Ind. Eng. Chem. Res. 1990,29, 691-696
69 1
Mass Transfer and Solubility of O2 and CH4 in Silicone Fluids Joo H. Lee and Neil
R.F o s t e r *
School of Chemical Engineering and Industrial Chemistry, University of New South Wales, P.O. Box 1 , Kensington, New South Wales 2033, Australia
Solubilities (C *) and mass-transfer coefficients @,a) of O2and CH, in silicone fluids were measured a t elevated temperatures (293-473 K) and pressures (10-70 bar) and a t different stirring speeds (1000-1600 rev-min-I). A transient absorption technique was utilized t o measure kLa and C *. T h e mass-transfer coefficients for O2 and CH4 increased with temperature, pressure, and stirring speed in the ranges examined; the mass-transfer coefficients of O2 are 10-50% higher than those for CH,. T h e solubilities of CH, are higher than those for 02,and a t low temperatures, the ratio of solubility of CH4to O2 is approximately equal to 2, while this ratio decreases with an increase in temperature.
1. Introduction There has been considerable interest recently in the potential of using bubble column and slurry reactors for chemical reactions involving gaseous reactants. In particular, those reactions that are highly exothermic and that require high reaction pressures and temperatures are well suited to these reactor types. The advantage of carrying out exothermic reactions in an inert liquid phase is that the removal of heat can be facilitated, thus enabling the reactor to be operated at higher levels of conversion while maintaining adequate temperature control. There is also potential for controlling the selectivity by manipulating the rates of mass transfer between the gas and liquid phases. Consequently, mass-transfer coefficients and solubilities of gases and their dependence on process conditions are required. However, few studies concerning the effects of pressure and temperature on volumetric liquid-side mass-transfer coefficients and solubilities have been reported. Furthermore, the limited information that is available is, at times, inconsistent. The purpose of the present study is to investigate the potential of using various silicone fluids as the (inert) liquid phase in bubble column and stirred tank reactors. In addition to the development of a data base for the rate of mass transfer and solubility of O2 and CH, in various silicone fluids, fundamental information relating the effects of pressure and temperature on the volumetric liquid-side mass-transfer coefficients, and solubilities, has been obtained. 2. Experimental Section This experimental technique involving batch gas absorption has been previously used by Deimling et al. (1984). The pressure of the enclosed gas phase in the reactor decreases with time because of the absorption. The volumetric mass-transfer coefficient, kLa, is estimated with this decrease in pressure with respect to time. After achieving equilibrium, the total pressure decrease allows the equilibrium solubility, C *, to be determined. The equations for the determinations of kLa and C * are derived in the Appendix. The equation used for kLa is
-[ -1 Pf
- Po
Pi - Po
In
[ “1
= kLa(t -
t’), for t > t’
P’- Pf
The gradient of a plot of the left-hand side of the above equation versus t - t’is the value of kLa. For the gas-liquid system with agitation, the time (mixing time) at which the dispersion can be assumed to be homogeneous is an important factor. In the present study, time t ’ was determined as the value beyond which kLa did not vary with t ’, because for t < t ’the value of kLa depends on time due to the nonhomogeneity. 0888-5885/90/2629-0691$02.50/0
By the ideal gas law, the equilibrium concentration, C,, is
’[
c,, = VL
NLo
VG + -(Pi RT
-
1
Pf)
3. Experimental S e t u p A schematic diagram of the experimental apparatus is shown in Figure 1. This apparatus is principally the same as that previously used by Alba1 et al. (1983, 1984) and Deimling et al. (1984). Experiments were carried out in two stainless steel autoclaves (1.05 X m3,0.3 X m3) without baffles, and the details of the vessel dimensions are shown in Figure 2 . The pressure transducer on the outlet line of the reactor was connected to the highspeed chart recorder. The agitator was driven by a belt drive hooked up to an electric adjustable-speed motor; stirring speed was measured by a stroboscope. The reactor was heated by a temperature-controlled furnace and a temperature-controlled aluminum heating block, and the gas- and liquid-phase temperatures were measured by K-type thermocouples. The liquid was degassed with a vacuum pump.
4. Experimental Procedure The reactor was filled with the required amount of liquid and heated to the desired temperature. After reaching thermal equilibrium as indicated by equal temperatures in the gas and liquid phases, the liquid was degassed by evacuation. The reactor was then slowly pressurized to the desired pressure with the gas, and then agitation was commenced. The total pressure of the gas phase was recorded as a function of time. The equilibrium pressure after absorption was considered as the presaturation pressure for the next run. Again the reactor was slowly pressurized to the next higher pressure. The procedure was repeated for the range of pressures investigated. The same procedure was used for different stirrer speeds, gases, temperatures, and liquids. Mass transfer and solubility in various silicone fluids were evaluated. These silicone fluids exhibit high oxidation resistance, heat stability, low vapor pressure, and high flash point (Dow Corning, 1974, 1976). The properties of the liquids are presented in Table I. The accuracy of the experimental results is estimated as A270 for solubility data and *5% for hLa. Both error estimates were calculated from the results of quadruplicate measurements. 5 . Results a n d Discussion 5-1. Solubility, C*. The solubilities of O2 and
CH, in silicone fluids have been plotted as a function of pressure for temperatures in the range 293-473 K (see Figures 3 and 4). C 1990 American Chemical Society
692 Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990 Table I. P r o p e r t i e s of t h e Silicone F l u i d s type viscosity at 25 "C, cSt flash pt, "C specific gravity at 25 "C viscosity temp coeff coeff of expansion, mL/(mL/"C)
200F 1CS 200F 100CS dimethylsiloxane polymer dimethylsiloxane polymer 100 1 315 33 0.818 0.960 0.41 0.60 0.001 34 0.000 96
surface tension a t 25 "C, dyn/cm volatility
17.4 bp 152 "C at 1 atm
-
20.9 0.5 wt 90 loss after 24 h at 150 "C
550F phenyl methylsilicone oil 125 308 1.07 0.76 0-149 "C: 0.000 75 149-204 "C: 0.00077 204-260 "C: 0.000 80 24.5 5.5 wt % loss after 48 h at 250 "C
_I
L
F i g u r e 1. Schematic flow diagram of the apparatus: 1,gas tank; 2, reactor; 3, agitator; 4, pressure transducer; 5, pressure indicator; 6, chart recorder; 7, thermocouples; 8, furnace; 9, furnace controller; 10, thermometer; 11, cold trap: 12, vent; 13, vacuum pump.
Figure 3. Solubilities of 0, and CH4 in 550F silicone fluid at various temperatures.
ti I
1 I. 6
Lc--4
L. 6 M
F i g u r e 2. Vessel dimensions (all dimensions in centimeters).
For both O2 and CH4, solubilities increase with an increase in pressure. All the data display linearity with zero intercept, which suggests that Henry's law is valid. Prausnitz (1969) reported a general equation relating solubility to temperature in the relatively simple case where the solvent is nonvolatile and where the solubility is sufficiently small to make the activity coefficient of the solute independent of the mole fraction: [-]p=K
IS2
(1-1)
where AS, = S2L - SZGand x 2 is the mole fraction of gaseous solute _at saturation. If AS, is negative, the solubility decreases with rising temperature: otherwise, it increases. AS', can be divided into two parts: IS,= (S,L - S,G) + ( S , L - S,L) (1-2) where SZL is the entropy of the (hypothetical) pure liquid a t the temperature of the solution.
PRESSURE
(
bar 1
F i g u r e 4. Solubilities of O2in 200F silicone fluids at various temperatures.
The first term on the right-hand side of eq 1-2 is generally negative because the entropy of a liquid is lower than that of a saturated gas at the same temperature. With the assumption of ideal entropy of mixing for the two liquids, the second term can be written as S2L -
S2L= -R In x2
(1-3)
Since x 2 < 1, the second term is positive, and the smaller the solubility, the larger this term must be. It therefore leads to the expection that gases that have very small solubility show positive temperature coefficients of solubility, whereas gases that have relatively high solubility show negative coefficients. The results in the present study confirm this general prediction. As shown in Figures 3 and 4, with 550F silicone fluid, the solubility of O2 (the lowest solubility in the present study) is almost independent of the temperature,
Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990 693 0.20 0
0.01
t
- Oxygen
IOOOrpm
Oxuoen
R
_--
I
IO
0
20
30 40 50 PRESSURE C bar 1
80
70
Figure 5. Effect of pressure on mass-transfer coefficient for O2and CH4-550F silicone fluid systems a t 323 K. 0.49 ~
[
0.08k 0
80
IO
50
1 80
Figure 7. Effect of pressure on mass-transfer coefficient for 0, and CH4-550F silicone fluid systems a t 473 K.
- Oxygen
o 1~10rpm
20 30 40 PRESSURE ( bar 1
'
0
IO bar
-
"
om[ 0
-
I 1
0
2
0
3 0 4 PRESSURE
(
0 5 0 bar 1
B
o
7
0
8
0
Figure 6. Effect of pressure on mass-transfer coefficient for O2and CH4-550F silicone fluid systems a t 373 K.
whereas for two different viscous 200F silicone fluids where the solubilities of O2 were relatively high, solubilities decreased with increasing temperature. The solubility data for CH, are higher than those for 02.At low temperatures, the ratio of solubility of CHI to O2 is approximately equal to 2, while this ratio decreases with increasing temperature. This relationship reflects the higher negative temperature solubility coefficient of CH, resulting from its relatively high solubility. 5-2. Mass-Transfer Coefficient, k L a . 5-2-1. Effect of P r e s s u r e . Various studies of the pressure effect on kLa have been reported in the literature. Yoshida and Arakawa (1968) and Phillips et al. (1961, 1973) reported a decrease in kLa with rising pressure. The pressure dependence was much more pronounced at lower stirring speeds. It was suggested that the results might be due to a change in the surface renewal rate or interfacial turbulence resulting from changes in surface tension due to the gas pressure. Teramoto et al. (1974) and Alba1 et al. (1983,1984) observed no dependence of kLa on pressure for various gas-liquid and gas-liquid-solid systems. The results were explained on the basis of no influence of pressure on the interfacial and bulk physical properties of the liquid. Recently, Deimling et al. (1984) and Karandikar et al. (1986) observed an increase in kLa with an increase in pressure. They explained the results on the basis that surface tension decreases as pressure increases (Reid et al., 1977), with the subsequent decrease in gas bubble size resulting in a large gas-liquid interfacial area and consequently higher kLa values. In the present study, the effect of pressure on kLa was studied for four different values of stirrer speeds (1000,
300
340
380 TEMPERATURE
(
420 K 1
480
500
Figure 8. Effect of temperature on mass-transfer coefficient for O2 and CH4-550F silicone fluid systems at 1200 rpm. '
0
n
IO
bar
. A 30 bar 0 50 bar
-
In \
"
0.02
300
340
---
380 TEMPERRTURE
420 (
480
503
K I
Figure 9. Effect of temperature on mass-transfer coefficient for 0, and CH4-550F silicone fluid systems a t 1400 rpm.
1200,1400, and 1600 rpm) in the pressure range 10-80 bar at various temperatures for the O2-550F silicone fluid and CH,-550F silicone fluid systems. The kLa data have been presented as a function of pressure in Figures 5-7. Under all conditions studied, dramatic increases in kLa values were observed with increasing pressure. These trends are similar to the results reported recently by Deimling et al. (1984) and Karandikar et al. (1986). As previous workers have suggested, the reason for this could be the decrease in surface tension with increasing pressure, which allows a large gas-liquid interfacial area and consequently higher hLa values.
694 Ind. Eng. Chem. Res.. Vol. 29, No. 4. 1990
m S T I R R I N G SPEED
(
revolutlon/mlnbte
)
F i g u r e 10. Effect of stirring speed on mass-transfer coefficient for O2and CH4-550F silicone fluid systems at 323 K.
5-2-2. Effect of Temperature. In Figures 8 and 9, kLa values for O2and CH, in 550F silicone fluid are represented as a function of temperature for the pressure range 10-50 bar. It can be seen from these data that kLavalues for both gases increase with rising temperature in the range of pressures studied. This result can be explained by the increase of gaseous molecular diffusivity with temperature and the decrease in liquid viscosity, which results in a high rate of diffusion of the gas into the liquid and the formation of smaller size bubbles. However, in a sparged agitated reactor, Suresh et al. (1988) showed diffusivity to have little effect on kL. In their study, the variation in diffusivity was brought about by a change in temperature. It was found that the variation of other physical properties such as viscosity, surface tension, and density, as a consequence of temperature variation, had relatively less effect on kL than the influence of diffusivity on kL. Unfortunately, since the mass-transfer coefficient, kL, and interfacial area, a, were not measured separately in the present study, the relationships between kL and physical properties such as viscosity, diffusivity, and surface tension were not examined. However, Suresh et al. (1988) also showed that lzLa increased slightly with an increase in temperature (353-373 K). Elstner and Onken (19811.. Yagi and Yoshida (19751, and Alba1 et al. (1983) reported that kLa decreased with an increase in viscosity in the range of stirrer speeds (600-1000 rpm) for both a sparged agitated reactor and a batch agitated reactor. The effect of temperature on hLa in the present study therefore can be explained by the increase in diffusivity, decrease in viscosity, and the formation of smaller size bubbles. 5-2-3. Effect of Stirring Speed. In a sparged agitated reactor, Sridhar and Potter (1980) showed that the stirrer speed had little effect on the interfacial area between 1250 and 1450 rpm at 423 K. Furthermore, Suresh et al. (1988) reported that the stirrer speed had no effect on kLa for the range of stirrer speeds (1OOO-15OOrpm) at 423 K. Contrary to t,he above result, Karandikar et al. (1986) observed that, at 423 and 498 K, kLa increased with an increase in specific 'power input in a batch agitated reactor. The specific power input is directly proportional to the stirrer speed, which was varied in their study from 700 to 1200 rpm. Since the power input by the stirrer was not measured in the present study, the effect of stirring speed which was relevant to P * / V L was estimated. The values of kLa for O2 and CH, in 550F silicone fluid are illustrated as a function of' stirrer speed in the pressure range 10-70 bar at 323, 373, and 473 K in Figures 10, 11 and 12. It was observed that kLa increased with an increase in stirring speed ilc)00-1600 rpm) in the range of temperatures
9.02 900
J
2003
'WO
STIRRING SPEEO : revolution/ni?uts 1
Figure 11. Effect of stirring speed on mass-transfer coefficient for O2 and CH4-550F silicone fluid systems a t 373 K.
F i g u r e 12. Effect of stirring speed on mass-transfer coefficient for O Land CH4-550F silicone fluid systems at 473 K.
(323-473 K). This result is consistent with that reported by Karandikar et al. (1986). This observation could be due to the increase in gas entrainment and the formation of a large number of smaller bubbles, thereby increasing the gas-liquid interfacial area and resulting in an increase in kLa. 6. Conclusions The results of this study show that solubilities, C *, and the mass-transfer coefficients, kLa, of O2 and CH, in silicone fluids are dependent on pressure, temperature. stirrer speed, and the properties of liquid. The equilibrium solubilities, C *, increased with pressure and could be expressed at constant temperature by Henry's law. The trends of the solubilities of O2 and CH, with respect to temperature are in agreement with theoretical predictions, in that gases that have limited solubility show positive temperature coefficients of solubility, whereas gases that have relatively high solubility show negative coefficients. The values of the mass-transfer coefficient, k,a, of CH, and O2 increased with temperature, pressure, and stirrer speed. The mass-transfer data obtained in the present study are to be used in a complementary investigation of the reaction of the gas components in the liquid phase using the same experimental apparatus.
Acknowledgment This project is funded in part by BHP MRL (Aust) Pty. Ltd. and the Australian Government under the auspices
Ind. Eng. Chem. Res., Vol. 29, No. 4,1990 695 of the Australian Research Council under Grant A 4a715554.
Nomenclature a = interfacial area, m2/m3 C * = equilibrium solubility of the gas in the liquid, m3 of gas
at STP/m3 of solution C,, = equilibrium concentration, km~lqm-~ Cieq = interfacial equilibrium concentration of solute gas, kmol~m-~ CL = solute gas concentration in the liquid, km~lam-~ H = Henry’s constant kLa = volumetric mass-transfer coefficient, l / s N = number of moles, kmol P = pressure, bar P’ = pressure at the mixing time, bar R = ideal gas constant, m3.bar.K-’.kmol-’ S2: = entropy of the gas S2 = entropy of the solute in the solution S = stirring speed, rev-min-’ T = temperature, K t = time, s t ’ = mixing time, s V , = volume of gas phase, m3 VL = volume of liquid phase, m3
Subscripts f = equilibrium state after absorption G = gas phase i = initial state before absorption L = liquid phase o = state of presaturation at a lower pressure
I)
[
where
(7) and also
cy
can be expressed as P: - P,
Therefore, by inserting eq 8 into eq 5, we obtain
[
- -p
f - p ~ In ] Pi - Po
[
p - p f ] = hLa(t - t’), f o r t > t’ P’- Pf
RT Pi - Pf = -(N
Gi - NGf)
VG Also, the equilibrium concentration C,, is
Appendix The equations for the determinations of kLa and C * are derived with the following assumptions. (1) T h e ideal gas law is valid in the pressure range of operation. (2) Henry’s law is valid for the absorption of the solute gas in the liquid. (3) While pressurizing the reactor with the gas, there is no absorption of gas. (4)During the experiment, the temperatures of the gas and liquid are equal and constant. ( 5 ) The vapor pressure of the liquid is negligibly small compared with the total pressure. (6) Mass-transfer resistance in the gas phase is negligible. (7) T h e liquid in the tank is well mixed. With these assumptions, the rate of solute gas uptake by the liquid is related to the rate of decrease in pressure according to
The differential mass balance for the liquid phase gives (2)
and the Henry’s law constant is given by
H = P/Cieq
I
The number of moles of the absorbed gas can be determined from the total uptake of gas by the liquid and can be evaluated by the ideal gas law as follows:
Greek Letter cy = constant in eqs 6 and 8
dNL/dt = VLkLa(Ci,, - C,)
By equating eq 1 and 2 and writing the concentrations in terms of pressure using eq 3 and 4 and integrating between the limits of pressure P ’at time t’and pressure P a t any time t , we obtain ( a + l ) k r a ( t - t ’1 = (cy + 1)(P- Po) - (Pi - Po) -(In (cy + l)(P’-Po) - (Pi -Po) (5)
(3)
By integrating eq 1, we obtain
(4)
Registry No. 02,7782-44-7; CHI, 74-82-8.
Literature Cited Albal, R. S.; Shah, Y. T.; Carr, N. L.; Schumpe, A. Mass Transfer in Multiphase Agitated Contactors. Chem. Eng. J . 1983,27, 61-80. Albal, R. S.; Shah, Y. T.; Carr, N. L.; Bell, A. T. Mass Transfer Coefficients and Solubilities for Hydrogen and Carbon Monoxide under Fischer-Tropsch Conditions. Chem. Eng. Sci. 1984, 39, 905-907. Dow Corning. Information about Silicone Fluids. Technical Data Sheet; Dow Corning Corporation: Mideland, MI, 1974; Bulletin NO. 22-069b. Dow Corning. Information about Silicone Fluids. Technical Data Sheet; Dow Corninp. Corporation: Midland, MI, 1976; Form No. 22-07lA-76. Deimling, A.; Karandikar, B. M.; Carr, N. L.; Shah, Y. T. Solubility and Mass Transfer of CO and H, in Fischer-TroDsch Liauids and Slurries. Chem. Eng. J . 1984, i 9 , 127-140. Elstner, F.; Onken, U. Effect of Liquid Phase Properties on Mass Transfer in Gas/Liquid Dispersions. Ger. Chem. Eng. 1981, 4, 84-89. Karandikar, B. M.; Morsi, B. I.; Carr, N. L.; Shah, Y. T. Effect of Water on the Solubility and Mass Transfer Coefficients of CO and H, in a Fischer-Tropsch Liquid. Chem. Eng. J . 1986,33,157-168. Phillips, K. L. Proposed Explanation for Apparent Dependence of Liquid Phase Mass Transfer Coefficients on Pressure. Can. J. Chem. Eng. 1973,51, 371-374. Phillips, K. L.; Sallem, E. R.; Spencer, J. F. T. Oxygen Transfer in Fermentations. Ind. Eng. Chem. 1961, 53, 749-754. Prausnitz, J. M. Molecular Thermodynamics of Fluid-Phase Equilibria; Prentice-Hall, Inc.: Englewood Cliffs, NJ, 1969. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties o f Gases and Liquids, 3rd ed.; McGraw-Hill Inc.: New York, 1977. Sridhar, T.; Potter, 0. E. Interfacial Areas in Gas-Liquid Stirred Vessels. Chem. Eng. Sci. 1980, 35, 683-695. Suresh, A. K.; Sridhar, T.; Potter, 0. E. Mass Transfer and Solubility in Autocatalytic Oxidation of Cyclohexane. AIChE J . 1988, 34, 55-68.
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
