Ind. Eng. Chem. Res. 1990, 29. 696-699
696
Teramoto, M.; Tai, S.;Nishi, K.; Teranishi, H. Effects of Pressure on Liouid-Phase Mass Transfer Coefficients. Chem. E m- . J . 1974. 8, 223-226. Yagi, H.; Yoshida, F. Gas Absorption by Newtonian and Non-Newtonian Fluids in Sparged Agitated Vessels. I n d . Eng. Chem. Process Des. Dev. 1975, 14, 488-493.
Yoshida, F.; Arakawa, S. Pressure Dependence of Liquid Phase Mass Transfer Coefficients. AIChE J . 1968. 14. 962-963.
Received for revieu May 23, 1989 Revised manuscript received September 29, 1989 Accepted October 27, 1989
COMMUNICATIONS A Semiempirical Model for the Oxidation of Cyclohexane T h e gas-liquid reactor data obtained on a typical complex, consecutive reaction system like the liquid-phase oxidation of cyclohexane in a semibatch manner is modeled on the basis of the surface renewal theory. T h e influence of mass transfer on the overall reaction rate is assessed. As the reaction proceeds, t h e reaction regime changes from one of slow reaction (oxidation of cyclohexane alone) to the fast reaction regime because of accumulation of the more reactive intermediate, cyclohexanone, which consumes more oxygen and leads t o a situation where mass-transfer limitations are experienced. Catalytic liquid-phase air oxidation of cyclohexane in acetic acid medium using cobalt acetate as the catalyst yields adipic acid in considerable yields (Tanaka, 1974). Oxidation proceeds with cyclohexanol and cyclohexanone as intermediates (eq 1). In such a typical gas-liquid reCsH12 cycbhexane
-
\I
+oxygen
C6H110H
cycbhexand
CsHloO cydd-texanone
HOOC(CH2)dCOOH (1)
adipic acid
action system, the reactants (cyclohexane and air) are placed in two different phases. The location of the reaction zone is important in the system, since this helps decipher the influence of mass transfer from chemical kinetics, which in turn helps in assessing the final product distribution. The gas distributes in the liquid in the form of small bubbles; the reaction may take place entirely in the film adjacent to the gas bubbles alone or both in the film and bulk liquid or in the bulk liquid alone. The concentration profiles of the gaseous reactant in the film gives a qualitative picture of the process (Danckwerts, 1970). Alternatively, evaluation of the reaction parameter ( M values would also indicate the reaction zone. The reaction parameter is defined for an (m,n)th-ordergeneral reaction (Brain, 1964) as follows: aA(g) + bB(1) products (2)
-
M = [ ( 2 / ( m+ l))km,nDAAlm-1Bgn]1’2/hL (3) When M < 0.0004, the reaction regime is known as an infinitely slow one, and practically no reaction takes place in the film; it takes place entirely in the bulk. If 0.0004 < M < 4, the reaction takes place both in the film and bulk (Levenspiel, 1972). These calculations were made for air oxidation of cyclohexane. M values were calculated to be of the order of 0.009 or less (Table I), indicating that the reaction is slow and takes place in the bulk liquid. Hence, the reaction should be free from mass-transfer limitations. Subsequently, the effect of the variation of stirrer speed on the reaction rate OS8H-5885/90/2629-0696$02.5O/u
constant is in contrast to this conclusion, when the reaction rate increased with stirring speed (Rao and Raghunathan, 1986), indicating the possible influence of mass transfer. It may be remarked that such observations (indicating the influence of mass transfer) were reported earlier also in the literature (Steeman et al., 1961; Alagy et al., 1974). To ascertain the nature of the reaction regime, we felt it necessary to study the oxidation of cyclohexanone, the intermediate product. Accordingly, the air oxidation of cyclohexanone to adipic acid in acetic acid medium was studied earlier (Rao and Raghunathan, 1985), which indicated a positive influence of the solvent concentration on the overall reaction rate constant. Such an effect (lower concentration of cyclohexanone favoring higher yields of adipic acid) was also reported recently by Shen and Weng (1988). Literature reports also indicate that cyclohexanone oxidizes much faster than cyclohexane (Berezin et al., 1966): k 2 / k l = 0.09 exp(5000/(RT)) (4) where k , is the reaction rate constant for the oxidation of cyclohexane to cyclohexanone and k 2 is that of cyclohexanone to adipic acid. The more oxidizing cyclohexanone in the presence of a higher concentration of the solvent would react much faster, causing a depletion of the reactant gas, which in turn transcends the reaction regime from one of kinetic controlled to diffusion controlled. Keeping these observations in mind, we have proposed in the present work the following model, similar to the “surface renewal model” of Inoue and Kobayashi (1968). Van de Vusse (1966) also reported a similar situation for consecutive reactions in a heterogeneous system for the chlorination of n-decane. To test the validity of the proposed model, we have used our experimental results published earlier on the oxidation of cyclohexane to adipic acid (Rao and Raghunathan, 1986).
The Model The situation in the reaction system is schematically represented in Figure 1 for a case where the surface layer thickness is 6 (Figure 1 is only a schematic presentation of the situation. The represented concentrations of cyclohexane in Figure 1 were neither measured nor calcu19YO American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990 697 Table I. Rate Constants and Reaction Parameters for Various Runsn run temD. K C,H,,:cat. Bo, kmol m-3 105k,,s-l 3.37 1.972 1oo:o.2 30 363 100:0.2 3.37 3.856 31 378 3.28 3.939 100:0.2 32 403 3.27 1.792 1OO:l.O 26 363 1OO:l.O 3.25 2.941 42 378 100:1.o 3.26 1.360 43 403 100:1.5 3.26 3.003 50 363 49 100:1.5 3.27 4.569 378 100:1.5 48 3.26 1.065 403
A;, kmol m-3
1OBDr,m2 s-l 0.904 1.133 1.435 0.904 1.133 1.435 0.904 1.133 1.435
0.057 35 0.060 45 0.065 41 0.057 35 0.060 45 0.065 41 0.057 35 0.060 45 0.065 41
.
103~ 7.933 11.540 9.444 7.449 9.902 5.533 9.628 12.568 4.896
aC6H12: AcOH = 1.0:3.33; rpm = 530; pressure = 0.5 M N m-2; volume of reaction mixture = 0.89 dm3 (Rao and Raghunathan, 1986).
Table 11. Phvsicochemical and Mass-Transfer Data for Various Runs" run C6H12:cat. 10-3p, kg m-3 103a, N m-l 103p, kg m-'s-l 103DBM,m 30 100:0.2 0.874 18.91 0.453 1.421 0.376 1.423 0.856 17.35 31 100:0.2 0.317 1.425 32 100:0.2 0.824 14.82 26 1OO:l.O 0.874 18.91 0.453 1.421 0.376 1.423 0.856 17.35 42 1OO:l.O 0.317 1.425 0.824 14.82 43 100:1.o 1.421 50 100:1.5 0.874 18.91 0.453 49 100:1.5 0.856 17.35 0.376 1.423 48 100:1.5 0.824 14.82 0.317 1.425
Ut, m
103H 2.714 2.830 3.074 2.714 2.830 3.074 2.714 2.830 3.074
s-l
0.1934 0.1883 0.1793 0.1934 0.1883 0.1793 0.1934 0.1883 0.1793
102kL,m s-l 0.0577 0.0680 0.0791 0.0577 0.0680 0.0791 0.0577 0.0680 0.0791
7,s
0.0345 0.0311 0.0587 0.0345 0.0311 0.0287 0.0345 0.0311 0.0287
C6H12:AcOH= 1.0:3.33; rpm = 530; pressure = 0.5 M N m?; volume of reaction mixture = 0.89 dm3.
lated). The gas-phase component (oxygen) diffuses from phase 1 (gas phase) to phase 2, reacting very little in the layer. Further, it reacts with the solute (cyclohexane) in the liquid phase, forming the intermediate, cyclohexanone. As the reaction proceeds, cyclohexanone accumulates in the bulk liquid and starts diffusing into the surface layer (Figure Ib). Subsequently, cyclohexanone reacts with oxygen and causes depletion of oxygen in the layer, since it reacts much faster with oxygen as compared to cyclohexane. The possibility of such a modified concentration profile for oxygen in the vicinity of the gas-liquid interface was also remarked by Suresh et al. (1988a,b). Thus, a fictitious situation is created where it looks as if the reaction is influenced by mass-transfer limitations without the actual concentration of oxygen in the bulk liquid approaching zero and manifests in increased overall reaction rate constants with an increase in stirrer speeds. In such situations where mass transfer with the chemical reaction is encountered, the results are usually analyzed with remarkable success by models of film theory or penetration theory (Astarita, 1967; Danckwerts, 1970). However, this kind of analysis of a complex and consecutive reaction scheme is indeed heavily computationally time consuming but definitely provides an insight into the reaction system. For this, the iterative computation of the progressive change of reactants was carried out in the present work. The model is based on the following assumptions: (i) reactions take place both in the surface layer and bulk liquid; (ii) the surface layer renews at every T seconds (where T is the surface renewal time and will be evaluated by Higbie's model), and mass transfer occurs from the surface to bulk by renewal of the surface layer; (iii) the concentration of the solute at the end of a renewal cycle will be the initial concentration for the next renewal cycle; and (iv) the reaction proceeds in both parts separately; however, the reaction in the layer follows secondorder kinetics and in the bulk liquid pseudo-first-order kinetics with respect to the solute. The concentration profiles in the surface layer and bulk liquid were separately evaluated. Dimensionless concentrations terms (concentration terms with asterisks) are used for ease of computation. Hence, B* = B / B o C* = C/Bo etc. (5)
A
21
a
Concn Profile
Time
-+
Figure 1. Progress of reaction and concentration profiles with accumulation of the intermediate (cyclohexanone).
The dimensionless time, 0, is defined as the actual time during the existence of a particular surface divided by the surface renewal time. Thus, 0=t/r 0
