Kinetics of Synthesis of Polyoxymethylene Dimethyl Ethers from Paraformaldehyde and Dimethoxymethane Catalyzed by Ion-Exchange Resin
Chemical Engineering Science 134 (2015) 758–766
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Chemical Engineering Science
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Kinetics of synthesis of polyoxymethylene dimethyl ethers from paraformaldehyde and dimethoxymethane catalyzed by ion-exchange resin
Yanyan Zheng, Qiang Tang, Tiefeng Wang n, Jinfu Wang n
Beijing Key Laboratory of Green Reaction Engineering and Technology, Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
HIGHLIGHTS
Kinetics of synthesis of PODEn from paraformaldehyde and methylal was studied. The transient molecular size distribution of PODEn follows Schulz–Flory model. The rate constants are the same for reversible propagation reactions of PODEn. The sequential reversible reactions to produce PODEn are exothermic. article info abstract
Article history: Polyoxymethylene dimethyl ethers (CH3–O–(CH2O)n–CH3, PODEn, n41) are new concerned environ- Received 1 February 2015 mental benign alternative components for diesel fuels. This work aimed to investigate the kinetics of Received in revised form synthesis of PODEn from paraformaldehyde and dimethoxymethane catalyzed by ion-exchange resin 27 May 2015 NKC-9. Experiments were conducted in a designed space, namely reaction temperatures (60, 70, and Accepted 30 May 2015 80 1C) vs. reaction times (2, 5, 10, 20, 30, 60, and 90 min), in a batch stirred autoclave. The transient Available online 12 June 2015 molecular size distribution of PODEn compounds from paraformaldehyde and methylal followed Schulz– Keywords: Flory distribution model. In this system, the concentration of formaldehyde in the homogenous solution Polyoxymethylene dimethyl ethers (CF) was nearly constant. The sequential reversible reactions to produce PODEn were verified to follow a Kinetics second-order kinetics for propagation and a first-order kinetics for depolymerization. The rate constants Schulz–Flory distribution of propagation (k ) and depolymerization (k ) and the reaction equilibrium constant K were the same Sequential reversible reactions p d n for the series of PODEn synthesis reactions. Respecting to 5 wt% dosage of NKC-9 resin catalyst, the pre- 7 –1 –1 exponential factors Ap for propagation and Ad for depolymerization were 1.84 10 L mol min and 6 –1 –1 5.36 10 min , respectively. The activation energy Ep (39.52 kJ mol ) for propagation was lower than –1 Ed (52.01 kJ mol ) for depolymerization, validating that the reversible reactions of producing PODEn compounds were exothermic. & 2015 Elsevier Ltd. All rights reserved.
1. Introduction matter with an aerodynamic diameter less than 2.5 mm) in air usually exceeds 100 mgm–3, which is seriously detrimental to The combustion of petroleum-derived fuels is an important human health (Lin et al., 2009). Reducing the emissions of source of key precursors to the formation of secondary organic precursors to secondary aerosol from gasoline and diesel vehicle aerosol (Hallquist et al., 2009; Volkamer et al., 2006; Worton et al., emissions is important for controlling the PM 2.5 levels and 2014). The accumulation of secondary organic aerosol in air improving environmental and air qualities in China (Huang et al., contributes to particulate pollution during haze events (Huang 2014). Diesel engines have a higher thermal efficiency than gaso- et al., 2014). In China, the concentration of PM 2.5 (particulate line engines. However, diesel exhaust is seven times higher in forming aerosol than gasoline exhaust (Gentner et al., 2012). Generally, the combustion of diesel is responsible for 65 90% of
n vehicular-derived secondary organic aerosol (Gentner et al., 2012). Corresponding authors. Tel.: þ86 10 62794132; fax: þ86 10 62772051. – – – – E-mail addresses: [email protected] (T. Wang), Polyoxymethylene dimethyl ethers (CH3 O (CH2 O)n CH3, [email protected] (J. Wang). PODEn, where n41), which are environmental benign alternative http://dx.doi.org/10.1016/j.ces.2015.05.067 0009-2509/& 2015 Elsevier Ltd. All rights reserved. Y. Zheng et al. / Chemical Engineering Science 134 (2015) 758–766 759 components for diesel fuels, are receiving increasing attentions in proposed an equilibrium molecular size distribution model based recent years (Burger and Hasse, 2013; Burger et al., 2010, 2012, on a sequential reaction mechanism, but did not study the kinetics
2013; Lumpp et al., 2011). Compared with the reference diesel fuel, in detail. The synthesis of PODEn from PF and DMM involved the the PM emissions are reduced by 18% with 10% blend and by 77% depolymerization of solid PF raw materials and sequential rever- with pure PODEn (Pellegrini et al., 2013). Among the PODEn sible chain propagation reactions, thus possessing very different oligomers, PODE3–5 compounds are the most ideal diesel additives, kinetic properties from other PODEn synthesis systems. while PODE2 does not fulfil the security criteria due to its low flash In the present work, the synthesis of PODEn from PF and DMM point, and PODEn 45 precipitate at low temperatures due to their catalyzed by NKC-9 acidic ion-exchange resins was conducted in high melting points (Zheng et al., 2013). Compared with methanol, the designed space, namely reaction temperatures (60, 70, and dimethyl ether (DME) and dimethoxymethane (DMM), the physi- 80 1C) and reaction times (2, 5, 10, 20, 30, 60, and 90 min), in a cochemical properties of PODE3–5 match well with that of petro- batch stirred autoclave. To the best of our knowledge, this article is leum diesel, thus allowing the use of PODE3–5 in modern diesel the first report on kinetics of synthesis of PODEn from DMM and PF engines without any change of the engine infrastructure catalyzed by ion-exchange resin. A kinetic model was developed (Pellegrini et al., 2013; Zheng et al., 2013). The application of assuming that the sequential reversible reactions to produce
PODEn is promising to relieving both air pollution and petroleum PODEn compounds follow a second-order kinetics for propagation shortage. and a first-order kinetics for depolymerization. Rate constants at
The PODEn compounds are prepared from end-group (–CH3, – different temperatures were obtained by least-squares aggression O–CH3) provider (DMM or methanol) and chain-group (–CH2O) of the experimental concentration of DMM as a function of provider (paraformaldehyde (PF), trioxane, or formaldehyde solu- reaction time. The Arrhenius parameters, including the pre- tion) over acid catalysts. Recent papers on synthesis of PODEn have exponential factor and activation energy, were calculated from focused on catalyst preparation and characterization, and process the rate constants at different temperature. optimization. Various acidic catalysts, including acidic ion- exchange resins (Wang et al., 2014; Zheng et al., 2013, 2014; Burger et al., 2012), ionic liquids (Wu et al., 2014), molecule sieves 2. Experimental (Zhao et al., 2011), and solid superacids (Li et al., 2015; Zhang et al.,
2014), have been employed in synthesis of PODEn. Burger et al. 2.1. Materials (2012) proposed that water reacts with ethers and form alcohols 4 during the synthesis of PODEn from DMM and trioxane in the acid- DMM (analytic reagent grade, 99 wt%) was purchased from catalyzed system. To illustrate the effect of water on the synthesis Alfa Aesar-Johnson Matthey. PF (polymer grade, 496 wt%) was of PODEn from DMM and PF, we investigated the product dis- purchased from Sinopharm Chemical Reagent Co., Ltd. The NKC-9 þ tribution with different dosages of water added in this work, as acidic ion-exchange resin (H type) was provided by Tianjin shown in Table 1. The results showed that water induced the Bohong Resin Technology Co., Ltd. – 4 hydrolysis of DMM and PODEn compounds forming methanol and PODE2 5 (industrial grade, 95%) were provided by a 10 kt/a formaldehyde. In particular, when the added dosage of water PODE industrial plant in Shandong Yuhuang Chemical (Group) Co., exceeded 5 wt%, the hydrolysis reactions became crucial, and Ltd. in China using the technology developed by our research fl significantly decreased the yield of PODEn products and increased group. In this technology, a uidized bed reactor was used to the complexity of product purification. To avoid introducing or produce PODEn from DMM and PF over solid acid catalyst. These fi generating water, DMM is a better end-group provider than PODE2–5 samples were further puri ed to analytic reagent grade methanol, while PF and trioxane are better chain-group provider (499%) and used as standard samples in quantitative analysis of than formaldehyde solution. PODEn product. Kinetics is of great importance for the molecular size distribu- tion regulation, process optimization and reactor design for 2.2. Experimental setup and procedure synthesis of PODEn. However, the studies on the kinetics of synthesis of PODEn are very limited. Burger et al. (2012) reported The schematic of the experimental setup for synthesis of PODEn the reaction kinetics of the heterogeneously catalytic formation of from PF and DMM catalyzed by NKC-9 is shown in Fig. 1. Previous
PODEn from DMM and trioxane, and proposed an adsorption- works (Zheng et al., 2013, 2014) showed that NKC-9 had a high based kinetic model to describe the results. Zhang et al. (2014) catalytic activity and good stability for the production of PODEn synthesized PODEn from methanol and formaldehyde solution and from PF and DMM. Therefore, NKC-9 was used in this work with a proposed a kinetic model based on an elimination mechanism. In dosage of 5.0 wt% relative to the mass of feedstocks (PFþDMM). our previous work (Zheng et al., 2014), we reported the synthesis To obtain a high conversion of formaldehyde and low yield of long of PODEn from DMM and PF over acidic ion-exchange resins and chain PODEn 4 5 compounds, the DMM/CH2O molar ratio of the feeding was set 2 (Zheng et al., 2013, 2014). Considering that the maximum tolerance temperature of NKC-9 resin was 100 1C, the Table 1 experiments were carried out in a designed space, namely the Compound distribution in PODEn products formed by DMM and PF with different reaction temperatures (T¼60, 70, and 80 1C) versus reaction times dosages of water added (80 1C, DMM/CH O molar ratio 3:1, 5 wt% NKC-9 resin as 2 (t¼2, 5, 10, 20, 30, 60, and 90 min), in a 0.5-L batch stirred catalyst). autoclave. Compound distribution Added dosage of water (wt%) To obtain reliable kinetic data, all the experiments were conducted strictly using the following procedures. Firstly, PF and 0 5 10 15 20 25 DMM were mixed and loaded into the reactor; then, the reactor
Methanol (wt%) 1.817 4.825 8.040 10.528 11.610 13.101 was sealed and heated; once the reactor temperature reached the Formaldehyde (wt%) 0.927 12.049 20.629 27.310 28.206 29.069 specific value, the catalyst (NKC-9 ion-exchange resin) was DMM (wt%) 67.291 60.061 53.934 48.985 48.017 47.518 released from the fragile bottle and then uniformly dispersed by PODE2 (wt%) 20.193 17.502 14.523 11.774 10.976 9.580 stirring at 500 rpm. This moment was considered as the starting PODE – (wt%) 9.626 5.516 2.873 1.403 1.192 0.732 3 5 time of reaction. The liquid phase was sampled at different PODEn45 (wt%) 0.146 0.044 0.000 0.000 0.000 0.000 reaction times for analysis. 760 Y. Zheng et al. / Chemical Engineering Science 134 (2015) 758–766
Fig. 2. Scheme of the formation of PODEn compounds from PF and DMM catalyzed over NKC-9 ion-exchange resin. Fig. 1. Schematic of the experimental setup for synthesis of PODEn from PF and DMM catalyzed over NKC-9.
2.3. Analysis Fig. 2. The NKC-9 strong acidic ion-exchange resin was made of polystyrene sulfonate. The featured sulfonic acid groups work as
The product distribution of the PODEn compounds was quantita- the reactive sites. In this scheme, the depolymerization of PF to tively analyzed using gas chromatography–mass spectrometry (GC– formaldehyde (reaction (1)) and the sequential chain propagation
MS). The product sample (0.5 mL) was diluted with 5 mL of unde- reactions of PODEn compounds (reactions (2) and (3)) occurred on cane. One microliter of the solution was injected into a Shimadzu the acid sites. The sequential chain propagation reactions are
2010 plus GC equipped with an MXT-5 column (5% diphenylþ95% reversible: DMM and PODEn react with formaldehyde to propa- dimethyl polysiloxane, 30 m 0.25 mm 0.1 mm) and a flame ioni- gate, and PODEn þ1 reversely depolymerize to PODEn and formal- zation detector (FID). The detailed temperature program of the GC dehyde. column was described elsewhere (Zheng et al., 2013, 2014). Nitrogen þ ð Þ H⇌ þ ð Þ was used as carrier gas. An Agilent G2579A MS was used to identify HO CH2O mH mCH2O H2O 1 the species with different residence times in the GC column. Although water can induce significant side reactions, the use of kp;1 DMMþCH2O ⇌ PODE2 ð2Þ anhydrous DMM (99%) and paraformaldehyde (496%) decreases the kd;1 water content to a very low concentration. Even if all the impurity in the feedstocks is water, the amount of water is o0.70 wt% in the kp;n PODEn þCH2O ⇌ PODEn þ 1ðn⪢1Þð3Þ feedstocks. Less than 1 wt% side-product methanol was formed and kd;n was neglected in further analysis. A set of relative mass correction where kp,j (j¼1, n) and kd,j (j¼1, n) are the rate constants of the factors of PODEn compounds (with DMM as reference) were mea- forward (propagation) and reverse (depolymerization) reactions, – sured using standard samples PODE2 PODE5.Itwasfoundthatthe respectively. For reactions (2) and (3), the values of k and k ¼ – p,j d,j relative mass correction factors for PODEn (n 2 5) is a geometrical were independent of j, as shown in Eqs. (4) and (5), which was series, which was similar to the results Burger et al. (2012) found validated by our previous study (Zheng et al., 2014) on molecular during their PODEn quantitative analysis. The relative mass correction size distribution model for the same process. factors for PODEn with longer polymerization degree were calculated ¼ ¼ ⋯ ¼ ¼ ð Þ by extrapolation. Using the above correction factors, the error in kp;1 kp;2 kp;n kp 4 carbon balance was within 73%. ¼ ¼ … ¼ ¼ ð Þ The concentration of formaldehyde was determined using kd;1 kd;2 kd;n kd 5 fi titration by the sodium sul te method provided by ASTM D2194- The theoretical molecular size distribution model of PODEn was 02 (2012). Different from Burger's attempt in PODEn system from developed based on the sequential reaction mechanism (Zheng DMM and trioxane (Burger et al., 2012), the titration by the et al., 2013, 2014). The molecular size distribution model followed sodium sulfite method used in this work could be calibrated and the Schulz–Flory distribution (Zheng et al., 2014): had a good reproducibility. The difference was attributed to the M þM ðn 1Þ an 1 different depolymerization properties of trioxane and PF in w ¼ DMM CH2O ð6Þ n M þM a ð1þaÞn sodium sulfite solution (Kiernan, 2000; Maurer, 1986). The repro- DMM CH2O ducibility experiments were conducted for three times for each where wn is the mass fraction of PODEn compound, MDMM is the sample, and the relative error was estimated to be within 73%. molecular weight of DMM, MCH2O is the molecular weight of formaldehyde, and a is a dimensionless factor equaling to the ratio of reacted amount of formaldehyde to initial amount of 3. Reactions and product molecular size distribution DMM.
NCH2O;R The scheme of the formation of PODEn compounds from PF and a ¼ ð7Þ N ; DMM catalyzed by NKC-9 ion-exchange resin is demonstrated in DMM 0 Y. Zheng et al. / Chemical Engineering Science 134 (2015) 758–766 761
The natural logarithm form of Eq. (6) is Based on Eq. (8),thevalueofa was determined from the slope or þ intercept of the line between ln(wn/(n 1.533)) and n.Thecalculated wn a 1 values of a from the slope and from the intercept are the same within ln ¼ n ln þ ln ð8Þ nþ1:533 aþ1 að2:533þaÞ the deviation 73%. The average of the calculated values of a from the slope and from the intercept was used. Fig. 3(d) presents the values of By analogy with the formation of poly-(oxymethylene) glycols a as a function of reaction time at 60, 70 and 80 1C. The corresponding (Burger et al., 2012), the sequential propagation mechanism leads value of a at different reaction times reflects the extent of chain to an equilibrium molecular size distribution of PODEn compounds propagation. The value of a gradually increased with increasing that depends on the factor a.Bydefinition, the factor a is reaction time until the equilibrium was approached, indicating the determined by conversion of formaldehyde and initial molar gradual shift of the product distribution to longer chains. In the range feeding ratio of DMM/CH2O. of 60–80 1C, the equilibrium value of a increased with increasing Although derived from equilibrium state (Zheng et al., 2014), reaction temperature. This was because depolymerization of PF to the theoretical molecular size distribution model was found to be formaldehyde was endothermic while propagation of DMM or PODEn applicable to transient state in the present work. As illustrated in was exothermic, and the whole reaction system showed an overall
Fig. 3, the plots of ln(wn/(nþ1.533)) exhibited a good linear weak endothermic effect, which accounted for the shift of the relationship with respect to n corresponding to the transient distribution to longer chains with increasing temperature. In another molecular size distribution of PODEn compounds in the design perspective, the increased temperature enhanced the equilibrium space, validating the application of the model at transient state. concentration of formaldehyde in solution, thus shifted the distribu-
This is because the values of kp and kd are independtent of n, tion to long chain, which was in consistent with to the results of which means the same reactivity of PODEn compounds indepen- Burger et al. (2012) on synthesis of PODEn from DMM and trioxane. dent of molecular size during the chain propagation. Using statistical method (Flory, 1940; Kissin, 1995; Schulz, 1999;
Tavakoli et al., 2008), the same reactivity of PODEn compounds 4. Kinetic modeling lead to transient molecular size distribution model the same expression with Eq. (6), accounting for the applicability of the In the kinetic modeling, the reaction system was assumed to molecualr size distribution model at transient state. have a constant volume with an average density of 1.0 g cm–3.
Fig. 3. Plots of ln(wn/(nþ1.533)) with respect to n and the calculated a value at different reaction times and different reaction temperatures (DMM/CH2O molar ratio of 2:1, dosage of NKC-9 at 5 wt%). 762 Y. Zheng et al. / Chemical Engineering Science 134 (2015) 758–766
Thus, the mass fraction (wi) and mole concentration (Ci) has the following relationship:
wi Ci ¼ ði ¼ F; 1; nÞð9Þ Mi where wi is the mass fraction of compound i relative to the total mass of all the homogeneous compounds (including homogenous formaldehyde, DMM, and PODEn compounds), Mi is the molecular weight of compound i, and Ci is the concentration of compound i. The subscripts F, 1 and n (41) refer to formaldehyde, DMM and
PODEn, respectively. Formaldehyde is a substance with complex existence forms in the PODEn solution (Maurer, 1986). In this work, the concentration of formaldehyde in the solution measured by titration with sodium sulfite included formaldehyde of different forms. The formaldehyde in different forms simultaneously react with PODEn propagating to PODEn þ 1 with the same reaction rate constant (Zhang et al., 2014). To simplifying the model, formaldehyde of Fig. 5. Equilibrium constant Kn at different temperatures for propagation of PODEn different forms in the solution were all included in the concentra- compounds (DMM/CH2O molar ratio of 2:1, dosage of NKC-9 at 5 wt%). tion of formaldehyde (CF) in the kinetics model. As shown in Fig. 4, CF increased at initial period before 10 min and then kept at a constant level, suggesting that depolymerization of paraformalde- The effects of internal and external diffusions on the conversion 1 hyde is not the rate limiting step. With a DMM/CH2O molar of formaldehyde at 60 min were investigated at 80 C with DMM/ feeding ratio of 2 and NKC-9 dosage of 5 wt%, the average value CH2O molar feeding ratio of 2 over 5 wt% NKC-9 catalyst, as shown 1 of CF was 0.901, 1.067 and 1.217 mol L at 60, 70 and 80 1C, in Fig. 6. The diffusion affected the conversion of formaldehyde at respectively. This indicated a favorable effect of higher tempera- 60 min when the reaction did not reach equilibrium. The effect of ture on the depolymerization of PF. According to the experimental internal diffusion was eliminated when the catalyst particle m data, CF was considered as a constant during the kinetic modeling diameter was smaller than 1000 m and that of external diffusion of the chain propagation of PODEn. The study on the kinetics of was eliminated at a stirring speed higher than 300 rpm. In this depolymerization of paraformaldehyde is complex and will be work, the experiments were carried out with catalyst particle considered separately in our future work. diameter of 800 mm and stirring speed of 500 rpm. Thus, the
The reversible chain propagation reactions of PODEn com- experimental data represented the intrinsic kinetics for the for- pounds followed a sequential reaction mechanism, and have the mation of PODEn from DMM and PF. following equilibrium constants: In this system, the amount of water introduced by feeding PF was less than 0.70 wt% relative to the mass of feedstocks. The
CPODE2 results showed that the methanol content at equilibrium in the K1 ¼ ð10Þ CDMMCF system was less than 1 wt%, indicating that the hydrolysis side-
reactions of DMM and PODEn played only a minor role and could C PODEn þ 1 be neglected, as discussed in Section 2.3. At DMM/CH2O molar Kn ¼ ðn⪢1Þð11Þ CPODEn CF feeding ratio of 2, the molecular size of PODEn was mainly in the range of n¼2–6, and the amount of PODEn 46 compounds could be The values of K at different temperatures were calculated from n neglected. To simplify the solution of the reaction rate matrix, the experimental equilibrium product distribution data, as shown PODE6 was assumed to be the terminal compound in the chain in Fig. 5. The experimental values of Kn was independent of n. This propagation of PODEn. agreed is well with the assumption that kp and kd are independent The chain propagation reaction of PODEn is condensation of of the molecular size. The average values of Kn were 313.9, 271.0 two molecules (PODE þCH O) into one molecule (PODE þ ). 1 n 2 n 1 and 243.2 at 60, 70 and 80 C, respectively. Supposing a first-order kinetics with respect to each reactant, the reversible chain propagation reactions follow a second-order kinetics for propagation and a first-order kinetics for depolymer- ization, the reaction rate matrix is expressed as
C d ¼ KC dt 2 32 3 kpCF k 0000C 6 d 76 1 7 6 76 7 6 kpCF kpCF kd kd 00076 C2 7 6 76 7 6 0 kpCF kpCF kd kd 0076 C3 7 ¼ 6 76 7 6 76 7 6 00 kpCF kpCF kd kd 0 76 C4 7 6 76 7 4 00 0 kpCF kpCF kd kd 54 C5 5 00 0 0 kpCF kd C6 ð12Þ
where K is the rate constant matrix, and C is the concentration matrix. The initial values for solving Eq. (12) are
1 Fig. 4. Concentration of formaldehyde in the homogenous solution (CF) at different ¼ ; ¼ ; ¼ ð ¼ – ÞðÞ t 0 CDMM c0 CPODEi 0 mol L i 2 6 13 reaction temperatures (DMM/CH2O molar ratio of 2:1, dosage of NKC-9 at 5 wt%). Y. Zheng et al. / Chemical Engineering Science 134 (2015) 758–766 763
Fig. 6. The effects of internal and external diffusions on conversion of formaldehyde at 60 min during synthesis of PODEn from PF and DMM (80 1C, DMM/CH2O molar feeding ratio of 2, 5 wt% NKC-9 catalyst).
XN The analytical solution of the above matrix, namely the con- 2 ESS ¼ ðCi;exp Ci;calÞ ð19Þ centration functions of PODE1–6, could be represented as i ¼ 1 iX¼ 6 λ where N is the number of the data points, Ci,ave is the average value ¼ β þ β ikd t ð Þ Cn f 1 1c0 c0 f i ie 14 of experimental value of Ci, and Ci,exp and Ci,cal are the experi- i ¼ 2 mental values and calculated values of Ci, respectively. For n¼1–6, f are ω, θ, η, ν, κ, δ, respectively. The Arrhenius parameters of propagation reaction of PODEn, The coefficients in the above solutions are expressed in matrix including the pre-exponential factor (Ap, Ad) and activation energy as follows: (Ep, Ed), were determined using the following Arrhenius equation
pffiffi pffiffi 2 : : : : 3 2 3 1 A A3 3A3 5 þ A3 þ A4 3A3 5 þ A3 þ A4 A3 5 þ A3 þ A4 A3 þ A4 A3 5 β 6 2 2 2 2 6 1 A 1 þ A 12ð1 A þ A Þ 12ð1 A þ A Þ 4ð1 þ A þ A Þ 4ð1 þ A þ A Þ 7 6 7 6 pffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffi pffiffiffi 7 6 λ 7 6 7 6 7 6 A 1 3A A 1 3A A 1 A A 1 A A 1 7 6 ω 7 6 2 2 2 2 2 7 6 7 6 1 A pffiffiffiffiffiffiA pffiffiffiffiffiffiA A A 7 6 7 6 : : 7 6 θ 7 6 A A 2 ð 3A 1ÞA 2 ð 3A 1ÞA 2 ðA0 5 1ÞA 2 2A 1 5 7 6 7 ¼ 6 pffiffiffi pffiffiffi 7 ð15Þ 6 η 7 6 2 1 0:5 1:5 0:5 1:5 1:5 1:5 7 6 7 6 A A ð2A 3ÞA ð2A þ 3ÞA A A 7 6 7 6 pffiffiffi pffiffiffi 7 ν : : : : : : 6 7 6 A3 A 1 ð 3 2A0 5ÞA 1 5 ð2A0 5 þ 3ÞA1 5 A 0 5 A0 5 7 6 7 6 pffiffiffi pffiffiffi 7 4 κ 5 6 : : : : : : : : 7 4 A4 1 ðA0 5 3ÞA 0 5 ðA0 5 þ 3ÞA 0 5 ð1 A0 5ÞA 0 5 ð1þA0 5ÞA 0 5 5 δ A5 1 1 11 1
as (20) where E lnðkÞ¼ lnðAÞ ð20Þ RT A ¼ KnCF ð16Þ
Given the experimental concentrations of PODEn compounds at different reaction temperatures (60, 70, and 80 1C) and different 5. Model validation and calculations reaction times (2, 5, 10, 20, 30, 60, and 90 min), the rate constants were estimated using least-squares regression. The coefficient of The concentrations of formaldehyde and PODE1–6 compounds 2 determination (R )defined by Eq. (17) was used to measure the at different operating conditions are listed in Table 2. The PODE2, agreement between the experimental and calculated data. PODE3, PODE4, PODE5 and PODE6 appeared one by one during the reaction period, which further validated the sequential propaga- TSS ESS R2 ¼ ð17Þ tion mechanism in this system. The rate constants kd at different TSS temperatures were obtained by least-squares aggression of the experimental concentration–time data of DMM using Eq. (14) with where total sum of squares (TSS) and explained sum of squares n¼1. The rate constants k at different temperatures were calcu- (ESS)aredefined as p lated from the corresponding Kn data. The Arrhenius parameters XN including the pre-exponential factor (Ap, Ad) and activation energy 2 TSS ¼ ðCi;exp Ci;aveÞ ð18Þ (Ep, Ed) respecting to 5 wt% dosage of NKC-9 resin catalyst were ¼ i 1 listed in Table 3. The values of Ap and Ad were 764 Y. Zheng et al. / Chemical Engineering Science 134 (2015) 758–766
Table 2
Concentrations of formaldehyde (CF) and PODE1–6 (C1–C6) in the designed space during synthesis of PODEn from PF and DMM catalyzed by NKC-9.
1 1 1 1 1 1 1 T (1C) t (min) CF (mol L ) C1 (mol L ) C2 (mol L ) C3 (mol L ) C4 (mol L ) C5 (mol L ) C6 (mol L )
60 0 0.758 12.802 0.000 0.000 0.000 0.000 0.000 2 0.801 12.802 0.141 0.001 0.000 0.000 0.000 5 0.867 11.988 0.659 0.029 0.001 0.000 0.000 10 0.901 11.193 1.224 0.107 0.008 0.001 0.000 20 0.901 10.907 1.407 0.145 0.014 0.001 0.000 30 0.901 10.585 1.602 0.194 0.021 0.003 0.000 60 0.904 10.171 1.833 0.264 0.034 0.005 0.001 90 0.903 9.292 2.250 0.435 0.076 0.015 0.003
70 0 0.853 12.645 0.000 0.000 0.000 0.000 0.000 2 0.927 11.890 0.613 0.025 0.001 0.000 0.000 5 0.978 11.356 1.004 0.071 0.005 0.000 0.000 10 1.065 11.001 1.244 0.112 0.009 0.001 0.000 20 1.067 10.450 1.585 0.192 0.021 0.003 0.000 30 1.087 10.040 1.813 0.261 0.034 0.005 0.001 60 1.078 9.436 2.110 0.377 0.061 0.011 0.002 90 1.083 8.771 2.548 0.627 0.140 0.036 0.009
80 0 1.004 12.666 0.000 0.000 0.000 0.000 0.000 2 1.075 12.186 0.398 0.010 0.000 0.000 0.000 5 1.158 10.981 1.271 0.118 0.010 0.001 0.000 10 1.208 10.238 1.718 0.230 0.028 0.004 0.001 20 1.217 9.526 2.079 0.362 0.057 0.010 0.002 30 1.221 9.363 2.153 0.395 0.066 0.013 0.002 60 1.211 8.620 2.542 0.620 0.137 0.035 0.009 90 1.223 8.429 2.625 0.685 0.162 0.044 0.012
Table 3
Rate constants of the propagation (kp) and depolymerization (kd) reactions of
PODEn compounds respecting to 5 wt% dosage of NKC-9 resin catalyst in the designed space.
k (min–1) Temperature (1C) Arrhenius parameters
60 70 80 E (kJ mol–1) A
7 –1 –1 kp 11.738 17.693 26.339 39.52 1.84 10 L mol min 6 –1 kd 0.037 0.065 0.108 52.01 5.36 10 min
Fig. 8. The parity plot of experimental data (Ci,exp) and calculated data (Ci,cal) using
DMM and PF as feedstocks at different reaction temperatures (DMM/CH2O molar ratio of 2:1, dosage of NKC-9 at 5 wt%).
The key assumption of the kinetic model is that the rate
constants of propagation (kp) and depolymerization (kd) were the same for the series of PODEn propagation reactions. To verify the prediction ability of the kinetic model, the concentrations of ¼ – Fig. 7. Arrhenius plots and Vant Hoff plots of the reversible propagation reactions PODE2–6 were calculated from Eq. (14) with n 2 6 as a function of of PODEn compounds in the designed space. the reaction time with the determined kd and kp from concentra- tion of DMM, and compared with the experimental data. The parity plot of the experimental and calculated concentrations of all 1.84 107 L mol 1 min 1 and 5.36 106 min 1, respectively. The compounds is shown in Fig. 8. The R2 value calculated by Eq. (17) 1 activation energy Ep (39.52 kJ mol ) was lower than Ed for all involved data points is 0.998, indicating a good agreement (52.01 kJ mol 1), indicating that the reversible propagation reac- between the experimental and calculated data. The comparison tions of PODEn were exothermic. Corresponding to the Kn values between the experimental and calculated concentrations of illustrated in Fig. 5, Vant Hoff plots are of great importance to PODE2–6 at different temperatures and reaction times is shown evaluate the accuracy of the reversible kinetics data. As shown in in Fig. 9. A good agreement was obtained for the experimental and
Fig. 7, both the Arrhenius and Vant Hoff plots of the reactions calculated concentrations of PODE2–6. present good linearity (R2 40.990), confirming that the kinetic To further verify the prediction ability of the kinetic model, a model proposed in this work had a good accuracy. mixture of DMM, PODE5 and PODE6 were used as feedstocks at Y. Zheng et al. / Chemical Engineering Science 134 (2015) 758–766 765
Fig. 10. Comparison between experimental and calculated C1–C8 data using a
mixture of DMM, PODE5 and PODE6 as feedstocks at 80 1C over 5 wt% dosage of NKC-9.
model proposed in this work based on chain propagation mechan- ism. These results show that kinetic model proposed in the present work has a good prediction ability, and can be used in
designing and scaling-up the process of PODEn synthesis.
6. Conclusions
The kinetics of synthesis of PODEn from PF and DMM catalyzed by NKC-9 acidic ion exchange resin was investigated in the designed space, namely reaction temperatures (60, 70, and 80 1C) and reaction times (2, 5, 10, 20, 30, 60, and 90 min), in a batch stirred autoclave. A kinetic model was proposed based on a sequential reversible reaction mechanism. The experimental results and theoretical analysis lead to the following conclusions:
(1) The transient molecular size distribution of PODEn compounds from PF and DMM followed Schulz–Flory distribution model.
(2) In the reversible sequential propagation of DMM and PODEn, the propagation reactions followed a second-order kinetics for propagation and the depolymerization reactions followed a
first-order kinetics. The rate constants for propagation (kp) and for depolymerization (kd), and the reaction equilibrium con- stant (Kn) were independent of PODEn molecular size. (3) Respecting to 5 wt% dosage of NKC-9 resin catalyst, the pre-
exponential factors Ap for propagation and Ad for depolymer- ization were 1.84 107 L mol–1 min–1 and 5.36 106 min–1, –1 respectively. While the activation energy Ep (39.52 kJ∙mol ) –1 for propagation was lower than Ed (52.01 kJ mol ) for depo- lymerization, validating that the reversible propagation reac- Fig. 9. Comparison between experimental and calculated C1–C6 data using DMM tions of PODEn compounds were exothermic. and PF as feedstocks at different reaction temperatures (DMM/CH2O molar ratio of 2:1, dosage of NKC-9 at 5 wt%).
80 1C over 5 wt% NKC-9 resin catalyst. The initial concentrations of Acknowledgments 1 1 DMM, PODE5 and PODE6 were 9.701 mol L , 0.995 mol L and 0.303 mol L 1, respectively. During the reaction, the formaldehyde The authors gratefully acknowledge the financial supports by concentration CF increased in the first 10 min and then kept almost the National Natural Science Foundation of China (No. 20606021). 1 unchanged at 1.209 mol L . Using the kd and kp data at 80 1Cin Table 3, the C –C data at different reaction times were calculated 1 8 References by extending Eq. (12) to include variables of C1–C8. Comparison between the experimental and calculated C1–C8 data using the Burger, J., Hasse, H., 2013. Multi-objective optimization using reduced models in mixture of DMM, PODE5 and PODE6 as feedstocks is shown in conceptual design of a fuel additive production process. Chem. Eng. Sci. 99, Fig. 10. The good agreement confirms the validity of the kinetics 118–126. 766 Y. Zheng et al. / Chemical Engineering Science 134 (2015) 758–766
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