Ind. E n g . Chem. Res. 1995,34, 3817-3825
3817
Influence of the IsobuteneMethanol Ratio and of the Methyl tert-Butyl Ether Content on the Reaction Rate of the Synthesis of Methyl tert-Butyl Ether Henk-Jan Panneman and Antonie A. C. M. Beenackers* Department of Chemical Engineering, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
The forward reaction rate constant of the MtBE synthesis was determined for different reaction mixture compositions. The forward rate constant decreases continuously with increasing isobutene/methanol ratio, while an increase in reaction rate constant is observed with a n increasing amount of MtBE in the reaction mixture. This effect has not been reported before. These so-called solvent effects could be explained by using a pseudo-homogeneous reaction rate model in combination with the transition state theory. Not only changes in activity of the initial state (reactants and ion exchange resin) but also changes in the activity of the activated complex turned out to contribute to the solvent effects observed. Changes in the rate caused by changes in the activity of the activated complex are not accounted for in the existing homogeneous and heterogeneous models such as the Langmuir-Hinshelwood model.
Introduction The synthesis of methyl tert-butyl ether (MtBE), catalyzed by macroporous strong acid ion-exchange resins, is of great commercial interest. MtBE is made via a liquid phase reaction of isobutene (IB) and methanol (MeOH) catalyzed by a strong acid, usually immobilized in an ion-exchange resin: CH,OH MeOH
+ (CH,),C=CH, IB
(CH,),COCH,
MtBE
A number of kinetic studies have been published (Ancillotti et al., 1977, 1978; Gicquel and Torck, 1983; Subramamian and Bhatia, 1987; Rehfinger and Hoffmann, 1990). A direct comparison of the reaction rate constants is often impossible, because of differences in reactant and inert concentrations, in conversion, and in type of ion-exchange resin applied. Particularly of interest is the influence of the feed composition and of the MtBE product concentration on the reaction rate constant. A good comparison of different MtBE formation rate models in MeOHAB systems is given by Rehfinger and Hoffmann (1990). However, in most studies only initial rates of different MeOWIB ratios in an inert solvent were measured. Therefore, no information is available about the influence of MtBE product concentration on the rate constant. Here, we report the initial rate constants for the synthesis of MtBE as a function of reaction mixture composition, and attempts have been made t o explain the observed effects in terms of changes in activity coefficients or Gibbs energies of the initial state and the transition state. Theory Depending on the solvent used, the mechanism of strong acid ion-exchange resins catalysis can be described in various ways ranging from homogeneous to heterogeneous catalysis. For homogeneous catalysis, complete swelling by a protophylic solvent, such as water or methanol, is required. The polymer-bound sulfonic acid is completely 0888-5885/95/2634-3817~09.00/0
dissociated. In addition, the kinetics will be more or less influenced by the accessibility of the reactants, the adsorption of reactants, the activated complex in the resin particles, and the intraparticle distribution of acid groups. The liquid phase synthesis of MtBE can be described by a pseudo-homogeneous reaction model. With this model, the reaction mechanism for strong acid resin catalysis is similar t o the mechanism of olefin hydration and of esterification, catalyzed by mineral acids. In heterogeneous catalysis, we ideally have a surface reaction, but in practice the accessibility depends on interactions close to the solventheactant'polymer interface. Also, the microenvironmentexerts an influence on the catalytic activated complex. A heterogeneous kinetic model has been successfully applied for the alkylation of benzene in an apolar reaction mixture (Buttersack et al., 1987). From the above, it follows that reactions in sulfonic acid ion-exchange resins usually are best characterized as quasi-homogeneousand quasiheterogeneous. If a heterogeneous kinetic model is applied, such as the Langmuir-Hinshelwood approach, the following assumptions are usually made: (1)all active sites have the same activity; (2) no interaction between substrate molecules and no environmentally dependent interaction; (3) the reaction mechanism is uniform and identical everywhere in the catalyst particle; and (4) no catalytic dependence regarding environment, acid concentration, and liquid composition. From our own results and from Ancillotti et al. (1978) it appears that (1)the acidity of the proton varies in the resin particle; (2) there is interaction between reactants and product; (3) the reaction rate is solvent dependent; (4) the kinetics depend on the microstructure of the catalyst; and ( 5 ) the catalytic activity and the rate constant depend on environment, number of acid groups, and liquid composition. The activity of the acid sites is nearly exclusively determined by solvation, if the solvent has a higher proton affinity than the reactant. Then, an active center will be identical with a single solvated site. The solvation will depend on microenvironment, acid concentration, and liquid composition. A pseudo-hetero1995 American Chemical Society
3818 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 geneous kinetic model was applied by Gicquel and Torck (1983), Subramanian and Bhatia (19871, and Rehfinger and Hoffmann (1990). Rates were explained in terms of absorption constants, activity coefficients of reactants, and a reversible first-order rate dependency on all species involved (Rehfhger and Hoffmann, 1990). Other rate dependencieson concentrations were obtained from computing the best fit of a number of rate expressions (AI-Jarallah, 1988; Subramanian and Bhatia, 1987). To describe our experimental results, a pseudo-homogeneous model turned out t o be superior to a pseudoheterogeneous model. In all our experiments, the concentrations of isobutene and methanol were such (IB/ MeOH ratio between 0.1 and 1)that the reaction follows a simple pseudo-first-order reversible rate law as derived from mechanistic studies on the hydration of olefins both with homogeneous acid catalysis (Nowlan and Tidwell, 1977; Chwang et al., 1977) and heterogeneous acid catalysis (Petrus et al., 1984, 1986; Panneman and Beenackers, 1992). Ancilotti et al. (1977,1978) used the same kinetic model for the etherification of isobutene. In isobutene/methanol mixtures (ratio 0.1-11, all protons of the sulfonic acid groups will be solvated by the polar methanol molecules. The reaction mechanism consists of the protonation of the olefin by these solvated protons, followed by the interaction of the carbonium ion with the nucleophile, methanol, available in large excess in the resin pores. The protonation is the ratecontrolling step. We consider the MtBE synthesis to be a pseudohomogeneous reaction. However, the reaction between isobutene and protons solvated by methanol and the subsequent reaction with a methanol molecule takes place in a heterogeneous environment, the macropores and micropores of the resin particles, and this certainly influences the reaction parameters. There are locations with relatively many acid groups where the solvated protons have a higher acidity than at places with only a few acid groups. Also, the reaction intermediate (activated complex) will be more or less stabilized by the polymeric environment. By using the transition state theory, it is possible to compute values for the Gibbs energy and the enthalpy and entropy of activation for the MtBE synthesis in resin particles. The use of these quantities, particularly AS*,can be of value to understand the kinetics in such a heterogeneous environment. Before the transition state theory can be applied, we have checked whether it can be used for the MtBE synthesis. From Denbigh (1981), it appears that errors can occur if EA has the magnitude of RT and if the reaction is highly exothermic without significant heat removal as in gas phase. In liquid phase MtBE synthesis, EA (90 k J mol-l) is large compared with R T (2.7 k J mol-l). In all experiments, the conversion was kept small, see Experimental Section, so that the temperature increase was less then 2 "C. The reaction rate depends on the activity of isobutene and the methanol solvated protons, at the reaction centers inside the resin particles. Under steady-state conditions, the activity in the resin particles and in the surrounding liquid will be the same for all components. Therefore, it is possible to explain changes in the rate, caused by changes in the liquid composition, in terms of changes in activity of one or more components. In general, the formation rate of MtBE is
and
K, =
aMtBE
=k + k
(2)
(%baMeOH
From literature (Streitwieser and Heathcock, 19761, it is known that ether decomposition is always acid catalyzed; therefore, we find UH+ in the reverse rate. The rate-determining step is the protonation of isobutene with zero-order rate dependence of methanol for the reaction mixtures we have used. From our experiments with a packed bed reactor, we can compute MtBE production rates and initial rate constants (see eq lo), using the following rate equation:
and
k* K, = CMtBE,equil -Cib,equil
k*-
(4)
Due to differences in the absolute values between activities and concentrations, rate constants have different values; therefore, k+, k*, and k1 are used respectively in eqs 1, 3, and 5. For the feed mixtures and temperatures used in our experiments, values of K , were computed from K,, the equilibrium constant based on mole fractions. The latter was obtained from an iterative procedure by using Ka from Colombo et al. (19831, K y computed with UNIFAC and K, = Ka/Ky. Values for the forward rate constant k* follow from K , and eq 3. According to the transition state theory (Denbigh, 1981; Connors, 1990) and from eqs 1 and 3, the rate can be expressed by
Changes in the experimentally determined forward rate constant (k*) due to changes in the reaction mixture composition or catalyst type will be explained from changes in y H + y i d y * . So we will not calculate individual values of y H + and y*. Starting from a reference mixture, a change in Yib can be estimated with UNIFAC and a change in YH+can be estimated from the experimentally determined acidity function, Ho.Finally, it is possible to compute the change in y*, the activity coefficient of the activated complex. The temperature dependency of the forward rate constant is described by both the Arrhenius equation:
k* = k, exp(-EAIRT)
(6)
and the Eyring equation (Denbigh, 1981; Connors, 1990): kBT
k* = exp(AS*/R)exp(-A€flRT) h
(7)
By plotting { M k d - 1 n W h ) - l n ( n } versus UT, it is
Ind. Eng. Chem. Res., Vol. 34, No. 11,1995 3819 ................................................................
7 F i
Table 1. Experimentally Determined Total Exchange Capacity of Resins Applied"
..............
a
Figure 1. Schematic representation of the experimental equipment.
possible to compute A@ from the slope and AS* from the interception.
Egperimental Section Equipment. A simplified flow scheme of the equipment is given in Figure 1. The reaction was conducted in a packed bed reactor. Two silver-coated tubular reactors of copper (length 0.15 m, i.d. 0.01 m) were used. The silver coating prevented catalyst deactivation. Both reactors could either be placed in series or be used separately, depending on the temperature and the amount and capacity of the catalyst in the reactors. Both reactors (labeled 4 and 5 in Figure 1)were filled with a narrow sieve fraction (dp = 0.75 x m) of a strong acid ion-exchangeresin. Measurement of the hydrogen capacity before and after experiments showed there was no decrease during the experiments. Two accurate metering pumps (Isco Model 314) (labeled 1 and 2 in Figure 1)were used: one for methanol or a mixture of methanol and MtBE and the other for liquefied isobutene. The flow rate of each pump was controlled within 0.1% by a computer, so mixtures of different composition could be metered to the reactor. A filter element with a pore diameter of 5 pm served as a static mixer (labeled 3). The reactor temperature was controlled to within f 0.1 "C by a thermostated water bath (labeled l l ) , which possessed a digital output connected to the computer. The product leaving the reactor was cooled down to 24 "C and passed through the 0.2-pL loop of a liquid injection valve (labeled 6) (Valco, 4CE-4WTS). Abackpressure regulator (labeled 8) (Tescom) kept the whole reactor system at 20 bar, resulting in a completely liquefied reaction mixture. A pneumatic actuator (labeled 7) (Valco), activated by the computer, switched the injection valve to evaporate 0.2 pL of liquid in a gas flow entering a gas chromatograph. The feed composition could be analyzed through a reactor bypass using two three-way valves (labeled 9 and 10). The samples were analyzed on a Perkin Elmer 3920B gas chromatograph. A 1.5-m, 1/8-in. stainless steel, i.d. m column containing 30% Carbowax 1540 2.1 x on Chromosorb W/AW (80-100 mesh) was used for separating the components. The injection valve and oven temperatures were 24 and 60 "C, respectively. A flame ionization detector (FIb) was applied. A n advantage of the constant volume liquid injection valve is that no internal standard is necessary. With
resin
exchange capacity (a),equiv kg-'
Amberlyst 15 Amberlyst CSP Amberlyst XE 307
4.6 4.3 4.4
Particle sieve fractions 0.71-0.81 mm.
experimentally obtained relative standard deviations below 0.1%, the accuracy of the applied analysis is extremely good (Marsman et al., 1989). The signal output of the FID was connected to a chromatographic integrator (Merck-Hitachi D2000) with a serial interface extension. The computer controlled the integrator, and the peak areas were sent to the computer by an RS232 interface. Safety precautions were taken by connecting temperature, pressure, and air flow sensors to the computer. The experiments were stopped automatically if set points were exceeded. Reagents. The resins were converted into the acid form using standard procedures. The catalysts were sieve-analyzed, and the different sieve fractions were separated. To prepare ion exchangers with protons partially substituted by sodium ions, we took the resin in the acid form with an exchange capacity known from titration, allowed it to swell in water, and added to it a calculated amount of sodium chloride. The system was allowed to stand for 24 h to reach equilibrium, and the ion exchanger was then washed with distilled water and dried a t 75 "C and reduced pressure. The remaining acid capacity was determined by titration. Dried resin particles burst if a strong polar liquid such as water or methanol was added. To avoid this problem, the catalyst particles were first wetted in 2-propanol. Then the propanol was displaced by adding methanol. All but one of the catalysts applied are commercially available sulfonated styrene-divinylbenzene copolymers. Amberlyst 15 and Amberlyst CSP were obtained from Rohm and Haas. The not commercially available catalyst, Amberlyst XE 307 from Rohm and Haas, was used because of its high thermal stability, which is due to the presence of chlorine in the resin. All catalysts were macroreticular. Information from the catalysts producers on the chemical and physical properties of the resins is rather scarce. The total hydrogen-exchange capacity of the dried resins is shown in Table 1. The theoretical maximum exchange capacity of XE 307 can be computed from an elemental analysis at 4.47 equiv kg-'. Isobutene, reagent grade, was supplied by Matheson (Gent, Belgium). Methanol and MtBE, both reagentgrade, were obtained from Janssen Chimica. Hammett's method (Hammett, 1970) to measure the acidity of heterogeneous catalysts (Rys and Steinegger, 1979) can also be applied to polar solvents in macroporous ion-exchange resins. The acidity function was determined by photometric detection of the dissociation of 4-nitroaniline ( ~ K B H=+1.0). That indicator has the right acidity constant for our experiments, and it shows reversible adsorption. The volatility and reactivity of isobutene made it impossible to use it for the measurements of the acidity of different feed mixtures. Consequently, we replaced isobutene by cyclohexene. The solubility parameter (both 1.5 x lo4) and dipole moment (1.67 and 1.5 x C m, respectively) of both molecules are compa-
3820 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 rable (Daubert and Danner, 1984);calculation of activity coefficients with UNIFAC gives almost identical values for methanol and the olefin, whether isobutene or cyclohexene is used. The base strength of isobutene exceeds that of cyclohexene. However, in binary mixtures with methanol, which has a much higher base strength, the base strength of the olefin is of minor importance. The acidity was measured for various solvent compositions. The W absorption of a solvent mixture was measured with an indicator and ca. 0.5 g of acid ionexchange resin. The experimentally determined Hammett acidity is given by
Ho = pKBH+ - lOg(1) (8) where I represents the ratio of protonated and neutral indicator concentration in a solvent mixture: (9) Procedure and Calculations. The necessary parameters for an experimental session were imported to the computer program controlling the reactor system. At each temperature, both the composition of the feed and the volumetric flow rate could be varied. After the input procedure, the equipment was started to perform the sequential experiments. On-line analysis of the product effluent started after a period equal to three times the residence time of the total system. Depending on the reproducibility of the peak areas of isobutene for a number of analysis (typically 5), the computer decided whether to repeat the analysis procedure or to start the next experiment. The experimental results were stored on disk for subsequent computing of the rate constants. The initial rate constants were computed from the performance equation of a packed bed reactor (Westerterp et al., 1984) with a first-order reversible reaction:
At each temperature, the isobutene conversion was determined for at least four volumetric flow rates. The initial concentrations were calculated from the volumetric flow rates, densities, and temperature. Special attention was paid to avoid heat transfer effects and both internal and external mass transfer effects. Most experiments were done with partially neutralized ion-exchange resins. The results shown in Figure 2 are obtained with Amberlyst CSP and u = 1.1 equiv kg-l. The MtBE production rate is four times lower than at full capacity, also the rate constant is capacity dependent as shown by us (Panneman and Beenackers, 1995) and is 4.65 times smaller. So the rate is about 20 times smaller than at full resin capacity. The heat development is also 20 times lower, and no mass transfer limitations do occur. At higher resin capacity, only experiments below 50 "C were used to compute energies of activation. The volumetric flow rate was always large so that the isobutene conversion was kept below 5%. Again, this lowers the heat production and avoids mass transfer limitations. Small conversions were also necessary to keep the variation in the mixture composition as small as possible so that initial rate constants as a function of solvent composition could be computed.
0.3
0.1
1.6 h
0.5
Xlb
8
1
I-)
I I
-
0
2
4
Olk"
6
0
C l b ( k r n o l rn-3)
Figure 2. Initial forward rate constants of the MtBE synthesis, in binary mixtures of isobutene and methanol; catalyst, Amberlyst CSP, u = 1.1equiv kg-l, T = 40 "C. (0) MtBE formation rates computed from the observed k* values (A) Literature values from Rehfinger and Hoffmann (1990).
Computations with a two-dimensional reactor model proved the absence of mass and heat transfer effects under the experimental circumstances described before. Thus, the intrinsic rate constants, k", are identical to the experimentally obtained apparent rate constants, k". Linear regression of rate constants versus the reciprocal temperature gives errors of 1-2% in EA and ko for Xib = 0.1 and errors of 2-4% in EA and ko for Xib = 0.5.
Results Effect of Isobutene Concentrationon Rate Constant. Figure 2 shows the results for binary feed mixtures of isobutene and methanol and macroporous Amberlyst CSP. To avoid heat and mass transfer problems, the capacity of Amberlyst CSP was reduced
to r~ = 1.1equiv kg-'. The initial forward reaction rate constant k* appears to decrease with increasing mole fraction of isobutene. In a feed mixture with an isobutene mole fraction of 0.5, the rate constant is about one-third below the value for a mixture with Xib = 0.1. The resulting MtBE formation rate of the forward reaction as obtained by using eq 3 is also shown in Figure 2. We compared our values with those of Rehfinger and Hoffmann (1990). Due to different experimental conditions, the absolute values of the rates differ. We used a temperature of 40 "C and 0 = 1.1 equiv kg-l, while Rehfinger and Hoffmann used 60 "C and a resin at full capacity. From the Arrhenius equation presented below, the ratio of the rate constant due to the difference in temperature can be calculated as 7.5. From our own experiments with Amberlyst CSP at full and reduced capacity, we compute a decrease in rate constant by a factor of 4.65. Thus, the values of Hoffmann were reduced by a factor of 7.5 x 4.65 to make them comparable to our own values. These data are also shown in Figure 2. The agreement of our data with those of Rehfinger and Hoffmann (1990) proves to be excellent. Whether the observed change in rate constant with isobutene concentration is caused by changes in the initial state (isobutene and the proton) andor by changes in the transition state follows from applying eq 5. The reaction mixture with Xib = 0.1 is called the reference mixture. The changes in the activity coefficient of isobutene were computed with UNIFAC (Fredenslund et d., 1977; Macedo et al., 1983). The results are accurate for these mixtures, see Colombo et al. (1983).
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 3821 1.1 1
0.9 0.8 0.7 0.6 0.9
0.8
0.7
0.6
0.5
0.5 0.1
0.4
0.2
X M ~ O H (-1
Xib
Figure 3. Ratio of proton and methanol activity coefficients relative to the reference mixture with Z M ~ O H= 0.9 a t T = 25 "C, in cyclohexene/methanol and isobutenelmethanol mixtures.
It is not possible to calculate the activity coefficient of a proton inside an ion-exchange resin. In fact, each proton has its own acidity, so we can only speak about a mean activity coefficient. All feed mixtures can be considered as polar, because XMEOH I 0.5. Also, the resin particles are preferably filled with methanol. Therefore, the variation in acidity is not very great, a reason why the ratio of activity coefficients of the indicator (YB) and the protonated indicator (YBH+) probably remains constant in good approximation (Rochester, 1970). If so, a change in the Hammett acidity gives a similar change in the mean activity coefficient of the proton in the resin. The relation between the proton activity and the Hammett acidity function(&) is (Hammett, 1970) (11) Values of HOwere obtained for mixtures of methanol and cyclohexene (ENE) a t 25 "C, with Amberlyst CSP as acid. The changes in the experimentally determined Hammett acidity values were used t o compute changes in the proton activity coefficient relative to the reference solvent mixture, Y H + ~ Y H + , ~ :
-YH+ - 10-(Ho-Ho,J
0.3
(12)
YH+,r
where XMeOH = 0.9 and XENE = 0.1 for the reference mixture. The results of these calculations for five binary mixtures of methanol and cyclohexene are shown in Figure 3. We see that the activity coefficient of the proton shows a nonlinear increase with the cyclohexene fraction. The activity coefficient of methanol in binary mixtures of methanol and cyclohexene was computed using UNIFAC. The change in the activity coefficient of methanol relative to the reference cyclohexene/methanol mixture, y/(y,r)MeOH is also shown in Figure 3. It can be concluded that the change in the proton activity coefficient almost equals the change in the activity coefficient of methanol in the same binary mixtures. According to Reichardt (1979) and Boyd (1969), the acidity of an acid not only changes due to a different acidity of another solvent composition but also because of its changing dielectric constant and the ability of the new species to solvate the acid. The changing Coulomb and dipole-dipole interactions, hydrogen bonding, and other forces between solvent molecules affect the acidity, i.e., the proton activity. In thermodynamics, these changes in interactions can be considered as changes in activity coefficients of the solvent molecules. So, the close relation between the change in Y M ~ O Hand the
0.4
0.5
0.6
(-1
Figure 4. Relative changes in the rate constant and in the activity coefficient of the initial state (IS) and the activated complex (AC) in binary isobutene/methanol mixtures, as a function of XibT = 40 "C. Table 2. Activation Parameters for Synthesis of MtBE (AG*at 50 "C)"
ion-exchange resin
Xib,
AmberlystXE 307 AmberlystXE 307 Amberlyst CSP Amberlyst CSP
10 50 10 50
%
ko, 107m3 EA, equiv-I kJ s-' mol-' 31 3.6 1.4 0.67
93.0 87.7 86.2 86.1
AlP, kJ mol-' 90.3 85.0 83.5 83.3
M*, J AG*, mol-' kJ K-' mol-' -91 -109 -117 -123
119.7 120.2 121.3 123.0
Feed: binary mixtures of isobutene and methanol. Arrhenius - TAS*. equation: k* = ko exp(-EA/RT), and AG* =
change in HOproves that in these polar feed mixtures all protons are indeed solvated by methanol. Figure 3 also shows the change in methanol activity coefficient with varying isobutene/methanol ratios. We showed already that some physical properties of cyclohexene and isobutene are of the same magnitude. Figure 3 proves that the change in YMeOH with composition is identical for binary mixtures with either cyclohexene or isobutene, respectively. So, a good approximation of the change in proton activity with composition in isobutene/methanol mixtures can be obtained from Hammett acidity values of Amberlyst CSP in cyclohexene/methanol mixtures. Now the change in activity coefficient of the initial state with respect to the reference mixture can be computed:
In Figure 4, both the change in reaction rate constant and activity coefficients of the reactants are shown with respect to the reaction mixture with 10% isobutene. If only the initial state would be responsible for the change in the rate constant, then a considerably higher decrease in the rate constant would be expected. This means that upon increasing the amount of isobutene in the reaction mixture, the activity coefficient of the activated complex will decrease. The Gibbs energy of the activated complex will become lower, and this gives a somewhat lower enthalpy of activation or a somewhat less negative entropy of activation, which means that the probability of formation of the activated complex is increased. We performed temperature-dependent experiments with Amberlyst CSP and Amberlyst XE 307, both with a reduced capacity of ca. 0.5 equiv kg-'. The kinetic experiments were carried out with feed mixtures containing 10% and 50% isobutene, respectively. The temperature was varied between 20 and 70 "C. The activation parameters are presented in Table 2.
3822 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 It appears that the change in EA and ko with solvent composition is resin-dependent. For Amberlyst XE 307, the energy of activation is considerably decreased; also ko shows a nine times decrease. Both changes compensate each other: at 50 "C, the rate constant k* changes from 2.8 x to 2.4 x m3 equiv-l s-l only, for Xib changing from 0.1 to 0.5. For amberlyst CSP, the energy of activation is independent of Xib, while ko decreases with 50%. The rate constant k* changes from m3 equiv-l s-l at 50 "C. 1.6 x to 0.8 x Rehfinger and Hoffmann (1990) find an activation energy for the forward reaction of 86.4 k J mol-'. This is approximately 10%larger than the mean value of the literature data, which could have been influenced by macropore diffusion. It can be concluded that the microenvironment in the neighborhood of the sulfonic acid group is of importance during the formation of the activated complex. Our results disagree with the statements of Rehfinger and Hoffmann (19901, who claim that there is no influence of cross-linking and of exchange capacity of the resin on the reaction rate and that the chemical reaction takes place in a pseudo-homogeneousmanner between molecules in the sorbed state in the gel phase. Our results not only show resin dependency but also prove to depend on the exchange capacity (Panneman and Beenackers, 1995). For each resin, solvent changes lead to different results, which cannot completely be explained by the change in activity of the reactants. Changes in the activity of the activated complex must play a role too. The latter changes are caused not only by changes in liquid composition in the resin phase but also by changes in the resin microenvironment proper. Table 2 shows for both resins that changing the mole fraction of isobutene from 0.1 to 0.5 gives a larger value of the Gibbs energy of activation, AG*, indicating a decrease in the rate constant. The change in AG* (dAG*) appears t o depend on the type of resin, the difference is the smallest for XE 307. This proves that the changes in the activities of the initial and transition state are resin dependent. For the polar feeds and the macroporous resins applied here, the expected change in the activity coefficient of both isobutene and the solvated protons, the initial state, is almost independent of the resin used. So, the difference in 6AGS between both resins probably is caused by the activated complex. The differences in polymeric structure and the notion, whether the remaining sulfonic acid groups of the partial neutralized resins are on the surface of the macropores or in the gellular microparticles, probably are the cause of the difference in dAGS between CSP and XE 307. For Amberlyst CSP, the entropy of activation appears to vary only, whereas for XE 307 both enthalpy and entropy changes occur upon variation of the feed composition. Unfortunately, we cannot conclude whether the enthalpy and entropy changes are caused by the initial or the transition state or by both states. Effect of MtBE on Rate Constant. To investigate the effect of MtBE on the forward rate constant, k*, we varied the mole fraction of MtBE in the feed, XMtBE, between 0 and 0.5. The rest of the feed consisted of equimolar quantities of isobutene and methanol: each was (1 - XMtBE)/2. The experimental conditions and results are shown in Table 3 and Figure 5. The forward reaction rate constant becomes higher if the amount of MtBE in the feed increases. A feed with 50%MtBE has a rate constant of about 2.4 times higher than a feed
Table 3. Initial Forward Reaction Rate Constants, k*, for Synthesis of MtBE as a Function of MtBE Contenta
XMtBE,
%
Amberlyst 15 u = 4.15 eqUiV kg-' T=40"C
Amberlyst 15 u = 0.61 equiv kg-l T = 70 "Cb
Amberlyst CSP o = 0.5 equiv kg-' T=60°C
7.3 8.4
5.6 6.8 7.9 8.5 11.2 13.6
2.3 2.5 2.9 3.7 4.5 5.4
0 10 20 30 40 50
10.1 11.0
14.6 18.1
a Feed: MtBE and equimolar amounts of isobutene and methanol. k*, m3 equiv-l s-l.
A
CSP, 0.5 ea hg.'; 6 0 %
0 '
1
2.5
-;
I
2
-
1.5
-
I
I
I
I
I
I
I
I
_-
amb.15, 7 0 %
.....
CSP. 60'C
- a m b . 1 5 , 40'C
I
4..
-
LI
>
1 -
/
without MtBE. The observed increase of the reaction rate constant is independent of the catalyst and of the proton exchange capacity of the resin. No experimental data are available from open literature. However, Rehfinger and Hoffmann (1990)used their kinetic model to construct a MtBE conversion diagram for different feed ratios. For feed stocks comparable to those reported in Table 3, the MtBE conversion rate decreases continuously with increasing conversion because of the decreasing isobutene concentration leading to a smaller forward rate and the increasing MtBE concentration giving a higher reversed reaction rate. Figure 6 shows the MtBE reaction rate of the reference mixture without MtBE (rMtBE,r) divided by the MtBE formation rate with MtBE (QftBE). This graph is based on the experimental rate constants shown in Table 3 in combinationwith a first-order reversible rate equation with a temperature-dependent equilibrium constant, K,. For all three catalysts, we observed a decrease in MtBE formation rate as a function of XMtBE. Also, a temperature effect is observed: the higher the temperature, the higher the decrease in rate. Therefore, the energies of activation are mixture dependent. The
Ind. Eng. Chem. Res., Vol. 34,No. 11, 1995 3823 3.0 k*/k'f
2.0
1
- k*/h:
-
-
- r/u,
I
I
I
Table 4. Activation Parameters for Synthesis of MtBE at 50 "Ca
1
ko, 107m3
(AC)
and
Y/Y, (-)
0.5
----
I
0 0
I
I
0.2 XHtBE
---- I
0.4
I
0.6
(-1
Figure 7. Relative changes in the rate constant, k*, and in the activity coefficients of the initial state and the activated complex (AC).
results computed by Rehfinger and H o h a n n (1990)for a comparable feed stock are also shown in Figure 6. The presence of a certain amount of MtBE in the feed can change the activity of both the initial state and the activated complex. It has influence on both the forward and reverse rate as can be seen from eq 5. UNIFAC calculations show that YMtBE is independent of the amount of MtBE in the feed. The value of K, remained the same for all mixtures applied. We determined the Hammett acidity of similar mixtures as applied here; only isobutene was replaced by cyclohexene. However, no significant increase of Ho was observed if MtBE was added. So the proton activity apparently is independent of the MtBE content. The activity coefficients of isobutene and methanol show only small changes if MtBE is added. This and the fact that methanol and MtBE have a comparable dipole moment f5.67 x and 4.17 x C m, respectively (Daubert and Danner, 198411 explain that Ho does not increase and that the proton activity is independent of the MtBE content. This is in contradiction to Rehfinger and Hoffmann (19901, who assume MtBE to be unpolar. We computed the changes in the activity coefficients of the initial state, y/y,(IS). In combination with the known changes in the rate constants, we could compute the changes in the ratio of the activity coefficient in the activated complex y/y,(AC) as a function Of XMtBE. The results are shown in Figure 7. The relative small changes in the activity of reactants and product would result in only small changes in the rate constant upon addition of MtBE to the reaction mixture. Due to the increasing importance of the reversed reaction with higher MtBE contents in the reaction mixture, the rate will continuously decrease as computed by Rehfinger and Hoffmann (1990). However, they do not take into account the increase in the forward rate constant we have observed. Probably this increase is caused by a considerable stabilization of the activated complex. It can be concluded that addition of MtBE decreases the Gibbs energy of the activated complex. It would be interesting to know whether the decrease in AG* is accompanied by a reduction in the enthalpy of activation or that the decrease is the result of a less negative entropy of activation. To answer this question, we performed temperature-dependent kinetic experiments with two feed mixtures. One feed contained an equimolar quantity of isobutene and methanol only, while the other contained 50% MtBE and 25% isobutene and methanol. The experiments were done with various strong acid ion-exchange resins: some were partially neutralized and another was at full proton capacity. For the results, see Table 4.
ion-exchange resin Amber1ystX.E 307 (0.45 equivkg) Amberlyst CSP (0.52equivkg) Amberlyst 15 (0.61 equivkg) Amberlyst 15 (4.0equivkg)
XMtBE,
%
0 50 0 50 0
50 0 50
equiv-' s-'
3.61 0.025 0.67 0.009 0.18 0.002 1.66 0.014
AS*,
EA,
e,J
kJ kJ mol-1 mol-'
mol-'
87.7 71.6 86.1
-109 -151 -123 -159 -135 -171
71.3
82.0 67.5 80.1 65.0
85 69 83 69 79 65 78 62
K-'
-114
-155
AG*, kJ mol-' 120.3 117.5 123.2 120.0 122.8 120.0 114.8 112.5
Feed: 50% isobutene and 50% methanol; 50% MtBE, 25% isobutene, and 25% methanol. a
The various resins show significant differences in both the activation parameters and the rate constants. However, the variation in the Gibbs energy of activation, AG*, between the two reaction mixtures, is almost independent of both the type of resin and its capacity, generally 6AG* is 2.5-3 kJ mol-I. This numerical value seems hardly significant; however, it results from large resin-independent changes in AlP and AS*, which cancel out for the greater part when computing AG*. Because there are large differences in the rate constants of the resins applied, one would not expect an uniform change in activation parameters upon addition of MtBE if this change in AG* would be caused by changes in the activity of the solvated protons or by changes in the microenvironment of the catalysts. Again, this provides evidence that the stabilization of the activated complex is mainly responsible for the increase in rate constant. The values of EA and A€F are about 15 k J mol-l lower, and the entropy of activation, AS*,becomes 40 J mol-' K-l more negative for feeds containing 50% MtBE. The lower enthalpy of the activated complex probably is not caused by another reaction mechanism with a lower energy barrier but most likely by a very pronounced solvation of the activated complex. This strong solvation of the activated complex leads to a loss of translational and rotational degrees of freedom. This is reflected in the value of the entropy of activation, which is more negative for mixtures with 50% MtBE.
Conclusions Experiments with different reaction mixtures showed that the initial rate constant of the synthesis reaction of MtBE from isobutene and methanol is influenced by solvent effects. Applying a pseudo-homogeneous rate model in combination with the transition state theory can explain these variations on the basis of changes in the activity of the reactants, the catalyst, and the activated complex. Existing pseudo-homogeneous models available from the literature consider changes in reactant activities only. In binary mixtures of methanol and isobutene, a decrease in forward reaction rate constant results from an increase of the isobutene content. This is caused by a stabilization of both isobutene and the activated complex on the one hand and by more active protons on the other hand. Temperature-dependent experiments with two strong acidic ion-exchangeresins showed the changes in the activation parameters t o be resin dependent. These resin-dependent variations in proton activity and in microenvironment in the gel-like structure of the microspheres, which influences the activated
3824 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995
complex, are not incorporated in existing LangmuirHinshelwood models. This also implies that isobutene is significantly present in the resin. The close correspondence between the change in proton activity as obtained from measured Hammett acidities and the change in activity coefficients of methanol in the same mixtures gives evidence that all protons of a strong acid ion-exchange resin are solvated by methanol. This is valid if XidXMeOH varies between 0.1 and 1. Addition of 50 mol % MtBE to an equimolar reaction mixture of isobutene and methanol gives an approximately 2.4 times higher forward rate constant, which is resin independent. We showed that addition of MtBE to the reaction mixture gives resin-independent changes in the activation parameters (enthalpy and entropy) that are mainly caused by changes in the activated complex. The dipole moments of methanol and MtBE are of the same magnitude, implying that both show rather similar behavior in the resin, resulting in minor changes in reactant and proton activity. The enthalpy and entropy of activation appear to decrease with about 15 and 40 J mol-l K-l, respectively. These changes can be understood from additional solvation of the activated complex by MtBE, resulting in a lower H . The latter implies that the solvent molecules lose translational and rotational degrees of freedom, which causes the observed decrease in entropy of activation. The presence of MtBE in reaction mixtures leads to higher rates than predicted by Rehfinger and Hoffmann (1990) and cannot be explained on the basis of existing homogeneous and heterogeneous rate equations, such as Langmuir-Hinshelwood.
Nomenclature ai = liquid phase activity of component i AC = activated complex B, BH+ = indicator, neutral or protonated (e.g., 4-nitroaniline) ci = concentration of component i, kmol m-3 d, = particle diameter, m E A = energy of activation (Arrhenius equation), J mol-l ENE = cyclohexene AG* = Gibbs energy of activation, J mol-' dAG* = change in Gibbs energy of activation for two different reaction mixtures, J mol-' h = Planck constant, J s Ho = Hammett acidity function AIP = enthalpy of activation, J mol-l IB, ib = isobutene, 2-methylpropene Z = ratio of protonated and neutral indicator B IS = initial state ka = apparent rate constant from an experiment, m3 equiv-I s-1 kl, k-1 = rate constants according to transition state theory, m3 equiv-1 s-1 k-, k- = rate constants for activity rate equation, mol equiv-l s-l k*, k*- = intrinsic rate constants from experiments, m3 equiv-1 s-l ko = pre-exponential factor of Arrhenius equation, m3 equiv-1 s-l kg = Boltzman constant, J K-I K, = equilibrium constant of the MtBE reaction based on activities K, = equilibrium constant based on concentrations, computed from K, K, = equilibrium constant of the MtBE reaction based on mole fractions
Ky= equilibrium constant based on activity coefficients MeOH = methanol MtBE = methyl tert-butyl ether ~ K B H=+acidity constant of the protonated indicator B R = gas constant ri = reaction rate of species i, mol equiv-l s-l AS* = entropy of activation, J mol-' K-l T = temperature, K w = dry weight of catalyst in the reactor during experiments, kg xL = mol fraction of species i Greek Symbols = molar extinction coefficientof component i, m3 kmol-1 cm-I yi = activity coefficient of component i Qv = volumetric flow rate, m3 s-1 (7 = specific capacity of dry resin, equiv k g:; ci
Superscripts = activated complex
*
Subscripts B, BH+ = indicator, neutral or protonated (e.g., 4-nitroaniline) ib = isobutene Hf = solvated protons MeOH = methanol MtBE = methyl tert-butyl ether r = reference reaction mixture
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Received for review August 30, 1994 Revised manuscript received April 13, 1995 Accepted July 11, 1995@
IE940517H
@
Abstract published in Advance ACS Abstracts, October 1,
1995.
