Supercritical Isomerization of n-Butane over Sulfated Zirconia. 2

Ind. Eng. Chem. Res. 2002, 41, 4941-4948

4941

Supercritical Isomerization of n-Butane over Sulfated Zirconia. 2. Reaction Kinetics† Bettina Sander and Bettina Kraushaar-Czarnetzki* Institute of Chemical Process Engineering CVT, University of Karlsruhe, Kaiserstrasse 12, 76128 Karlsruhe, Germany

The kinetics of the isomerization of n-butane over a commercial sulfated zirconia catalyst have been studied. Experiments were performed in a fixed-bed reactor with both pure and diluted n-butane as a feed, at pressures between 4.6 and 8.1 MPa, and at weight hourly space velocities between 0.6 and 170 h-1, which is equivalent to a range of modified residence times between 5000 and 71 000 kg‚s/m3. Earlier studies have shown that the catalyst is stable under supercritical conditions, however, in a narrow temperature regime only. Therefore, the reaction temperature was kept constant in this kinetic study at a value of 488 K. It is shown that the reaction is kinetically inhibited at high concentrations of n-butane in the feed, whereas mass transport may become a limiting factor in the highly diluted system. Three models will be presented, which are suitable for a robust and accurate description of the kinetics in broad pressure and concentration ranges. Introduction Supercritical processing is a well-established technology for the separation of compounds. An important application comprises the extraction and workup of temperature-sensitive life-science products. For this purpose, carbon dioxide and propane are used as supercritical solvents because they are medically welltolerated and exhibit a low critical temperature. Numerous physical and thermodynamic data of these solvents and their mixtures with biochemical or pharmaceutical substances have been collected over the past few years. In reacting systems, however, many different species are usually involved of which the physical properties are not well-known. It is also important that temperature and pressure are not just used to adjust a thermodynamic state as in separation technology. These parameters, in the first instance, are used to control the reactions rates, and it may well be that thermodynamic and kinetic requirements are conflicting for many reactions. So far, however, this research area has barely been explored. We are particularly interested in the possibilities of prolonging catalyst lifetimes and of increasing throughputs of heterogeneously catalyzed reactions by performing the process under supercritical reactions. We have investigated the isomerization of n-butane over a catalyst which suffers from rapid deactivation through coke deposition under gas-phase conditions. In the first part of our study,1 we have evaluated the catalytic performance of this catalyst (sulfated zirconia) in a broad range of supercritical reaction conditions using a fixedbed reactor and pure n-butane as a feed. The reaction temperature was found to be the decisive parameter with respect to the catalyst stability. However, within certain temperature limits, it is possible to process stationary isobutane and to increase the production † Dedicated to Prof. Jens Weitkamp on the occasion of his 60th birthday. * Corresponding author. Phone: +49-721-3947/4133. Fax: +49-721-608 6118. E-mail: [email protected].

capacity of isobutane with a factor of at least 10 as compared to gas-phase conditions. In this part, we report on the kinetics of the isomerization of n-butane under supercritical conditions. The catalyst employed consists of extrudates of nonpromoted sulfated zirconia and is of the same origin as the catalyst used in the previous study. The concentration range of n-butane was broadened by feeding mixtures of nbutane with nonreactive propane. We will show that a very simple reaction scheme can serve as a basis for the analysis of the data, and we will present three suitable kinetic models. However, this study also revealed some weaknesses of the catalyst, a commercially available material which has not been developed and optimized for this specific application under supercritical conditions. Our future work will thus also be devoted to the formulation catalysts with the aim of improving the activity and transport properties. Experimental Section Catalyst. Commercially available cylindrical extrudates of sulfated zirconium hydroxide [Zr(OH)4] bound to alumina with a diameter of 2.45 mm and an average length of 3 mm (MEL Chemicals, MEL XZO707/03) were used as catalyst precursors. Prior to use, the extrudates were calcined in air for 3 h at 873 K (heating rate of 2.5 K/min) to obtain sulfated zirconia. In the calcined state, the amount of alumina binder was 20 wt %, and the sulfur content was 2.6 wt %. For further data about the catalyst, we refer to part 1 of this study.1 To monitor the possible effects of mass-transfer limitations, additional experiments were carried out with small catalyst particles which were obtained from crushing the extrudates and sieving out a fraction with diameters ranging between 0.215 and 0.3 mm. Unit. A continuous flow unit with a fixed-bed reactor of an internal diameter of 15 mm and a length of 350 mm was used for the catalytic experiments. The catalyst bed consisted of catalyst particles diluted with SiC particles of 0.2 mm diameter in a volumetric ratio of 1:1. In addition, the rest of the reactor was filled with pure SiC particles of 0.5 and 1.0 mm diameter. This reactor packing ensures that the feed has the desired

10.1021/ie020300k CCC: $22.00 © 2002 American Chemical Society Published on Web 08/31/2002

4942

Ind. Eng. Chem. Res., Vol. 41, No. 20, 2002 Table 1. Critical Constants of Pure n-Butane and Mixtures of n-Butane and Propane and Reaction Conditions at Constant Reduced Density of Gr ) 0.42′ n-butane content xB (% vol, NTP)

critical parameters pC (MPa), TC (K)

reaction conditions pR (MPa), TR (K)

100 47 30 10

3.8, 425 4.3, 401 4.4, 389 4.3, 377

4.6-8.1, 488 5.6, 488 6.0, 488 6.6, 488

Results and Discussion

Figure 1. Critical temperatures and pressures of mixtures of n-butane and propane as a function of the mole fraction of n-butane.

temperature when contacting the catalyst bed and that the temperature gradient within the catalyst bed is negligible (∆Tmax ) 2 K) during all measurements. Also, dilution of the extrudates with small SiC particles enables that a plug flow profile is obtained as indicated by the Peclet number of the catalyst bed (Peax ) 1.37) and the high ratio R of the reactor diameter to the mean particle diameter (R ) 12). Further details about unit and product analysis and descriptions of start-up and processing procedures have been given elsewhere.1 Reaction Conditions. As shown earlier, the reaction temperature is the decisive parameter with respect to the stability of the catalyst. Stationary isomerization of n-butane over sulfated zirconia is possible only in a narrow temperature regime around 488 K.1 Therefore, all kinetic experiments reported here were carried out at this temperature of 488 K. The amount of catalyst was varied between 1.3 and 11.5 g to adjust modified residence times between 5000 and 71 000 kg‚s/m3. The corresponding weight hourly space velocities ranged between 0.6 and 170 h-1. Note that definitions are given at the end of this paper. Using pure n-butane as a feed, the concentration was varied by changing the pressure in the range from 4.6 to 8.1 MPa. This measure, however, allows only for a limited concentration variation and inevitably results in a simultaneous change of the density and other related fluid properties. Therefore, mixtures of n-butane with 53%, 70%, and 90% by volume of propane were also employed as feeds. The volumetric concentrations refer to normal pressure and temperature (NTP; 273 K and 0.1013 MPa). Propane is completely miscible with both n-butane and the reaction products, and it is not reactive by itself over sulfated zirconia at temperatures below 523 K. In Figure 1, critical temperatures and pressures of butane-propane mixtures are plotted as a function of the mole fraction of n-butane.2 Pitzer’s threeparameter correlation for the compressibility factor has been used to calculate the reaction pressure required for a given reduced fluid density Fr at a fixed reaction temperature of 488 K.3 The feed compositions used in this study, their critical constants, and the reaction conditions chosen are listed in Table 1. The carbon balance was checked regularly by comparing the compositions of the reactor effluent and the reactor bypass. Typically, the carbon balance summed up to 100 ( 4%. Data out of this limit were not taken into consideration.

Thermodynamics. The isomerization (n-butane T isobutane) is a reversible reaction. The Gibbs functions (∆Gf) and the heats of formation (∆Hf) of n-butane and isobutane as well as the enthalpy of the reaction (∆Hr) are known for temperatures of 400 and 500 K.4 These data enable the calculation of the Gibbs function for the reaction and the equilibrium constant expressed in terms of fugacities (Kf) at these temperatures. To predict the effect of pressure on the equilibrium conversion, it is necessary to know the fugacity-pressure ratios of the reactant and product. Reid et al. provide these ratios as a function of reduced pressures and temperatures.3 From these data, we determined the values for 488 K and the pressure range between 4.6 and 8.1 MPa and found that the acentric factors and, correspondingly, the fugacities of n-butane and isobutane were almost identical. It follows that the equilibrium constants Kf and Kx, the former expressed in terms of fugacities and the latter based on mole fractions, have the same value. The equilibrium composition is independent of the pressure. The temperature dependence can be calculated using the van’t Hoff equation. At a reaction temperature of 488 K, the equilibrium constant Kx has a value of 1.22 and the equilibrium conversion of n-butane was calculated to be 55%. The maximum conversion observed in our experiments amounted to 45%. Hence, thermodynamic limitations can be excluded. Effect of n-Butane Concentration. Using pure, supercritical n-butane as a feed, it is observed that increasing the reaction pressure results in a drop in catalyst activity.1 The question arises as to whether this phenomenon must be ascribed to a pressure or to a concentration effect. However, the maximum pressure applied in our experiments was 8.1 MPa. At pressures below 10 MPa, changes in the rate coefficients are generally less than 10% and can be neglected.5 Moreover, the activation volume of the isomerization reaction should have a value close to zero because the number of molecules does not change and the partial molar volumes of n-butane and isobutane are of similar magnitude. It is, therefore, reasonable to suppose that the rate coefficients are independent of the pressure. We ascribe the observed activity loss at increasing pressure to a concentration effect. To broaden the concentration range of n-butane in the feed and to study concentration effects without simultaneously changing the (reduced) fluid density, additional kinetic experiments were carried out with mixtures of n-butane and propane. A set of data obtained with three different feed compositions at 488 K and a fixed reduced fluid density of Fr ) 0.42 is depicted in Figure 2. The plots show that higher conversion levels are achieved at a given residence time when the n-butane concentration in the feed is reduced. Note that the pressure required to install a certain reduced fluid density of the feed mixture increases with

Ind. Eng. Chem. Res., Vol. 41, No. 20, 2002 4943 Scheme 1

Figure 2. Conversion of n-butane as a function of the modified residence time at 488 K. Concentrations of n-butane in the feed: 10%, 30%, and 100% by volume at NTP.

Figure 3. Selectivity to isobutane versus n-butane conversion at 488 K. Filled symbols: 100% by volume of n-butane at Fr ) 0.41 (4.6 MPa), Fr ) 0.65 (6.1 MPa), Fr ) 0.99 (8.1 MPa). Open circles: 47% by volume (NTP) of n-butane at Fr ) 0.42. Open squares: 30% by volume (NTP) of n-butane at Fr ) 0.42.

decreasing concentration of n-butane (Table 1). Hence, the data in Figure 2 give clear evidence of a concentration effect. They give, however, no clue of whether the inhibition of the catalyst is caused by n-butane itself, by one of the reaction products, or by an intermediate. Because isobutane was formed with a selectivity of at least 80% in all experiments, it is most convenient to ascribe the inhibition to one of the major components in the reaction mixture, i.e., n-butane or isobutane, rather than to a byproduct or to a postulated species. Selectivity and Reaction Scheme. The isomerization of n-butane over sulfated zirconia is a very selective reaction. At supercritical conditions, the selectivities to isobutane are somewhat lower than those in the gas phase, and they increase when the concentration of n-butane in the feed is decreased. The byproducts are propane and pentanes in almost equimolar amounts. In Figure 3, the integral (reactor) selectivities to isobutane are plotted versus the conversion of n-butane for different feed concentrations. Extrapolation of the data of the integral selectivity to zero conversion yields the differential selectivity which is independent of the reactor type and mixing pattern. In the supercritical isomerization of n-butane, the differential selectivity at zero conversion is below 100%. This indicates that byproducts are formed in at least one parallel reaction. In addition, byproducts must be formed from isobutane

in at least one consecutive reaction because the selectivity to isobutane decreases with increasing conversion at all reaction pressures and feed compositions applied in our study. Scheme 1 accounts for these observations in a simple and straightforward manner. It consists of a combination of parallel and consecutive reaction paths. In the parallel reactions, n-butane is converted to isobutane (path 1 f 2) and to the byproducts propane and pentanes (path 1 f 3). Isobutane is an intermediate and can also form byproducts (path 2 f 3). Note that it is not our aim to provide a mechanistic interpretation. Data from a processing study provide no information about reacting surface species in situ. The simple scheme described above accounts only for the observable product distributions in the fluid at the outlet of the reactor. These product distributions are used to identify rate-determining reaction pathways and to provide a quantitative description of the kinetics. For the sake of robustness, the reaction scheme is as simple as possible, and the number of fitting parameters is kept at a minimum. Kinetic Models. The analysis of the data was based on the assumption of ideal plug flow in the reactor. This is justified in view of the dimensions of the catalyst bed and the magnitudes of the feed flows applied in the experiments. The concentration change of a component i can be written as (definitions and a list of symbols are provided in the appendix)

dCi dtm

)

∑ij νi,ijrmij

(1)

To find suitable mathematical expressions of the reaction rates rm12, rm13, and rm23 (see Scheme 1), three different kinetic models were tested, and the concentration profiles along the reactor were calculated. This was done by choosing a set of start values for the model parameters and subsequently varying these parameters by the Levenberg-Marquardt algorithm until function F defined by eq 2 reached a minimum.

F)

∑

3

∑

number of exptl points i)1

(

)

(Ci,exp - Ci,cal)2 σi

(2)

Based on a lower detection limit of 0.02 mol/m3 of the concentrations in the analytical equipment used and assuming an error of 0.05 in the measured concentrations, the following equation was used to estimate the standard deviation σi:

σi ) 0.02 mol/m3 + 0.05Ci

(3)

Replicate measurements were carried out only for single operating points. For 10 vol % of n-butane in the feed, the confidence interval for the measured n-butane concentration at 40 000 kg‚s/m3 was calculated. With the mean being equal to 137 mol/m3, the confidence interval would amount to (10.2 mol/m3 if Student’s

4944

Ind. Eng. Chem. Res., Vol. 41, No. 20, 2002

Table 2. Reaction Coefficients and Reaction Orders Referring to Scheme 1 model 1

reaction path i f j

a

1f2

kmija ni,ij

2.4 × 10-5 0.8

1f3

kmija ni,ij

4.4 × 10-17 8.6 × 10-5

2f3

kmija ni,ij

2.4 × 10-7 1.6

model 2 kmijb ni,ij n2,ij kmijb ni,ij n2,ij kmijb ni,ij n2,ij

1.21 × 10-4 0.7 0.3 8.3 × 10-12 2.5 6.2 × 10-14 1.2 × 10-5

model 3 kmij (mol‚kg-1‚s-1) KB (m3‚mol-1) KIso (m3‚mol-1) kmij (mol‚kg-1‚s-1) KB (m3‚mol-1) KIso (m3‚mol-1) kmij (mol‚kg-1‚s-1) KB (m3‚mol-1) KIso (m3‚mol-1)

1.1 × 10-2 7.4 × 10-4 3.0 × 10-6 3.9 × 10-21 7.4 × 10-4 3.0 × 10-6 6.7 × 10-1 7.4 × 10-4 3.0 × 10-6

kmij in units of (mol‚m3)-ni,ij‚(mol‚kg-1‚s-1). b kmij in units of (mol‚m3)-ni,ij‚(mol‚kg-1‚s-1), respectively, (mol‚m3)-ni,ij+n2,ij‚(mol‚kg-1‚s-1).

factor t was chosen for a statistical probability of 95.4%. This example shows that the assumptions made for the estimation of the standard deviation (eq 3) are justified. With a simple first-order kinetic model, it is not possible to account for the experimental results and the observed negative concentration effect. Several types of rate expressions have been evaluated. Finally, three models turned out to be appropriate. Model 1 represents the most general approach because both the kinetic constants kmij and reaction orders ni,ij were used as free model parameters. The reaction rates are defined as

Model 1

rm12 ) km12CnB1,12

(4)

rm13 ) km13CnB1,13

(5)

2,23 rm23 ) km23CnIso

(6)

In model 2, inhibition of the reaction by isobutane was postulated by attributing a negative reaction order to the concentration of isobutane. The exponent n2,12 in power law rate expression rm12 has a negative value.

Model 2

2,12 rm12 ) km12CnB1,12 C-n Iso

(7)

rm13 ) km13CnB1,13

(8)

2,23 rm23 ) km23CnIso

(9)

Likewise, model 3 implies interpretation in advance. Here, saturation of the catalyst surface with n-butane and isobutane and inhibition of rate-determining surface reactions were postulated. The rate expressions chosen for model 3 display similarity with LangmuirHinshelwood kinetics. The formal “adsorption constants” KB and KIso are model parameters.

Model 3

rm12 )

km12KBCB 1 + KBCB + KIsoCIso

(10)

rm13 )

km13KBCB 1 + KBCB + KIsoCIso

(11)

rm23 )

km23KIsoCIso 1 + KBCB + KIsoCIso

(12)

We emphasize again that the form of the mathematical expressions (4)-(12) has been fixed in advance. These expressions are not the output of the regression but rather the input. The output only comprises the values of the model parameters. The calculated values of the reaction constants and the reaction orders are sum-

Figure 4. Comparison of measured and calculated reactant concentrations as a function of the modified residence time. Feed: 30% by volume (NTP) of n-butane in propane. Models are based on the reaction in Scheme 1.

marized in Table 2. It should be noted that all rate coefficients and “adsorption constants” reported there are really independent of all reactant concentrations. The quality of the models can be checked by comparing them with experimental data. As an example, measured reactant concentrations obtained from a mixture of 30% by volume (NTP) n-butane in propane are depicted in Figure 4 together with the calculated concentration profiles. All three models provide a satisfactory description of the experimental results. The best results, however, are obtained with models 2 and 3, whereas model 1 slightly underestimates the conversion of n-butane and the concentration of isobutane at high residence times. Simplification of the Reaction Scheme. We have discussed before that the selectivity pattern of isobutane (Figure 3) indicates the occurrence of both parallel reactions and reactions in series. However, the impact of the parallel reaction of n-butane to byproducts (path 1 f 3) must be small because the selectivity at zero conversion is very high. Likewise, one could argue that the consecutive reaction of isobutane is of minor importance because the slope of the selecitivity with conversion is very small. The values of the corresponding rate coefficients (Table 2) in models 1 and 2 are, indeed, at least more than 2 orders of magnitude smaller than km12, the coefficient of the isomerization rate. The values obtained with model 3 show a comparable trend. The product (km12KB) of the isomerization rate is much larger than the corresponding terms km13KB or km23KIso in the rate expressions of the byreactions. We therefore tested simplifications of the reaction in Scheme 1 by either omitting the consecutive pathway (2 f 3) or the parallel pathway (1 f 3), thereby yielding

Ind. Eng. Chem. Res., Vol. 41, No. 20, 2002 4945 Scheme 2

Scheme 3

Schemes 2 and 3. The coefficients and reaction orders calculated on the basis of these simplified reaction patterns are summarized in Tables 3 and 4, respectively. In Figures 5 and 6, reactant concentrations are plotted versus the residence time to compare measured and calculated results. Scheme 3 consisting only of two reactions in series provides the best agreement (Figure 6). Further model validation can be carried out either by numerical methods (e.g., the F test) or by graphical residual analysis. The graphical method was chosen in this work. The residuals from the fitted model are the differences between the responses observed at each modified residence time and the corresponding prediction of the response computed using the regression function. The residual δ of a component i can be expressed by eq 13:

δi ) Ci,exp - Ci,cal

(13)

The plot of δ versus the modified residence shows whether the residuals are distributed randomly. Figure 7 refers to the consecutive reaction depicted in Scheme 3. In the case of n-butane and isobutane, the residuals exhibit both positive and negative deviations. In contrast, the residuals of the byproducts (Figure 7c) are not normally distributed. All three models slightly underestimate the production of byproducts. However, this holds as well when the other two reaction schemes are applied. As an example, Figure 8 displays the residuals obtained after application of Scheme 1 for a set of data points. The distribution of residuals of the byproducts (Figure 8c) is almost identical with that in Figure 7c. However, for the other species in the reaction mixture, the combination of model 1 with the reaction in Scheme 1 (consecutive and parallel reactions) shows the most pronounced deviations from normal distribution of the residuals. The analysis of Scheme 2 (parallel reactions) is not shown, but the results are very close to those obtained with Scheme 3 (consecutive reactions). Although differences are small, it can be concluded that Scheme 3 provides the best basis for a regression. Because accurate kinetic experiments under supercritical reaction conditions are cumbersome and timeconsuming, the number of data is limited. Therefore, more detailed analyses, e.g., by statistical methods, are not meaningful here to discriminate between the reaction schemes and the rate models. Generally, however, the values of the residual δ are very small as compared to the total concentrations in the effluent mixture. Every combination of Schemes 1-3 with models 1-3 would provide a sufficiently accurate quantitative description of the kinetics within the operational window under

investigation. This is worth noticing because different “mechanistic assumptions” have been implemented in the rate expressions regarding the inhibition of the isomerization at high n-butane concentrations in the feed. In contrast to the effluent concentrations, the product selectivity is a derived magnitude which is related to the conversion of n-butane. Deviations must be most pronounced at very low conversions. The preferred reaction scheme (Scheme 3, consecutive reactions) predicts an isobutane selectivity of 100% for conversions approaching zero. The deviation from the experimental, extrapolated values (typically between 82 and 99%), although obvious, should not be overestimated. Mass Transport Limitations. The odd reaction orders in n-butane and isobutane that were determined from our models can be taken as a hint for the absence of external mass transport limitations because ratedetermining film diffusion would result in reaction orders of the value unity. Because the pressure drop strongly increases in the supercritical system when the velocity of the fluid flow is increased, it was not possible to check on the effects of external mass transport by experiment. Instead, Carberry numbers were calculated for various n-butane concentrations in the feed and at a temperature of 488 K, thereby assuming a reaction order of unity for simplicity. The values obtained (Ca < 0.05) indicated that film mass transfer is not rate limiting in this system. This situation may change at higher reaction temperature in combination with low n-butane concentrations. To check whether pore diffusion controls the consumption rate of n-butane, we performed control experiments with smaller catalyst particles. Small catalyst particles (diameter between 0.2 and 0.3 mm) and noncrushed extrudates were found to display the same apparent activity until the concentration of n-butane in the feed was 10 vol % or less. For the catalyst extrudates, we also estimated the value of the effective diffusion coefficients from the coefficients of Knudsen and binary diffusion of n-butane, taking a measured particle porosity of 0.486 and an estimated tortuosity of 4 into account. These values (e.g., Deff ) 2.2 × 10-8 m2/s at 488 K) were used to estimate the Weisz number, assuming for simplicity a reaction order of unity in n-butane. The results confirmed that pore diffusion becomes rate limiting only when the concentration of n-butane in the feed is 10 vol % or less at 488 K reaction temperature (Wz ) 0.17). At higher n-butane concentrations, the values of the Weisz numbers remain well below the limit of Wz ) 0.15 (e.g., Wz ) 0.1 for 30 % by volume of n-butane at 488 K); hence, pore diffusion is sufficiently fast in relation to the kinetically inhibited reaction. However, with increasing reaction temperature, the transition from the kinetically to mass transport controlled regime shifts to higher n-butane concentrations. Above 533 K, Weisz numbers are larger than 0.2 even when the highest feed concentration, i.e., pure n-butane at a pressure of 8.1 MPa, is processed. In the analysis of the reaction kinetics as discussed in the previous sections, we accounted for the limiting effects of pore diffusion at low n-butane concentrations. Only data from experiments at 488 K and with feed mixtures containing more than 10 vol % n-butane were considered to fit the model parameters.

4946


Table 3. Reaction Constants and Reaction Orders for a Kinetic Scheme Consisting Only of Parallel Reactions (Scheme 2) model 1

model 2

model 3

reaction path i f j

a

1f2

kmija ni,ij

3.3 × 10-5 0.7

1f3

kmija ni,ij

4.6 × 10-12 2.6

kmijb ni,ij n2,ij kmijb ni,ij n2,ij

1.8 × 10-4 0.7 0.3 8.3 × 10-12 2.5

kmij (mol‚kg-1‚s-1) KB (m3‚mol-1) KIso (m3‚mol-1) kmij (mol‚kg-1‚s-1) KB (m3‚mol-1) KIso (m3‚mol-1)

3.2 × 10-2 3.3 × 10-4 3.8 × 10-3 3.1 × 10-4 3.3 × 10-4 3.8 × 10-3


Table 4. Reaction Constants and Reaction Orders for a Kinetic Scheme Consisting Only of Two Reactions in Series (Scheme 3) model 1

model 2

model 3

reaction path i f j

a

1f2

kmija ni,ij

6.2 × 10-5 0.6

2f3

kmija ni,ij

3.2 × 10-9 2.4

kmijb ni,ij n2,ij kmijb ni,ij n2,ij

1.0 × 10-4 0.7 0.2 4.3 × 10-10 2.8

kmij (mol‚kg-1‚s-1) KB (m3‚mol-1) KIso (m3‚mol-1) kmij (mol‚kg-1‚s-1) KB (m3‚mol-1) KIso (m3‚mol-1)

1.1 × 10-2 7.2 × 10-4 9.5 × 10-6 2.2 × 10-1 7.2 × 10-4 9.5 × 10-6


Figure 5. Comparison of measured and calculated reactant concentrations as a function of the modified residence time. Feed: 30% by volume (NTP) of n-butane in propane. Models are based on a reaction scheme with parallel reactions only (Scheme 2).

Conclusions The isomerization of n-butane over robust sulfated zirconia catalysts in the supercritical state could be a promising alternative to the current hydroisomerization technology involving highly sensitive catalysts which require continuous chlorination. Although the supercritical isomerization is kinetically inhibited at high n-butane concentrations in the feed, the space time yields of isobutane are still much higher as compared to reaction in the gas phase. We have analyzed the kinetics of the reaction in a broad range of n-butane concentrations, reaction pressures, and residence times. A simple reaction scheme consisting of two reactions in series, i.e., the isomerization of n-butane and the consecutive reaction of isobutane to the byproducts propane and pentanes, can serve as a basis for the kinetic description of the system. Three different sets of rate equations were evaluated: model 1 consisting of simple power law expressions, model 2 assuming product inhibition, and model 3 of the Langmuir-Hinshelwood type assuming surface saturation of the catalyst by n-butane and isobutane. With all

Figure 6. Comparison of measured and calculated reactant concentrations as a function of the modified residence time. Feed: 30% by volume (NTP) of n-butane in propane. Models are based on a reaction scheme with consecutive reactions only (Scheme 3).

approaches, rate coefficients and “adsorption constants” could be obtained which are independent of all reactant concentrations. Models 2 and 3 are slightly superior; however, all models provide a satisfactory agreement between experimental and calculated concentration profiles. This example illustrates that a good fit of experimental data does not prove the validity of the assumptions made because different models can be used to describe the same experimental results. Rather, a model reflects what has been put in it before. Although this finding is not new, we stress this point because it is tempting to overinterpret the physical meaning of the mathematical expressions in a kinetic model. A kinetic inhibition of the supercritical isomerization was observed at high n-butane concentrations in the feed, whereas pore diffusion limited the rate at low concentrations. To improve the process, future work will also focus on the development of the catalyst. The activity should be enhanced to reduce the kinetic inhibition and to enable processing at lower tempera-

Ind. Eng. Chem. Res., Vol. 41, No. 20, 2002 4947

Figure 7. Graphical residual analysis. Models are based on a reaction scheme with consecutive reactions only (Scheme 3). Feed: 30% by volume (NTP) of n-butane in propane; (a) δ(nbutane), (b) δ(isobutane), (c) δ(byproducts).

Figure 8. Graphical residual analysis. Models are based on the reaction in Scheme 1. Feed: 30% by volume (NTP) of n-butane in propane; (a) δ(n-butane), (b) δ(isobutane), (c) δ(byproducts).

Appendix: Definitions and Symbols ture, be it by addition of transition-metal promotors or by reduction of the amount of binder in the extrudates. In addition, the shape, size, and pore size distribution of the catalyst bodies must be adjusted such that the pressure drop and transport limitations are minimized at supercritical conditions.

Acknowledgment The authors thank the German Research Foundation (DFG) for financial support and MEL Chemicals for providing the catalyst.

The residence time is the quotient of the reactor volume and volumetric flow into the reactor. In the case of heterogeneously catalyzed reactions, it is useful to define a modified reactor residence time (MRT)

MRT ) mCat/V˙ (kg‚s/m3)

(14)

which is related to the catalyst mass rather than to the reactor volume. When mixtures of n-butane and propane are used as a feed, the MRT refers to the total volumetric flow. In contrast, the weight hourly space velocity (in units of h-1) is defined as the quotient of the feed mass flow without diluent and the total catalyst mass.

4948


The definition (14) of the MRT refers to the total catalyst mass including nonreactive binder and to the volumetric flow at reaction conditions. The conversion of n-butane (X) and the reactor selectivity to isobutane (Siso) are defined as

X)

(m ˘ B)in - (m ˘ B)out (m ˘ B)in

(15)

and

Siso )

(m ˘ iso)out (m ˘ B)in - (m ˘ B)out

(16)

The definitions above contain the following symbols: Nomenclature m ˘ B ) mass flow rate of n-butane (kg/h) m ˘ iso ) mass flow rate of isobutane (kg/h) m ˘ Cat ) total mass of catalyst including binder (kg) V˙ ) total volumetric flow rate into the reactor at reaction conditions (m3/s) In addition, tables and eqs 1-13 in the text contain the following symbols:

Nomenclature p ) pressure (MPa) T ) temperature (K)

Fr ) reduced density ) (density at reaction conditions)/ (critical density) Ci ) concentration of species i (mol/m3) kmij ) rate constant of the reaction ij (for units, see Tables 2-4) ni,ij ) reaction order in reactant i in the reaction ij rmij ) rate of the reaction ij (see Schemes 1-3) based on the total catalyst mass (mol/s‚kg) νi,ij ) stoichiometric coefficient of species i in reaction ij (νi,ij < 0 when species i is consumed; νi,ij > 0 when species i is formed) σi ) standard deviation with respect to the concentration of species i (mol/m3)

Literature Cited (1) Sander, B.; Thelen, M.; Kraushaar-Czarnetzki, B. Supercritical Isomerization of n-Butane over Sulfated Zirconia. 1. Catalyst Lifetime. Ind. Eng. Chem. Res. 2001, 40, 2767. (2) Kreglewski, A.; Kay, W. B. The Critical Constants of Conformal Mixtures. J. Phys. Chem. 1969, 73, 3359. (3) Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The properties of gases and liquids, 4th ed.; McGraw-Hill: New York, 1988. (4) Stull, D. R.; Westman, E. F.; Sinke, G. C. The chemical thermodynamics of organic compounds; Wiley: New York, 1969. (5) Van Eldijk, R.; Asano, T.; Le Noble, W. J. Activation and Reaction Volumes in Solution (2). Chem. Rev. 1989, 89, 549.

Received for review April 16, 2002 Revised manuscript received July 8, 2002 Accepted July 10, 2002 IE020300K

Supercritical Isomerization of n-Butane over Sulfated Zirconia. 2

Recommend Documents