions between groups,K

b Debye–Hückel parameter

d density,kg﹒m-3

F objective function

I ionic strength,mol﹒kg-1

M mumber of data types

Ms,imolar mass of solvent,kg﹒mol-1

m molality,mol﹒kg-1

N number of components or number of data points

n number of formaldehyde groups

p pressure,kPa

q UNIFAC surface parameter

r UNIFAC size parameter

T temperature,K

wQweighting factor

xitrue mole fraction of component in liquid phase

yitrue mole fraction of component in vapor phase

α relative volatility

γ activity coefficient

ε relative dielectric constant

Subscripts

A anion

C cation

cal calculated result

exp experimental result

FA formaldehyde

HF hemiformal

HFnpoly(oxymethy1ene) hemiformal

ME methanol

MG methylene glycol

MGnpoly(oxymethylene) glycol

TOX 1,3,5-trioxane

W water