Article pubs.acs.org/IECR
Reaction Kinetics of the Formation of Poly(oxymethylene) Dimethyl Ethers from Formaldehyde and Methanol in Aqueous Solutions Niklas Schmitz, Jakob Burger,* and Hans Hasse Laboratory of Engineering Thermodynamics, University of Kaiserslautern, 67663 Kaiserslautern, Germany S Supporting Information *
ABSTRACT: Poly(oxymethylene) dimethyl ethers (OME) are attractive oxygenated fuel additives and physical solvents for the absorption of carbon dioxide. This works studies the synthesis of OME from formaldehyde and methanol in aqueous solutions. The reaction kinetics of OME formation is studied experimentally in a stirred batch reactor on a laboratory scale using the heterogeneous catalyst Amberlyst 46. The influences of the ratio of formaldehyde to methanol, the amount of water, and the temperature (303.15−363.15 K) are investigated. A model of the reaction kinetics is developed that differentiates two competing reaction mechanisms. The model explicitly accounts for the intermediates poly(oxymethylene) hemiformals and poly(oxymethylene) glycols.
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INTRODUCTION Poly(oxymethylene) dimethyl ethers (OME) are a class of oxygenates that reduce soot formation in diesel engines.1,2 In addition, OME are also attractive as fuels in direct oxidation fuel cells3,4 and as physical solvents for the absorption of carbon dioxide from natural gas.5 All known synthesis routes for the OME production start from methanol, which in turn is produced from synthesis gas.6,7 Hence, the synthesis of OME is an opportunity for producing fuels and chemicals on the basis of renewable feedstocks.8 The chemical structure of OME is H3C−O−(CH2O)n−CH3 with n ≥ 2. OME are synthesized from two different reactants, one providing the methyl end group and the other providing the monomer unit formaldehyde. In the early work of Gresham and Brooks9 and Boyd,10 OME were prepared from methylal and various formaldehyde reactants. For the OME production from methylal and trioxane, Burger et al. investigated the chemical equilibrium and the reaction kinetics11 and conceptually designed a production process.12,13 The reactants methylal and trioxane have to be produced, however, from formaldehyde and methanol in intermediate process steps.14,15 The direct synthesis of OME from formaldehyde and methanol in aqueous solutions is an interesting short-cut in the value added chain.16 Water is present in this system, because formaldehyde is conventionally supplied in aqueous solutions. Further, water is a coupled product of the OME formation from formaldehyde and methanol. In this system, the selectivity toward OME is limited by competing reactions of formaldehyde, methanol, and water toward poly(oxymethylene) hemiformals and poly(oxymethylene) glycols.15,17−19 In the literature, there are only a few contributions to the reaction kinetics and the chemical equilibrium in the aqueous system. Drunsel et al. investigated the reaction kinetics of methylal synthesis from a reactant mixture comprising formaldehyde, methanol, and a small amount of water.15 Methylal can be seen as a OME of chain length n = 1. This work uses the term OME exclusively for chain lengths n ≥ 2. As © 2015 American Chemical Society
the amount of formaldehyde was small in the reactant mixtures from Drunsel et al., they did not observe the quantifiable formation of OME.15 Zhang et al. investigated the reaction kinetics of OME synthesis from formaldehyde and methanol using different acidic heterogeneous catalysts.20,21 Their kinetic models do not, however, explicitly account for the complex behavior of formaldehyde in solutions of methanol and water, where formaldehyde is bound in the oligomers poly(oxymethylene) hemiformals and poly(oxymethylene) glycols. In our previous work, we investigated the chemical equilibrium of OME synthesis from formaldehyde and methanol in aqueous solutions, also taking the formation of poly(oxymethylene) hemiformals and poly(oxymethylene) glycols into account.16 A production process of OME from formaldehyde and methanol, which also takes into account the downstream process, was filed by Ströfer et al.22 In the present work, the experimental basis of the reaction kinetics is extended and a model is adjusted to the results. The heterogeneous catalyst Amberlyst 46, an acidic ion-exchange resin, is used. The model is consistent with the previously published model of the chemical equilibrium16 and explicitly accounts for the formation of poly(oxymethylene) hemiformals and poly(oxymethylene) glycols. The literature indicates that there are at least two competing mechanisms for the OME formation.11,15 They are differentiated and quantified in this work. The model of the reaction kinetics is essential for a reliable reactor design for a production process of OME from formaldehyde and methanol in aqueous solutions.
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FUNDAMENTALS Chemical Reactions. In solutions of methanol (MeOH, H3C−OH) and water (H2O), formaldehyde (FA, CH2O) is bound in the oligomers poly(oxymethylene) hemiformals (HFn, Received: Revised: Accepted: Published: 12553
October 27, 2015 December 2, 2015 December 4, 2015 December 4, 2015 DOI: 10.1021/acs.iecr.5b04046 Ind. Eng. Chem. Res. 2015, 54, 12553−12560
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Industrial & Engineering Chemistry Research HO−(CH2O)n−CH3) and poly(oxymethylene) glycols (MGn, HO−(CH2O)n−H).15,17−19 The oligomerization of formaldehyde with water is described by reactions 1 and 2. FA + H 2O ⇌ MG1 FA + MGn − 1 ⇌ MGn
between the true composition and the overall composition is given in the Supporting Information.
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EXPERIMENTS Chemicals and Catalyst. Paraformaldehyde (>0.95 g/g) was purchased from Carl Roth. Methanol (>0.999 g/g) and
(1)
n≥2
(2)
Formaldehyde and methanol react similarly, which is described by reactions 3 and 4. FA + MeOH ⇌ HF1 FA + HFn − 1 ⇌ HFn
Table 1. Overview of the Temperature and the Overall Initial Composition of the Kinetic Experiments K1−K11
(3)
n≥2
(4)
The chemical equilibrium of reactions 1−4 is far on the side of the products; i.e., the amount of monomeric formaldehyde in equilibrium is very small. Reactions 1−4 occur at all pH levels and have considerable reaction rates without the addition of any catalyst.15,17−19 By contrast, the following reactions occur only in the presence of acids. The formation of methylal (MAL, H3C−O− (CH2O)−CH3) is given by reaction 5,15 which is an acetalization reaction. H+
HF1 + MeOH HooI MAL + H 2O
(5)
For the formation of the long-chain OME with n ≥ 2, different mechanisms are discussed in the literature. In analogy to the formation of methylal, OME of chain lengths n ≥ 2 could be formed by an acetalization of poly(oxymethylene) hemiformals (n ≥ 2) and methanol according to reaction 6.15 H+
HFn + MeOH HooI OMEn + H 2O
n≥2
(6)
H+
H+
FA + OMEn − 1 HooI OMEn
(7)
n≥3
m̃ FA/m̃ MeOH (g/g)
x̃(m) H2 O (g/g)
x̃(m) MAL (g/g)
x̃(m) OME2−8 (g/g)
K1 K2 K3
363.15
0.86 0.62 0.93
0.05 0.04 0.22
0.05 0.05 0.02
0.03 0.02 0.01
K4 K5 K6
333.15
0.89 0.47 0.82
0.03 0.04 0.21
0.04 0.04 0.01
0.02 0.01 0.00
K7 K8 K9
303.15
0.85 0.57 0.81
0.03 0.02 0.22
0.01 0.01 0.00
0.00 0.00 0.00
K10
363.15
1.48
0.03
0.40
0.04
K11
333.15
1.44
0.05
0.38
0.01
methylal (>0.99 g/g) were purchased from Sigma-Aldrich. Ultrapure water was produced with a Milli-Q water purification system from Merck. Methanolic and aqueous formaldehyde solutions were prepared by dissolving paraformaldehyde in methanol and water, respectively. This is described in previous work.16 The ion-exchange resin Amberlyst 46 from Rohm and Haas was used as heterogeneous catalyst. This catalyst reduces the formation of the side products dimethlyl ether and methyl formate.11,16 Both side products are only observed in traces at elevated temperatures.16 Prior to every experiment, the wet catalyst was dried for 1 day in a vacuum oven at a pressure 4.11,16 The overall mass fraction of formaldehyde was determined by the sodium sulfite titration method with hydrochloric acid as titer. The overall mass fraction of water was determined by Karl Fischer titration. For both titrimetric methods, the relative errors are less than 2%.16 For all analyzed samples, the sum of the overall mass fractions was between 0.97 and 1.03 g/g. This indicates a good quality of the multicomponent analysis. To provide consistent data sets for model development, all mass fractions were normalized to a sum of 1 g/g by proportional weighing. Apparatus and Experimental Procedure. The kinetic experiments were carried out in a stirred batch reactor. The experimental setup is described in previous work.16 For the
The formation of OME is also described by a sequential growth mechanism from methyal to OME2 and OMEn by way of adding monomeric formaldehyde according to reactions 7 and 8.11,20,23,24 FA + MAL HooI OME 2
T (K)
(8)
For the OME synthesis from trioxane and methylal, i.e., in the absence of methanol and water, only reactions 7 and 8 are possible. To differentiate between both mechanisms (acetalization and growth) in the present system, it is necessary to explicitly account for the poly(oxymethylene) hemiformals and poly(oxymethylene) glycols. For describing the chemical equilibrium, both mechanisms are linear-dependent; i.e., both mechanisms lead to the same results for the equilibrium composition. A differentiation of the mechanisms is however essential for the quality of the kinetic model. This will be discussed on the basis of the experimental results of the present work. True Composition and Overall Composition. In aqueous and methanolic solutions of formaldehyde, two different ways of describing the composition are used. Overall concentrations are found when the unstable poly(oxymethylene) hemiformals and poly(oxymethylene) glycols completely decompose into formaldehyde, methanol, and water. The true species concentrations also quantify all poly(oxymethylene) hemiformals and poly(oxymethylene) glycols. A detailed description of the mathematical relations 12554
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Industrial & Engineering Chemistry Research kinetic experiments, the reactor was filled with the liquid reactant mixture, pressurized with nitrogen (absolute pressure >2 bar to prevent boiling of the mixture), and equilibrated to reaction temperature overnight. Then the catalyst was added and the reaction started. The catalyst was either added to the reacting mixture in dry form by removal of a clamp from a ductile plastic tube that is mounted on top of the reactor or, alternatively, in methanolic solution through the filling valve. The way of adding the catalyst did not significantly affect the experimental results. Consecutive samples of the liquid phase at different time intervals were taken with a riser pipe. The time of the first sample was set as the starting time of the reaction (t = 0). The time gap between the addition of the catalyst and the first sample was not longer than 1 min. The stirrer speed was approximately 400 rpm in the experiments. In a preliminary experiment, the stirrer speed was reduced to approximately 225 rpm, which did not significantly affect the experimental results. After every experiment, the capacity of the catalyst (amount of acid sites per dry mass) was determined. The catalyst was rinsed well with water to remove all organic substances. The rinsed catalyst was given into deionized water, and the amount of acid sites was determined using caustic soda solution for the neutralization of the dissociated protons of the acid sites and back-titration with hydrochloric acid. This method was adapted from the work of von Harbou et al.25 Experimental Program. The reaction kinetics were primarily studied starting from reactant mixtures containing formaldehyde, methanol, and water. The investigated temperatures were 303.15, 333.15 and 363.15 K. At each temperature, three experiments were carried out varying in the ratio of formaldehyde to methanol and the amount of water. These experiments are named K1−K9. As all reactions in the system are reversible, the OME yield on a process scale can be increased by recycling of methylal into the reactor. For this reason, two kinetic experiments were carried out, in which the reactant mixture also comprised a significant amount of methylal (K10 and K11). The investigated temperatures were 333.15 and 363.15 K. Table 1 summarizes the settings of all experiments in the present work and indicates how the parameters were varied. Small amounts of the reaction products methylal and OME are already present for every experiment at t = 0, because the catalyst was added prior to taking the first sample. The mass of dry catalyst was between 12 and 14 g. The initial mass of the liquid reacting mixture was about 700−750 g. The liquid mass is a step function of the time, which is caused by consecutive removing of samples. The mass of the dry catalyst and the time-dependent mass of the liquid reacting mixture are given for each experiment in the Supporting Information. Experimental Results. The numerical results for the experimental concentration profiles (overall mass fractions over time) and the experimentally determined catalyst capacity are given for each experiment in the Supporting Information. The profiles for the experiments at 363.15 K are discussed below, along with the development of the model.
Figure 1. Overall concentration profiles of kinetic experiment K1 (T = 363.15 K): (a) formaldehyde (▲), water (●), methanol (▼), methylal (□), and OME2 (△) and (b) OME3 (○), OME4 (▽), OME5 (▷), and OME6 (◇). Pseudohomogeneous model: solid lines (−).
Table 2. Parameters for the Calculation of the Reaction Rate Constants kA(T) (reactions 5 and 6) and kG(T) (reactions 7 and 8) Using the Correlation ln kl/(mol/mol H+ s) = al + bl/ (T/K), l ∈ {A, G} kl
al
bl
kA kG
19.959 31.046
−6669.9 −8906.6
accessible for every component in the reaction mixture. This assumption is often valid for ion exchange catalysis in aqueous systems, because the catalytic agent is the dissociated proton and not the undissociated sulfonic acid group.26 A pseudohomogeneous model has previously been successfully applied for the synthesis of methylal from formaldehyde and methanol in aqueous solutions.15 The material balance for the time-dependent amount of substance ni(t) of any true component i is given by eq 9
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MODELING Model Equations. For modeling of the reaction kinetics of the OME synthesis from formaldehyde and methanol in aqueous solutions, a pseudohomogeneous approach is used. The active sites of the ion exchange catalyst are assumed to be homogeneously distributed in the liquid phase and freely
NR
ni(t ) = nĩ (t =0) +
∑ νijξj(t ) j=1
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Figure 2. Arrhenius plot for the reaction rate constant kA(T) . Rate constants fitted to every experiment individually (○). Rate constants fitted to all three experiments at each temperature (●). The solid line indicates the correlation of this work according to eq 20.
where ñi(t=0) is the overall amount of substance of component i at the beginning of the experiment, NR is the number of reactions, νij is the stoichometric coefficient of every true component i in reaction j, and ξj(t) is the molar extent of reaction j. From eq 9, the true amounts of substance at the beginning of the experiment ni(t=0) are inherently calculated by the model; see below. As the formation of poly(oxymethylene) hemiformals and poly(oxymethylene) glycols is very fast compared to the formation of methylal and all OME,15 it is assumed that reactions 1−4 are instantaneous. The molar extents of these reactions are determined by the mole-fraction-based chemical equilibrium constants, as given in eqs 10−13, at any point of time (Bodenstein principle). This assumption has been previously proposed for the synthesis of methylal from formaldehyde and methanol in aqueous solutions.15 x MG1 K1(T ) = x FAx H2O (10) K 2, n(T ) =
K3(T ) =
x MGn x FAx MGn−1
Figure 3. Overall concentration profiles of kinetic experiment K10 (T = 363.15 K): (a) formaldehyde (▲), water (●), methanol (▼), methylal (□), and OME2 (△) and (b) OME3 (○), OME4 (▽), OME5 (▷), and OME6 (◇). Pseudohomogeneous model without growth reactions (kG = 0): solid lines (−). If a significant amount of methylal is present in the reactant mixture, the pseudohomogeneous acetalization mechanism alone is not able to describe the experimental results. A good description of experiment K10 is only possible if the growth reactions are included. This is shown in Figure 6.
n≥2 (11)
x HF1
+
x FAxMeOH
K4, n(T ) =
x HFn x FAx HFn−1
In eq 14, mcat is the mass of dry catalyst, cHcat is the catalyst capacity, and rj is the rate of reaction j. The initial conditions for solving eq 14 are given in eq 15.
(12)
n≥2
ξj(t =0) = 0
(13)
In eqs 10−13, Kj(T) are the temperature-dependent molefraction-based chemical equilibrium constants of reactions 1−4. The subscript j refers to the numbering of the reactions in this paper, followed by the oligomer chain length n, if necessary. In addition, xi is the true mole fraction of component i. The formation of the acetals methylal and all OME (reactions 5−8) is kinetically controlled. The rates of change of the molar extents of these reactions are given by eq 14. dξj dt
+
H rj = mcat ccat
j ∈ {5, (6, n), 7, (8, n)}
j ∈ {5, (6, n), 7, (8, n)}
(15)
The initial conditions in eq 15 ensure that the model inherently calculates the true composition at t = 0 from the measured overall composition at t = 0 using the material balance in eq 9 and the algebraic eqs 10−13. The rates of reactions 5−8 are given by the kinetic expressions in eqs 16−19. They are intensive with respect to + the total number of acid sites (mcatcHcat). ⎞ ⎛ 1 xMALx H2O⎟ r5 = k5(T )⎜x HF1xMeOH − K5(T ) ⎠ ⎝
(14) 12556
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DOI: 10.1021/acs.iecr.5b04046 Ind. Eng. Chem. Res. 2015, 54, 12553−12560
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Industrial & Engineering Chemistry Research ⎛ ⎞ 1 r6, n = k6, n(T )⎜⎜x HFnxMeOH − xOMEnx H2O⎟⎟ K 6, n(T ) ⎝ ⎠
acetalization reactions 5 and 6. In these calculations, the rate constant kG for the growth reaction is set to zero. At each investigated temperature, the rate constant kA is fitted to all three experiments carried out at this temperature. The parameters aA and bA, as given in Table 2, are fitted to the rate constants kA obtained for each temperature. The corresponding Arrhenius plot is given in Figure 2. To give an impression of the scattering, rate constants fitted to each experiment individually are also shown in Figure 2. The outlier at the lowest temperature is caused by the low reaction rates of this experiment (see concentration profile of experiment K9 in the Supporting Information). For this experiment, the changes in the overall composition of the reaction mixture are too small to determine kA precisely. Figure 3 shows the experimental concentration profiles for experiment K10, for which the reactant mixture also comprises a significant amount of methylal. In addition, model results are shown using only the acetalization mechanism with the rate constant kA of the acetalization as given in Table 2; i.e., the rate constant kG for the growth reactions is set to zero. It can be seen that the model predicts the concentration profile for methylal qualitatively wrong. Furthermore, it was not possible to adjust kA in such a way that all experiments are described satisfactorily. Obviously, the pseudohomogeneous acetalization mechanism alone is not able to describe the kinetic behavior of the reaction system, if also a significant amount of methylal is present in the reactant mixture. As discussed in the Introduction, there is also a competing reaction mechanism. Therefore, we assume a superposition of the acetalization mechanism and the growth mechanism. For this reason, the rate constant kG was additionally fitted to the kinetic profiles obtained from experiments K10 and K11. In this adjustment, the rate constant for the acetalization reactions is kept constant as given in Table 2. The parameters aG and bG are fitted to the rate constants kG obtained for each temperature. The resulting parameters aG and bG are also given in Table 2. A simultaneous fit of both kA and kG to all experiments in the present work did not improve the quality of the model.
n≥2 (17)
⎛ ⎞ 1 r7 = k 7(T )⎜x FAxMAL − ·xOME2⎟ K 7(T ) ⎝ ⎠ ⎛ ⎞ 1 r8, n = k 8, n(T )⎜⎜x FAxOMEn−1 − xOMEn⎟⎟ K8, n(T ) ⎝ ⎠
(18)
n≥3 (19)
In the calculations, the chain length of OME is limited to n = 8 and the chain length of poly(oxymethylene) hemiformals and poly(oxymethylene) glycols is limited to n = 10. Increasing the maximal chain lengths does not significantly affect the model results. The number of adjustable parameters is reduced by the following assumptions. The reaction rate constants k5(T) and k6,n(T) of the acetalization reactions 5 and 6 are set equal and named kA(T) . For the growth reactions 7 and 8, the reaction rate constants k7(T) and k8,n(T) are also set equal and named kG(T). The temperature dependence of the reaction rate constants is correlated by eq 20, an Arrhenius expression with parameters al and bl. ln kl(T ) = al +
bl T /K
l ∈ {A, G}
(20)
The determination of the two temperature-dependent reaction rate constants kA(T) and kG(T) is described in details in the subsequent section. Correlations for the chemical equilibrium constants for every reaction Kj(T) are adapted from previous work;16 see the Supporting Information for details. Since reactions 1−4 are assumed to be in chemical equilibrium and the reactions 5−8 are modeled as kinetically controlled, a system of differential−algebraic equations (DAE) has to be implemented and solved. This was done using the software gProms Model Builder V. 3.7.1 (Process Systems Enterprise) and the gProms solver “DASOLV” as integrator for the DAE system. The determination of the rate constants kA and kG was likewise carried out with the software gProms. The software uses a maximum-likelihood method for the parameter estimation. The uncertainty of the measured overall mass fractions over time is considered by a constant relative variance model with relative errors for the overall mass fractions as given in the analytics subsection. Reaction Mechanism and Parameter Estimation. Figure 1 shows the experimental overall concentration profiles for experiment K1. It can be seen that all OME are formed at the same time and without delay. OME up to n = 6 could be detected after t = 88 s. It is concluded that all OME are formed rather by the acetalization mechanism (reaction 6) than by the growth mechanism (reactions 7 and (8)). At the beginning of the experiment, long-chain poly(oxymethylene) hemiformals (n ≥ 2) are already present in the mixture that react with methanol to OME of similar chain length after the addition of the cataylst. By contrast, the growth mechanism is a sequential mechanism. A time-delayed formation of long-chain OME (n ≥ 2) would be expected but could not be observed experimentally. The experimental concentration profiles of experiments K1− K9 are used to estimate the reaction rate constant kA for the
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DISCUSSION Figure 1 compares the experimental overall concentration profiles with the model results for experiment K1. In the model calculation, both the acetalization reactions and the growth reactions are accounted for with rate constants, as given in Table 2. The model describes the simultaneous formation of all OME with good accuracy. The influences of a decreased ratio of formaldehyde to methanol (cf. Figure 4), an increased overall mass fraction of water (cf. Figure 5), and an increased overall mass fraction of methylal in the reactant mixture (cf. Figure 6) are also described with good accuracy. For all experiments carried out at different temperatures in the present work, the accuracy of the model is also good. This is shown in the Supporting Information. For every experiment, the composition in chemical equilibrium is described well. This agreement supports the quality of the previously published model of the chemical equilibrium.16 To differentiate between both competing reaction mechanisms, the calculated reaction rates r6,2 (formation of OME2 by acetalization) and r7, r8,2 (formation and depletion of OME2 by growth mechanism) are shown in Figure 7 for experiment K1. It can be seen that the reaction rates r7 and r8,2 are strongly dominated by the reaction rate r6,2. Hence, if methylal and OME are not present in the reactant mixture, the growth 12557
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Figure 5. Overall concentration profiles of kinetic experiment K3 (T = 363.15 K): (a) formaldehyde (▲), water (●), methanol (▼), methylal (□), and OME2 (△) and (b) OME3 (○), OME4 (▽), and OME5 (▷). Pseudohomogeneous model: solid lines (−).
Figure 4. Overall concentration profiles of kinetic experiment K2 (T = 363.15 K): (a) formaldehyde (▲), water (●), methanol (▼), methylal (□), and OME2 (△) and (b) OME3 (○), OME4 (▽), and OME5 (▷). Pseudohomogeneous model: solid lines (−).
OME (n ≥ 2) are formed from formaldehyde and methanol rather by acetalization of poly(oxymethylene) hemiformals (n ≥ 2) and methanol than by sequential addition of monomeric formaldehyde into growing OME of shorter length. However, if also a significant amount of methylal is present in the reactant mixture, both mechanisms were found to superimpose. The model consequently includes both the acetalization and the growth reactions and describes the experimental concentration profiles with good accuracy. The developed model is simple, as only two temperature-dependent kinetic parameters (the reaction rate constants kA and kG) had to be adjusted to experimental data. The chemical equilibrium constants are taken from previous work.16 The results of this work enable a reliable reactor design for a production process of OME from formaldehyde and methanol in aqueous solutions.
mechanism is of minor importance. The growth mechanism is, however, important for experiment K10, for which the corresponding calculated reaction rates are shown in Figure 8. Caused by the high amount of methylal in the reactant mixture, the reaction rate r7 is the dominant reaction rate for the OME2 formation.
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CONCLUSION The reaction kinetics of the OME synthesis from formaldehyde and methanol in aqueous solutions was studied. Experiments were carried out in a stirred batch reactor on a laboratory scale using Amberlyst 46 as heterogeneous acidic catalyst at varying temperatures and varying reactant compositions. Two experiments were carried out in which the reactant mixture also comprised a significant amount of methylal. The experimental concentration profiles were used to develop a pseudohomogeneous kinetic model for the formation of OME in the present reaction system. The model explicitly accounts for the formation of poly(oxymethylene) hemiformals and poly(oxymethylene) glycols in methanolic and aqueous solutions of formaldehyde and is consistent with a previously published model of the chemical equilibrium. It was found that
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b04046. Numerical results of the experimental concentration profiles, correlations for the calculation of the chemical 12558
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Figure 7. Calculated reaction rates r6,2 (formation of OME2 by acetalization) and r7, r8,2 (formation and depletion of OME2 by growth mechanism) for experiment K1.
Figure 6. Overall concentration profiles of kinetic experiment K10 (T = 363.15 K): (a) formaldehyde (▲), water (●), methanol (▼), methylal (□), and OME2 (△) and (b) OME3 (○), OME4 (▽), OME5 (▷), and OME6 (◇). Pseudohomogeneous model with acetalization and growth reactions: solid lines (−). In contrast to Figure 3, the growth reactions are considered here. This leads to a good description of the kinetic behavior.
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Figure 8. Calculated reaction rates r6,2 (formation of OME2 by acetalization) and r7, r8,2 (formation and depletion of OME2 by growth mechanism) for experiment K10.
HF MAL MeOH MG OME
equilibrium constants, and comparison between experimental concentration profiles and model results for all experiments that are not shown in the main body of this publication (PDF)
Symbols and Indices
al, + bl cHcat H+ kj Kj mcat m̃ i n ni ñi NR νij rj t T
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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poly(oxymethylene) hemiformal methylal methanol poly(oxymethylene) glycol poly(oxymethylene) dimethyl ethers
ACKNOWLEDGMENTS This work was funded by the German Ministry of Food and Agriculture (BMEL) through grant 22403914. NOMENCLATURE
Abbreviations
DAE FA
differential−algebraic equations formaldehyde 12559
correlation parameters catalyst capacity (amount of acid sites per dry mass) proton (acid-catalyzed) reaction rate constant of reaction j mole fraction-based chemical equilibrium constant mass of dry catalyst overall mass of component i oligomer chain length true amount of substance of component i overall amount of substance of component i number of reactions stoichiometric coefficient of component i in reaction j rate of reaction j time temperature DOI: 10.1021/acs.iecr.5b04046 Ind. Eng. Chem. Res. 2015, 54, 12553−12560
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(20) 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. (21) 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. Catal. 2014, 113, 459−470. (22) Ströfer, E.; Hasse, H.; Blagov, S. Method for producing polyoxymethylene dimethylethers from methanol and formaldehyde. Patent WO2006134088, 2006. (23) Zheng, Y.; Tang, Q.; Wang, T.; Wang, J. Kinetics of synthesis of polyoxymethylene dimethyl ethers from paraformaldehyde and dimethoxymethane catalyzed by ion-exchange resin. Chem. Eng. Sci. 2015, 134, 758−766. (24) 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. (25) von Harbou, E.; Yazdani, A.; Schmitt, M.; Großmann, C.; Hasse, H. Reaction kinetics for reactive distillation using different laboratory reactors. Ind. Eng. Chem. Res. 2013, 52, 624−637. (26) Chakrabarti, A.; Sharma, M. M. Cationic ion exchange resins as catalyst. React. Polym. 1993, 20, 1−45.
xi True mole fraction of component i x̃(m) overall mass fraction of component i i ξj molar extent of reaction j
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DOI: 10.1021/acs.iecr.5b04046 Ind. Eng. Chem. Res. 2015, 54, 12553−12560
