Ind. Eng. Chem. Res. 1997, 36, 3391-3399
3391
Kinetic Investigation of Isobutane Selective Oxidation over a Heteropolyanion Catalyst Se´ bastien Paul,† Ve´ ronique Le Courtois,‡ and Dominique Vanhove*,§ Laboratoire de Ge´ nie Chimique et d’Automatique, Ecole Centrale de Lille et ENSCL, BP 48, 59651 Villeneuve d’Ascq, France
The Mars and Van Krevelen model can be applied to all the steps of the oxidation of isobutane by oxygen over a heteropolyanion catalyst. The reaction scheme includes both direct (from isobutane) and indirect (via methacrolein) methacrylic acid production. The determinant multiresponse criterion has proved very efficient in the simultaneous estimation of all parameters of this complex model which perfectly fits the measured partial pressures of isobutane, methacrolein, and methacrylic acid in a large range of experimental conditions. The reaction of isobutane with the oxidized sites is the rate-limiting step of the process. Temperature and the oxygen-to-hydrocarbon ratio do not affect selectivities for the main products. The methacrolein transformation is 50 times faster than the isobutane reaction but is a factor of degradation, whereas methacrylic acid is stable. To improve selectivity, the transformation from isobutane to methacrylic acid has to be favored. Moreover, a higher propensity of catalysts for hydrocarbon activation should increase productivity. 1. Introduction The methyl methacrylate (MAM) is a very useful monomer leading by polymerization to poly(methyl methacrylate) (PMMA). The most significant commercial process technology used to date for the manufacture of MAM is the acetone cyanohydrin process. However, the disposal of the ammonia hydrosulfate produced and the handling of HCN are sources of substantial increase in the cost of MAM manufacture. Due to the great success in using n-butane to synthesize maleic anhydride [1], many works on alkanes activation have recently emerged. This work is included in that trend, and the reaction studied is the selective oxidation of isobutane (iBu) into methacrolein (MACO) and methacrylic acid (AMA) over heteropolycompoundsbased catalysts (HPA). Many recent works have actually shown the possibility of a future industrial development of such catalysts for this reaction [2-16]. It has to be noted that further oxidation of MACO into AMA and esterification of AMA into MAM are well-known reactions. For a number of reasons, the direct oxidation of isobutane into AMA is a very interesting alternative to the currently used process. First, the raw material is much cheaper than acetone and therefore the cost of production of MAM could be reduced significantly. Second, this process avoids the formation of cumbersome byproducts. Finally, it requires no dangerous substances. It has been shown that HPAs are selective in the direct oxidation of iBu to AMA and MACO but their level of activity is low [2-16]. Moreover, most of the studies have stated that the global selectivity for MACO and AMA decreases with an increase of the conversion of iBu. This accounts for the poor AMA and MACO yieldsless than 10%scurrently encountered in the researchers’ experiments. Modifications of the chemical composition and structure of the HPA have been extensively studied [17-23], but the kinetics of the selective oxidation of isobutane * Corresponding author. † E-mail:
[email protected]. ‡ E-mail:
[email protected]. § E-mail:
[email protected]. S0888-5885(96)00683-5 CCC: $14.00
is not known. Nevertheless, works on the kinetics of the oxidation of isobutyric acid to AMA have been published [24-27]. The purpose of this study is therefore to establish the kinetic equation of the isobutane reaction in order to improve the understanding of the behavior of the catalyst. The second objective is to devise a tool for assessing the effect of changes in composition or structure on the performances of catalysts. It is hoped that this will lead to a better rationale in catalyst formulation. The reaction rate equations obtained could also be used to model and hence improve reactor performance. To reach this objective, a kinetic analysis of the effect of each separate variable will be undertaken in view to select the possible forms of the kinetic law, then to discriminate them, and to give a first estimation of kinetic parameters. Finally, in a global approach, experiments at various experimental conditions will be used to obtain the most likely and precise values of parameters and to establish a formal scheme of the reaction. 2. Experimental Section 2.1. Preparation of the Catalyst. The catalyst used is a cesium-ammonium mixed salt of the 11molybdo-1-vanadophosphoric acid. It was prepared in two steps: the acid synthesis and its further cation exchange. At first, H4PMo11VO40 was synthesized by a method derived from Watzenberger’s works [28]: a (1.65 M) MoO3, (0.075 M) V2O5, and (0.23 M) H3PO4 aqueous solution was prepared by heating at reflux temperature for 24 h. The volume of the solution was then reduced by half in a vacuum. After total evaporation of the remaining water at 120 °C, a dark orange solid (H4PMo11VO40) was collected. In a second step, 0.168 mol of H4PMo11VO40 was added gradually to 300 mL of deionized water under continuous stirring. To the dark-red translucent solution obtained were added with great caution 0.112 mol of Cs2CO3 in water, leading to a CO2 release. A second solution of 0.374 mol of NH4Cl in 100 mL of water was added to the first one under constant stirring. The obtained slurry was evaporated as above to collect a pale orange solid. It was then ground into a fine powder. © 1997 American Chemical Society
3392 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 Table 1. Experimental Data balance sample
T (°C)
tc (s)
piBu0 (atm)
pO20 (atm)
XiBu
XO2
SAMA
SMACO
O
C
Sel
piBu0/pO20
B B B B B B B B B A A A A A A A A A A A A A A A A A B B B
301 301 302 321 321 322 337 342 342 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 350 352 352
3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 3.6 3.6 3.6
0.26 0.50 0.26 0.50 0.26 0.26 0.26 0.26 0.50 0.02 0.09 0.09 0.09 0.09 0.09 0.09 0.13 0.16 0.17 0.06 0.09 0.03 0.17 0.17 0.17 0.26 0.26 0.26 0.50
0.130 0.130 0.050 0.130 0.050 0.130 0.050 0.130 0.130 0.010 0.045 0.080 0.065 0.045 0.010 0.130 0.065 0.080 0.065 0.065 0.200 0.065 0.010 0.065 0.350 0.130 0.050 0.130 0.130
0.014 0.010 0.011 0.016 0.018 0.024 0.026 0.041 0.031 0.033 0.039 0.043 0.040 0.036 0.017 0.047 0.039 0.034 0.028 0.039 0.047 0.035 0.010 0.024 0.043 0.036 0.031 0.053 0.040
0.080 0.110 0.139 0.196 0.235 0.138 0.374 0.260 0.405 0.192 0.227 0.148 0.163 0.201 0.385 0.104 0.247 0.197 0.206 0.110 0.071 0.048 0.364 0.160 0.065 0.231 0.483 0.361 0.558
0.354 0.262 0.327 0.325 0.400 0.416 0.406 0.446 0.355 0.348 0.413 0.393 0.414 0.409 0.396 0.371 0.434 0.428 0.432 0.372 0.369 0.318 0.317 0.426 0.421 0.422 0.405 0.434 0.370
0.375 0.436 0.469 0.355 0.392 0.300 0.310 0.233 0.281 0.321 0.238 0.204 0.224 0.245 0.426 0.179 0.242 0.252 0.251 0.214 0.183 0.275 0.528 0.308 0.199 0.220 0.290 0.192 0.237
1.031 1.048 0.986 0.999 0.948 0.991 0.872 0.987 0.986 0.972 0.993 0.993 0.992 0.990 0.962 1.001 0.981 0.989 0.984 0.992 0.998 0.995 0.932 0.985 1.001 0.927 0.855 0.934 0.982
1.000 0.999 0.999 0.997 0.994 0.999 0.993 0.994 0.996 1.002 1.001 0.990 0.994 0.998 0.998 0.998 0.992 1.016 1.000 0.990 0.992 1.001 1.002 0.998 0.993 0.995 0.990 0.997 1.001
0.964 0.875 0.923 0.824 0.742 0.955 0.779 0.880 0.879 1.072 1.017 0.813 0.863 0.946 0.886 0.967 0.824 1.852 0.999 0.800 0.860 1.043 1.204 0.921 0.867 0.881 0.763 0.954 1.030
2.00 3.85 5.20 3.85 5.20 2.00 5.20 2.00 3.85 2.00 2.00 1.13 1.38 2.00 9.00 0.69 2.00 2.00 2.62 0.92 0.45 0.46 17.00 2.62 0.49 2.00 5.20 2.00 3.85
The same preparation was repeated twice in order to obtain two samples of catalyst: A and B. The specific areas have only been measured before thermal treatments and reactionsrespectively 42.7 and 64.5 m2/g for samples A and B. The recovery of catalyst samples for specific areas determination after the test has not been possible. Heteropolyanions are very sensitive to temperature. A thermal pretreatment has been used in a view to stabilize catalytic performance. In that purpose, sample A has been kept at 360 °C for 5 h under a fixed nitrogen flow, whereas sample B has been stabilized by a 30 h run at the following operating conditions: iBu/O2/H2O/ N2 ) 26/13/12/49, tc ) 3.6 s, 320 °C. 2.2. Apparatus. The experimental investigations were conducted in a tubular isothermal fixed-bed reactor. It consists of a 35 cm long (12 mm i.d.) 316 stainless steel tube immersed in a bath of molten salt providing uniform heating. The temperature profilesmeasured with a thermocouple sliding inside an axial 4 mm (o.d.) tubeshas shown a 15-cm-high isothermal section. The experiments were carried out only in this part of the reactor. A blank test realized with a carborundum-filled reactor has shown negligible transformation at the reaction temperature (300-350 °C). The heat of reactions at 350 °Csfrom 110 to 631 kcal/ molscan lead to extreme temperature gradients [29]. Thus, in order to maintain an isothermal catalytic bed, differential conditions of conversion were kept and dilution with silicon carbide powder (100 µm) was used. The fixed bed thus consists of three 5 cm layers: the catalytic bed made of 3 mL of catalysts3.6 gsdiluted in silicon carbide (1:1 by volume) was sandwiched between two identical pure silicon carbide layers. The reactor was fed with isobutane (0.12-1.56 NL/ h), air or oxygen (0.06-2.1 NL/h), and nitrogen by a set of Brooks mass flow controllers. Liquid water was provided by a Gilson 302 pump used in its lower range (0.3-0.6 mL/h). The partial pressures of isobutane and
oxygen were in the range of 0.02-0.5 and 0.01-0.35 atm, respectively. The iBu/O2 ratio was thus in the range of 0.45-17. In all experiments, the partial pressure of water was kept fixed at 0.12 atm. The contact time tc was defined as the ratio of the apparent volume of catalyst (i.e., 3 mL) to the gas flow rate at the NTP conditions. It was set at two different values, i.e., 1.8 and 3.6 s. 2.3. Analysis of the Reactants and Products. The concentrations of each component (except water) at the inlet and outlet of the reactor were determined by on-line gas chromatography. Two “instantaneous” mass balances, based on the conversions of the reactants (isobutane and oxygen) and in the oxidized products, were then calculated. The oxygen consumption due to the water formation can be deduced from the elementary balances established for the transformation of isobutane in each oxidized product, the excess of hydrogen giving water. These calculations do not depend on the effective mechanism of the reactions. The oxygen balance (BO) is much more sensitive and thus has much more significance than the carbon one’s (BC) at low conversion conditions (Table 1). The sum of selectivities (BS) was also checked. Samples of the outlet flow were simultaneously injected into two gas phase chromatographs, using two calibrated thermostated loops. To prevent the condensation of products, the effluent was kept at 250 °C. The inlet flow was sampled with another loop and analyzed in a chromatograph equipped with two thermal conductivity detectors (TCD), whereas the analysis of the outlet flow was carried out with the same equipment as well as in another chromatograph equipped with a flame ionization detector (FID). O2, N2, CO, CO2, isobutane, and lower alkanes were separated out through two successive columns and analyzed by the TCD. The first column (2 m long, 1/8 in. o.d.), filled with Porapak Q, was kept at 135 °C to separate CO2 and isobutane from the other components,
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3393
which in their turn were separated out through a 3-mlong 13X molecular sieve column (1/4 in. o.d.). The carrier gas used was helium at a 30 NmL/min flow rate. The temperature of the detectors was maintained at 100 °C. Water and possible heavy impurities were trapped before analysis in two precolumns filled with MgSO4 and Spherosil. The separation of the oxygenated products (i.e., acrolein, methacrolein, acetic acid, acrylic acid, and methacrylic acid) was carried out on a 3 m long, 1/8 in. o.d. LAC 2R446 column. The temperature program consisted of three isothermal periods: 2 min at 40 °C, 2 min at 60 °C, and 19 min at 160 °C, separated by two heating periods at a 10 °C/min rate. The injector and the flame ionization detector were kept at 200 °C. The carrier gas used was nitrogen at a 30 NmL/min flow rate. Absolute calibrations for all products were made by injecting liquid (FID) or gaseous (TCD) standard mixtures of the above-mentioned products. A complete analysis of inlet and outlet flows was achieved in 45 min. 2.4. Procedure of Calculations. The C and O balances are usually very close to 100% (Table 1). However, the sum of the selectivities is very sensitive to low fluctuations of C balance especially at low isobutane conversion. This is essentially caused by the experimental lack of accuracy in isobutane conversion in this case (very little difference between two large peaks). Thus, in order to avoid erratic results when determining the kinetic parameters, the isobutane conversion used for modeling was taken as the sum of the product yields. This approximation seems to be justified in view of the good C (always greater than 99%) and O balances (100 ( 5%). The reaction rate for each reactant or product can be evaluated by the global balance on the catalytic bed:
(pi0 - pi)Vcata Fi0Xi ) ri ) tcmRT m for the reactants, i.e., i ) iBu or O2 (1) and
rj )
pjVcata
FiBu0Yj
) tcmRT m for the products, i.e., j ) MACO or AMA (2)
Due to the low conversions, the reactor was considered homogeneous with respect to the reactants. Thus, for kinetic exploitation, the partial pressures of oxygen and isobutane in the whole reactor were taken as the average values between the inlet and the outlet. This assumption appears to be roughly consistent with both zero and first kinetic orders in integral reactors. The rate hence obtained is therefore a mean reaction rate inside the reactor. 3. Results and Discussion 3.1. Kinetics of Isobutane Disappearance. In order to establish the complete kinetic model for AMA production, 29 experiments were carried out over the two samples A and B. The effects of all the variables, i.e., partial pressures of reactants, reaction temperature, and contact time, were investigated. The steady state is observed after a run of several hours, leading to a perfect stability for operating conditions and effluent concentrations. The
Figure 1. Influence of the partial pressure of isobutane on isobutane reaction rate. Sample A: T ) 350 °C, tc ) 1.8 s (b, pO2 ) 0.01 atm; O, pO2 ) 0.065 atm).
experimental data reported in Table 1 result from several successive identical analyses obtained after this stabilization period. 3.1.1. Apparent Partial Orders. In a first approach, the variations of the isobutane reaction rate with isobutane and oxygen inlet concentrations were studied. These experiments were carried out over sample A at 350 °C with a contact time tc ) 1.8 s. In Figure 1, the effect of variations in isobutane partial pressure on the reaction rate is represented for two different constant oxygen concentrations. It is seen that the reaction rate linearly varies in a first step and then reaches a plateau, the level of which depends on the oxygen pressure. Therefore, the partial kinetic order for isobutane evolves from one to zero when the hydrocarbon concentration is increased. This evolution, which is not due to a limitation in oxygen partial pressure (always above 6 × 10-3 atm), indicates the competition for access to the catalytic sites, the number of which varies with the oxygen concentration. It cannot be represented using a power-law kinetic equation. Figure 2 reports the variation of isobutane reaction rate with oxygen partial pressure at constant isobutane partial pressure. The conclusions are not as clear as those given previously, but, once again, a shift in order is observed. As a matter of fact, the oxygen apparent partial order changes from a positive value at low concentration to zero for the higher values. This result is verified for two different hydrocarbon concentrations. Here again, the partial pressure of isobutane always stays above 0.08 atm; there is therefore no using up of the reactant. As previously, a homogeneous kinetic model cannot match these data. 3.1.2. Kinetic Models. It has been shown that the variations of the isobutane reaction rate with the hydrocarbon and oxygen concentrations imply a surface saturation phenomenon. Two standard hypotheses of kinetic models are commonly used in oxidation catalysis. The first assumption is that the hydrocarbon reacts with active sites (oxidized sites), the number of which decreases as the hydrocarbon partial pressure increases. This model is known as the Mars and Van Krevelen model [30]. A second hypothesis consists of the equilibrated adsorption of isobutane on the catalyst’s surface
3394 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997
Figure 2. Influence of the partial pressure of oxygen on isobutane reaction rate. Sample A: 350 °C, 1.8 s (b, piBu ) 0.09 atm; O, piBu ) 0.17 atm).
and its further reaction with the oxygen provided by the gas phase. This model is known as the Eley-Rideal model [31]. In each case, the reaction rate increase is stopped at high hydrocarbon partial pressures. Another usual mechanism, generally used in catalytic hydrogenation, considers adsorption equilibria for both reactants and reaction between adsorbed species (LangmuirHinshelwood). In these assumptions, the dependency of the reaction rate on the partial pressure of one reactant is identical whatever the other reactant concentration is. Figures 1 and 2 clearly show that this model is not relevant to our data. The Mars and Van Krevelen model is based on the redox dynamics of the catalyst’s sites, reduced by reaction with the hydrocarbon coming from the gas phase and further reoxidized by the gaseous oxygen, according to the following scheme: kr
iBu + cata-ox 98 products + cata
Ns
kKpiBupO2n2 N 1 + KpiBu s
(4)
It is interesting to note that, in this case, the apparent partial order for oxygen must be constant, which is not experimentally observed. As previously observed concerning the Mars-Van Krevelen model, the accessible kinetic parameter will be kNs. The discrimination between these two models can be easily confirmed by linearization of the previous equations. This leads to
1 1 1 ) + r (k N )p n2 (k N )p n1 o s O2 r s iBu
s
The balance on catalytic sites at steady state leads to the following equation (see note):
krpiBun1 + kopO2n2
r)
1 1 ) r (kN )p
iBu + nO2 f products
r)
adsorption and rapid desorption or low-coverage byproducts, the reaction rate is then expressed by
(5)
for the Mars and Van Krevelen model and
ko
cata + nO2 98 cata-ox
krkopiBun1pO2n2
Figure 3. Inverse of isobutane reaction rate vs inverse of isobutane partial pressure. Sample A: 350 °C, 1.8 s (b, pO2 ) 0.01 atm; O, pO2 ) 0.065 atm).
(3)
Ns cannot be easily determined. Consequently, the values of the estimated kinetic parameters are the product of turnover number frequency by sites concentration: krNs, koNs. In the case of the Eley-Rideal model: K
iBu + cata \ y z cata-iBu k
cata-iBu + nO2 98 cata + products iBu + nO2 f products when applying Langmuir assumptions for isobutane
O2
n2
(
1+
1 KpiBu
)
(6)
for the Eley-Rideal equation. As can be seen, the two models are not identical and the discrimination can be done, for instance, by means of the origin’s ordinate of the curves 1/r versus 1/pO2n2 at constant piBu. This ordinate will be positive and variable, depending on isobutane partial pressure, if Mars and Van Krevelen’s model fits and zero if EleyRideal’s model is verified. From several values of both oxygen and isobutane partial orders tested, it has been found that the best linearity is observed for n1 ) n2 ) 1 (Figures 3 and 4). This result is not surprising as far as isobutane is concerned, whereas it is more difficult to explain directly for oxygen. Figure 3 presents straight lines that do not pass through the origin; the Eley-Rideal model is hence not valid. Furthermore, the straight lines observed for different concentrations are rather parallel (Figures 3 and 4). Consequently, the Mars and Van Krevelen model seems to be pertinent to the experimental data.
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3395 Table 2. Mars-Van Krevelen Rate Constants for Isobutane Consumption Issued from Regression at Different Temperatures sample B B B B A
T (°C)
krNs (mol/atm/g/h)
koNs (mol/atm/g/h)
300 320 340 350 350
6.84 × 1.20 × 10-3 2.35 × 10-3 3.06 × 10-3 3.81 × 10-3
3.54 × 10-3 6.15 × 10-3 1.07 × 10-2 1.51 × 10-2 1.76 × 10-2
10-4
Figure 4. Inverse of isobutane reaction rate vs inverse of oxygen partial pressure. Sample A: 350 °C, 1.8 s (b, piBu ) 0.09 atm; O, piBu ) 0.17 atm).
Figure 6. Arrhenius plot of reaction rate constants determined at constant temperatures and tc ) 3.6 s (O, ln koNs for sample B; b, ln krNs for sample B; 4, ln koNs for sample A; 2, ln krNs for sample A).
Figure 5. Inverse of isobutane reaction rate vs inverse of the square root of oxygen partial pressure. Sample A: 350 °C, 1.8 s (b, piBu ) 0.09 atm; O, piBu ) 0.17 atm).
By way of verification, the hypothesis of dissociative adsorption of oxygen (oxygen partial order equal to 0.5) is presented on Figure 5. This plot is not a straight line; this assumption is therefore invalidated. 3.1.3. Determination of the Activation Energies. The activation energies of both stepssreduction and oxidation of the catalystswere determined using the experiments over sample B. They were carried out at different temperatures (300, 320, 340, and 350 °C) and various feed compositions. The values of the rate constants krNs and koNs (Table 2) were obtained by linearization at each temperature and plotted on an Arrhenius diagram (Figure 6). The excellent linearity of these representations validates the significance of the values of the rate constants and leads to the corresponding activation energies, i.e., Er ) 21.6 kcal/mol and Eo ) 20.6 kcal/mol. These values are consistent with the usual data for oxidation reactions.
Figure 7. Comparison between experimental and calculated isobutane partial pressuressMars-Van Krevelen model, all experiments (O, sample A; 4, sample B).
The rate constants found from the experiments over sample A at 350 °C are shown in the same figure. It is of interest to note that both are greater than those obtained from sample B at the same temperature. This result has been attributed to a difference in site concentration between the two samples. This may be related to specific area variations or surface modifications during the various pretreatments of samples described in the Experimental Section.
3396 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 Table 3. Parameters of the Mars and Van Krevelen Model for Isobutane Consumption Issued from Regression on All Experiments krNs at T ) 350 °C (mol/atm/(g of cat A)/h)
koNs at T ) 350 °C (mol/atm/(g of cat A)/h)
Er (kcal/mol)
Eo (kcal/mol)
h
RSS
3.7 × 1.3 × 10-4
1.9 × 5.3 × 10-4
22 4
21 6
1.30 0.04
6 × 10-6
parameter standard deviation
10-2
10-3
Then, in order to verify the applicability of the kinetic model to both samples (A and B), to take an advantage from all experiments, and to obtain more reliable and precise parameters, a correcting factor of the activity, h ) NsA/NsB, has been introduced and the regression has been conducted on the experimental errors on the most imprecise measured variable. The five parameters (kr350°CNsA, ko350°CNsA, Er, Eo, h) are then simultaneously determined using a nonlinear regression method (Marquardt’s method [32]). The primary experimental data being partial pressures of reactants and products issued from chromatographic analyses, the regression has been made on the sum of the squared differences between experimental and calculated values of the outlet isobutane partial pressure expressed by 29
o.f. )
(piBu - pˆ iBu)i2 ∑ i)1
(7) Figure 8. Influence of isobutane conversion on yields and selectivity for valuable productssall experiments (2, MACO yield; O, AMA yield; b, AMA and MACO yield; 4, global selectivity for AMA and MACO).
with
pˆ iBu ) piBu0 -
22.4tckokr piBu pO2
NsA
Vcata(kr piBu + ko pO2)
Scheme 1
for sample A (8) and
pˆ iBu ) piBu0 -
22.4tckokr piBu pO2 NsA V (k p + k p ) h cata
r
iBu
o
O2
for sample B (9) For an optimal estimation of the parameters, the following reparametrization was applied:
[(
ki ) kiTm exp
Ei 1 1 R Tm T
)]
(10)
Here Tm is equal to 623.15 K. The results of the regression (Table 3) exhibit a good agreement with the estimations obtained by the sequential procedure (Arrhenius diagram), especially for the activation energies. Moreover, the validity of these values is confirmed by the particularly low standard deviations of the parameters obtained unless the degree of freedom is low. Figure 7 shows an excellent agreement between experimental and calculated values for all temperature, contact time, and feed composition conditions. From the obtained values, one can conclude that the reoxidation step is much faster than the reaction of the hydrocarbon on the surface. Therefore, the reaction rate cannot be notably increased when high oxygen partial pressures are used, giving rapidly a zero order. This conclusion explains the choice of high hydrocarbon-tooxygen ratios in this reaction, with a view to increase the productivity and decrease contact times.
3.2. Analysis of the Reaction Network. 3.2.1. Reaction Scheme and Kinetic Equations. Figure 8 shows the dependence of MACO and AMA yields on the conversion of isobutane for all experiments (samples A and B). It also reports the selectivity into valuable products (sum of AMA and MACO). It is of interest to note that in the complete range of the operating conditions used (O2/iBu ratio, 0.45-17; temperature, 300-350 °C) the evolutions of methacrylic acid and methacrolein conversions are directly related to the conversion of isobutane in single curves. The effect of the concentration of each reactant on each step of the reaction scheme is hence identical. Therefore, the same kinetic model can be applied to all the steps. Moreover, the absence of temperature effect on yields shows that the effect obtained in varying temperature is the same on each kinetic constant, that is to say, that the activation energies of rate constants are equal at each step of the reaction. Several mechanistic conclusions can also be drawn from Figure 8. At the initial stage of reaction (very low conversions), MACO, AMA, and products of degradation are all produced, but the fast consecutive transformation of MACOswhich rapidly reaches a quasi-steady-state concentrationsleads to an increase in AMA formation. Last, consecutive degradation of these products is
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3397
observed. As suggested by an earlier study [14], MACO is hence an intermediate in AMA formation. These conclusions lead to a general reaction network (Scheme 1). As shown below, the rates of product formation can be derived from the adopted scheme.
rMACO )
dpMACO ) dt k1ko piBu pO2 - (k3 + k4)ko pMACO pO2 Ns (11) kr piBu + ko pO2
dpAMA ) dt k3ko pMACO pO2 + k2ko piBu pO2 - k5ko pAMA pO2 Ns (12) kr piBu + ko pO2
rAMA )
These time-dependent expressions were related to the isobutane disappearance equation by dividing eqs 11 and 12 by eq 3. The integration of the derived equations leads to
pˆ MACO )
[( )
pˆ iBu K1 piBu0 1 - K3 - K4 p 0 iBu
(
)
K1K3 K3 + K4 - 1 K5 - 1
piBu0 K2 + pˆ AMA )
( )] pˆ iBu
K3+K4
-
piBu0
(13)
[( ) ( ) ] pˆ iBu
piBu0
pˆ iBu
-
piBu0
Figure 9. Comparison between experimental and calculated values for MACO partial pressuressall experiments, multiresponse criterion.
K5
+
K1K3 × piBu0 (K3 + K4 - 1)(K3 + K4 - K5)
[( ) pˆ iBu
0
piBu
( )] pˆ iBu
K3+K4
-
K5
0
piBu
(14)
It can be noted that the Ki parameters do not depend on the sample surface area. 3.2.2. Parameters Estimation. The model consists of the eqs 8, 9, 13, and 14; its adequacy has been tested by means of the experimental data. This involves the estimation of the 10 parameters in these four equations. All of them could be determined by sequential regression, first on piBu using eqs 8 and 9, then on pMACO using eq 13, and finally on pAMA with eq 14. Such a procedure could lead to bad precision on the last estimated parameter, in this instance K5. Therefore, to come to an optimal fit between experiments and calculations and to preserve the statistical significance of the parameters, it is preferable to include simultaneously all the independent responses in the objective function used in the regression. The estimation then becomes a multiresponse problem usually based upon a weighted leastsquares criterion as the objective function:
o.f. ) aΣ(pˆ iBu - piBu)i2 + bΣ(pˆ MACO - pMACO)i2 + cΣ( pˆ AMA - pAMA)i2 However, this criterion does not account for eventual correlations between responses and uses weighting
|
Figure 10. Comparison between experimental and calculated values for AMA partial pressuressall experiments, multiresponse criterion.
factors a, b, and c, which have to be the inverse of the variances of each response. The variances on the isobutane, MACO and AMA partial pressures are a priori different, due to the various sensitivities of analytical apparatus, and they cannot be easily determined. Thus, to avoid a more or less arbitrary choice of the weighting factors, a different approach using the determinant criterion proposed by Box and Draper [33], taking into account the different variances of the responses and their correlation, has been chosen. The determinant which has to be minimized is given in eq 15.
Σ( pˆ iBu - piBu)i(pˆ MACO - pMACO)i Σ(pˆ iBu - piBu)i(pˆ AMA - pAMA)i Σ(pˆ iBu - piBu)i2 Σ(pˆ MACO - pMACO)i(pˆ AMA - pAMA)i ∆ ) Σ(pˆ iBu - piBu)i(pˆ MACO - pMACO)i Σ( pˆ MACO - pMACO)i2 Σ(pˆ iBu - piBu)i(pˆ AMA - pAMA)i Σ( pˆ MACO - pMACO)i(pˆ AMA - pAMA)i Σ(pˆ AMA - pAMA)i2
|
(15)
3398 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 Table 4. Parameters Issued from the Multiresponse Regression K1 0.56
K2
K3
0.25
23.4
K4 28.7
K5
(krNsA)350°C
(koNsA)350°C
Er
Eo
h
DET
0
3.9 ×
2.0 × 10-2
21.2
20.0
1.40
3.31 × 10-18
10-3
Table 5. Kinetic Parameters of Each Step of the Model (k1NsA)350°C
(k2NsA)350°C
(k3NsA)350°C
(k4NsA)350°C
(k5NsA)350°C
(k6NsA)350°C
(koNsA)350°C
Er
Eo
h
0.0022
0.000 98
0.091
0.112
0
0.000 741
0.020
21.2
20.0
1.40
Scheme 2
This multiresponse method has previously shown good efficiency in the treatment of complex kinetic reaction schemes [34]. The minimization of the criterion based on all experiments and responses was carried out by the numerical Newton-Raphson’s method. The results of the regression are reported in Table 4. Figures 9 and 10 show the excellent agreement between experimental and calculated values. The standard deviations on isobutane, methacrolein, and methacrylic acid partial pressures reach very low values: 4.6 × 10-4, 1.5 × 10-4, and 3 × 10-4 atm, respectively. This proposed reaction scheme is therefore representative of the experiments. It is interesting to note that the optimization leads to the zero value for the relative rate constant of the AMA degradation step. This means that the rate of this reaction is negligible at low isobutane conversion in the operating conditions used. K1 and K2 are the initial selectivities of the catalyst for MACO and AMA formation. The initial global selectivity for valuable products is therefore above 80%. This confirms the high selectivity of the catalyst at low isobutane conversion. In addition, the value of K3 + K4 shows the fast transformation of MACO compared with the isobutane one (around 50 times more reactive). In this transformation, the degradation of MACO, leading to carbon oxides and C2-C3 oxygenated products and represented by K4, appears to be rapid: the selectivity is 43% over this catalyst, according to these calculations. Results obtained by other authors in the catalytic oxidation of MACO show high activity and selectivity in AMA formation at a lower temperature [35]. Our recent works have shown the high activity and the moderate selectivity of this transformation in our experimental conditions on this catalyst. The value of selectivity we obtained in this way can be assigned to a high sensitivity of MACO at high temperature. All the kinetic parameters of the model are summarized in Table 5 and Scheme 2. 4. Conclusions It has been found that the Mars and Van Krevelen kinetics applies to the reactions occurring between isobutane, MACO, AMA, and oxygen on a HPA catalyst. The rate-limiting step appears to be the reaction of isobutane on the oxidized surface of the catalyst. The state of the catalyst could then be near fully oxidized, except at a very low concentration of oxygen. It is stated that the total selectivity for methacrolein and methacrylic acid only depends on the conversion of
isobutane and can be influenced neither by the hydrocarbon-to-oxygen ratio nor by temperature in the 300350 °C range. The general reaction scheme proposed and the kinetic equations derived from it fit well with the experimental data. Both direct and indirect pathways from isobutane to methacrylic acid are thus significant. Methacrolein appears to be very reactive compared with isobutane and its degradation plays an important role in the final yield in AMA. On the contrary, methacrylic acid seems to be very stable and its degradation is negligible at low conversion. At present, catalysts have a low activity and a poor selectivity at high conversion. The findings of this study suggest that an increase in productivity could be obtained by favoring hydrocarbon activation rather than oxygen incorporation. Moreover, selectivity could be enhanced by avoiding the production (or desorption) of methacrolein, which seems to be fragile in the current operating conditions, and by favoring the direct pathway leading to methacrylic acid. In a further study, these equations could be used for simulating new reactor configurations with a view to optimizing operating conditions. Acknowledgment ELF ATOCHEM is gratefully acknowledged for financial and technical support. All the reaction rates for transformation of reactants and intermediate products have to be included in the sites balance for an exact description of the dynamic behavior of the catalyst. This procedure leads to a kinetic equation containing an excessive number of parameters which cannot be correctly determined in a sequential kinetic analysis. With respect to the high value of isobutane partial pressure in comparison with intermediates partial pressures, the corresponding terms have been omitted in the sites balance and then do not appear in the denominator of rate expressions. Nevertheless, a global regression upon all responses and using the rigorous Mars-Van Krevelen equation has been done, giving no significant variations in the quality of regression and in the parameter values. Abbreviations and Notations Abbreviations AMA: methacrylic acid BO: oxygen balance BC: carbon balance BS: sum of selectivities DET: determinant HPA: heteropolyacid or -anion iBu: isobutane MACO: methacrolein MAM: methyl methacrylate PMMA: poly(methyl methacrylate) RSS: residual sum of squares
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3399 Notations Eo: activation energy for the reoxidation step (Mars and Van Krevelen model) (kcal/mol) Er: activation energy for the reduction step (Mars and Van Krevelen model) (kcal/mol) Fi0: inlet molar flow rate of reactant i (mol/h) K: isobutane adsorption equilibrium constant (Eley-Rideal model) (atm-1) k: turnover frequency for the reaction of adsorbed isobutane (Eley-Rideal model) (mol/atm/site/h) Ki (i ) 1-5): relative reaction rate constant for the reaction step j kj (j ) 1-5): turnover frequency for the reaction step j (mol/ atm/site/h) ko: turnover frequency for the reoxidation step (Mars and Van Krevelen model) (mol/atm/site/h) kr: turnover frequency for the reduction step (Mars and Van Krevelen model) (mol/atm/site/h) m: weight of the catalyst sample (g) n1: partial order for isobutane n2: partial order for oxygen NsA, NsB: concentrations of sites in samples A and B (sites/g) pˆ i: calculated outlet value of the partial pressure in component i (atm) p j i: mean partial pressure in component i inside the reactor (atm) pi0: inlet partial pressure for component i (atm) pi: outlet partial pressure for component i (atm) ri, rj: mean reaction rate for a reactant i (disappearance) or a product j (formation) (mol/h/g) Si: selectivity for product i T: reaction temperature (K) tc: contact time (s), defined in the experimental part Vcata: apparent volume of the catalyst sample (mL) Xi: conversion of reactant i Yj: yield in product j
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Received for review October 24, 1996 Revised manuscript received May 30, 1997 Accepted June 3, 1997X IE960683K
X Abstract published in Advance ACS Abstracts, July 15, 1997.
