Kinetic Model for Homogeneously Catalyzed Halogenation of Glycerol

Article pubs.acs.org/IECR

Kinetic Model for Homogeneously Catalyzed Halogenation of Glycerol Cesar A. de Araujo Filho,† Tapio Salmi,*,† Andreas Bernas,† and J.-P. Mikkola†,‡ †

Department of Chemical Engineering, Process Chemistry Centre, Laboratory of Industrial Chemistry and Reaction Engineering, Åbo Akademi University, FI-20500 Turku/Åbo, Finland ‡ Department of Chemisty, Chemical-Biochemical Center, Technical Chemistry, Umeå University, SE-90187, Umeå, Sweden ABSTRACT: A new kinetic model for the halogenation of polyalcohols (e.g., chlorination of glycerol with gaseous HCl in the presence of homogeneous acid catalysts) was developed. The model is based on a reaction mechanism, which includes esterification and epoxidation steps followed by halogenation steps. The principle of quasi-steady state was applied to the ester and ionic intermediates appearing in the model and rate equations were derived. Furthermore, some simplified cases of the rate equations were considered, such as immediate water removal from the reaction mixture and analytical solutions for the simplified kinetic models were derived. The model was verified against experimental data obtained from laboratory-scale semibatch reactors. The conclusion is that the model worked very well, predicting correctly the glycerol conversion and the product distribution of α-, β-, α,β- and α,γ-chlorinated products. The kinetic model can be used for the design of reactors for homogeneously catalyzed halogenation.

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INTRODUCTION The production of biodiesel via the transesterification route has recently attracted significant attention giving rise to a new source of renewable fuels. Furthermore, the most abundant byproduct of this process (∼10 wt %) is glycerol, the market of which is today rather saturated after the start-up of several plants for biodiesel production around the world,1 consequently, leading to drastic price drop of particularly low-quality glycerol.1,2 In fact, companies such as Dow and Procter and Gable have shut down their glycerol production units.3 Several processes alternatives are currently under study4−7 with the aim of transforming glycerol to other valuable chemicals. The present work focuses on its chlorination using gaseous hydrochloric acid in the presence of a mild organic acid catalyst, aiming to produce α,γ-dichlorhydrin. Although old reports of this reaction date from 1941,8 the kinetics and mechanism have remained unexplored for many years due to the high price of glycerol.9 As a matter of fact, the current process for production of dichlorhydrin is part of the epichlorhydrin synthesis chain. It constitutes of the chlorination of propylene using allyl chloride, where a mixture of (30%) α,γ and (70%) α,β −dichlorhydrin is obtained.10 Nevertheless, this process presents few drawbacks such as low chlorine atom efficiency, expensive waste treatment and raw material.9,11,12 Moreover, the product distribution is not favorable, since α,β-dichlorhydrin is 10 times less reactive than α,γ in giving epichlorhydrin.10 Therefore, the selectivity is a crucial issue in our system, since a mixture of different chlorinated compounds is obtained by the end of the reaction. The product distribution can be primarily steered by the reaction time: because of the consecutive nature of the chlorination process, short reaction times favor the formation of α-monochlorhydrin, while α,γ-dichlorhydrin is preferred, as the reaction time increases. In the classical process of glycerol chlorination, temperatures of 90−110 °C are applied. Although © 2013 American Chemical Society

the increase of the reaction temperature favors the formation of α,γ-dichlorhydrin, the catalyst boiling point dictates the operation policy. Small amounts of β-chlorhydrin are formed, but this product is not able to react further in the presence of a mild acid catalyst, while α-monoclorohydrin undergoes further chlorination to α,β- and α,γ- dichlorhydrins. No threechlorinated products have been observed. In addition, water has been found to have a retarding effect on the reaction rate.11,13,14 The overall reaction scheme can thus be summarized in Figure 1. Recently, Tesser et al. (2007) have presented experimental data and proposed a reaction mechanism and a kinetic model for the homogeneously catalyzed chlorination of glycerol in the presence of a dissolved acid catalyst, such as acetic, propionic, and malonic acids. They suggest that an esterification step

Figure 1. Overview of glycerol chlorination reaction. Received: Revised: Accepted: Published: 1523

September 25, 2012 December 23, 2012 January 7, 2013 January 7, 2013 dx.doi.org/10.1021/ie302610v | Ind. Eng. Chem. Res. 2013, 52, 1523−1530

Industrial & Engineering Chemistry Research

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Figure 2. Proposed reaction mechanism.

followed by the formation of an epoxide intermediate is the key step in the reaction mechanism.15 This might explain the experimentally observed fact that β-chlorhydrin does not react further in the process, since it is not able to form any epoxide intermediate. Tesser et al. (2007) focus mainly on kinetic models, in which a rate-determining step is assumed in the reaction mechanism, and on systems, in which all the water formed is kept in the reactor with the aid of a reflux condenser. In this paper, we expand the treatment to more general cases, for which it is characteristic that the quasi-steady state hypothesis is applied to the reaction intermediates and water is partially or completely removed from the reaction system. The model is applied to the experimental data of Tesser et al. (2007) as well as to the data of our own.

(2)

rI1 = r2 − r3 − r4 = 0

(3)

rI2 = r6 − r7 − r8 = 0

(4)

For the proton transfer step 0, the quasi-equilibrium hypothesis gives c K 0 = catH ccatcH (5) Furthermore, for the catalyst, the following total balance is valid: ccatH + ccat = ccat,0 (6)

■

where ccat,0 is the initial concentration of the catalyst. A combination of eqs 5 and 6 gives the effective catalyst concentration ccat0 ccat = 1 + K 0c H (7)

REACTION MECHANISM AND RATE EQUATIONS Figure 2 depicts the proposed reaction mechanism for the chlorination of glycerol (A) using a mild acid catalyst (cat). Based on it, it was possible to derive rate equations according to four overall reaction routes (N1, N2, N3, and N4). The chemical symbols present in Figure 2 are explained in the Notation section. In the reaction scheme above, W is water, E1 and E2 are the ester intermediates, I+1 and I+2 are the epoxide intermediates and α, β, αβ, αγ are the chlorinated products (Figure 1). In step 0, the acid catalyst receives a proton originating from HCl. Proton transfer steps are known to be very rapid; therefore, it is assumed that this step is in quasi-equilibrium during the chlorination process. The other steps 1−8 are assumed to determine the overall rates and quasi-steady state hypothesis is applied to the intermediate species (E1, E2, I1+, I2+). The set of stoichiometric numbers gives the experimentally observed overall reactions, which are displayed below the mechanistic scheme. The principle of quasi-stationary state implies that the generation rates of the intermediates are set to zero, since the intermediates formed rapidly react further to the products observed in the liquid phase. We obtain rE1 = r1 − r2 = 0

rE2 = r5 − r6 = 0

Acids are, in general, not very eager to receive a proton; thus, K0 is small and ccat ≈ ccat0. For the sake of brevity, the following abbreviations are introduced: a1 = k1cAccatH, a−1 = k−1cWcH, a2 = k2cH, a−2 = k−2ccat, a3 = k3cCl, a−3 = k−3cα, a4= k4cCl, a−4 = k−4cβ a5 = k5cαccatH, a−5 = k−5cWcH, a6 = k6cH, a−6 = k−6ccat, a7 = k7cCl, a−7 = k−7cαβ, a8 = k8cCl, a−8 = k−8cαγ. Now eqs 1−4 can be rewritten and reorganized to a1 − (a−1 + a 2)c E1 + a−2c I1 = 0

(8)

a 2c E1 − (a−2 + a3 + a4)c I1 + a−3 + a−4 = 0

(9)

a5 − (a−5 + a6)c E2 + a−6c I2 = 0

(10)

a6 + a−7 + a−8 − (a−6 + a 7 + a8)c I2 = 0

(11)

According to the calculations of Tesser et al. (2007), the equilibria of the actual chlorination reactions are strongly shifted toward the products, and therefore, the reaction steps 3, 4, 7, and 8 are approximated to be irreversible here. On the other hand, it is very generally accepted that esterifications are reversible

(1) 1524

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main reactions consume equimolar amounts of H+ and Cl−, as revealed by the reaction scheme, steps 2−4 and 6−8. Consequently, it is reasonable to assume that cH = cCl = cHCl (i.e., corresponding to the saturation concentration of HCl in the liquid phase). Based on this reasoning, the rate equations can be condensed to

chemical processes; thus, all the other steps in the reaction sequence are taken as reversible. By setting a−3 = a−4 = a−7 = a−8 = 0, the equation system is simplified. The system is fully linear with respect to the concentrations of the intermediate species. A general solution for this kind of reaction sequence is provided, for instance, by Murzin and Salmi16 (2005). For the particular case considered here, the equation system is solved as follows: cE1 is solved from eq 9 with respect to cI1, (a−3 = a−4 = 0) giving c E1 =

(a−2 + a3 + a4)c I1 a2

r3 =

k 3′ccatcAc HCl 2 D34

(22)

r4 =

k4′ccatcAc HCl 2 D34

(23)

r7 =

k 7′ccatcαc HCl 2 D78

(24)

r8 =

k 8′ccatcαc HCl 2 D78

(25)

(12)

which is inserted in eq 8 and the concentration of I1+ can be obtained a1a 2 c I1 = a−1a−2 + (a−1 + a 2)(a3 + a4) (13) For reaction steps 3 and 4, the rates are r3 = k 3c I1cCl

(14)

r4 = k4c I1cCl

(15)

where D34 = ccatcW + (α′cW + β′)cHCl and D78 = ccatcW + (γ′cW + δ′) cHCl. Water has a retarding effect on the reaction rate, even though the overall reaction rate was presumed to be irreversible here. This is due to the fact that the esterification step included in the mechanism is reversible. The term ccatcW in the denominators of the rate expressions can be diminished by removing water continuously from the reaction system. If water continuously escapes from the system, either through vacuum distillation or through a membrane, cW approaches 0 in the denominators of eqs 22−25 and all rate equations obtain the form rj = kj*ccatcHClcA/α, where kj* corresponds to k′3/β′, k4′/β′, k′7/δ′, k′8/δ′, and cA/α is cA or cα. Based on the rate equations obtained and the underlying hypotheses behind them, it can be concluded that the important parameters in the validation of the reaction mechanism are, besides the reaction temperature and the liquid-phase reactant concentrations (cA, cα), the catalyst concentration and the partial pressure of HCl, since the pressure of HCl dictates the liquidphase concentrations of H+ and Cl− ions. By varying the operation policy of the chlorination reactor, from complete water removal to complete water reflux, the role of water in the reaction mechanism can be revealed. The proposed reaction mechanism yielded rate equations, which all have the same formal reaction order with respect to HCl, but the numerical size of parameter α′ can be different from that of parameter γ′, as well as the numerical value of β′ with the highest probability differs from that of δ′. Thus, the partial pressure of HCl can have an impact on the relative product distribution, as the product yields are considered as a function of the reactant (glycerol) conversion.

After introducing the original notations, the rate equations become r3 = (K 0k1k 2k 3ccatc H 2cAcCl)/(k −1k −2ccatc Hc W + (k −1c W + k 2)(k 3 + k4)c HcCl)

(16)

r4 = (K 0k1k 2k4ccatc H 2cAcCl)/(k −1k −2ccatc Hc W + (k −1c W + k 2)(k 3 + k4)c HcCl)

(17)

To obtain operative forms of the rate equations, the following notations are introduced: k3′ = K0K1K2k3, k4′ = K0K1K2k4, α′ = (k3 + k4)/k−2, β′ = K2(k3 + k4)/k−1. The rate equations become now r3 =

k 3′ccatcAc HcCl ccatc W + (α′c W + β′)cCl

(18)

r4 =

k4′ccatcAc HcCl ccatc W + (α′c W + β′)cCl

(19)

A closer examination of the reaction mechanism reveals that steps 5−8 are formally completely analogous with steps 1−4; step 5 corresponds to step 1, step 6 corresponds to step 2, etc. and component α corresponds to component A. Thus, no separate derivation of rate equations is needed, but just the following set of notations is introduced: k7′ = K0K5K6k7, k8′ = K0K5K6k8, γ′ = (k7+k8)/k−6, δ′ = K6(k7 + k8)/k−5. The rate expressions for steps 7 and 8 become r7 = r8 =

k 7′ccatcαc HcCl ccatc W + (γ ′c W + δ′)cCl

■

(20)

k 8′ccatcαc HcCl ccatc W + (γ ′c W + δ′)cCl

COMPONENT GENERATION RATES AND MASS BALANCES The stoichiometric scheme for the overall reactions and components are displayed in Figure 3. From the scheme, the production and consumption rates of the components are obtained as follows: rA = −r3 − r4 (26)

(21) +

−

Now the issue of the concentrations of H and Cl is raised. HCl is continuously bubbled through the system under vigorous stirring, thus it is reasonable to assume that the liquid phase is at any moment saturated with respect to HCl. Since HCl is a very strong acid, it is completely dissociated. A very minor amount of H+ is bound to the catalyst (catH+), but this amount is established at the very initial state of the process. Therefore, the 1525

rα = r3 − r7 − r8

(27)

rβ = r4

(28) dx.doi.org/10.1021/ie302610v | Ind. Eng. Chem. Res. 2013, 52, 1523−1530


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dci = ri dt

(37)

for all liquid-phase components. For HCl, the saturation concentration (a constant value) is used in eq 37. In the general case, the coupled ordinary differential equations are solved numerically. For the ideal case, where water is selective and immediately removed from the system, cW = 0, ccat = constant, and cHCl = constant throughout the reaction, the following rate equations are obtained

Figure 3. Stoichiometric scheme for components and overall reactions.

rαβ = r7

(29)

rαγ = r8

(30)

rHCl = −r3 − r4 − r7 − r8

(31)

r3 = k 3*cA

(38)

rW = r3 + r4 + r7 + r8

(32)

r4 = k4*cA

(39)

These expressions are used in the mass balances of the components in the semibatch reactor system displayed in Figure 4.

r7 = k 7*cα

(40)

r8 = k 8*cα

(41)

which de facto is a first order kinetic system. In the right-hand side of the mass balances, the term riVL always appears. For instance, (r3 + r4)VL becomes (k3* + k4*)cAVL = (k3* + k4*)nA, where nA is the amount of substance. The mass balances of the components can now be transformed to dnA = − (k 3* + k4*)nA dt

(42)

dnα = k 3*nA − (k 7* + k 8*)nα dt

(43)

dnβ dt Figure 4. Principal setup of the semibatch reactor.

dnαβ dt

For the perfectly backmixed semibatch reactor, through which HCl is continuously bubbled, the general mass balance for an arbitrary component (A, α, HCl etc) is written as NA i GL

dni + rV i L = ni′ + dt

dnαγ dt

dni dt

(45)

= k 8*nα

(46)

nA /n0A = exp( −at )

dnGi dt

k 3* [exp( −bt ) − exp( − at )] a−b

(48)

nβ /n0A =

k4* [1 − exp( −at )] a

(49)

k 3*k 7* [(1 − exp( −bt ))/b − (1 − exp(−at )) a−b

/ a] (36)

nαγ /n0A =

that is, the difference between the HCl inflow and outflow corresponds to its consumption rate. For the case of complete reflux, the liquid volume can be considered rather constant,10 and the general mass balance equation is simplified to

(47)

nα /n0A =

nαβ /n0A =

(35)

gives, after assuming the quasi-steady state, n0Gi′ − nGi′ = −rV i L

= k 7*nα

(34)

for A, α, β, αβ, and αγ, respectively. For HCl, the interfacial flux (NiAGL) deviates from zero, but ni′ = 0 (no liquid phase flow out from the system). For HCl in the gas and liquid phases, a quasi-steady state is assumed. A combination of eq 33 with the gas-phase mass balance for HCl, n0Gi′ = NA i GL + nGi′ +

(44)

This system of linear ordinary differential equations can be easily solved analytically. The solution is obtained with the following initial conditions: nA = n0A at t = 0; ni = 0 at t = 0 for all the other components. Under these premises, the solution becomes (a = k3* + k4* and b = k7* + k8*)

(33)

The symbols are explained in the Notation. The organic liquidphase components are in batch, since they have low volatilities at the reaction temperatures; thus, eq 33 is reduced to rV i L =

= k4*nA

(50)

k 3*k 8* [(1 − exp( −bt ))/b − (1 − exp(−at )) a−b / a]

(51)

The analytical solution reveals interesting features. The amount of the monochlorinated component (α) passes through 1526



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Table 1. Values of Estimated Parameters in Kinetic Modeling of Glycerol Chlorination k3′ (l mol−1·min−1) k4′ (l mol−1·min−1) k7′ (l mol−1·min−1) k8′ (l mol−1·min−1) β′ (mol·L−1) δ′ (mol·L−1) R2 (%)

T = 80 °C

T = 90 °C

T = 100 °C

T = 110 °C

T = 120 °C

9.36 × 10−04 5.45 × 10−05 6.55 × 10−07 1.81 × 10−04 0.57 1.43 99.89

3.98 × 10−03 2.64 × 10−04 5.03 × 10−06 5,48 × 10−04 2.05 2.62 99.33

1.26 × 10−02 1.01 × 10−03 5.75 × 10−06 1.25 × 10−03 6.33 4.06 99.51

4.30 × 10−02 3.30 × 10−03 3.29 × 10−05 2.23 × 10−03 17.50 6.91 99.59

1.70 × 10−01 1.54 × 10−02 7.77 × 10−05 2.89 × 10−03 50.70 10.30 99.13

Figure 5. Chlorination of glycerol at varied temperatures. (a) 80 °C, (b) 90 °C, (c) 100 °C, (d) 110 °C, (e) 120 °C. Symbols: (●) glycerol, (■) αmonochlorhydrin, (▲)β-monochlorhydrin, (⧫) α,γ-dichlorhydrin, (*) α,β -dichlorhydrin. Solid line = model prediction.

The amount of the β-chlorinated product increases monotonously toward the limit

a maximum, which is obtained from eq 48 by differentiation and setting the time derivative of the concentration of α to zero:

tmax =

ln(a /b) a−b

n∞ β /n0A =

(52)

This time is inserted in eq 48, which gives the maximum αconcentration: nα max /n0A =

k 3* [(a /b)b /(b − a) − (a /b)a /(b − a)] a−b

k4* a

(54)

since this molecule is not able to react further. Also the amounts of the dichlorinated components (αβ and αγ) increase monotonously, approaching the following limit values at long reaction times:

(53) 1527



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n∞ αβ /n0A =

k 3*k 7* ab

(55)

n∞ αγ /n0A =

k 3*k 8* ab

(56)

Equations 50 and 51 reveal that a plot of the concentrations of the dichlorinated products (αβ vs αδ) should give a straight line. This result is valid for the semibatch reactor also for the case of the general forms of the rate equations, since division of the mass balance of αβ with that of αγ gives

dcαγ

=

dcαβ

k8 k7

(57)

which after integration yields (c0αβ = 0 and c0αγ= at t = 0) cαγ =

k8 cαβ k7

Figure 6. Arrhenius plot for the kinetic parameters estimated using malonic acid as catalyst.

(58)

■

Table 2. Values of Activation Energies and Pre-exponential Factors for the Using Malonic Acid

NUMERICAL APPROACH The model was tested with the aid of nonlinear regression analysis, by checking the fit of the model to experimental data. The following objective function was minimized in the regression analysis: Q=

∑ (ciexp ,t − ci ,t )2 k

Ea(kJ/mol) ln A

r3

r4

r7

r8

147.5 32.3

159.4 33.5

132.1 20.0

80.7 8.1

(59)

where exp refers to experimental data and ci (i = A, α, β, αβ, αγ) is predicted by the model. The underlying differential eqs 37 were solved by a backward difference method implemented in a stiff ODE-solver during the parameter estimation. A Levenberg− Marquardt algorithm was used in the minimization of the objective function. The results were checked by standard statistical analysis as well as contour and sensitivity plots of the parameters. The overall fit of the model was checked by the degree of explanation defined by R2 = 1 −

∑ (ciexp , t − ci , t )2 ∑ (ciexp , t − ciav , t )2

(60)

where cieav,k is the average value of the experimentally recorded concentrations. The software Modest17 was used in all parameter estimations.

Figure 7. Arrhenius plot for parameters β′ and δ′.

■

Table 3. Values of Estimated Parameters in Kinetic Modeling of Glycerol Chlorination

MODEL VALIDATIONCOMPARISON WITH EXPERIMENTAL DATA In Tesser et al. 2007, the molar fraction versus time data for experiments conducted at five different temperatures using malonic acid catalyst are presented. These data were used for the estimation of the kinetic parameter involved in the system of differential equations described by eqs 22−25) and eqs 26−32. In the parameter estimation procedure, the liquid phase concentration of HCl was set to 10 mol % and the catalyst concentration was 8 mol %. The values of the estimated parameters are shown in Table 1. In this solution, it can be seen that there is some variation in the magnitude of the values due to the rather large number of parameters. However, at all temperatures the degree of explanation exceeded 99%, which is extraordinarily large. The fit of the experimental data to the kinetic model is presented in Figure 5.

k3′ k4′ k7′ k8′ β′ δ′ R2 (%)

2.16 × 10−02 1.39 × 10−03 1.29 × 10−09 1.01 × 10−03 1.74 × 1001 1.91 × 1000 97.00

Figure 6 presents an Arrhenius plot for the kinetic parameters estimated, and Table 2 shows the values of energy of activation and pre-exponential factors calculated from them. An Arrhenius plot of the parameters β′ and δ′ is presented in Figure 7 in order to depict the accuracy of the model. 1528



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Figure 8. Chlorination of glycerol at 105 °C. Symbols: (●) glycerol, (■) αβγ-monochlorhydrin, (▲)β-monochlorhydrin, (⧫) α,γ-dichlorhydrin, (*) α,β -dichlorhydrin. Solid line = model prediction.

r T t V α′,β′,γ′,δ′

A similar mathematical treatment was done using our own data from experiments in glycerol chlorination using 11 mol % of acetic acid as a catalyst. The results of the parameter estimation are shown in Table 3 and the data fitting is presented in Figure 8. The figure contains data fittings from two separate experiments at identical conditions. The degree of explanation is 97% and a similar fit of the data was obtained.

Subscripts and Superscripts

■

G i j L 0 ∞

CONCLUSIONS A more general model for the homogeneously catalyzed halogenation of polyalcohols with hydrogen halides was introduced. Reaction mechanisms with multistep rate control were presumed and rate equations were derived, starting from first principles, and they were validated with the aid of experimental data from glycerol chlorination in a laboratoryscale reactor. The model explained well the experimental data, and it can be used for prediction of the behavior of halogenation reactors.

■

rate temperature time volume merged parameters in rate equations

gas phase component index general index liquid phase initial quantity limit value

Abbreviations

A E I+ α β αβ αγ

AUTHOR INFORMATION

■

Corresponding Author

*Tel.: +358 2 2154427. Fax: +358 2 2154479. E-mail: Tapio. Salmi@abo.fi.

glycerol ester intermediate ionic intermediate 1-monochlorhydrin 2-monochlorhydrin 1,2-dichlorhydrin 1,3-dichlorhydrin

REFERENCES

(1) Yazdani, S. S.; Gonzalez, R. Anaerobic fermentation of glycerol: A path to economic viability for the biofuels industry. Curr. Opin. Biotechnol. 2007, 18, 213−219. (2) Asad-ur-Rehman; Saman Wijesekara, R. G.; Nomura, N.; Sato, S.; Matsumura, M. Pre-treatment and utilization of raw glycerol from sunflower oil biodiesel for growth and 1,3-propanediol production by Clostidium butyricum. J. Chem. Technol. Biotechnol. 2008, 83, 1072−1080. (3) McCoy, M. Glycerin surplus. Chem. Eng. News 2006, 84 (6), 7. (4) Ripoll, V.; Belkhodja, S.; Santos, V .E.; García-Ochoa, F. Enhanced 1,3-propanediol production by glycerol fermentation pathway by Escherichia blattae using different pH strategies. New Biotechnol. 2012, 29, S52−S53. (5) Adhikari, S.; Fernando, S. D.; Haryanto, A. Hydrogen production from glycerol: An update. Energy Convers. Manage. 2009, 50, 2600− 2604. (6) Melero, J. A.; Vicente, G.; Paniagua, M.; Morales, G.; Muñoz, P. Etherification of biodiesel derived glycerol with ethanol for fuel formulation over sulfonic modified catalysts. Bioresour. Technol. 2012, 103, 142−151. (7) Zakaria, Z. Y.; Linnekoski, J.; Amin, N. A. S. Catalyst screening for conversion of glycerol to light olefins. Chem. Eng. J. 2012, Article in Press. (8) Conant, J. B.; Quayle, O. R. Glycerol α-monochlorhydrin. Org. Syn. Coll. 1941, 1, 294. (9) Bell, B. M.; Briggs, J. R.; Campbell, R. M.; Chambers, S. M.; Gaarestroom, P. D.; Hippler, J. G.; Hook, B. D.; Kearns, K.; Kenney, J. M.; Kruper, W. J.; Schreck, D. J.; Theriault, C. N.; Wolfe, C. P. Glycerin

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is a part of the activities at the Åbo Akademi Process Chemistry Centre within the Finnish Centre of Excellence Programmes (2000−2011) by the Academy of Finland.

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NOTATION A surface area aj merged parameter in the derivation of rate equations a,b merged parameters in analytical solutions c concentration D denominator in rate equation K equilibrium constant k reaction rate constant k′, k* transformed rate constants N diffusion flux N stoichiometric number n amount of substance n′ flow of amount of substance Q objective function in nonlinear regression R2 degree of explanation 1529



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as a renewable feedstock for epichlorhydrin production. The GTE process. Clean 2008, 36 (8), 657−661. (10) Carrà, S.; Santacesaria, E.; Morbidelli, M.; Schwarz, P.; Divo, C. Synthesis of epichlorhydrin by eliminatio of hydrogen chloride from chlorhydrins 1. Kinetic aspects of the process. Ind. Eng. Chem. Process Des. Dev. 1979, 18 (3), 424−433. (11) Luo, Z.-H.; You, X.-Z.; Li, H.-R. Direct preparation kinetics of 1,3dichloro-2-propanol from glycerol using acetic acid catalyst. Ind. Eng. Chem. Res. 2009, 48, 446−452. (12) Wang, L. L.; Liu, Y. M.; Xie, W. Highly efficient and selective production of epichlorohydrin through epoxidation of allyl chloride with hydrogen peroxide over Ti-MWW catalyst. J. Catal. 2007, 246, 205− 214. (13) Tesser, R.; Santacesaria, E.; Di Serio, M.; Di Nuzzi, G.; Fiandra, V. Kinetics of glycerol chlorination with hydrochloric acid: A new route to α,γ-dichlorhydrin. Ind. Eng. Chem. Res. 2007, 46, 6456−6465. (14) Lee, S. H.; Song, S. H.; Park, D. R.; Jung, J. C.; Song, J. H; Woo, S. Y; Song, W. S.; Kwon, M. S; Song, I. K. Solvent-free direct preparation of dichloropropanol from glycerol and hydrochloric acid in the presence of H3PMo12−xWxO40 catalyst and/or water absorbent. Catal. Commun. 2008, 10, 160−164. (15) March, J. Advanced Organic Chemistry; Wiley: New York, 2001. (16) Murzin, D.; Salmi, T. Catalytic Kinetics; Elsevier: Amsterdam, 2005. (17) Haario, H. MODESTUser’s Guide; Profmath Oy: Helsinki, 2007.

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Kinetic Model for Homogeneously Catalyzed Halogenation of Glycerol

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