1824
Ind. Eng. Chem. Res. 1991,30, 1824-1828
y = response Y = yield of MA Y = vector of responses = least-squares estimate Registry No. PO, 1314-56-3; MA, 108-31-6;Mo, 7439-98-7; Ce, 7440-45-1; H(CH2),H, 106-97-8;V, 7440-62-2.
Literature Cited Box, G. E. P.; Hunter, W. C.;Hunter, J. S. Statistics for Experimenters; Wiley: New York, 1978; Chapters 10 and 12. Buchanan, J. S.; Sundaresan, S. Kinetics and Redox Properties of Vanadium Phosphate Catalysts for Butane Oxidation. Appl. Catal. 1986, 26, 211-226. Cavani, F.; Centi, G.; Trifiro, F. The Chemistry of Catalysts Based on Vanadium-Phosphorus Oxides Note IV Catalytic Behaviour of Catalysts Prepared in Organic Medium in the Oxidation of C4 Fraction. Appl. Catal. 1984,9, 191-202. Cavani, F.; Centi, G.; Manenti, I.; Trifiro, F. Catalytic Conversion of C, Hydrocarbons on Vanadium-Phosphorus Oxide: Factors Influencing the Selectivity of l-Butene Oxidation. Ind. Eng. Chem. Prod. Res. Deu. 1985a, 24, 221-226. Cavani, F.; Centi, G.; Trifiro, F. Study of n-Butane Oxidation to Maleic Anhydride in a Tubular Flow Stacked-Pellet Reactor. Influence of Phosphorus on the Selectivity. Appl. Catal. 1985b, 15, 151-160. Centi, G.; Fornasari, G.; Trifiro, F. On the Mechanism of n-Butane Oxidation to Maleic Anhydride: Oxidation in Oxygen-Stiochiometry-Controlled Condtions. J . Catal. 1984a, 89, 44-51. Centi, G.; Manenti, I.; Riva, A.; Trifiro, F. The Chemistry of Catalysts Based on Vanadium-Phosphorus Oxides Note I11 Catalytic Behaviour of Different Phases in 1-Butene Oxidation to Maleic Anhydride. Appl. Catal. 1984b,9, 177-190. Centi, G.; Trifiro, F.; Ebner, J. R.; Franchetti, V. M. Mechanistic Aspects of Maleic Anhydride Synthesis from C4 Hydrocarbons over Phosphorus Vanadium Oxide. Chem. Reu. 1988,88,55-80. Davies, 0. L. The Design and Analysis of Industrial Experiments; Longman Group: New York, 1978; Chapter 11.
Draper, N. R.; Smith, H. Applied Regression Analysis, 2nd ed.; Wiley: New York, 1981; pp 1-125. Hodnett, B. K. Vanadium-Phosphorus Oxide Catalysts for the Selective Oxidation of C4 Hydrocarbons to Maleic Anhydride. Catal. Rev. Sci. Eng. 1985, 27 (3), 373-424. Hodnett, B. K.; Delmon, B. Factors Influencing the Selectivity of Vanadium-Phosphorus Oxide Catalysts for n-Butane Oxidation to Maleic Anhydride. Appl. Catal. 1985, 15, 141-150. Hucknall, D. J. Selective Oxidation of Hydrocarbons; Academic Press: London, 1974; Chapter 4. Katsumoto, K.; Marquis, D. M. US. Patent 4 132 670, 1979. Khuri, A. I.; Cornell, J. A. Response Surfaces Designs and Analyses; Marcel Dekker: New York, 1987; Chapters 1, 2, 3, and 5. Kittrell, J. R.; Erjavec, J. Response Surface Methods in Heterogeneous Kinetic Modelling. Ind. Eng. Chem. Process Des. Deu. 1968, 7 (3),321-327. Moser, T. P.; Schrader, G. L. Selective Oxidation of n-Butane to Maleic Anhydride by Model V-P-0 Catalysts. J . Catal. 1985,92, 216-231. Rao, M. S.; Iyengar, S. S. In Computer Modelling of Complex Biological Systems; Iyengar, S. s.,Ed.; CRC Press: Boca Raton, FL, 1984; pp 29-53. Smith, J. M. Chemical Engineering Kinetics, 3rd ed.; McGraw-Hill: New York, 1981; Chapter 11. Varma, R. L.; Saraf, D. N. Oxidation of Butene to Maleic Anydride I. Kinetics and Mechanism. J . Catal. 1978,55, 361-372. Varma, R. L.; Saraf, D. N. Selective Oxidation of C, Hydrocarbons to Maleic Anhydride. Ind. Eng. Chem. Prod. Res. Deu. 1979, 18 (11, 7-13. Wellauer, T. P.; Cresswell, D. L.; Newson, E. J. Optimal Policies in Maleic Anhydride Production through Detailed Reactor Modelling. Chem. Eng. Sci. 1986, 41 ( 4 ) , 765-772. Wenig, R. W.; Scharder, G. L. Vanadium-Phosphorus-Oxygen Industrial Catalysts for n-Butane Oxidation: Characterization and Kinetic Measurements. Ind. Eng. Chem. Fundam. 1986, 25, 612-620. Receiued for review July 2, 1990 Reuised manuscript received February 6, 1991 Accepted February 12,1991
Selective Oxidation of 11 -Butane to Maleic Anhydride. 2. Identification of Rate Expression for the Reaction Shyamal K. Bej and Musti S. Rao* Department of Chemical Engineering, Indian Institute of Technology, K a n p u r 208 016,
U.P., India
The modeling of the selective oxidation of n-butane t o MA has been done in a systematic manner. Both Langmuir-Hinshelwood and redox models have been proposed and tested with differential rate data. Four redox models have been fitted to the experimental data. Discrimination among these models has been achieved with the use of a sequential experimental design. T h e redox model having first-order dependency on n-butane partial pressure and zero-order dependency on oxygen partial pressure was found to be the most appropriate. 1. Introduction
The selective oxidation of n-butane to maleic anhydride (MA) is a complex reaction from the mechanistic and modeling point of view. Besides the main reaction of selective formation of MA from n-butane, two other side reactions, viz., the complete oxidation of n-butane and of MA to oxides of carbon, take place simultaneously. Different types of models have been proposed by different investigators (e.g., Wohlfahrt and Hofmann (1980), Centi et al. (19851, Buchanan and Sundaresan (1986), Lerou and Weiher (1986), and Schneider et al. (1987)). Wohlfahrt and Hofmann (1980), Centi et al. (1985), and
* T o whom correspondence should be addressed. 0888-5885/91/2630-1824$02.50/0
Buchanan and Sundaresan (1986) have proposed different forms of redox models for this reaction. An adsorption model has been proposed by Lerou and Weiher (1986). Though a number of studies are available on the modeling of this reaction, there is some doubt regarding the order of reaction with respect to oxygen and also the activation energy. In this present work we have tried to clarify some of these doubts by systematic modeling studies. The reaction has been studied over a Mo- and Ce-promoted VPO catalyst (P/V atomic ratio = 1.0s; weight ratio of Mo/V = 0.06; weight ratio of Ce/V = 0.0221, the optimum composition of which was established in part 1 of this series. The catalyst had a surface area of 20 m2/g. The details of catalyst preparation were also given in part 1 of this series. 0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991 1825 Table I. Concentrations of the Components Involved in the Rate Equations and Rate of temp, O C 370
390
410
inlet concn, vol % n-butane oxygen 0.60 21.95 0.94 19.77 1.20 17.68 1.50 15.58 1.80 13.57 21.78 0.59 0.90 19.68 1.21 17.80 1.54 15.80 1.80 13.47 21.68 0.60 19.55 0.90 1.22 17.50 15.44 1.50 13.26 1.80
outlet concn, vol % n-butane oxygen 21.71 0.54 0.86 19.47 1.14 17.42 1.42 15.24 1.70 13.15 0.55 21.63 0.84 19.42 1.13 17.44 1.40 15.28 1.72 13.18 0.56 21.50 0.84 19.29 1.14 17.16 1.44 15.14 1.70 12.84 ~
2. Experimental Section The setup used for the present study was the same as that described in part 1 of this series except that oxygen and nitrogen gases were used separately instead of air. The experiments were performed and the products were analyzed according to procedures described in part l of this series.
~~
Table 11. Values of Parameters for Models 1-4 model K," K," RSS Temperature = 370 "C 0.2169 0.2254 X 1 0.3060 0.1980 X 2 0.0985 0.2214 0.2348 0.1689 X lo-' 3 0.0553 0.1407 X 4 0.0308 0.2445
3. Results and Discussion The general scheme of the reaction can be represented by a combination of series and parallel reactions as follows:
(1)
n-butane
MA
-Butane Depletion rate of n-butane concn*'01 % depletion, g-mol/(g.h) n-butane oxygen x 103 1.2114 0.57 21.83 19.62 1.8055 0.90 17.55 2.1209 1.17 2.4604 1.46 15.41 1.75 13.36 2.9357 21.71 2.3296 0.57 0.87 19.55' 2.7238 1.17 17.62 4.0466 4.7088 1.47 15.54 1.76 13.40 5.0342 0.58 21.59 3.7777 0.87 19.42 4.6764 17.33 6.2457 1.18 15.29 7.0716 1.47 13.05 7.5654 1.75
(1)
oxides of carbon a
In the present investigation we have conducted detailed modeling studies of the fmt reaction (i). For that we have conducted experiments under such conditions that MA is the only product of the reaction. From preliminary experiments it is observed that the reaction carried out below 410 O C and at low conversion of n-butane leads to very high selectivity (>96%) toward MA. Under such conditions, the above complex reaction is reduced to a simplified form as n-butane MA (2) Both Langmuir-Hinshelwood models and redox models can be proposed for the reaction. We have derived four redox models and three Langmuir-Hinshelwood models for this reaction. The derivation of the redox models is based on the general principles as discussed by Thomas and Thomas (1967). The reaction. can be written in the following stepwise manner:
KI
O,+R-X
B + xL !- MA + R (3) where B, MA, R, and X stand for n-butane, maleic anhydride, reduced state of the catalyst, and oxidized state of the catalyst, respectively. The rate a t which n-butane is depleted to form MA on site X is given by -dpe/dt = K & Y x (4) where p B is the partial pressure of n-butane a t a time t, 8x is the fraction of surface occupied by X, and m is the
I)
1 2 3 4
Temperature = 390 "C 0.3990 0.4878 0.1619 0.4174 0.0937 0.4298 0.4467 0.0523
0.2007 X 0.2077 X 0.2141 X 0.2212 x
1 2 3 4
Temperature = 410 O C 0.6848 0.5447 0.7356 0.1791 0.1022 0.7222 0.8219 0.0575
0.1432 X 10" 0.1315 X IO" 0.1347 X 10" 0.1473 X 10"
10" 10" 10" 10"
Units: g-mol/(g.h.atm).
order of the reaction with respect to n-butane. Similarly, the rate a t which oxygen is consumed at the site R for the oxidation of R to X is given by -dp02/dt = KIP8PR
(5)
where po, is the partial pressure of oxygen, dR is the fraction of surface occupied by R, and n is the order of reaction with respect to oxygen. If a moles of oxygen are required for the oxidation of 1 mol of n-butane to MA, then a t steady state oxygen balance on site X gives aK&eX
= KIP6$R
(6)
or aK$Bex = K&(l
- 8x1
(7)
Rearrangement of the above equation gives the following final form: -rg
=
KIKzPBP6, KlP8, + 'YK2PB
(8)
There is very little doubt regarding the value of m. Most of the previous investigators, viz., Centi et al. (1985),Buchanan and Sundaresan (1986),and Centi et al. (19881, have established the value of m as 1.0. However, there is much doubt regarding the value of n. In the present investigation we have assumed the value of m as 1.0 but four different values of n, viz., 1.0, 0.5,0.25, and 0 for models 1, 2, 3, and 4,respectively. The Langmuir-Hinuhelwood models have been derived
1826 Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991 Table 111. Posterior Probabilities of Models (Initial Prior Probability for Each Model = 0.25) posterior probability of temD, O C discrim stage total no. of exDts model 1 model 2 model 3 370 1 0.210 0.240 0.260 5 0.010 0.110 2 6 0.310 0.305 I 3 0.108 0.294 4 0.100 8 0.290 5 9 0.095 0.280 6 10 0.090 0.248 0.256 0 252 390 1 5 0.350 2 0.002 0.130 6 0.340 3 i 0.120 0.325 4 8 0.117 5 9 0.110 0.320 10 U.106 6 0.315 0.254 9 0.257 410 1 0.246 13.320 2 6 0.001 0 080 c 3 0.070 0.320 0.310 4 8 0 060 0.306 5 9 0.056 0 0% 0.306 6 10
on the lines the modeling of the propylene oxidation reaction in Tan et al. (1988). Model 5. For this model, a single site mechanism is considered. It is assumed that all sites have affinities for n-butane and oxygen. Then we get the following form of the Langmuir-Hinshelwood model.
In this model, it is also assumed that each adsorbed molecule occupies only one site. Model 6. In this model two different sites-one with affinity for n-butane and the other with affinity for oxygen-are considered. The occupancy of one site by a single molecule is also assumed here. With these assumptions, the Langmuir-Hinshelwood model becomes -rB =
K2KAKRPBP02 (1 -k KAPo1)(1 + KRPB)
(10)
Model 7. Here, besides the assumption of two different sites as in model 6, the occupancy of a pair of adjacent sites by each oxygen molecule has been considered. Then the Langmuir-Hinshelwood equation becornes
model 4 0.290 0.570 0.587 0.605 0.614 0.630 0.244 0.520 0.540 0.560 0.570 0.580 0.243 0.590 0.610 0.630 0.637 0.655
The values of the parameters for models 1-4, as estimated by least-squares technique at various temperatures, are given in Table 11. From the values of parameters (not shown here) it appeared that the Langmuir-Hinshelwood models did not fit the rate data well since the estimated parameters were found to be negative. On the other hand, all the redox models seem to fit the experimental results well. This is quite reasonable since only lattice oxygen rather than adsorbed oxygen of the catalyst is involved in the reaction. This has also been reported by Srivastava (1988) for other selective oxidation reactions. The values of residual sum of squares (RSS) for all the redox models are also given in Table 11. Since the RSS are very close to each other, it is not possible to discriminate among the redox models based on minimum RSS criterion. In order to discriminate among the four redox models, we have applied the Bayesian method of discrimination among rival models. The details of this method are given by several authors (e.g., Box and Hill (1967), Roth (19651, and Prasad and Rao (1977)). The Bayes' theorem states that (13) :=1
The notations used for developing the Langmuir-Hinshelwood models are as follows: KA is the oxygen adsorption equilibrium constant, KR is the n-butane adsorption equilibrium constant, and K2 is the rate constant for n-butane oxidation. Experiments were carried out at temperatures of 370, 390, and 410 "C under differential conditions. The experimental conditions and responses of the experiments are given in Table I. The rates are calculated by use of the relation -rB = A x / ( A ( W / F ) )
(12)
Where AX and A( WIF) represent conversion and contact time, respectively. The value of concentration used in the rate equation is the average of the inlet and outlet concentrations of the respective component. The difference between the inlet and outlet concentrations ranged up to 1070,substantiating the differential operation of the reactor. With these values, all the above seven models have been tested.
where Ai (i = 1,..., r ) denotes the ith model, B denotes the data, P(Ai)denotes the prior probability of the ith model, and P(B/A,) denotes the likelihood for the ith model. A knowledge of prior probabilities for various models is required. If there is no information regarding the prior probabilities, equal probabilities for all the models are assigned. A knowledge of the error structure is required for calculating the likelihood. Once the observations and design matrix are substituted into the expression for the probability density function, (p.d.f.1, the resulting expression, which is a function of k and u2, is called the likelihood. With the use of the estimated parameters of Table 11, the likelihoods were calculated. Equal prior probabilities were assigned and the posterior probabilities were calculated at three different temperatures (370, 390, and 410 " C ) on the basis of the results of five experiments a t each temperature. From the values of the posterior probabilities after five preliminary runs, it was difficult to discriminate among the models on the basis of the existing data. When it is not possible to discriminate among rival models from the available data, it is necessary to design
Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991 1827 Table IV. Values of Parameters of Model 4 Based on All Runs temperature, OC 370 390 410 0.0586 0.0643 K1,g-mol/(gatm.h) 0.03362 0.4339 0.7841 K2,g-mol/(gatmh) 0.2383 Table V. Comparison of Activation Energies with Those Reported in the Literatum value of activation energy, source kcal/mol our investigation El 12.60 E2 25.90 Buchanan and Sundaresan (1986) E2 = 27.71 E2 = 10.77 Centi et al. (1985) E2 17.24 Schneider et al. (1987)
further experiments that will provide maximum discrimination. While several criteria are available, we have chosen Box and Hill's criterion (Box and Hill, 1967) for the design of experiments for model discrimination. The design criterion to be maximized is given by
-
Partial pressure of n-butane,atm
5
O-Ol75 0.02 0.0225 0025 0.0275 003 0.0.4
2
-@
E
8 0.06.
c
01.2-
Figure 1. Experimental region and settings for experiments for sequential model discrimination at 370 OC. e
Partial pressure of n-butane , a t m 0.0225 0.025 0.0275 0.03
~-o,o~0175 0.02 c b)
E2 0.06 c 0
$0.06
I 2
-.-po.10 0
-
Figure 2. Experimental region and settings for experiments for sequential model discrimination at 390 O C .
After N experimental runs, one selects the ( N + 1)th run a t those operating conditions that maximize D. In the above model, T stands for probability, 2 for the common variance of the N observations, u t and u? are variances for the predicted values of +1 under models i and j , respectively, and 91f)+l and are the predicted values of YN+1 under models i and J, respectively. After conducting the ( N + 1)th run, the current posterior probabilities for various models are calculated from the Bayes' theorem by using the following probability density function for a single observation
Partial pressure ot n - b u t a n e d m g>,&0175 002 04225 0025 0.0275 0,03
(&@
C
L
fEl
where yN+1 is the value of the response obtained from actual experiment under the ( N + 1)th experimental conditions. The variance for the predicted values of yN+l under model i is calculated by the procedure given by Box and Hill (1967). After conducting ( N + 1)th run, the posterior probabilities are calculated and if discrimination is not achieved successfully, further experiments are designed sequentially. The experimental settings of the discriminatory runs for three temperatures, viz., 370,390, and 410 "C,are shown in Figures 1,2, and 3, respectively. The current values of posterior probabilities for the models after each discriminatory run are shown in Table 111. From the results it is evident that the reaction is dependent on a very low power of oxygen concentration. Models having first-order and half-order dependency on oxygen concentration can be safely discarded for all the temperatures. Moreover, though models 3 and 4 are closely competing with each other, model 4 is superior to model 3 for all the temperatures. Therefore, model 4 having zero-order dependency on oxygen concentration seems to be the most appropriate one for the reaction. As seen from Figure 1, it is confirmed that experiments conducted at
Figure 9. Experimental region and settings for experiments for sequential model discrimination at 410 "C.
a constant n-butane partial pressure of 0.03 atm, but varying partial pressures of oxygen from 0.04 to 0.10 atm, support model 4. Finally, parameters for this particular model (model 4) are estimated considering all runs for each temperature. This is given in Table IV. Activation energies are also calculated on the basis of an Arrhenius plot (Table V). The activation energy for the oxidation of n-butane to MA obtained in the present study is comparable to the value reported by Buchanan and Sundaresan (1986). 4. Conclusions
The selective oxidation of n-butane to MA can be better described by redox models over Langmuir-Hinshelwood models. The experimental data best fit a redox model having zero-order dependency on oxygen partial pressure and first-order dependency on n-butane partial pressure. The model is given by -rB
=
KIKflB K1+ ffKflB
In previous studies there was much confusion regarding the order of the reaction with respect to oxygen. The estimated rate constants based on this particular model showed an Arrhenius dependency on temperature. The
1828 Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991
calculated activation energy for the oxidation of n-butane to MA is 25.9 kcal/mol, which is comparable to the value reported by Buchanan and Sundaresan (1986). The activation energy for the oxidation of the reduced catalyst is 12.6 kcal/mol. The value of this activation energy was not available in the literature. Nomenclature
D = Box and Hill’s design criterion f = function k = parameters K1 = rate constant for the oxidation of reduced catalyst K 2 = rate constant for n-butane oxidation KA = oxygen adsorption equilibrium constant KR = n-butane adsorption equilibrium constant m = order of reaction with respect to n-butane n = order of reaction with respect to oxygen N = experimental trial P(A,) = prior probability for the ith model P(B/A,) = likelihood for the ith model p , = partial pressure of ith component P, = probability density function under model i r = number of models r g = rate of reaction of n-butane R = reduced state of catalyst W / F = contact time X = oxidized state of catalyst X = conversion in eq 12 y = predicted value of response Greek Symbols OR =
fraction of surface occupied by R
8x = fraction of surface occupied by X x = probability x,, = posterior probability of ith model (i = 1-4) after conducting j experiments g2
=
common variance of n observations predicted values of observations under model
u,*= variance of 1
Registry No. MA,108-31-6;H(CH2),H, 106-9743
Literature Cited Box, G. E. P.; Hill, W. J. Discrimination Among Mechanistic Models. Technometrics 1967,9 (l),57-71. Buchanan, J. S.;Sundaresan, S.Kinetics and Redox Properties of Vanadium Phosphate Catalysts for Butane Oxidation. Appl. CataE. 1986,26,211-226. Centi, G.; Fornasari, G.; Trifiro, F. n-Butane Oxidation to Maleic Anhydride on Vanadium-Phosphorus Oxides: Kinetic Analysis with a Tubular Flow Stacked-Pellet Reactor. Ind. Eng. Chem. Prod. Res. Dev. 1985,24,32-37. Centi, G.; Trifiro, F.; Ebner, J. R.; Franchetti, V. M. Mechanistic Aspects of Maleic Anhydride Synthesis from C, Hydrocarbons over Phosphorus Vanadium Oxide. Chem. Rev. 1988,88,55-80. Lerou, J. J.; Weiher, J. F. Paper presented a t Pittsburgh/Cleveland Catalysis Society Meeting, 1986. Prasad, K. B. S.; Rao, M. S.Use of expected likelihood in sequential model discrimination in multiresponse systems. Chem. Eng. Sci. 1977,32, 1411-1418. Roth, P. M. Design of Experiments for Discriminating Among Rival Models. Ph.D. Thesis, Princeton University, Princeton, NJ, 1965. Schneider, P.; Emig, G.; Hofmann, H. Kinetic Investigation and Reactor Simulation for the Catalytic Gas-phase Oxidation of nButane to Maleic Anhydride. Ind. Eng. Chem. Res. 1987,26, 2236-2241. Srivastava, R. D. Heterogeneous Catalytic Science; CRC Press: Boca Raton, FL, 1988; pp 41-49. Tan, H. S.; Downie, J.; Bacon, D. W. The Kinetics of the Oxidation of Propylene Over a Bismuth Molybdate Catalyst. Can. J.Chem. Eng. 1988,66,611-618. Thomas, J. M.; Thomas, W. J. Introduction to the Principles of Heterogeneous Catalysis; Academic Press: London, 1967;Chapter 8. Wohlfahrt, K.; Hofmann, H. Kinetics of the synthesis of maleic anhydride from n-butane. Chem. Ing. Tech. 1980, 52 (lo), 811-814. Received for review July 2, 1990 Revised manuscript received February 6, 1991 Accepted February 12, 1991
