Chemical Equilibrium of the Synthesis of Poly(oxymethylene) Dimethyl

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Chemical Equilibrium of the Synthesis of Poly(oxymethylene) Dimethyl Ethers from Formaldehyde and Methanol in Aqueous Solutions Niklas Schmitz, Fabian Homberg, Jürgen Berje, Jakob Burger, and Hans Hasse Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b01148 • Publication Date (Web): 02 Jun 2015 Downloaded from http://pubs.acs.org on June 15, 2015

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Industrial & Engineering Chemistry Research

Chemical Equilibrium of the Synthesis of Poly(oxymethylene) Dimethyl Ethers from Formaldehyde and Methanol in Aqueous Solutions Niklas Schmitz, Fabian Homberg, Jürgen Berje, Jakob Burger,∗ and Hans Hasse Laboratory of Engineering Thermodynamics, University of Kaiserslautern, Germany E-mail: [email protected]

Abstract Poly(oxymethylene) dimethyl ethers (OME) reduce the soot formation during the combustion process, when added to diesel fuels. OME are a Gas-to-Liquid (GtL) option as they can be produced via methanol from natural gas or renewable feedstocks. This work deals with the synthesis of OME from the educts formaldehyde and methanol in aqueous solutions. The studied mixtures are complex reacting systems in which besides OME, also poly(oxymethylene) glycols and poly(oxymethylene) hemiformals are present. The chemical equilibrium of the OME formation is studied in a stirred batch reactor varying in the educts’ overall ratio of formaldehyde to methanol and the amount of water and varying the temperature between 333.15 K and 378.15 K. A mole fraction-based, as well as an activity-based model of the chemical equilibrium of the OME formation are developed, which explicitly account for the formation of poly(oxymethylene) glycols and poly(oxymethylene) hemiformals. Information on the latter reactions from literature are confirmed by NMR experiments in the present work. ∗

To whom correspondence should be addressed

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Introduction The oxygenates poly(oxymethylene) dimethyl ethers (OME) are oligomers of the chemical structure H3 C−O−(CH2 O)n −CH3 with n ≥ 2. Their addition to diesel fuel reduces the soot formation during the combustion process. 1 In contrast to methanol or dimethylether, which are also discussed as oxygenated diesel fuel additives, 1,2 no modification of the diesel engine is necessary, when OME (n = 3-5) are added to diesel fuels. 3 In addition to that, OME are also discussed as an alternative to methanol in direct oxidation fuel cells. 4,5 Different synthesis routes for the production of OME are discussed. All of them start from methanol, which in turn is produced from synthesis gas. 6 Hence, the production of OME is a Gasto-Liquid (GtL) technology. 2 There is large number of articles (e.g. 7–18 ) and patents from China concerning OME, as China is the largest coal producer in the world and is seeking for an option to produce liquid fuels from coal. Synthesis gas may however also be produced from renewable feedstocks. For this reason OME can also be produced on the basis of biomass. 19 Two kinds of educts are necessary for the synthesis of OME: first, an educt that provides the methyl end group of OME (e.g. methylal, methanol) and second, an educt that provides the monomer unit formaldehyde (e.g. trioxane, aqueous- or methanolic formaldehyde solution). Table 1 lists an overview over the educts used by different authors in the literature on the OME synthesis. In earlier work, 3,20–22 we measured and modeled the chemical equilibrium and reaction kinetics of the OME synthesis from methylal and trioxane using an acidic heterogeneous catalyst and presented a conceptual design of a production process. The reaction of methylal and trioxane over an acidic catalyst produces OME with a very high selectivity and without coupled products. Both educts have to be produced however from methanol and formaldehyde in additional process steps. 3,23,24 This is why other educt combinations are also interesting, c.f. Table 1. Particulary interesting is the use of methanol and formaldehyde in aqueous solutions, as these are the cheapest of all educts. Zhang et al. investigated the OME synthesis from the educts methanol and aqueous formalde2 ACS Paragon Plus Environment

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hyde solution over an acidic heterogeneous catalyst. 10,11 In this system the selectivity of formaldehyde towards OME is limited by the competing reactions of formaldehyde with methanol and water towards poly(oxymethylene) glycols and poly(oxymethylene) hemiformals. 25–27 Zhang et al. did not mention these competing reactions. Drunsel et al. investigated chemical equilibrium and reaction kinetics for the synthesis of methylal from methanolic formaldehyde solutions with a small amount of water over an acidic heterogeneous catalyst. 24,28 This is interesting, as methylal could be seen as OME of chain length n = 1. In this work, however, the term OME will only be used for chain lengths n ≥ 2. As the amount of formaldehyde was small in their educt mixtures, Drunsel et al. did not observe the quantifiable formation of OME. 24,28 For conceptual process design, a reliable model for the chemical equilibrium of the OME formation from formaldehyde and methanol in aqueous solutions is needed, which accounts for all components in the reaction system. In the present work, experimental data on the equilibrium in such systems are measured and two models are developed, which describe the chemical equilibrium of the OME synthesis, including the formation of poly(oxymethylene) glycols and poly(oxymethylene) hemiformals.

Chemical reactions In aqueous- and methanolic formaldehyde solutions, formaldehyde (FA, CH2 O) is almost completely bound in the oligomers poly(oxymethylene) glycols (MGn , HO−(CH2 O)n −H) and poly(oxymethylene) hemiformals (HFn , HO−(CH2 O)n −CH3 ). Formaldehyde and water (H2 O) react and form poly(oxymethylene) glycols according to reactions (1) and (2). 28 −− ⇀ FA + H2 O ↽ − − MG1 − ⇀ FA + MGn−1 − ↽ − − MGn ; n ≥ 2


(1) (2)


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Similarly, formaldehyde reacts with methanol (MeOH, H3 C−OH) and forms poly(oxymethylene) hemiformals according to reactions (3) and (4). 28 − ⇀ FA + MeOH − ↽ − − HF1

(3)

−− ⇀ FA + HFn−1 ↽ − − HFn ; n ≥ 2

(4)

The chemical equilibrium and the reaction kinetics of reactions (1) to (4) are well described in literature. 25–28 The above reactions occur at all pH levels and have considerable reaction rates even at neutral conditions without the addition of any catalyst. 25 By contrast, the following reactions occur only in acidic environment. The formation of methylal (MAL, H3 C−O−(CH2 O)−CH3 ) is given by reaction (5). This reaction is an etherfication reaction and the coupled product water is formed. H+

−− ⇀ HF1 + MeOH ↽ − − MAL + H2 O

(5)

For the chain elongation from methylal to OME2 and OMEn , formaldehyde is added in reactions (6) and (7). H+

− ⇀ FA + MAL − ↽ − − OME2 H+

−− ⇀ FA + OMEn−1 ↽ − − OMEn ; n ≥ 3

(6) (7)

In this work, two side products were observed: trioxane (TRI) and methyl formate (MEFO). Their formation can formally be explained by reactions (8) and (9). 21 H+

− ⇀ 3 FA − ↽ − − TRI H+

2 FA −−→ MEFO


(8) (9)

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True composition and overall composition As the unstable components poly(oxymethylene) glycols and poly(oxymethylene) hemiformals are present in the studied mixtures, two different ways of describing the composition are used: the true composition and the overall composition, respectively. Overall concentrations are the concentrations of formaldehyde, methanol, water, methylal and OME that are found when the unstable poly(oxymethylene)glycols and poly(oxymethylene) hemiformals completely decompose into formaldehyde, methanol and water. The true species concentrations are those obtained by noninvasive analysis, also quantifying poly(oxymethylene) glycols and poly(oxymethylene) hemiformals.

Experiments on the OME synthesis Chemicals and catalyst Paraformaldehyde (> 0.95 g/g) was purchased from Carl Roth. Methanol (> 0.999 g/g) was purchased from Sigma Aldrich. Ultrapure water was produced with a Milli-Q water purifaction system from Merck. OME2 to OME4 (both > 0.97 g/g) were provided by BASF SE. Methanolic and aqueous formaldehyde solutions were prepared by dissolving paraformaldehyde in methanol and water, respectively. The rate of depolymerization was enhanced by heating the reaction mixture to 333.15 K for methanolic solutions and to 353.15 K for aqueous solutions and by the addition of a few drops of base (sodium methoxide solution for methanolic solutions and sodium hydroxide solution for aqueous solutions). The solutions were stirred over night with a magnetic stirrer at constant temperature as given above. Then the solutions were filtered to remove undissolved paraformaldehyde. The heterogeneous ion exchange resin Amberlyst 46 from Rohm and Haas was used as acidic catalyst for the OME synthesis. This catalyst shows a reduced formation of the side products dimethlylether and methyl formate. 21 Before each experiment, the catalyst was dried in a vacuum



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oven at a pressure < 10 mbar and a temperature of 343.15 K as the catalyst is supplied in wet from. This enables an accurate determination of the dry mass of catalyst used in each experiment and avoids uncontrolled carryover of water into the reaction system.

Analysis The overall mass fractions of methanol, methylal and all OME (up to n = 8) in chemical equilibrium were analyzed with gas chromatography (GC) using 1-4-dioxane as internal standard and a flame ionization detector (FID). The calibration was carried out using the pure components methanol, methylal and OME2 to OME4 . For OME with n > 4, the calibration factors are extrapolated assuming that the FID signal is linear in the number of carbon atoms of the molecule. More details on the GC method are given in the supporting information. The relative errors for the overall mass fractions are less than 5% for methanol and less than 2% for methylal and OME2 to OME4 . This was checked by the analysis of samples that were prepared gravimetrically containing formaldehyde, methanol, methylal and OME2 to OME4 . The accuracy for all OME with n > 4 could not be tested but the uncertainty is assumed to be below 5%. 21 The overall mass fraction of formaldehyde in chemical equilibrium was analyzed by the sodium sulfite titration method using hydrochloric acid as titer with an accuracy of 2%. 29 The overall mass fraction of water in chemical equilibrium was analyzed using Karl Fischer titration. Analysis of test samples (water in methanol) shows relative errors of 2% for the water mass fraction. The consistency of the results was further checked by the summation of all overall mass fractions in chemical equilibrium, which is between 0.97 g/g and 1.03 g/g for all experiments. All overall mass fractions were then normalized by proportional weighing to a sum of 1 g/g to provide a consistent set of data for the model development.

Apparatus and experimental procedure The chemical equilibrium was measured in a stirred batch reactor manufactured from borosilicate glass and stainless steel. A schematic of the reactor is given in Figure 1. The reactor has a volume 6 ACS Paragon Plus Environment

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of 1.5 L and is thermostated with a double jacket (TIC) connected to an oil bath (H1). The temperature is measured with a Pt 100 resistance thermometer with an accuracy of ± 0.05 K. The pressure is measured with a membrane pressure indicator with an accuracy of ± 0.1 bar (PI). The stirrer ensures the homogeneity of the reacting mixture. The catalyst is added to the reacting mixture from a ductile tube that can be divided into two compartments with a clamp (S1). Educt mixtures were prepared by mixing of methanolic- and aqueous formaldehyde solution in different ratios before the reactor was filled through the valve V1. Then the reactor was sealed pressure-tight and pressurized with a nitrogen atmosphere (absolute pressure in the reactor at least 2 bar) to prevent boiling of the mixture. Then the catalyst was released into the reactor by removing the clamp and the reaction starts. The reacting mixture is kept at least for six hours at each reaction temperature to ensure that the chemical equilibrium is established. This was checked by consecutive sampling and preliminary analysis. Test experiments with reaction times up to 48 hours did not yield different results for the equilibrium composition. Samples were drawn through the sampling valve V2. After studying the equilibrium at one temperature, the mixture was brought to the next temperature, for which the measurement procedure was repeated.

Experimental program The educt mixtures comprise three overall components: formaldehyde, methanol and water. Thus, considering that the sum of all overall mass fractions must be unity, there are two degrees of freedom for an unambiguously characterization of the overall composition of the educt mixture. The overall ratio of formaldehyde to methanol (per mass) and the overall mass fraction of water are chosen as independent variables. The compositions of the educt mixtures that were investigated in this work are illustrated in Figure 2. A wide range of compositions for the educt mixtures is covered. Additionally, an educt mixture from an experiment of Drunsel 24 is shown, in which the formation of OME was not observed. For each educt mixture E1 to E11, the chemical equilibrium was studied at four different temperatures: 333.15 K, 348.15 K, 363.15 K and 378.15 K. In each experiment, the total mass of 7 ACS Paragon Plus Environment


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liquid educts was about 800 g, the total mass of dry catalyst was about 40 to 50 g, the exact data are given in the supporting information.

Experimental results Numerical results for the overall mass fractions in chemical equilibrium for all experiments are given in the supporting information. The discussion of the experimental results is carried out below along with the discussion of the model.

NMR experiments Quantitative 13 C-nuclear magnetic resonance (NMR) spectroscopy is used to investigate the chemical equilibrium of the formation of poly(oxymethylene) glycols and poly(oxymethylene) hemiformals (reactions (1) to (4)) in the presence of actetals, such as methylal and OME, as no such information was previously available in literature. For this purpose, aqueous- and methanolic formaldehyde solution, respectively, were mixed with methylal and the true species distribution at 293.15 K was determined from the NMR spectra. The overall composition of the investigated mixtures is given in the captions of Figure 8 for the methanolic system and Figure 9 for the aqueous system, respectively. The NMR experiments are carried using a 400 MHz spectrometer from Bruker. Technical details on the NMR experiments and the spectra including the peak identification are given in the supporting information.

Mole fraction-based model of the chemical equilibrium In this section a mole fraction-based model of the chemical equilibrium is presented. The mole fraction-based approach is however not consistent if the model is combined with a model of the vapor-liquid equilibrium (VLE), e.g. for describing reactive distillation. For this reason, a second model with chemical equilibrium constants based on activities is presented in the subsequent


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section. The mole fraction-based chemical equilibrium constant Kx (T ) of a reaction with NC components is given by Eq. (10), NC

Kx (T ) = ∏ xiνi

(10)

i=1

where xi is the true mole fraction of each component in chemical equilibrium and νi is the stoichiometric coefficient of each component i. Eq. (10) is valid for each of the reactions (1) to (7). The algebraic sign of νi is positive for the products on the right-hand side of reactions (1) to (7) and negative for the educts. A two-step procedure is used to determine the mole fraction-based chemical equilibrium constants from the measured overall composition in the experiments of the OME synthesis. Step one is the model-based calculation of the true mole fractions of poly(oxymethylene) glycols and poly(oxymethylene) hemiformals in chemical equilibrium. For this purpose a mole fractionbased model of the chemical equilibrium of the formation of poly(oxymethylene) glycols and poly(oxymethylene) hemiformals (reactions (1) to (4)) is applied. The mole fraction-based chemical equilibrium constants of reactions (1) to (4) are taken from Hahnenstein et al., 25 c.f. Table 2 for temperature-dependent correlations of the chemical equilibrium constants. In the calculations, the measured overall compositions in chemical equilibrium are taken as educt compositions and reactions (1) to (4) are brought to the equilibrium via simulation using Eq. (10). Methylal and the OME are treated as chemically inert in this step. In these calculations, the chain length of poly(oxymethylene) glycols and poly(oxymethylene) hemiformals is limited to n = 10. For both, the calculated true mole fraction never exceeded the order of 10−4 mol/mol at chain length n = 10. In step two, the true mole fractions of all components including the OME are inserted into Eq. (10) to determine the mole fraction-based chemical equilibrium constants of reactions (5) to (7). For each temperature, the chemical equilibrium constants are calculated as the arithmetic mean of all 11 different educt mixtures. The relative standard deviation of ln(Kx ) at each temperature is smaller than 10% for the formation of methylal (reaction (5)) and smaller than 2% for the formation of OME2 to OME4 (reactions (6) and (7)). The rather large relative standard deviation for the 9 ACS Paragon Plus Environment


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formation of methylal results from the low sensitivity of the corresponding chemical equilibrium constant on the calculated overall mass fractions in chemical equilibrium. In a representative example (experiment E1 at 333.15 K), increasing ln(Kx ) for the formation of methylal by 10% results in a maximum absolute deviation in the calculated overall mass fractions in chemical equilibrium of 0.01 g/g. The chemical equilibrium constants Kx (T ) are plotted in a logarithmic diagram over the inverse temperature (van’t Hoff plot) in Figure 3 for reaction (5) and in Figure 4 for reactions (6) and (7). In Figure 4, it can be seen that the chemical equilibrium constants Kx (T ) of the OME formation (reactions (6) and (7)) do not depend on the chain length n. This was also previously observed for the OME synthesis from methylal and trioxane. 21 The absolute values of Kx (T ) are however different. This can be explained by the different chemical environments (non aqueous vs. aqueous). Further, Burger et al. have noted that the absolute values of Kx (T ) for the OME synthesis from methylal and trioxane may have a large experimental error. 21 The temperature dependence of the chemical equilibrium constants is modeled by the correlation in Eq. (11), the integrated van’t Hoff equation with parameters A and B.

ln Kx (T ) = A +

B T /K

(11)

The parameters A and B for the formation of methylal (reaction (5)) are fitted to the chemical equilibrium constants given in Figure 3. The parameters of one common equilibrium constant for all reactions (6) to (7) (formation of all OME) are fitted to the arithmetic mean of the determined chemical equilibrium constants Kx (T ) (calculated at each investigated temperature) for the formation of OME2 (reaction (6)), OME3 (reaction (7), n = 3) and OME4 (reaction (7), n = 4). The model is shown as solid line in Figure 3 and Figure 4, respectively. The resulting parameters A and B, both for the formation of methylal and all OME, are given in Table 3. The reaction enthalpy ∆R h is estimated from the van’t Hoff parameter B with Eq. (12), ∆R h = −R · B 10 ACS Paragon Plus Environment

(12)

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where R denotes the universal gas constant. The estimated reaction enthalpy is -25.2 kJ/mol for the formation of all OME (reactions (6) to (7)), i.e. the reactions are slightly exothermic. Because of the rather high standard deviation of ln(Kx ) for the formation of methylal (reaction (5)), the reaction enthalpy of this reaction is not estimated. Despite the uncertainty, the absolute value of the reaction enthalpy of the methylal formation is however in the same small order as for the OME formation.

Model validation For experiment E1 at 333.15 K, the experimentally determined overall mass fractions in chemical equilibrium are compared to the model calculations in Figure 5. In the calculations, the chain length of OME is limited to n = 8, as this is the largest OME chain length that is detected analytically. Increasing the OME chain length up to n = 10 did not significantly affect the model results. In Figure 5, it can be seen that the agreement between experiment and model is good. Parity plots, including all experiments, for the calculated and the experimentally determined overall mass fractions are given in Figure 6. They show good agreement between experiments and model. The arithmetic mean value of the absolute deviations between experimental and calculated overall mass fractions is 0.0047 g/g. This shows that the model is able to accurately describe the chemical equilibrium for all investigated educt mixtures and temperatures. In addition, Figure 7 shows the comparison between the model calculations and the experimental results of Drunsel. 24 The model results for this experiment are fully predictive, as this experiment was not included in the parameter estimation process. Again, the agreement between experiment and model is good. The model confirms that OME are not formed in quantifiable amounts, as has been observed by Drunsel 24 (the calculated overall mass fraction of OME2 is in the order of 10-4 g/g). Consequently, the model also accurately describes the chemical equilibrium in the studied educt mixtures with low overall mass fractions of formaldehyde. The mole fraction-based model of the chemical equilibrium in the subsystem formaldehyde, methanol and water 25 (i.e. the formation of poly(oxymethylene) glycols and poly(oxymethylene) 11 ACS Paragon Plus Environment


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hemiformals) is used for the calculation of the true mole fractions in chemical equilibrium. To check whether the chemical equilibrium constants of the model are also reliable if acetals, such as methylal and OME, are present in the mixture, the model predictions (treating methylal as inert component) of the true molar ratio of poly(oxymethylene) glycols and poly(oxymethylene) hemiformals) of different chain lengths to methylal are compared to those obtained from the NMR experiments. The results are shown in Figure 8 for the methanolic system and in Figure 9 for the aqueous system. The model predictions show only little deviation from the experiments. Thus, the mole fraction-based model of the chemical equilibrium in the system formaldehyde, methanol and water 25 is able to describe the true mole fractions, also when acetals are present.

Activity-based model of the chemical equilibrium The approach for modeling of the chemical equilibrium using activity-based chemical equilibrium constants is similar to the mole fraction-based equilibrium model. In this case Eq. (10) is replaced by Eq. (13), NC

NC

i=1

i=1

Ka (T ) = ∏ aνi i = ∏(xi · γi )νi

(13)

where, additionally to Eq. (10), ai is the activity of any true component i in chemical equilibrium and γi is the corresponding activity coefficient. To describe the activity coefficients, the UNIFACbased activity coefficient model of the system formaldehyde, water, methanol and methylal by Kuhnert et al. 29 is adopted and augmented by OME. OME of chain length n are modeled by the already available groups methylal (H3 C−O−(CH2 O)−CH3 ) (one occurence) and formaldehyde (CH2 O) (n − 1 occurrences). Hence the calculation of the OME activity coefficients is fully predictive. A three step-procedure is used to determine the activity-based chemical equilibrium constants from the measured overall composition in the experiments of the OME synthesis. Step one is the model-based calculation of the true mole fractions in chemical equilibrium. Activity-based chemical equilibrium constants of reactions (1) to (4) (i.e. the formation of poly(oxymethylene) 12 ACS Paragon Plus Environment

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glycols and poly(oxymethylene) hemiformals) are taken from Drunsel et al., 28 c.f. Table S17 in the supporting information. The measured overall compositions in chemical equilibrium are taken as educt compositions and reactions (1) to (4) are brought to the equilibrium via simulation using Eq. (13). Methylal and OME are treated as chemically inert in this step. The chain length of poly(oxymethylene) glycols and poly(oxymethylene) hemiformals is limited to n = 10. The calculated product compositions are the true mole fractions of each component in chemical equilibrium. In step two, the activity coefficients of all true components are calculated from the true mole fractions using the UNIFAC-model. In step three, the true mole fractions and the activity coeffcients are inserted into Eq. (13) to determine the activity-based chemical equilibrium constants Ka for reactions (5) to (7). For each temperature, the chemical equilibrium constants are calculated as the arithmetic mean of all 11 different educt mixtures. The relative standard deviation of ln(Ka ) at each temperature is smaller than 13% for the formation of methylal (reaction (5)) and smaller than 3% for the formation of all OME (reactions (6) and (7)). The van’t Hoff plots for the activity-based chemical equilibrium model are given Figure 12 for the formation of methylal (reaction (5)) and in Figure 13 for the formation of OME (reactions (6) to (7)). The van’t Hoff parameters A and B for the formation of methylal (reaction (5)) are fitted to the chemical equilibrium constants given in Figure 12. The parameters of a common equilibrium constant for all reactions (6) to (7) (formation of all OME) are fitted to the arithmetic mean of the chemical equilibrium constants Ka (T ) (calculated at each investigated temperature) for the formation of OME2 (reaction (6)), OME3 (reaction (7), n = 3) and OME4 (reaction (7), n = 4). The resulting parameters A and B, both for the formation of methylal and all OME, are given in Table S18 in the supporting information. Figure 14 shows a comparison between experimental results and calculations using the activitybased chemical equilibrium model for the overall mass fractions in chemical equilibrium for experiment E1 at 333.15 K. The agreement between experiment and model is good. The arithmetic mean value of the absolute deviations between experimentally determined overall mass fractions in chemical equilibrium and calculated overall mass fractions is 0.0063 g/g, i.e the activity-based



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model does not increase the accuracy compared to mole fraction-based model. Parity plots for the overall mass fractions in equilibrium using the activity-based model are given in the supporting information. A comparison between the NMR experiments and the activity-based chemical equilibrium model (true species distribution) is also given in the supporting information and shows good agreement.

Discussion Figure 10 shows four equilibrium compositions calculated with the mole fraction-based chemical equilibrium model for three different educt compositions and two different temperatures. In the right column, the chain length distribution (per mass) of OME in the chemical equilibrium is given as additional pie chart for each equilibrium composition. The educt mixtures in rows one and two differ in the overall ratio of formaldehyde to methanol. Increasing this ratio shifts the chemical equilibrium towards longer chain lengths of OME and consequently less methylal is formed. The reason is that the reactions of the formation of all OME (reactions(6) and (7)) use formaldehyde as educt, which is present in higher quantities in row two. Row three differs from the row two in the amount of water. It can be seen that the presence of water decreases the overall mass fractions of methylal and OME in chemical equilibrium. As water is a product of the formation of methylal (c.f. reaction (5)), the chemical equilibrium of this reaction is shifted to the educt side. In addition, water bounds formaldehyde in poly(oxymethylene) glycols reducing the formaldehyde available for OME formation and thus leading to rather shorter OME chain lengths. The influence of temperature is shown in row four (T = 378.15 K), in which the composition of the educt mixture is identical to row three (T = 333.15 K). The influence of the temperature on the equilibrium composition is negligible. This result is confirmed by the low reaction enthalpies for the formation of methylal and all OME (reactions (5) to (7)). An important result is the influence of the composition of the educt mixture on the combined mass fraction of OME in equilibrium. This is illustrated in Figure 11. High yields of OME are


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obtained for a high overall ratio of formaldehyde to methanol and a low overall amount of water in the educt mixture.

Conclusion In this work the chemical equilibrium of the OME synthesis from formaldehyde and methanol in aqueous solutions was studied. Experiments to determine the compositions in chemical equilibrium at varying educt compositions and temperatures were carried out in a stirred batch reactor using a heterogeneous acidic catalyst. Two different models (mole fraction-based and activity-based) for describing the chemical equilibrium were developed in this work. Both models explicitly account for the formation of poly(oxymethylene) glycols and poly(oxymethylene) hemiformals using literature models 25,28,29 of the chemical equilibrium in the system formaldehyde, methanol and water. NMR experiments confirmed that these models of the chemical equilibrium give reliable results, also in the presence of acetals. The ratio of two OME of different chain lengths in chemical equilibrium was found to be independent of the OME chain length, i.e. the mole fraction-based chemical equilibrium constant for the formation of all OME is independent of the OME chain length. High yields of OME were obtained for a high overall ratio of formaldehyde to methanol and a low overall amount of water in the educt mixture. The temperature was found to have negligible influence on the equilibrium composition. This work shows that the direct synthesis of OME from the educts formaldehyde and methanol in aqueous solutions is a promising alternative to the synthesis from the intermediates trioxane and methylal. The yields of OME are comparably smaller, but the production processes for trioxane and methylal are omitted. The model for the chemical equilibrium is essential for the conceptual design of a process producing OME from the educts formaldehyde and methanol in aqueous solutions and is an important basis for future comparison of both synthesis routes.



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

Nomenclature Abbreviations: FA

Formaldehyde

FID

Flame Ionization Detector

GC

Gas Chromatograph

GtL

Gas-to-Liquid

HF

Poly(oxymethylene) hemiformal

MEFO

Methyl formate

MeOH

Methanol

MG

Poly(oxymethylene) glycol

NMR

Nuclear Magnetic Resonance

OME

Poly(oxymethylene) Dimethyl Ethers

PI

Pressure Indication

TIC

Temperature Indication and Control

TRI

Trioxane

UNIFAC

Universal Quasichemical Functional Group Activity Coefficients

VLE

Vapor-Liquid Equilibrium

Symbols and indices: ai

Activity of component i

A, B, C, D Temperature correlation parameters

γi

Activity coefficient of component i

H+

Proton (Acid-catalyzed)

∆R h

Reaction enthalpy

Ka

Acitvity-based chemical equilibrium constant

Kx

Mole fraction-based chemical equilibrium constant 16 ACS Paragon Plus Environment

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Page 17 of 34

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


m˜ i

Overall mass of component i

n

Oligomer chain length

ni

True amount of substance of component i

NC

Number of components

νi

Stoichiometric coefficient of component i

R

Universal gas constant ( = 8.3145 J/(mol·K))

T

Temperature

xi

True mole fraction of component i

(m)

x˜i

Overall mass fraction of component i

Acknowledgement J. B. is grateful for financial support by BASF SE.

Supporting Information Available • Experiments on the OME synthesis: Numerical results • Gas chromatography: Configuration, Extrapolation of the calibration factor • NMR spectroscopy: Configuration, Spectra and peak identification, Numerical results • Activity-based model of the chemical equilibrium: Parameters and correlations for the calculation of Ka (T ) for each reaction, Parity plots, Comparison between NMR experiments and activity-based model of the chemical equilibrium This material is available free of charge via the Internet at http://pubs.acs.org/.



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

References 1. Lumpp, B.; Rothe, D.; Pastötter, C.; Lämmermann, R.; Jacob, E. Oxymethylene ethers as diesel fuel additives of the future. MTZ 2011, 72, 34–38. 2. Fleisch, T. H.; Sills, R. A. Large-scale gas conversion through oxygenates: beyond GTL-FT. Studies in Surface Science and Catalysis, Natural Gas Conversion VII, Proceedings of the 7th Natural Gas Conversion Symposium 2004, 147, 31–36. 3. Burger, J.; Siegert, M.; Ströfer, E.; Hasse, H. Poly(oxymethylene) dimethyl ethers as components of tailored diesel fuel: Properties, synthesis and purification concepts. Fuel 2010, 89, 3315–3319. 4. Devaux, D.; Yano, H.; Uchida, H.; Dubois, J.-L.; Watanabe, M. Electro-oxidation of hydrolysed poly-oxymethylene-dimethylether on PtRu supported catalysts. Electrochim. Acta 2011, 56, 1460–1465. 5. Baranton, S.; Uchida, H.; Tryk, D. A.; Dubois, J. L.; Watanabe, M. Hydrolyzed polyoxymethylenedimethylethers as liquid fuels for direct oxidation fuel cells. Electrochim. Acta 2013, 108, 350–355. 6. Fiedler, E.; Grossmann, G.; Kersebohm, D. B.; Weiss, G.; Witte, C. Methanol, Ullmann’s Encyclopedia of Industrial Chemistry; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, Germany, 2000. 7. Li, X. Y.; Yu, H. B.; Sun, Y. M.; Wang, H. B.; Guo, T.; Le Sui, Y.; Miao, J.; Zeng, X. J.; Li, S. P. Synthesis and application of polyoxymethylene dimethyl ethers. Appl. Mech. Mater. 2013, 448-453, 2969–2973. 8. Shi, M.; Liu, D.; Zhao, G.; Fang, D.; Luo, W.; Liu, W.; Liu Hongwei,; Wang, J.; Li, C. Catalytic synthesis of polyoxymethylene dimethyl ethers from methanol and formaldehyde. CIESC J. 2013, 64, 931–935. 18 ACS Paragon Plus Environment

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9. Wang, L.; Wu, W.-T.; Chen, T.; Chen, Q.; He, M.-Y. Ion-exchange resin-catalyzed synthesis of polyoxymethylene dimethyl ethers: A practical and environmentally friendly way to diesel additive. Chem. Eng. Commun. 2014, 201, 709–717. 10. Zhang, J.; Fang, D.; Liu, D. Evaluation of Zr-alumina in production of polyoxymethylene dimethyl ethers from methanol and formaldehyde: Performance tests and kinetic investigations. Ind. Eng. Chem. Res. 2014, 53, 13589–13597. 11. Zhang, J.; Shi, M.; Fang, D.; Liu, D. Reaction kinetics of the production of polyoxymethylene dimethyl ethers from methanol and formaldehyde with acid cation exchange resin catalyst. React. Kinet. Mech. Cat. 2014, 11, 459–470. 12. Zhao, Q.; Wang, H.; Qin, Z.-f.; Wu, Z.-w.; Wu, J.-b.; Fan, W.-b.; Wang, J.-g. Synthesis of polyoxymethylene dimethyl ethers from methanol and trioxymethylene with molecular sieves as catalysts. J. Fuel Chem. Technol. 2011, 39, 918–923. 13. Zheng, Y.; Tang, Q.; Wang, T.; Liao, Y.; Wang, J. Synthesis of a green fuel additive over cation resins. Chem. Eng. Technol. 2013, 36, 1951–1956. 14. Zhao, Y.; Xu, Z.; Chen, H.; Fu, Y.; Shen, J. Mechanism of chain propagation for the synthesis of polyoxymethylene dimethyl ethers. J. Energ. Chem. 2013, 22, 833–836. 15. Wu, Q.; Wang, M.; Hao, Y.; Li, H.; Zhao, Y.; Jiao, Q. Synthesis of polyoxymethylene dimethyl ethers catalyzed by Brønsted acid ionic liquids with alkanesulfonic acid groups. Ind. Eng. Chem. Res. 2014, 53, 16254–16260. 16. Wu, J.; Zhu, H.; Wu, Z.; Qin, Z.; Yan, L.; Du, B.; Fan, W.; Wang, J. High Si/Al ratio HZSM5 zeolite: an efficient catalyst for the synthesis of polyoxymethylene dimethyl ethers from dimethoxymethane and trioxymethylene. Green Chem. 2015, 17, 2353–2357. 17. Fang, X.; Chen, J.; Ye, L.; Lin, H.; Yuan, Y. Efficient synthesis of poly(oxymethylene)



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dimethyl ethers over PVP-stabilized heteropolyacids through self-assembly. Sci. China Chem. 2015, 58, 131–138. 18. Fu, W. H.; Liang, X. M.; Zhang, H.; Wang, Y. M.; He, M. Y. Shape selectivity extending to ordered supermicroporous aluminosilicates. Chem. Commun. 2015, 51, 1449–1452. 19. Zhang, X.; Kumar, A.; Arnold, U.; Sauer, J. Biomass-derived oxymethylene ethers as diesel additives: a thermodynamic analysis. Energy Procedia 2014, 61, 1921–1924. 20. Burger, J.; Hasse, H. Multi-objective optimization using reduced models in conceptual design of a fuel additive production process. Chem. Eng. Sci. 2013, 99, 118–126. 21. Burger, J.; Ströfer, E.; Hasse, H. Chemical equilibrium and reaction kinetics of the heterogeneously catalyzed formation of poly(oxymethylene) dimethyl ethers from methylal and trioxane. Ind. Eng. Chem. Res. 2012, 51, 12751–12761. 22. Burger, J.; Ströfer, E.; Hasse, H. Production process for diesel fuel components poly(oxymethylene) dimethyl ethers from methane-based products by hierarchical optimization with varying model depth. Chem. Eng. Res. Des. 2013, 91, 2648–2662. 23. Grützner, T.; Hasse, H.; Lang, N.; Siegert, M.; Ströfer, E. Development of a new industrial process for trioxane production. Chem. Eng. Sci. 2007, 62, 5613–5620. 24. Drunsel, J.-O. Entwicklung von Verfahren zur Herstellung von Methylal und Ethylal. Ph.D. thesis, TU Kaiserslautern, Kaiserslautern, 2012. 25. Hahnenstein, I.; Albert, M.; Hasse, H.; Kreiter, C. G.; Maurer, G. NMR spectroscopic and densimetric study of reaction kinetics of formaldehyde polymer formation in water, deuterium oxide, and methanol. Ind. Eng. Chem. Res. 1995, 34, 440–450. 26. Hahnenstein, I.; Hasse, H.; Kreiter, C. G.; Maurer, G. 1H- and 13C-NMR-spectroscopic study of chemical equilibria in solutions of formaldehyde in water, deuterium oxide, and methanol. Ind. Eng. Chem. Res. 1994, 33, 1022–1029. 20 ACS Paragon Plus Environment

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27. Maiwald, M.; Fischer, H. H.; Ott, M.; Peschla, R.; Kuhnert, C.; Kreiter, C. G.; Maurer, G.; Hasse, H. Quantitative NMR spectroscopy of complex liquid mixtures: methods and results for chemical equilibria in formaldehyde−water−methanol at Temperatures up to 383 K. Ind. Eng. Chem. Res. 2003, 42, 259–266. 28. Drunsel, J.-O.; Renner, M.; Hasse, H. Experimental study and model of reaction kinetics of heterogeneously catalyzed methylal synthesis. Chem. Eng. Res. Des. 2012, 90, 696–703. 29. Kuhnert, C.; Albert, M.; Breyer, S.; Hahnenstein, I.; Hasse, H.; Maurer, G. Phase equilibrium in formaldehyde containing multicomponent mixtures: Experimental results for fluid phase equilibria of (formaldehyde + (water or methanol) + methylal)) and (formaldehyde + water + methanol + methylal) and comparison with predictions. Ind. Eng. Chem. Res. 2006, 45, 5155–5164.



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

Table 1: Overview of the literature reporting on the synthesis of OME from different educts Educt 1

Educt 2

Authors

Burger et al. 3,20–22 , Fu et al., 18 Shi et al. 8 , Wang et al. 9 , Wu et al. 15 , Wu et al. 16 Methylal Paraformaldehyde Li et al. 7 , Zhao et al. 14 , Zheng et al. 13 Methanol Trioxane Fang et al., 17 Zhao et al. 12 Methanol Aqueous formaldehyde solution Zhang et al., 10,11 This work Methylal

Trioxane

Table 2: Parameters for the calculation of the mole fraction-based chemical equilibrium constant Kx (T ) for the formation of poly(oxymethylene) glycols and poly(oxymethylene) hemiformals (reactions (1) to (4)) using the correlation: ln Kx (T ) = A + B/(T /K). 25 Reaction (1) (2) (n = 2) (2) (n ≥ 3) (3) (4)

A

B

-2.3250 -2.3105 -2.4334 -1.9020 -2.2496

2579.0 3139.9 3039.4 3512.0 3008.8

Table 3: Parameters for the calculation of the mole fraction-based chemical equilibrium constant Kx (T ) for the formation of methylal and all OME (reactions (5) to (7)) using the correlation: ln Kx (T ) = A + B/(T /K). Reaction

A

B

(5) (6) & (7)

0.8147 -2.4154

340.25 3029.6


Page 22 of 34

Page 23 of 34

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


H2 V1

V2

S1 PI TIC

H1 Figure 1: Schematic of the reactor used for the measurement of the chemical equilibrium. V1: filling valve, V2: sampling valve, H1: thermostat, H2: sample cooler, S1: catalyst feeding, TIC: temperature indication and control, PI: pressure indication



0.4

0.3 E2

H O

E6

E3

0.2

(

2

xm

)

/ (g/g)

E4

E11

E10

Dru 0.1 E5 E8 0.0

0.0

0.4

E7 E1

0.8 /

E9

1.2

m m FA

1.6

MeOH

Figure 2: Overall ratio of formaldehyde to methanol (per mass) and overall mass fraction of water of the educt mixtures E1 to E11 (◦) for which the chemical equilibrium is studied in the present work. In addition, an educt mixture of Drunsel is shown () who did not observe the formation of OME. 24

K

x

2.0

ln

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

Page 24 of 34

1.8

1.6

2.6

2.7

2.8

2.9

3.0

3.1

T

1000 / ( /K)

Figure 3: Experimentally determined mole fraction-based chemical equilibrium constant Kx (T ) of the formation of methylal () according to reaction (5) in a logarithmic plot over the inverse temperature (van’t Hoff plot). The solid line (-) indicates the model and the error bars indicate the standard deviation over all experiments.


Page 25 of 34

7.5

x

7.0

ln K

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


6.5 6.0 5.5 5.0

2.6

2.7

2.8

2.9

3.0

3.1

T

1000 / ( /K)

Figure 4: Experimentally determined mole fraction-based chemical equilibrium constant Kx (T ) of the formation of OME2 (△) according to reaction (6), OME3 (◦) and OME4 (▽) according to reaction (7) in a logarithmic plot over the inverse temperature (van’t Hoff plot). The solid line (-) indicates the model, which is independent of the OME chain length. The error bars indicate the standard deviation over all experiments.



92 % 92 %

76 %

94 %

0.4 Exp.

Kx-Model

0.3

95 %

0.2

0.1

4

0.0

F W A a t M er e O H M A L O M E O 2 M E O 3 M E

overall mass fraction / (g/g)

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

Page 26 of 34

Figure 5: Comparison between the experiment and model results using the mole fraction-based equilibrium constants for the overall mass fractions in chemical equilibrium for experiment E1 at 333.15 K.


Page 27 of 34

i,Model

(a)

0.4 0.3 0.2

x

(m)

/ (g/g)

0.5

0.1

0.0

0.1

0.2 (m)

x

i,Exp

i,Model

(m)

/ (g/g)

0.2

0.3

0.4

0.5

/ (g/g)

(b)

0.1

x

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


0.0

0.1 (m)

x

i,Exp

0.2

/ (g/g)

Figure 6: Parity plots for the overall mass fractions in chemical equilibrium for all investigated educt mixtures and temperatures. The model calculations are carried out using the mole fractionbased model of the chemical equilibrium. (a) Formaldehyde (N), water (•), methanol (H), methylal (), (b) OME2 (△), OME3 (◦), OME4 (▽)



92 % 92 %

0.6

Exp.

Kx-Model

0.5 0.4 0.3 0.2 0.1 0.0

A L M

M

e

W a

te

O H

r

76 %

F A


76 %

92 %

92 %

Figure 7: Comparison between the experiment and the model results using the mole fraction-based equilibrium constants for the overall mass fractions in chemical equilibrium for the experiment of Drunsel 24 at 333.15 K.

Exp.

Kx-Model

2

i

/

n

MAL

3

n

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

Page 28 of 34

1 0

MeOH HF1

HF2

HF3

Figure 8: Comparison between NMR experiment and mole fraction-based chemical equilibrium model 25 for the true molar ratios of methanol and poly(oxymethylene) hemiformals (n = (m) (m) 1 − 3) to methylal at 293.15 K. Overall composition: x˜FA = 0.3633 g/g, x˜MeOH = 0.4189 g/g, (m)

(m) 2O

x˜MAL = 0.2044 g/g, x˜H

= 0.0134 g/g.


Page 29 of 34

92 % 92 %

76 %

1.0 Exp.

0.5

i

/

n

MAL

Kx-Model

n

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


0.0 MG

1

MG

MG

2

3

MG

4

Figure 9: Comparison between NMR experiment and mole fraction-based chemical equilibrium model 25 for the true molar ratios of poly(oxymethylene) gylcols (n = 1 − 4) to methylal (m) (m) (m) at 293.15 K. Overall composition: x˜FA = 0.2322 g/g, x˜H O = 0.5679 g/g , x˜MAL = 0.1999 g/g. 2



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

Educt composition

Overall mass fractions in chemical equilibrium

Page 30 of 34

Chain length distribution of OME (per mass)

OME FA

OME3

OME4

H2O mFA/mMeOH = 0.47 = 0 g/g x(m) HO 2

T = 333.15 K

MeOH

MAL

OME2

OME>5 OME FA

mFA/mMeOH = 1.41 x

(m) H2O

= 0 g/g

OME5 OME2 OME4

T = 333.15 K MAL

H2O

OME3

MeOH

OME5 OME>5

OME MAL

FA

mFA/mMeOH = 1.41

OME4

x(m) = 0.2 g/g HO

OME2

2

T = 333.15 K

MeOH

OME3 H2 O

OME5 OME>5

OME MAL

FA

mFA/mMeOH = 1.41

OME4

x(m) = 0.2 g/g HO

OME2

2

T = 378.15 K

MeOH

OME3 H2O

Figure 10: Compositions in equilibrium for different educt compositions and temperatures (c.f. left column). Middle column: Overall mass fractions of different species corresponding to the educt composition and temperature given in the left column. Right column: Chain length distribution (per mass) of OME. The calculations are carried out using the mole fraction-based chemical equilibrium model.


Page 31 of 34

0.3

xm (

)

H O

/ (g/g)

(

)

H O

=0.1 g/g

2

OME

)

xm

0.2

xm (

=0 g/g

2

xm (

0.1

)

H O

=0.3 g/g

2

0.0 0.5

1.0

1.5

m m /

FA

MeOH

Figure 11: Combined overall mass fraction of OME2 to OME8 in chemical equilibrium dependent on the composition of the educt mixture. The calculations are carried out using the mole fractionbased model of the chemical equilibrium at 333.15 K.

3.0

a

2.8

ln K

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


2.6 2.4 2.2 2.0

2.6

2.7

2.8

2.9

3.0

3.1

T

1000 / ( /K)

Figure 12: Activity-based chemical equilibrium constant Ka (T ) of the formation of methylal () according to reaction (5) in a logarithmic plot over the inverse temperature (van’t Hoff plot). The solid line (-) indicates the model and the error bars indicate the standard deviation over all experiments.



6.0

a

5.5

ln K

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

Page 32 of 34

5.0 4.5 4.0 3.5 3.0

2.6

2.7

2.8

2.9

3.0

3.1

T

1000 / ( /K)

Figure 13: Activity-based chemical equilibrium constant Ka (T ) of the formation of OME2 (△) according to reaction (6), OME3 (◦) and OME4 (▽) according to reaction (7) in a logarithmic plot over the inverse temperature (van’t Hoff plot). The solid line (-) indicates the model, which is independent of the OME chain length. The error bars indicate the standard deviation over all experiments.


Page 33 of 34

92 % 92 %

76 %

94 %

0.4 Exp.

Ka-Model

0.3

0.2

0.1

4

0.0

F W A a t M er e O H M A L O M E O 2 M E O 3 M E


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


Figure 14: Comparison between the experiment and model results using the activity-based equilibrium constants for the overall mass fractions in chemical equilibrium for experiment E1 at 333.15 K.


95 %

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

Page 34 of 34

Model


Exp.

Experiments

Modeling For Table of Contents only


Validation

Chemical Equilibrium of the Synthesis of Poly(oxymethylene) Dimethyl

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