Chemical Equilibrium and Reaction Kinetics of the Heterogeneously

Article pubs.acs.org/IECR

Chemical Equilibrium and Reaction Kinetics of the Heterogeneously Catalyzed Formation of Poly(oxymethylene) Dimethyl Ethers from Methylal and Trioxane Jakob Burger,*,† Eckhard Ströfer,‡ and Hans Hasse† †

Laboratory of Engineering Thermodynamics, University of Kaiserslautern, Kaiserslautern 67663, Germany Chemical and Process Engineering (GCP), BASF SE, Ludwigshafen 67056, Germany

‡

S Supporting Information *

ABSTRACT: Poly(oxymethylene) dimethyl ethers (OMEs) are attractive components for tailoring diesel fuels. They belong to the group of oxygenates that reduce soot formation in the combustion when added to diesel fuels and can be produced on a large scale based on gas-to-liquid technology. This work deals with a particularly favorable route for their large scale production in which they are formed from methylal and trioxane. Reaction kinetics and chemical equilibrium of the OME formation via this route were studied in a batch reactor using the ion-exchange resin Amberlyst 46 as heterogeneous catalyst at temperatures between 323 and 363 K and for a wide range of feed compositions. An adsorption-based kinetic model is presented that represents both reaction kinetics and equilibrium well.

■

INTRODUCTION It is well-known that diesel engines have, due to their high thermal efficiency, revolutionized transportation. Environmental and linked regulatory issues have driven the development of low emission diesel engines. Still, even in modern high performance diesel engines, the formation of soot during the combustion remains a problem. Oxygenated compounds (molecules that contain oxygen in their structure), such as methanol or dimethyl ether (DME), are known to reduce soot formation during the combustion, when added to diesel fuels.1 Promising oxygenates for the use as diesel fuel additives are poly(oxymethylene) dimethyl ethers (OMEs). In contrast to methanol or DME, their physical properties allow the use in modern diesel engines without significant change of the engines infrastructure.2,3 OMEs can be produced from the sole feedstock methane on the basis of gas-to-liquid technology.2 Recently, many patents for the production of OMEs from various educts were filed, e.g., refs 4−8. The value-added chain and different routes for the production of OMEs are discussed in more detail by Burger et al.2 If methanol or water are present in the process, the OME purification is difficult because many side-products are formed.2 One particular favorable route is therefore the production of OMEs from the well-known and water-free intermediates methylal (dimethoxy methane) and trioxane, which are reacted over an acidic heterogeneous catalyst. We recently proposed a process for this route.2,9 To design the process and determine the production costs of OMEs, a quantitative model of the reaction kinetics and the chemical equilibrium of the OME formation from these intermediates is required. The present paper provides this model based on comprehensive experimental studies. In the literature there is only little quantitative data on the OME formation. Recently, Zhao et al.10 synthesized OMEs from trioxane in methanolic solutions producing water as a side © 2012 American Chemical Society

product. Selectivities of OMEs of different chain lengths and conversions of trioxane are compared for several molecular sieves employed as catalysts. The presence of methanol and water leads to the formation of hemiformals and methylene glycols. This complex reaction system is different from the system of the present work in which water-free and methanolfree educts are used. For the OME formation from methylal and trioxane, Arvidson et al.11 give few reaction equilibrium data taken at very high methylal/trioxane ratios for a homogeneously catalyzed reaction. We have previously published equilibrium data at low methylal/trioxane ratios using the ion-exchange resin Amberlyst 36 as a heterogeneous catalyst.2 Neither of the works provides a model of the equilibrium. In the present work, experimental data were collected systematically in the laboratory to finally derive a model which is able to describe the kinetics and the equilibrium of the OME formation from methylal and trioxane.

■

REACTIONS Chemical System. Poly(oxymethylene) dimethyl ethers (OMEn) have the general structure H3C−O−(CH2−O)n−CH3 and are oligomers of the monomer formaldehyde (FA, structure OCH2). The simplest OME is methylal (n = 1, DMM, often also referred as dimethoxymethane). In neutral environment the OMEs are chemically stable. At least up to n = 6 they are liquids at ambient conditions. In acidic environment DMM and OMEs react with monomeric formaldehyde. H+

DMM + FA HooI OME 2 Received: Revised: Accepted: Published: 12751

(1)

June 6, 2012 August 30, 2012 August 31, 2012 August 31, 2012 dx.doi.org/10.1021/ie301490q | Ind. Eng. Chem. Res. 2012, 51, 12751−12761

Industrial & Engineering Chemistry Research H+

OMEn − 1 + FA HooI OMEn

n>2

Article

completely to methanol and the poly(oxymethylene) hemiformals that are found in the analysis. Two side products were observed which occur independent of educt contamination: methyl formate (MEFO, HCOOCH3) and dimethyl ether. Methyl formate is formed in acidic environment from formaldehyde in a Tischenko reaction.17

(2)

This reaction scheme is analogous to formation of poly(oxymethylene) glycols in aqueous solutions of formaldehyde.12 Reactions 1 and 2 are reversible and lead to an equilibrium chain distribution which mainly depends on the overall formaldehyde concentration in the solution. Increasing the formaldehyde concentrations shifts the distribution to longer chains. In this work, the formaldehyde is provided by trioxane (TRI, (CH2O)3cyc), a cyclic, anhydrous form of formaldehyde. At ambient conditions trioxane is a chemically stable solid. In the literature the trioxane breakup is often described as the acidcatalyzed, reversible formation of three monomeric formaldehyde segments.13−15 H+

TRI HooI 3FA

H+

2FA ⎯→ ⎯ MEFO

Dimethyl ether is formed, besides reaction 8, by the decomposition of methylal. H+

DMM ⎯→ ⎯ DME + FA

■

This equation is rather a formal description than a chemical mechanism as trioxane has to split up into three monomers at a time.16 This becomes even more unlikely when the backward reaction is considered: the formation of trioxane by the collision of three formaldehyde molecules. A more probable mechanism of the trioxane breakup is that the ring breaks at one position so that a linear trioxymethylene chain is formed that, in the OME system, could be inserted into another OME chain according to the overall eq 4. H+

n>3

EXPERIMENTS Chemicals and Catalysts. Methylal (Grinard reaction grade, >0.99 g/g) was purchased from Sigma Aldrich. Trioxane (polymer grade, >0.995 g/g), OME2 (technical grade, 0.98 g/ g), OME3 (technical grade, 0.95 g/g), and OME4 (technical grade, 0.97 g/g) were provided by BASF. In this work two strong acidic ion-exchange resins from Rohm and Haas were used, Amberlyst 36 (dry) and Amberlyst 46. Both catalysts are small spheric beads with a diameter of about 1 mm. Stationary sulfonic groups attached on a polymer matrix function as active sites. The difference between the two catalysts is the degree of sulfonation: whereas Amberlyst 46 is sulfonated only on the surface, Amberlyst 36 features also sulfonic groups within the micro pores of the matrix. The capacity of Amberlyst 36 is higher.18 Amberlyst 46 is shipped in wet form. As water is causing side reactions, it was removed before the experiments. For this purpose the catalyst was dried in two steps: first one day at a temperature of 333 K at atmospheric pressure and finally one week in a vacuum oven at 368 K at a pressure of about 5 mbar. After the drying process, the catalyst was stored in the vacuum oven at a temperature of 323 K before it was used in the experiments. Analysis. All samples taken in the experiments were analyzed using gas chromatography. A Restek Rtx-200 capillary column with a FID detector was used in a Hewlett-Packard HP6890 gas chromatograph. More details are given in the Appendix. The calibration was carried out by injecting the pure components including the OMEs up to chain length OME4. OMEs up to OME8 could be quantified. For calibration the peak area/mol ratio obtained from the calibration of methylal, OME2, OME3, and OME4 was extrapolated linearly up to OME8. The accuracy of the mass fractions determined by this analytical method is about ±0.005 g/g (absolute deviation). For methylal, trioxane, OME2, OME3, and OME4 the relative error in the mass fraction is smaller than 1%. This was checked by analyzing test samples that were prepared gravimetrically. For the side products methanol, methyl formate, and dimethyl ether the relative error is smaller than 5% due to their small mass fraction in connection with the mass-based analysis method. A relative error of 5% must also be assumed for the long chain OMEs which could not be tested for accuracy. Formaldehyde is analyzed using titration by the sodium sulfite method.13 That method was developed for aqueous and

(4)

For describing the chemical equilibrium the choice of the mechanism is not significant. The kinetic experiments of this work did not yield any direct evidence on the mechanism. During the modeling of the kinetics both descriptions (3) and (4) were tested. It was found that assumption on the mechanism is not significant for the quality of the kinetic model. This will be discussed in more detail in the modeling section. The formal description (3) in combination with reactions 1 and 2 was finally chosen in this work. It will be shown later that this assumption is suited for describing the kinetics of the OME formation from methylal and trioxane. Side Reactions. If water is present, it reacts with the ethers in an acid-catalyzed reaction forming alcohols. An example is the reaction of methylal with water to form hemiformal (HF1, H3C−O−CH2−OH) and methanol (ME, H3C−OH). H+

DMM + H 2O HooI HF1 + ME

(5)

Methanol and hemiformal form poly(oxymethylene) hemiformals (HFn, H3C−O−(CH2−O)n−H) in the presence of formaldehyde.13 ME + FA ⇌ HF1

HFn − 1 + FA ⇌ HFn

(6)

n>1

(7)

In acidic environment methanol further forms dimethyl ether (DME, H3C−O−CH3) in a dehydration reaction. H+

2ME ⎯→ ⎯ DME + H 2O

(10)

Note that reaction 10 can be considered to be the first reaction of the series of reactions 1 and 2. Under what conditions side reactions 9 and 10 occur and how they can be suppressed is explained in the experimental section.

(3)

TRI + OMEn − 3 HooI OMEn

(9)

(8)

To inhibit reactions 5−8, water and methanol should be removed from the educts as far as possible. In the experiments described later in this paper there is always a strong methylal surplus, so the equilibrium of Rreaction 5 is shifted far to the product side and remaining traces of water react almost 12752

dx.doi.org/10.1021/ie301490q | Ind. Eng. Chem. Res. 2012, 51, 12751−12761

Industrial & Engineering Chemistry Research

Article

the upper compartment above the clamp and can be released into the reactor at any time by removing the clamp. First the premixed educts were filled into the reactor trough valve V1. Then the reactor was sealed and the stirrer was started. Finally, the reactor was heated up to the desired temperature and a temperature controller ensured isothermal conditions. Then the catalyst was added to start the reactions. Preliminary Catalyst Selection. During preliminary tests both catalysts were used to react methylal and trioxane to OMEs. With Amberlyst 36 the side products dimethyl ether and methyl formate were obtained in orders of 1−2 mass % in the solution whereas the main reactions reached about 90% of the equilibrium conversion even at temperatures as low as 300 K. With Amberlyst 46 neither methyl formate nor dimethyl ether could be detected with gas chromatography at any time in the transient regime up to the time when the reaction equilibrium of the main reactions was reached. This holds for all studied temperatures that were up to 363 K. For this reason the catalyst Amberlyst 46 was chosen for all following experiments. The different behavior of side product formation for the two different catalysts can be explained with their different degree of sulfonation. Amberlyst 36 is sulfonated inside the micropores. Small formaldehyde molecules, which are important for side product formation, might accumulate in micropores with active sites, resulting in a higher probability of side product formation. Amberlyst 46, in contrast, is not sulfonated in the micropores. Note that even for Amberlyst 46 at temperatures above 340 K both dimethyl ether and methyl formate could be detected after long times of the order of 10 times the 90% equilibrium conversion. Thus, the side product formation is strongly reduced but not completely avoided by using Amberlyst 46. This should be kept in mind if the catalyst is filled used in processes with closed recycle streams. Experimental Program and Procedure. In most of the experiments methylal and trioxane were used as educts. When the ratio of these two educts is varied, the overall fraction of formaldehyde (supplied by trioxane) in the system can be changed. As mentioned before, the OME distribution in the equilibrium is mainly dependent on the overall formaldehyde fraction and can therefore be changed by varying the educt ratio. In a later process the OME reactor may be fed not only with methylal and trioxane but also with recycled OME2 or long chain OMEs.2 Nevertheless any possible equilibrium composition in the reaction system 1−3 can always be characterized unambiguously by one trioxane/methylal ratio, as all species could react back to these two educts. Therefore, only the trioxane/methylal ratio was varied to examine the influence of the composition on the equilibrium. However, some kinetic experiments which contained OME2 and long chain OMEs in the feed were carried out. The experimental program was chosen to provide data in the region of states that are most interesting for the industrial production of OMEs as fuel additives; hence they cover only a comparatively small range of educt ratios and temperatures. In the kinetic experiments the ratio of mass of catalyst and mass of reaction solution was also varied. To study the reaction equilibrium, two feed mixtures EQ1 and EQ2 were prepared and mixed with catalyst in the reactor. The initial masses of the feed mixtures and the catalyst are given in Table 1. After the reactor was sealed, a temperature of 323.06 K was held for 1 h at a stirrer speed of 107 rpm. After the equilibrium was reached (checked by consecutive

methanolic solutions and cannot be directly applied to the OME system. We therefore tried to adapt the method to the OME system, cf. the Appendix. However, the method could not be calibrated in the OME system and the reproducibility of the analysis results turned out to be poor. The relative error of the method was estimated to be at least ±20% (relative deviation). The formaldehyde concentrations obtained from this method were therefore considered not to be reliable enough and only used in the development of the quantitative models when this was unavoidable, cf. the modeling section for more details. The quality of the multicomponent analysis was always checked by 100% tests. The sum of all component mass fractions was between 0.98 and 1.02 g/g. Only for mixtures with a high content of long chain OMEs was the sum sometimes higher, but it did not exceed 1.04 g/g. To provide consistent data for the model adaption, all measured mass fractions were normalized to a sum of 1 g/g. All concentrations reported here are normalized. Spot tests for water with Karl Fischer titration were all negative. All hemiformals decompose into methanol and formaldehyde during the analysis19 and could therefore not be quantified. Apparatus and General Procedure. The equilibrium and the kinetics were measured in a stirred batch reactor made of stainless steel. A schematic of the reactor is shown in Figure 1.

Figure 1. Schematic of the stirred batch reactor used to measure the equilibrium and the kinetics, volume 2.2 L. H1: oil bath. H2: sample cooling. TIC: temperature measurement and control. PI: pressure measurement. V1: inlet valve. V2: sampling valve. S1: catalyst supply with hose clamp.

The reactor has a volume of 2.2 L. It is thermostated using a jacket connected to an oil bath (H1). The temperature is measured by a Pt100 resistance thermometer (TIC) with an accuracy of ±0.05 K. The pressure is measured by a membrane pressure indicator with an accuracy of ±0.1 bar (PI). Liquid phase samples are taken using a riser pipe through valve V2 and a water cooling (H2). The catalyst is kept from being withdrawn by a filter (F1). A stirrer ensures a homogeneous reacting mixture. The catalyst supply consists of a PTFE tube mounted on the top of the reactor, which is sealed at the opposite end. The tube is ductile and can be divided into two compartments by squeezing it with a hose clamp (S1). The catalyst is filled into 12753



■

MODEL The experimental data on reaction equilibrium and kinetics from the present work was used to develop a model. The influence of pressure on the results is neglected as the reaction takes place only in the liquid phase. As no activity model for the liquid phase is presently available for the given system, all model equations are based on mole fractions. Note that due to similar structure and nonpolar behavior of all species except formaldehyde the nonideality in the liquid phase is expected to be not important. To model the heterogeneous reaction, different compositions are considered. The composition in the bulk phase is denoted by the mole fraction vector x, the composition at the surface of the catalyst is denoted by the mole fraction vector θ. All compositions determined experimentally are bulk compositions. Bulk Equilibrium. In the equilibrium experiments the composition in the bulk liquid phase was determined at different temperatures and initial trioxane/methylal ratios. The mole fraction based equilibrium constant of the OME 2 formation Reaction 1 is defined as

Table 1. Feed Specifications for the Experiments EQ1 and EQ2 (Methylal (DMM), Trioxane (TRI), and the Catalyst Amberlyst 46 (A46)) initial mass/g EQ1 EQ2

mass ratios

DMM

TRI

A46

DMM/TRI

(DMM+TRI)/A46

319 226

106 107

21.9 21.9

3.00 2.10

19.4 15.2

Article

sampling), the composition in the liquid reaction phase was analyzed. This procedure was repeated at 338.08, 353.10, and 363.12 K. The reactor pressures were about 1.5 bar for 323 K, 1.9 bar for 338 K, 2.6 bar for 353 K, and 3.5 bar for 363 K. They are not important as long as they are high enough to prevent the reacting mixture from boiling, which was always the case. To study reaction kinetics, a set of experiments with the educts methylal and trioxane was performed. During each experiment the temperature was held constant and time profiles of the composition of the liquid phase were measured as follows. After isothermal conditions in the sealed reactor were established, a sample of the liquid phase was taken to determine the initial composition of the mixture, which is not the same as the feed composition due to evaporation of methylal during the filling process. Then the catalyst was added and the time measurement was started (t = 0). Samples of the liquid phase were drawn in intervals of 3−30 min, depending on the catalyst-to-solution ratio and the progress of the experiment. Table 2 gives an overview of the experiments and indicates how different parameters were varied. The stirrer speed was set to 106−120 rpm in the experiments, which was the maximal allowable range. At higher stirrer speed, the setup started to vibrate. Lowering this speed to about 75 rpm did not change the results. The kinetic experiments in Table 2 are useful to study the forward reactions of all previous defined chemical equilibrium reactions as at the beginning of the experiment no reaction products are present. In the OME process it is also important to cleave recycled OMEs.2 To account for this, three additional experiments were performed. Methylal was no longer mixed with trioxane, but with OMEs. In experiment KIN7 pure OME2 was used. In experiments KIN8 and KIN9 a mixture of long chain OMEs with (n ≥ 4) was used. Table 3 gives the settings of these experiments. Experimental Results. Numerical data for the equilibrium compositions and the time dependent compositions taken during the kinetic runs are presented in the Supporting Information.

K2 =

EQ xOME 2 EQ EQ x DMM ·x FA

(11)

xEQ i

with denoting the mole fraction of component i in the equilibrium. The constants for the formation reaction 2 of the longer OMEs are defined as Kn =

EQ xOME n

n>2

EQ EQ xOME ·x FA n−1

(12)

For the trioxane decomposition in reaction 3 the constant is defined as KTRI =

EQ x FA

3

EQ x TRI

(13)

The values of the equilibrium constants K are calculated directly from the compositions determined in the experiments. In a first step, the ratio between the Kn, n ≠ 2, and K2 is examined. EQ

EQ

xOME ·x DMM Kn = EQ n EQ K2 xOMEn−1·xOMEn−1

(14)

The results are shown in Figure 2. The values of the ratios are clearly independent of the temperature and the initial composition (the markers are superimposed). The outlier for n = 8 might come from analytical or experimental errors. As all

Table 2. Overview of the Kinetic Experiments KIN1−KIN6a initial mass/g KIN1 KIN2 KIN3 KIN4 KIN5 KIN6 a

mass ratios

T/K

N/rpm

DMM

TRI

A46

DMM/TRI

(DMM +TRI)/A46

323.06 323.06 338.08 338.08 353.10 353.10

106 109 120 120 109 106

341 379 337 382 338 601

167 125 167 134 167 200

4.6 3.0 4.0 4.0 1.5 3.0

2.05 3.03 2.02 2.85 2.03 3.00

111 168 125 129 330 267

Feed: methylal (DMM), trioxane (TRI), catalyst Amberlyst 46 (A46); temperature T, stirrer speed N. 12754



Article

Table 3. Overview of the Kinetic Experiments KIN7−KIN9a initial mass/g KIN7 KIN8 KIN9

T/K

N/rpm

DMM

OME2

323.06 338.08 353.10

109 109 109

261 290 289

276

mass ratio LC

A46

(DMM + OME)/A46

291 290

0.51 3.0 2.0

1053 194 290

a

Feed: methylal (DMM), OME2, mixture LC, catalyst Amberlyst 46 (A46); temperature T, stirrer speed N. Composition of mixture LC: OME4 0.392 g/g, OME5 0.298 g/g, OME6 0.157 g/g, OME7 0.071 g/g, OME2,3 0.052 g/g, OME>7 0.030g/g.

K 2* =

K n* =

EQ xOME 2 EQ EQ 1/3 x DMM ) ·(x TRI

EQ xOME n EQ EQ 1/3 xOME ) ·(x TRI n−1

(18)

n>2 (19)

From eq 15 it follows that Figure 2. Ratio of equilibrium constants Kn/K2 for different temperatures and feed compositions EQ1 (unfilled markers), EQ2 (filled markers): squares, T = 323.15 K; circles, T = 338.15 K; triangles, T = 353.15 K; diamonds, T = 363.15 K. The markers are superimposed, thus difficult to distinguish.

* K 2* = K3* = ... = K n* = K OME

(20)

ratios are close to unity, it is simply assumed that the absolute values of the equilibrium constants for different chain lengths are equal. (They might still be temperature dependent). K 2 = K3 = ... = K n = K OME (15) More sophisticated descriptions do not increase the quality of the final model significantly. The numerical values of KOME depend on the analytical results for xEQ FA and are, hence, subject to large errors, cf. the van t’Hoff plot in Figure 3. The most important property derived

Figure 4. Experimental values of the constant K*OME in a logarithmic plot over the inverse temperature (van t’Hoff plot) for the two feeds EQ1 (unfilled markers) and EQ2 (filled markers). The model is indicated by a solid line (−).

The numerical results for KOME * are presented in Figure 4. From K*OME and KOME, the equilibrium constant KTRI can be calculated. KTRI

ln Kj(T ) = aj +

(16)

+

OMEn − 1 +

H 1 TRI HooI OMEn 3

n>2

bj T /K

(22)

was used to model KOME, K*OME, and KTRI. The concentration dependency of the K’s is in the range of the measurement uncertainty and is therefore not included in the model. The coefficients a*OME and b*OME were fitted to all eight experimental values of K*OME (two feed mixtures, four temperatures each, as described in the experimental section). The experimental values of KOME * are calculated as the arithmetic mean of all K2* to K8* resulting from eqs 11 and 12. The coefficients aOME and bOME were fitted to the values of KOME analogously. The coefficients aTRI and bTRI were calculated to meet eq 21. All parameters of the bulk equilibrium model are given in Table 4. In Figures 3

from the model is, however, the chain length distribution of the OMEs. By reformulating the equilibrium reactions to H+ 1 TRI XooY OME 2 3

(21)

Note that KTRI and KOME are subject to large scattering due to the uncertainties of the FA analysis but K*OME is not. The van’t Hoff equation

Figure 3. Experimental values of the constant KOME in a logarithmic plot over the inverse temperature (van t’Hoff plot) for the two feeds EQ1 (unfilled markers) and EQ2 (filled markers). The model is indicated by a solid line (−).

DMM +

⎛ K * ⎞3 = ⎜ OME ⎟ ⎝ K OME ⎠

(17)

we obtain a system of equations that describes the chain length distribution with equilibrium constants that are independent of the formaldehyde concentration. They are given by 12755



Article

Table 4. Parameters for the Bulk Equilibrium: ln Kj = aj + bj/ (T/K) Kj

aj

bj

KOME * KOME KTRI

−0.2699 0.3221 −1.7759

297 1292 −2986

cleaved in the reactor. In the design of an OME process an compromise between these two effects has to be found. The work of Zhao et al.10 showed that the chain length distribution of OMEs in the equilibrium varies for different catalysts. Thus, we want to stress that the equilibrium model of the present work should only be used when Amberlyst 46 is employed as catalyst. Pseudohomogeneous Kinetic Model. In a first approach the reaction kinetics were modeled with a pseudohomogeneous model. The active sites of the catalyst are considered to be homogeneously distributed in the liquid phase and freely accessible to all components. The reaction rates of the reactions depend on the temperature, the number of active sites and the bulk composition. The mathematical formulation of the model and the parameter fitting procedure is described in the Appendix. In Figure 6 a typical composition profile of a kinetic experiment is shown together with the fitted pseudohomoge-

and 4 the model is indicated by a straight line. It should be noted that despite the fact that the model can only predict the formaldehyde concentrations with low accuracy, the concentrations of DMM, TRI, and OMEs are predicted reliably. Discussion Reaction Equilibrium. For given feed composition and temperature, the composition in the chemical equilibrium can be calculated with numerical software. The equations required for the solution are the definitions of the equilibrium constants (eqs 11−13) and the stoichiometry of the reactions. Figure 5 shows as an example four different

Figure 6. Concentration profiles of experiment KIN2 (cf. Table 2). Experimental values: markers. Pseudohomogeneous model: solid lines.

neous model. The educts methylal and trioxane are consumed and OMEs of different chain length emerge. For reasons explained above no measured formaldehyde concentrations are shown, but only the model results. It is found experimentally that all OMEs are formed simultaneously. This is a contradiction to the sequential mechanism of chain growth presented by reactions 1 and 2. It could be possible that these reactions are very fast compared to the trioxane decomposition. This would lead to the observed simultaneous formation of OMEs of different chain lengths. Hereby it does not matter which one of the two trioxane decomposition descriptions (3) and (4) is assumed. To check this possible explanation, experiment KIN7 is considered. Methylal and OME2 that includes traces of trioxane, are used as educts. If the OME formation reactions 1 and 2 would be rather fast, first a typical OME chain distribution would arise, followed by a slow trioxane reaction. The experimental values and the prediction by the model are shown in Figure 7 and for components of small mass fractions enlarged in Figure 8. The expectations from the pseudohomogeneous model are, however, not fulfilled. In the experiment the OMEs do not emerge as fast as predicted by the model. They emerge at the same speed at which trioxane is decomposed. Note that the decrease in the trioxane concentration is very small, and thus difficult to discern in the Figure 8, as the trioxane concentration was already close to the equilibrium in the feed solution. In fact, in all performed kinetic experiments it was observed that the OME equilibrium composition arises in about the same time in that trioxane is formed or decomposed, independent of the feed composition.

Figure 5. Mass fractions (represented by areas of pie slices) of the reacting species in chemical equilibrium in the system methylal + trioxane. MTR is the methylal/trioxane mass ratio in the feed. The formaldehyde fraction is a slice between DMM and OME2 and not discernible. The slices for OME3−OME5 are those that are most interesting for the production of fuel additives.

equilibrium compositions (given in mass fractions) as calculated with the model. The top and bottom row represent two different temperatures. There is practically no temperature dependency. The results in the left and right column differ in the methylal/trioxane mass ratios (MTR) in the feed. At both considered MTRs (2.0 and 3.0 g/g, respectively) the acetals (DMM and OMEs) are dominating. The monomeric formaldehyde fraction in the equilibrium is between 0.002 and 0.003 g/g and not discernible in the plot in Figure 5, the trioxane fraction is between 0.01 and 0.02 g/g. Increasing the trioxane fraction in the feed, i.e., reducing the methylal/trioxane ratio, leads to a shift toward longer chain OMEs in the equilibrium (cf. Figure 5). The methylal and OME2 fractions are reduced. Trioxane and formaldehyde fractions are slightly increased. OME3, OME4, and OME5 are considered to be favorable as diesel fuel additives.2 A high concentration of trioxane in the feed, not only increases the concentration of these OMEs in equilibrium but also increases the fraction of OMEs of chain length n > 5 that have to be recycled after separation and 12756



Article

model used here, it is assumed that the overall reaction rate is controlled by the sorption processes (a) and (c), whereas the surface reactions (b) are considered to be fast and in equilibrium. Note that the different trioxane decomposition descriptions (3) and (4) cannot be differentiated under this assumption. The adsorption is described by the rate controlled processes kiads

S + A i HoodesI S‐‐‐A i

(23)

ki

Figure 7. Concentration profiles of experiment KIN7 (cf. Table 3). Experimental values: markers. Pseudohomogeneous model: solid lines. The result shows that despite the favorable fit shown in Figure 6 the pseudohomogeneous model is not applicable.

for all A i ∈ {FA, TRI, DMM, OME 2 , OME3, ..., OMEn}

in which S represents a free active site of the catalyst and S---Ai the adsorbed component Ai. The desorption processes are represented by the backward reactions of (23). On the surface the adsorbed components react according to the following equations. K 2S

S‐‐‐DMM + S‐‐‐FA ⇌ S‐‐‐OME 2 + S

(24)

K nS

n>2

S‐‐‐OMEn − 1 + S‐‐‐FA ⇌ S‐‐‐OMEn + S

(25) Figure 8. Concentration profiles of experiment KIN7 (cf. Table 3) enlarged. Experimental values: markers. Pseudohomogeneous model: solid lines. The result shows that despite the favorable fit shown in Figure 6 the pseudohomogeneous model is not applicable.

S KTRI

S‐‐‐TRI + 2S HoooI 3S‐‐‐FA

(26)

The total number of active sites is constant and calculated from the catalyst mass and capacity. The number of free sites varies. Further, it is assumed that these reactions are very fast compared to the sorption processes (23) and that they are in equilibrium. The adsorption rate rads i of the component Ai is proportional to the mole fraction xi of Ai in the bulk, and the fraction θS of free sites.

The pseudohomogeneous model is therefore not capable to describe the formation of OMEs from methylal and trioxane (forward reaction) and their decomposition (backward reaction) in a consistent way. Adsorption-Based Kinetic Model. The catalyst Amberlyst 46 used in the present work is a cationic ion-exchange resin. The way these resins act as catalyst is different in aqueous and nonaqueous systems.20 In aqueous systems the catalytic agent is the hydrated proton, which can leak into the solution. This results in a pseudohomogeneous behavior of the catalyst. In water-free systems, in contrast, the catalytic agent is the undissociated sulfonic acid group. In this case the catalysis must occur together with diffusion, adsorption and desorption processes.20 This explains why the pseudohomogeneous model is not able to reproduce the experimental results from the present work, although it has often been used successfully for describing kinetics of reactions catalyzed with cationic ionexchange resins (e.g., see refs 21 and 22). Therefore, an adsorption−desorption based modified Langmuir−Hinshelwood−Hougen−Watson (LHHW) model23 is used in this work to describe the reaction kinetics. The adsorption−desorption based kinetic model consists of three steps: (a) adsorption of the educts from the bulk phase on the catalyst surface, (b) reaction of the adsorbed species on the surface, and (c) desorption of the products back to the bulk phase. In the original LHHW model the surface reaction (b) is assumed to be the rate determining step. The adsorption (a) and desorption (c) processes are considered to be very fast so that adsorption equilibrium is established. For the reasons discussed above the original LHHW model would be inadequate for describing the experimental results from the present study. To succeed in this, in the modified LHHW

riads = kiads(T ) ·xi·θS

(27)

kads i

The proportionality constant is the adsorption rate constant of component Ai. The desorption rate rdes i is given by rides = kides(T ) ·θi

(28)

in which θi is the fraction of active sites that are occupied by component Ai. The variable kdes denotes the desorption rate i constant of component Ai. The rate of change of the amount ni of component Ai in the bulk is given by the difference of desorption and adsorption rate dni H+ = mcat ·ccat ·(rides − riads) dt

(29) +

where mcat is the total mass of catalyst and cHcat the active sites per mass catalyst (capacity). In adsorption equilibrium the bulk phase is stationary and the following holds: riads = rides

(30)

The adsorption equilibrium constant equals the adsorption rate constant divided by the desorption rate constant. K iAD(T ) = 12757

kiads(T ) kides(T )

=

θi xi·θS

(31)



Article

reactions. Therefore, the remaining four parameters had to be globally fitted to the kinetic experiments. As initial guesses the adsorption equilibrium constants were set to values, in a way so that the fraction of free active sites in the equilibrium was about + 0.1 mol/mol. The capacity cHcat was assumed to be 0.43 mol H+/ kgcat as given by the supplier of the catalyst.18 The temperature dependency of the four parameters is again modeled according to eq 22. The correlation parameters aj and bj were fitted globally to the experiments KIN1−KIN6 (cf. Table 2) and KIN7 (cf. Table 3). The objective of the fit was to minimize the sum of all squared errors of the mole fractions of every component except of formaldehyde. Tables 5 and 6 list all

The very fast surface reactions of the adsorbed species (24)− (26) lead to a permanent reaction equilibrium on the catalyst surface which is described by reaction equilibrium constants K 2S(T ) = K nS(T ) =

θS·θOME2 θDMM·θFA

(32)

θS·θOMEn

n>2

θOMEn−1·θFA

S KTRI (T ) =

(33)

θFA 3 θTRI·θS2

(34)

The adsorption-based kinetic and equilibrium model presented above has many parameters. For every chemical species Ai in the bulk phase there are two independent, temperature dependent parameters that describe the adsorption/desorption processes. Here, the adsorption rate constant AD kads are chosen as i and the adsorption equilibrium constant Ki des parameters. The desorption rate constant ki follows from eq 31. For every surface reaction j there is one temperature dependent equilibrium constant KSj . For the given system of 10 chemical species in the bulk and 8 surface reactions there is a total of 28 independent, temperature dependent parameters. To reduce this very large number of parameters, the following assumptions are used. First, methylal and all OMEs are treated equally throughout the model. All adsorption constants, as well as the equilibrium constants of their formation reactions are set equal and named with the index OME. ads ads ads ads k OME = kDMM = k OME = k OME 2 n

(35)

AD K OME

(36)

=

AD KDMM

=

AD K OME 2

S K OME = K 2S = K nS

=

AD K OME n

n>2

Table 5. Adsorption and Desorption Rate Constants of the Adsorption-Based Reaction Kinetic Model: ln Ki/(mol/ (s·mol of H+)) = aj + bj/(T/K) ki

ai

bi

−1 kads OME/s −1 kads /s TRI −1 kdes OME/s des −1 kTRI/s

9.0878 5.2380 9.0878 4.5523

−2074 −1021 −2074 −2278

a Fitted to kinetic data. constants.

b

a b

Calculated from adsorption equilibrium

Table 6. Adsorption Equilibrium and Surface Reaction Equilibrium Constants of the Adsorption-Based Reaction Kinetic Model: ln Kj = aj + bj/(T/K)

a

Kj

aj

bj

KAD OME KAD TRI KSOME KSTRI

0 0.6857 −0.3636 −0.4045

0 1257 35 −472

a b

Fitted to kinetic data. bCalculated from bulk equilibrium data.

(37)

the resulting parameters of the model. In Figures 9−12 examples for comparisons between the model and the experiments are given (experiments KIN1, KIN3, KIN7). The quality of the fit is similar for all experiments KIN1−KIN7.

Further, the adsorption rate and adsorption equilibrium constants of formaldehyde and trioxane are set equal. ads ads k TRI = kFA

(38)

AD AD KTRI = KFA

(39)

By specifying the equilibrium constants of the surface reactions KSj and the adsorption equilibrium constants KAD j , we also describe the bulk equilibrium. The previously defined bulk equilibrium constants KOME and KTRI could be calculated from eqs 31−34, resulting in the following relations. S AD K OME = K OME ·KTRI

KTRI =

⎛ 1 ⎞2 ⎟ AD ⎝ KTRI ⎠

S KTRI ·⎜

(40)

(41)

Figure 9. Concentration profiles of experiment KIN1 (cf. Table 2). Experimental values: markers. Adsorption-based model: solid lines.

The assumptions lead to a considerable simplification of the model. Only four independent, temperature dependent model parameters have to be fitted to experimental kinetic data: kads OME, AD AD S S kads TRI, KOME, and KTRI. The parameters KTRI and KTRI result from eqs 40 and 41 and ensure that the previously determined bulk equilibrium is properly described. As all components except methylal are unstable when brought in contact with the catalyst, it was not possible to measure the adsorption equilibria separately from the chemical

Discussion Reaction Kinetics. The agreement between the adsorption-based model and the data from experiments KIN1−KIN7 is good. The model is able to reproduce the simultaneous formation of OMEs of different chain lengths. The rate limiting steps are the adsorption and desorption processes of all components. New species are not formed one after another, but simultaneously. This is particularly demonstrated in experiment KIN7 (cf. Figures 11 and 12), in 12758



Article

predicted by the model. This might have different reasons. The equilibrium as well as the sorption rates could depend on composition. Bigger molecules could adsorb at different rates as smaller ones. The model assumes that all OME have the same adsorption rate constant. Further the reaction volume is bigger in these experiments (about 600 mL compared to about 500 mL in the other experiments.) This might have changed the fluid dynamics in the reactor. The total volume of catalyst in the reactor was very small compared to the volume of the bulk phase. If only a small number of catalyst beads are trapped in a dead zone in the reactor for some time, there could be an influence on the reaction rate. The good agreement of the model with the experimental data of kinetic experiments for large times indicates that the kinetic data and the equilibrium data are consistent. It is again stressed that the kinetic model of this work and its parameters should only be applied for water-free systems and the catalyst Amberlyst 46. Zhao et al.10 who used a system containing methanol and water, found that the chain length of the OMEs may influence the mechanism of their formation at the surface of catalytic molecular sieves. This finding could not be confirmed for the chemical system and the catalyst of this work.


■

CONCLUSION In the present work the OME formation reactions from methylal and trioxane were studied. Equilibrium and kinetic data were measured using a stirred batch reactor and the heterogeneous catalyst Amberlyst 46, which minimizes side product formation. The concentrations of all main components in the chemical equilibrium are described well by a model developed in the present work. A pseudohomogeneous kinetic model was not able to represent the experiments for strongly varying initial compositions. An adsorption-based model which differentiates between sorption processes and surface reaction processes succeeded to represent the results properly. The sorption processes are the rate determining steps in the model, whereas the surface reactions are comparatively fast. The new model is important for developing a new process for the production of the innovative fuel additive OME.


Figure 12. Concentration profiles of experiment KIN7 (cf. Table 3) enlarged. Experimental values: markers. Adsorption-based model: solid lines.

■

which a completely different feed mixture (DMM and OME2) is used. For experiments KIN8 and KIN9, which were not included in the fit, the model is fully predictive. There are slightly larger deviations (cf. Figure 13 showing the results for experiment KIN8). The fraction of methylal in the equilibrium is slightly underpredicted. The experiment is slightly slower than

APPENDIX

Gas Chromatography (GC)

The Hewlett-Packard HP6890 GC was equipped with Restek Rtx-200 column (530 μm i.d., 30 m). The carrier gas was helium with a column flow of 2.0 mL/min. The injector was used in split-mode with a split ratio of 15. The samples were quantified using the internal standard method using tetrahydrofuran (THF) as standard. The temperature profile is given in Table 7. Table 7. Temperature Profile with Ramps Used for GC Analysis

init ramp ramp ramp ramp ramp

Figure 13. Concentration profiles of experiment KIN8 (cf. Table 3). Experimental values: markers. Adsorption-based model: solid lines. 12759

slope/(°C/min)

final value/°C

hold time/min

70 70 69 69 10

50 70 130 230 250 270

6.0 2.5 3.5 2.0 6.0 10.0



Article

Determination of Formaldehyde Concentration

For the given system of eight reactions the model has eight temperature dependent parameters, the reaction rate constants kfj. To reduce the number of parameters, the rate constants of the seven reactions 1 and 2 are assumed to be equal and named kfOME. The temperature dependences of kfOME and kfTRI are correlated with eq 22. The correlation parameters aj and bj (cf. eq 22) were fitted globally to the experiments KIN1−KIN6 (cf. Table 2) and KIN7 (cf. Table 3). The objective of the fit was to minimize the sum of all squared errors of the mole fractions of every component except of formaldehyde. Table 8 lists the parameters resulting from the fit.

Formaldehyde concentrations are usually determined by titration with the sodium sulfite method.13 In aqueous and methanolic solutions the sodium sulfite method yields the overall formaldehyde concentration (including the formaldehyde bound in the reaction products of formaldehyde with water and methanol). The monomeric formaldehyde concentration in these solutions is low. The present analytical problem differs strongly from that standard problem. Formaldehyde is mainly present as monomer in the solutions studied here. Furthermore, we are interested in the concentration of monomeric formaldehyde rather than in the overall concentration. The sodium sulfite method is applied as described by Walker.13 Hydrochloric acid (1 mol/L) is used as titer. The end point at pH 9.4 is determined using a pH electrode. In the solutions studied here the result includes not only the monomeric formaldehyde but also the fraction of formaldehyde that is bound to methanol. Even though methanol is only a side product, the reaction of formaldehyde with methanol cannot be completely neglected as its equilibrium is far on the product side. To estimate the monomeric formaldehyde concentration from the measured overall concentration, a model of the chemical equilibrium in the system formaldehyde + methanol is needed. In this work the activity based equilibrium model of Kuhnert et al.24 is used. To calculate the activities of the reacting components, it is assumed that the binary interactions between any component and OME are equal to the binary interactions between the species and methylal that has been already included in the model of Kuhnert et al. As the methanol concentration in the experiments was rather low, the detected formaldehyde was found to be mainly monomeric formaldehyde.

Table 8. Rate Constants of the Pseudohomogeneous Model: ln kfj/(mol/(s·mol H+)) = aj + bj/(T/K)

■

⎛ ⎞ 1 xOMEn⎟ r2 = knf (T )⎜xOMEn−1·x FA − K n(T ) ⎝ ⎠

(43)

⎛ ⎞ 1 f r3 = k TRI (T )⎜x TRI − x FA 3⎟ KTRI(T ) ⎝ ⎠

■

0 −1871.1

ASSOCIATED CONTENT

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

NOMENCLATURE

Abbreviations

A46 DME FA FID GC HFn DMM ME MEFO OME OMEn TRI

Amberlyst 46 dimethyl ether formaldehyde flame ionization detector gas chromatograph hemiformal of chain length n methylal (dimethoxymethane) methanol methyl formate poly(oxymethylene) dimethyl ethers OME of chain length n trioxane

Symbols and Indices

aj Ai bj + cHcat H+ i j kads i kfj kdes i Kj K*j KSj

(44)

The variables kjf are the temperature dependent rate constants of the reactions. The use of the bulk equilibrium constants Kj ensures consistency to the bulk equilibrium model. The rate of change of the mole number ni of component Ai in the bulk is dni H+ = mcat ·ccat ·∑ νi jrj dt j

bj

Tables: bulk equilibrium compositions (Table S1), kinetic composition profiles (Tables S2−S10). Figures: comparisons of kinetic models and experiments (Figures S1−S5). This material is available free of charge via the Internet at http://pubs.acs. org/.

In the pseudohomogeneous approach the active sites of the catalyst are assumed to be homogeneously distributed in the bulk phase and freely accessible. The reaction rates depend on mole fractions of the educts and products in the bulk. For reactions 1−3 the rates rj are given by the following expressions.

(42)

aj 18.42 −1.29

S Supporting Information *

Pseudohomogeneous Kinetic Model

⎞ ⎛ 1 r1 = k 2f(T )⎜x DMM ·x FA − xOME2⎟ K 2(T ) ⎠ ⎝

kfj kfOME kfTRI

(45)

where vji is the stoichiometric coefficient of component Ai in reaction j. 12760

temperature correlation parameter place holder component temperature correlation parameter catalyst capacity proton, acidic component index reaction index adsorption rate constant reaction rate constant desorption rate constant bulk equilibrium constant bulk equilibrium constant altern surface equilibrium constant dx.doi.org/10.1021/ie301490q | Ind. Eng. Chem. Res. 2012, 51, 12751−12761

Industrial & Engineering Chemistry Research KAD i mcat ni p rads i rdes i rj S t T xi xEQ i θi θS vji

■

Article

reference: chemical equilibria and reaction kinetics of formaldehydewater-1,3,5-trioxane. Anal. Bioanal. Chem. 2006, 385, 910−917. (17) Bernard, K. A.; Atwood, J. D. Evidence for C-0 Bond Formation, Aldehyde Decarbonylatlon, and Dimerization by Reaction of Formaldehyde and Acetaldehyde with trans-ROIr(CO)(PPh3)2. Organometallics 1987, 7, 235−236. (18) Rohm and Haas Company, Amberlyst Polymeric Catalysts, Data sheet. 2005. (19) Hasse, H. Dampf-Flüssigkeits-Gleichgewichte, Enthalpien und Reaktionskinetik in formaldehydhaltigen Mischungen; Dissertation, University of Kaiserlautern, 1990. (20) Chakrabarti, A.; Sharma, M. Cationic ion exchange resins as catalyst. React. Polym. 1993, 20, 1−45. (21) Schmitt, M.; Hasse, H. Chemical Equilibrium and Reaction Kinetics of Heterogeneously Catalyzed n-Hexyl Acetate Esterification. Ind. Eng. Chem. Res. 2006, 45, 4123−4132. (22) Pöpken, T.; Götze, L.; Gmehling, J. Reaction Kinetics and Chemical Equilibrium of Homogeneously and Heterogeneously Catalyzed Acetic Acid Esterification with Methanol and Methyl Acetate Hydrolysis. Ind. Eng. Chem. Res. 2000, 39, 2601−2611. (23) Hougen, O. A.; Watson, K. M. Chemical Process Principles; John Wiley: New York, 1947. (24) 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.

adsorption equilibrium constant mass of dry catalyst amount of component Ai in the bulk pressure adsorption rate component Ai desorption rate component Ai reaction rate of reaction j surface time temperature mole fraction in bulk mole fraction in bulk equilibrium mole fraction on the catalyst surface mole fraction free active sites stoichiometric coefficient

REFERENCES

(1) Natarajan, M.; Frame, E. A.; Naegeli, D.; Asmus, T.; Clark, W.; Garbak, J.; Gonzales, M.; Liney, E.; Piel, W.; Wallace, J. Oxygenates for Advanced Petroleum-Based Diesel Fuels: Part 1. Screening and Selection Methodology for the Oxygenates. SAE Pap. 2001, 2001− 01−3631. (2) 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. (3) Lumpp, B.; Rothe, D.; Pastötter, C.; Lämmermann, R.; Jacob, E. Oxymethylene Ethers as Diesel Fuel Additives of the Future. MTZ 2011, 72, 34−38. (4) Ströfer, E.; Hasse, H.; Blagov, S. Verfahren zur Herstellung von POMDME aus Methanol und Formaldehyd. Patent DE 1020050277020, 2006. (5) Ströfer, E.; Schelling, H.; Hasse, H. Verfahren zur Herstellung von Polyoxymethylendialkylethern aus Trioxan und Dialkylether. Patent DE 102005027690, 2005. (6) Hagen, G.; Spangler, M. Preparation of Polymethylene Dimethyl Ethers by Reaction of Dimethylether with Formaldehyde over Heterogeneous Catalysts. Patent WO 00/29364, 2000. (7) Hagen, G.; Spangler, M. Preparation of Polymethylene Dimethyl Ethers by Acid-activated Catalytic Conversion of Methanol with Formaldehyde. Patent WO 00/29365, 2000. (8) Hagen, G.; Spangler, M. Preparation of Polymethylene Dimethyl Ethers by Catalytic Conversion of Formaldehyde Formed by Oxidation of Dimethyl Ether. Patent US 6392102, 2000. (9) Schelling, H.; Ströfer, E.; Pinkos, R.; Haunert, A.; Tebben, G.; Hasse, H.; Blagov, S. Verfahren zur Herstellung von POMDME. Patent WO 2006/045506, 2006. (10) Zhao, Q.; Wang, H.; Wu, Z. F. Q. Z. W.; Wu, J. B.; Fan, W. B.; Wan, J. G. Synthesis of polyoxymethylene dimethyl ethers from methanol and trioxymethylene with molecular sieves as catalysts. J. Fuel Chem. Technol. 2011, 39, 918−923. (11) Arvidson, M.; Fakley, M. E.; Spencer, M. S. Lithium Halideassisted Formation of Polyoxymethylene Dimethyl Ethers from Dimethoxymethane and Formaldehyde. J. Mol. Catal. 1987, 41, 391−393. (12) Ott, M. Reaktionskinetik und Destillation formaldehydhaltiger Mischungen; Shaker: Aachen, 2004. (13) Walker, J. F. Formaldehyde, 3rd ed.; Reinhold Publishing Corp.: London, 1964. (14) Albert, M. Thermodynamische Eigenschaften formaldehydhaltiger Mischungen; Shaker: Aachen, 1999. (15) 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. (16) Maiwald, M.; Grützner, T.; Ströfer, E.; Hasse, H. Quantitative NMR spectroscopy of complex technical mixtures using a virtual 12761


Chemical Equilibrium and Reaction Kinetics of the Heterogeneously

Recommend Documents