rI = reaction rates respectively for total disappearance of n-pentane, hydrocracking, and isomerization, mol/hr g of catalyst rc = reaction rate for coke formation, g of coke/hr g of catalyst R ~ ( z , st ,) = weighting function for modeling error s = spatial variable in filtering equations t’,t = chronological time, hr t = dimensionless time x = state of the system i = optimal estimate of the state x y = measureddata YA~YB,YH,YW, = respective mole fractions of n-pentane, isopentane, and n-pentane converted to cracking products and hydrogen z = spatial distance (dimensionless reactor length) = rA,rH,
z” = reactor length, cm
Greek Letters = fouling parameter, (g of catalyst/g of coke)”2 6 = Dirac delta function 6 t j = Kronecker delta c = bed porosity, cm3 of void/cm3 of bed 7 = error in measuring device t 1 , t ~= modeling errors PB = bulk density of catalyst, g/cm3 R = reactor cross section, cm2 cp = catalyst activity cy
Literature Cited Ajinkya, M. B., Ray, W. H., Seinfeld, J. H., Yu, T. K., in press. Butt, J. B., First International Symposium on Chemical Reaction Engineering, Washington, D. C., 1970. Froment, G. F., De Pauw, R. P., paper presented at the American Institute of Chemical Engineers Meeting, New Orleans, La., March 1973, Paper 79e. Gavalas, G. R.. Seinfeld, J. H., Chem. Eng. Sci., 24,265 (1969) Gavalas, G. R.. Hsu, G. C., Seinfeld, J . H., Chem. Eng. Sci., 27, 329 (1972a). Gavalas, G. R., Hsu, G. C., Seinfeld, J . H., Chem. Eng. J., 4, 77 (1972b). Goldman, S.F., Sargent, R. W. H.,Chem. Eng. Sci., 26, 1535 (1971). Hwang, M., Seinfeld. J. H., Gavalas. G. R., J. Math. Anal. Appl., 39, 49 (1972). Joffe, B. L., Sargent, R. W. H., Trans. inst. Chem. Eng., 50,270 (1972). Kmak, W. S.,paper presented at the American Institute of Chemical Engineers Meeting, Houston, Tex., March 1971. Kmak, W. S.,paper presented at the American Institute of Chemical Engineers Meeting, New Orleans, La., March 1973. Larnbrecht, G. C., Nussey. C., Froment, G. F., Proc. lnt. Symp. Chem. React. Eng., 2nd, 7972, 82-19 (1972). McGreavy, C.,Vago, A., Paper presented at the American Institute of Chemical Engineers Meeting, New York, N. Y . , 1972. Ogunye, A. F., Ray, W. H., AlChEJ., 17,43, 365 (1971a). Ogunye, A. F., Ray, W. H., lnd. Eng. Chem., Process Des. Develop., 18, 410,416 (1971b). Ray, W. H., Proceedings IFAC Conference on Distributed Parameter Systems, June 1971, Paper No. 10-5. Seinfeld, J. H., Chen, W. H., Chem. Eng. Sci., 26, 753 (1971).
Received for review M a r c h 5 , 1973 Accepted November 6, 1973
Mechanism of Vapor-Phase Oxidation of Anthracene over Vanadium Pentoxide Catalyst Periasami Subramanian and M. S. Murthy* Department of Chemical Engineering, lndian Institute of Science, Bangalore 560012, lndia
Models based on redox, Langmuir-Hinshelwood, and Rideal mechanisms were tested for elucidiation of the mechanism of vapor phase oxidation of anthracene over vanadium pentoxide catalyst in the temperature range 270-360”. A two-stage redox mechanism was found as the best model. The reaction was found to be first order with respect to anthracene and oxygen partial pressures.
Introduction Many investigators have studied the kinetics of vaporphase oxidation of anthracene over vanadium pentoxide catalyst and have fitted their data to empirical equations (Andreikov and Rus’yanova, 1967; Rus’yanova, et al., 1966). Recently Subramanian and Murthy (1972) applied the redox mechanism to elucidate the kinetics of this reaction. The kinetics and mechanism of gas-solid catalytic reactions are generally explained on the basis of Langmuir-Hinshelwood and Rideal mechanisms. However, the application of these mechanisms to anthracene oxidation over vanadium pentoxide catalyst has not been reported thus far. In the present investigation, various possible mechanisms are tested in order to find which mechanism explains the experimental data satisfactorily. Experimental Section The experimental set-up used, the catalyst, and the analytical procedure employed have been discussed in our earlier paper (Subramanian and Murthy, 1972). 112
Ind. Eng. Chem., Process Des. Develop., Vol. 13,No. 2, 1974
The effect of temperature, time, mole ratio, and partial pressure of anthracene and oxygen on the conversion and rate of reaction was investigated in the temperature range 270-360”, in which the secondary reactions were found to be negligible. Discussion The various mechanisms tested are summarized in Table I. The mechanisms are discussed elsewhere (Subramanian and Murthy, 1974). However, derivation of empirical models from the redox model is discussed below. Sampson and Shooter (1965) suggested two possible mechanisms for the oxidation of hydrocarbons. The first involves a slow interaction of oxygen ions, which are formed by dissociation of chemisorbed oxygen with hydrocarbon and the second involves a reaction between molecular oxygen and hydrocarbon. For these two cases, the rate equations are given by
Table I: Models Tested for Fitting Kinetic Data Model Assumptions/reaction mechanism
Rate equation
Two-stage redox mechanism. First-order reaction with respect to anthracene and oxygen concentrations ( a = 0 = 1).
rA
=
Ki P A K Z P o K I P A KzPoz
2
Two-stage redox mechanism. Half-order reaction with respect to anthracene and oxygen concentrations ( a = 0 = 0.5).
rA
=
K ~ P A " ~ ' K5 ~ P o ~ K ~ P A Q ' K2Po,O
3
Two-stage redox mechanism. Half-order reaction with respect to anthracene concentration and first-order reaction with respect to oxygen concentration ( a = 0 . 5 ; 6 = 1).
rA
=
KIPAO'K2P02 K i p ~ " ' KzPo,
4
Two-stage redox mechanism, with additional assumption that oxygen dissociates.
rA
=
KIPAK~PO;,~ K~PA f KzPo,O'
5
Two-stage redox mechanism, with additional assumption that desorption rate of oxygen is not negligible.
YA
=
rA
=
rA
=
7-A
=
1
+
+
+
kikzP~P02
kd
+ kzpo2 + 1 . 5 k i p ~
1
+ (ksIki)PA + 1 . 5 ( k 2 ~ / k n P o , )
1
+ (ki/kd)PA -k 1 . 5 ( k i P ~ / h z P o ~ )
1
+ (ki/kd)PA + 1 . 5 ( k i P ~ / k z P o , )
1
+ 1.5(kiP.~/hrPo2)+ 1 5 ( k i P ~ P o /
Three-stage redox mechanism
+
ClaHlo C-ox "8, (CIIH1O) - C-ox(s) kl Cl,H802(g) HzO(g) (CI4Hl,) - C-oxis) +
6
C-red
+
+ C-red
+ 1.502(g) -% C-OX
+
+
C14Hlo(g) C-ox -% (C14H802) - C-red@) HzO(g) (CiiH802) - C-red(s) -% Cia&Oz(g) C-red 1.502(g) "i,C-ox C-red
7
+
+
8
+
+
ClaHlo(g) C-ox -%- Cl4H8O2(g) HzO) (H20) - C-red(s) H20(g) C-red C-red 1 .502(g)-% C-ox
+
+
+
10
ClaHlo(g) C-ox hl_ HzO(g) (ClaH802) Kd (C14H80?)-C-red(s) C14H80z(g) C-red
11
kiPA
+
ClaHlo(g) c-ox " 1 ,Cl&Oz(g) C-red 1.502(g)ka_ (Oz) - C-red(s) C-red (On) - C-red(s) L?_ C-ox
+
C-red
kiPA
- C-red(s)
9
+
kaPA
+
+
- C-red(s)
rA =
kipa
KdkiPoJ
+ 1 5 0 2 ( g ) -% C-ox
Langmuir-Hinshelwood model. Equilibrium concentrations of oxygen and hydrocarbon are assumed established on the surface, with reaction occurring between adsorbed reactants.
rA
=
krKAKoPAPoz
[I -b K o P o z -k KAPA]'
Rideal mechanism. Equilibrium concentration of oxygen is assumed established on the surface, with reaction occurring between adsorbed oxygen and gas-phase hydrocarbon.
rA =
13
Empirical model
rA
=
kPAPo:J
14
Empirical model
FA
=
kPAPo2
15
Empirical model
rA
=
KiPA
12
r.A a fie,P.APO.
(2) where f ( e ) refers to the equilibrium electron availability a t the surface. The concentration of the oxygen ions on the surface of t h e catalyst is given by (Subramanian and Murthy, 1972)
[C-oxI = KJ'oLd/(KIPAa
+
KZPo,')
(3)
If K1 is the proportionality constant in models 1 and 4, eq 1and 2 and models 1 and 4 are similar provided
K,I(KiPA"
+
KzPoL')
=
[C-OXI/P~,'
f,@)
Such a relation between f ( e ) , PA, and Po, may be possi-
krKoPAPoi 1 KoPo,
+
ble. Therefore the following equations (models 13 and 14) were also tested IA = kPAPO?O' r k = kPAP, Model 1 can be reduced to a pseudo-first-order expression (model 15) (Subramanian and Murthy, 1974).
Comparison of Various Models The constants of the rate equations for various models were estimated by the method of linear least squares. The rates corresponding to initial conditions were employed in these estimations. For evaluation of the models, the folInd. Eng. Chem.,
Process Des. Develop., Vol. 13,No. 2, 1974 113
Table 11: Values of the Nonintrinsic Parameter NonTemp, intrinsic Standard Model "C parameter error Confidence interval 3
4
11
270 300 330 340 350 360
-0.4716 0.06136 - 0.5291 0.03482 -0,4927 0.03320 0.4923 0.00912 -0.5226 0,04012 - 0.4942 0.00732
-0.6133 to -0.6095 t o -0.5260 to -0.5134 to -0.6158 to -0.5111to
-0.3298 -0.4486 -0.3726 -0.4712 -0.4299 -0.4773
270 300 330 340 350 360
- 0.3582 - 0.6129
0 ,07746 0.03876 -0.4313 0.03316 -0.3775 0 ,00921 - 0.6016 0.04126 - 0.4597 0,07071
-0.5371 t o - 0.3025 to -0,5079 to -0.3987t0 -0.6969 t o -0.6231to
-0.1792 - 0,5234 - 0.3547 -0.3566 -0.5063 -0.2964
270 300 330 340 350 360
- 0.4872
0.09592 0.03606 0.02863 0.02241 0.01931 0.01621
-0.7105t0 -0.6811 to -0.6953 t o -0,7936 t o -0,6806 to -0.4805 to
-0.2578 -0.5095 - 0.5602 -0.6878 -0.5895 -0.4040 -0.6324 -0.1899 -0.5397 -0.5231 -0.2368 -0.5342
-
-0.5953 - 0.6277 - 0.7407 - 0.6350 -0.4422
12
270 300 330 340 350 360
- 0.6891
0.02451 0.03462 - 0,5633 0.01034 0 ,02830 -0.5884 - 0.2679 0.01346 - 0.5862 0.02246
-0.7457 to -0,3499 t o -0.5871 to -0.6538 to -0.2990t0 -0.6380 t o
13
270 300 330 340 350 360
-0.5714 -0.4171 - 0.4897 - 0.5152 - 0,3781 - 0.5261
0,07809 0.04472 0.09036 0.06120 0,04870 0.03546
-0,6479 -0,5181 - 0.6939 -0.6535 -0,4888 -0.5341
t o -0.3950 t o -0.3160 to - 0.2855 to - 0.3769 t o -0.2674 t o -0,5180
14
270 300 330 340 350 360
-0.5412 - 0.4529 -0.4931 - 0.5034 - 0.4343 - 0.5134
0.00781 0.00458 0,00906 0.00616 0.00510 0.00361
-0,5589 -0,4633 -0.5136 - 0.5173 -0,4458 -0.5216
to -0.5236 to -0.4426 to -0.4726 t o - 0.4895 to -0.4228 t o -0.5053
15
270 300 330 340 350 360
- 0.6108 0.07803 -0.3061 0,04273 -0.4518 0.08821 - 0.5952 0.05981 - 0,2208 0.04022 - 0.6314 0.03463
-0,7872 -0,4021 -0,6518 -0,7304 -0.3117 -0,7097
to -0.4344
- 0.2699
-0.2096 -0.2525 -0.4600 -0.1299 to -0.5531
to to to to
lowing criteria were employed: (1) since the rate constants represent some reaction steps, the values of the constants should not be negative; (2) all the constants should exhibit temperature sensitivity and can be represented by the Arrhenius-type equation; and (3) the model should represent the experimental data satisfactorily. From the values of various constants of these models, the following conclusions can be drawn. Criterion 1. Models 2 and 5-10 do not satisfy this criterion, since all values of one of the rate constants are always negative within 5% confidence limits. The values of the rate and equilibrium constants of models 1, 3, 4, and 11-15, on the other hand, are positive at all temperatures studied. Criterion 2. Values of the rate and equilibrium constants for all models except 1, 3, 4, 13, 14, and 15 were scattered showing no specific trends. Some of the parameters of these models could not exhibit a clear-cut temperature sensitivity. These values present a haphazard trend with change in temperature and cannot be correlated by the Arrhenius equation. Criterion 3. A nonintrinsic parameter method was employed in the selection of the best model. Mezaki and Kit114
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 2, 1974
trell (1966) proposed this method to discriminate between two rival models (C and D) proposed for the vapor-phase catalytic dehydrogenation of secondary butyl alcohol. This method is based on the estimation of the magnitude of the nonintrinsic parameter, X, given by
z
X(rD
-
rc)
(4)
where
r being the observed rate value. Now, if rc represents the data adequately, then
z=-
0.5(rD - r c )
+
6
on the other hand, if r D gives a better fit, then
2 = 0 . 5 ( r ~- r C )
+
t
(7)
In eq 6 and 7, e represents the random error. Thus if model C represents the data satisfactorily, then the confidence interval of X includes -0.5 and model D is rejected and, vice-versa, if the confidence interval of X includes +0.5. Models 2 and 5-10 were not discriminated by this method, as they failed to satisfy the first two criteria. Models 3 , 4 , and 11-15 were compared with model 1. Table I1 gives the values of X obtained for various models when they were compared with model 1, a t various temperatures. It is evident that model 1 is supported overwhelmingly in all cases. The confidence interval of X in none of these cases is anywhere near +0.5. Model 1 reproduces the experimental data with a standard deviation of only &1.75%. For all other models, the standard deviation is much higher than that of model 1. Hence it can be concluded thatimodel 1 (two-stage redox model with (Y = P = 1) is superior to all other models in explaining the vapor-phase oxidation of anthracene to anthraquinone on vanadium pentoxide catalyst. The Arrhenius plot and the activation energies for the individual steps are given elsewhere (Subramanian and Murthy, 1972). Summary a n d Conclusions Redox, Langmuir-Hinshelwood, and Rideal mechanisms were tested to elucidate the kinetics and mechanism of the vapor-phase oxidation of anthracene over vanadium pentoxide catalyst. The various models were compared on the basis of three criteria and were finally discriminated by making use of a nonintrinsic parameter method. The two-stage redox model (the substance to be oxidized reduces the catalyst, which in turn is oxidized by oxygen from the feed) was found to be the best. The reaction was found to be first order with respect to anthracene and oxygen partial pressures. Nomenclature k l = rate constant for catalyst reduction step, mol/g min mm kz = rate constant for catalyst reoxidation step, mol/g min mm k,, kd, and k , = adsorption, desorption, and reaction rate constants, respectively K A , KO,and Kd = equilibrium constants for adsorption of anthracene, adsorption of oxygen, and desorption of anthraquinone, respectively PA = partial pressure of anthracene, mm PO, = partial pressure of oxygen, mm Pa = partial pressure of anthraquinone, mm rA = rate of reaction, mol of anthracene/g min a = order of reaction with respect to anthracene
fl = order of reaction with respect to oxygen A = nonintrinsic parameter
Literature Cited
Rus'yanova, N. D., Kostromin, A. S., et a/., Chem. Absfr., 64, 19354e (1966). Sampson, R . J., Shooter, D., Oxid. Combust. Rev., 1, 225 (1965). Subramanian, P.,Murthy, M . S., Ind. Eng. Chem., Process Des. Develop. 11, 242 (1972). Subramanian P., Murthy, M. S., Chem. Eng. Sci.. in press, 1974.
Andraikov. E. I., Rus'yanova. N. D., Koks, Smola, Gaz, 12 ( q l ) , ' 289 (1967); Chem. Abstr. 6 9 , 6 6 3 8 ~(1968). Mezaki, R., Kittrell, J. R., Can. J. Chem. Eng., 44, 285 (1966).
Received f o r review March 5, 1973 Accepted November 6, 1973
Gas Absorption with Heat Effects. 1. A New Computational Method John R. Bourne,* Urs von Stockar, Technisch-chemisches Laboratorium ETH, CH-8006 Zurich, Switzerland
and George C. Coggan Gamma Associates Ltd., Nottingham, Great Britain
A dynamic simulation method has been applied to determining the state of a stagewise gas absorption column. The unsteady state heat and mass balances for each real stage have been integrated up to the steady state, taking into consideration all possible heat effects for physical gas absorption. The new method resulted in stable convergence of the two point boundary value problem and was superior to the method employed earlier. After a description of this improved method, the earlier studies of the influences of typical operating and system variables upon the capacity of an absorber have been extended. The transport capacity of the gas phase for heat, solvent evaporation, the L/G ratio, the solvent feed temperature, and the feed gas humidity were investigated. The limitation of the absorber capacity through the formation of a temperature plateau has been confirmed and extended to the case of a column, where both absorption and desorption occur. The proper description of these phenomena has proved possible only by correctly formulating the heat and mass transport phenomena and using dynamic simulation for their solution.
Introduction Because of the generally strong dependence of the solubility of the solute gas on temperature, the temperature distribution in an absorption tower should be considered when determining its capacity. The heat effects, influencing this temperature profile, are (1) heat of absorption of the solute, leading to a rise in the temperature of the liquid phase; (2) partial evaporation of the solvent, tending to lower the liquid temperature, provided that the solvent is volatile, e.g., water; under certain conditions, the reverse processes (condensation and heating) occur; (3) transfer of sensible heat by direct contact between gas and liquid phases; (4) transfer of sensible heat between the fluids in the column and cooling coils and/or the column wall. Temperature in turn influences the degrees of heat and mass transfer thermodynamically, through the phase equilibrium relationships, e.g., the solubilities, and kinetically, through variations of the transfer coefficients, e.g., plate efficiencies in the case of stagewise gas-liquid contact. The overall effect of temperature variations on a gas absorption process can be very significant. Typical conditions for substantial heat effects are the following. (a) Normal and high values for the enthalpy changes, when solute and solvent are transferred between phases. (b) The equilibrium partial pressures of solute and solvent are highly dependent upon the temperature. Exceptions to this generalization are, however, systems where a fast, quantitative chemical reaction occurs. The following mixtures, for example, have equilibrium partial pressures for the solute which are so small that their temperature
dependence is of little significance: HCl/H20, C02/MEA, COa/DEA, HCHO/H20 (Stockar, 1972). Such absorptions are often conducted without cooling. (c) Absorption towers operate predominantly adiabatically, especially when they process large volumes of gas, i.e., at industrial scale. The following two types of simplification were introduced many years ago to aid the theoretical treatment of gas absorption. (1) Isothermal process, whereby the temperature of the liquid phase was assumed to be everywhere the same, e.g., equal to its inlet value. This method implicitly ignored all heat effects and produced the simplest calculations, e.g., on a McCabe-Thiele diagram. (2) Simple adiabatic model, whereby the heat of solution was assumed to manifest itself only in the liquid phase. Its temperature could then be determined, as a function of solute concentration, from a simple adiabatic energy balance. The real situation, resulting from the factors described earlier, exhibits however a high degree of interaction between all factors and does not allow simplifying approximations (Coggan and Bourne, 1969). Rather a digital computer should be applied to a comprehensive generalized model of the absorption process. Our earlier method, however, resulted sometimes in difficult convergence and therefore a degree of uncertainty. It is therefore the objective of this paper to show a better, more certain computational method, to test its capacities and convergence properties, and to draw some further generalizations about the nature of heat effects in gas absorption. In the second part (Bourne, e t al., 1974), the accuracy and reliability of the method developed here will be demonstrated Ind. Eng. Chem.,
Process
Des. Develop., Vol.
13, No. 2, 1974
115
