Designing a Cyclohexane Oxidation Reactor J. Alagy, P. Trambouze,* and H. Van Landeghem lnstitut Francais du Petrole, C.E.D.I. B.P. No. 3. 69390 Vernaison, France
As part of the development of a liquid-phase cyclohexane oxydation process, various aspects of the reactor design have been investigated: fundamental research on the influence of mass-transfer phenomena on reaction selectivity, laboratory and development research on the use of boric acid as a coreagent, and hydrodynamic research to determine the optimum reactor configuration. First a simplified reaction scheme was established which led to a not too complicated mathematical model. This model was not available at the time when the pilot plant began operating. Therefore a further simplified model was adopted, so that the results of a one-reactor stage pilot plant enabled the design of a multistage industrial unit. These two approaches compared favorably and the industrial construction proved also to conform to forecasts.
I. Introduction The direct partial oxidation of hydrocarbons in the liquid phase presents a chemical reaction scheme which is extremely complex and often poorly understood. The transfer of oxygen from the gas to the liquid phase complicates further the overall phenomena. As part of our efforts to develop a cyclohexane oxidation process, we felt that we should go further in understanding just what happened during these transformations into the liquid phase. One of the reasons for this was that designing a reactor required various data that we were lacking. In particular, we wondered how conversion and selectivity were influenced by parameters such as temperature, residence time, gas flow rate, and stirring. In order to proceed as rigorously as possible, we developed a mathematical model based on both kinetic data concerning cyclohexane oxidation and mass-transfer information obtained from research on cyclododecane oxidation. A nonlinear regression had to be performed in order to determine the value of seven parameters used in this model, but independent estimates were available for all of these parameters, thus simplifying the work on regression while, above all, making the numerical values thus obtained more meaningful. At the same time and for the sake of respecting deadlines, we used a more pragmatic procedure to scale-up the initial pilot-plant results. This enabled us, in particular, to estimate the influence of the stage effect in a cascade of perfectly stirred reactors. In the present article, we will begin by reviewing the simplified reaction scheme developed from a preliminary kinetic study. Then we will sum up the main conclusions reached concerning the influence of the mass transfer on liquid-phase hydrocarbon oxidations as revealed by experiments with cyclododecane. These data will enable us to compile a relatively simple mathematical model to describe cyclohexane oxidation. After a brief description of the formal computing of the influence of the stage effect, we will conclude by mentioning some hydrodynamic studies that became necessary before an industrial reactor could be built. 11. Experimental Methods The studies we have just mentioned were carried out in two types of equipment. (i) The chemical kinetics studies and especially the physical kinetics studies were performed in semicontinuous equipment with mechanical stirring. The device used in particular for cyclododecane oxidation was a small cylindrical vessel with a capacity of about 1.5 l., equipped with a stirring system (turbine + baffles) standardized
according to Rushton, et al. (1950). Turbine rotation speed was variable, and the installation was equipped with gas flow rate, temperature, pressure, and volume measuring instruments. (ii) The pilot-plant cyclohexane oxidation studies were performed in a 150-1. cylindrical reactor (Figure 1). stirring was generated by gas injection a t the bottom of the column and by tangential injection, a t the top of the column, of a liquid flow taken from the bottom of the column. In both cases, the reaction procedure was followed by sampling the liquid phase and chemically titrating for acidity and hydroperoxides, and by using gas chromatography to determine alcohols, ketones, and secondary products. Further details on these techniques can be found in the work of Burguieu (1972) and Busson (1966). 111. Reaction Scheme Liquid-phase hydrocarbon oxidation proceeds according to a radical mechanism that has been described very often (for example, by Emanuel, et al., 1967). The kinetic expressions describing this mechanism reveal reaction orders between zero and first order for both oxygen and hydrocarbons. In addition, the overall reaction rate is known to be proportional to the square root of the decomposition rate of the radical-generating compound. In the case of an autoxidation, Le., one in which the radical-generating compound itself is created by the transformation being performed, these compounds are intermediate hydroperoxides. T o obtain preliminary information about these autoxidations, we studied the oxidation of cyclododecane which is a close relation to cyclohexane. Its autoxidation takes place under identical conditions a t a rate that is very close to the ones obtained for other hydrocarbons of industrial importance (Burguieu, 1972; Emanuel, et al., 1965; Reich and Stivala, 1969). A study of the influence of the mass transfer and its interaction with the chemical kinetics provided conclusions that were valid for cyclohexane, but it should be pointed out that the vapor pressure of cyclododecane is such that a t 150 to 180°C it is possible to operate a t atmospheric pressure, thus considerably facilitating experimental work. Generally speaking, the reaction scheme for naphthenic hydrocarbon oxidation can be written as hydrocarbon
-
alcohol
(I)
hydroperoxide ketone
--+ acid -+
by-products
This reaction scheme was simplified in various ways durInd. Eng.
Chem., Process Des. Develop., Vol. 13, No. 4 ,
1974
317
Purge
I
1
T
n------u
Figure 2. Calculated curves used for the estimations of Hatta number and interfacial area.
Figure 1. Sketch of the pilot plant continuous reactor.
might be a tendency for ketones and alcohols to accumulate at this spot and cause a drop in selectivity. Therefore, it can be seen that knowing the exact location of the reaction is primordial for understanding the phenomenon to a satisfactory degree. To determine where this reaction is located, we used the film theory. The oxygen fraction passing through the liquid film without having reacted ( f ) and the oxygen flux a t the gas-liquid interface (@02)were calculated as follows.
ing the study on cyclododecane. In general, we used scheme 11.
ROH RH
I
-
L V RO
byproducts
For cyclohexane oxidation, this scheme is further complicated by the presence of boric acid. As suggested by Bashkirov, et al. (1961), in the case of n-paraffins, we used this reactant to partially esterify the alcohol formed so as to slow down its oxidation. In this case, the reaction scheme becomes
+ HBO, ROH
rboric esters
In this respect, special mention should be made of the work of Spielman (1964), who compared from the point of view of selectivity the reaction scheme I11 with a simple consecutive one.
IV. Studying the Influence of Mass Transfer The influence of mass transfer on a chemical reaction (or vice versa) has received abundant attention (Astarita, 1967; Danckwerts, 1970) from both the theoretical and experimental standpoints. However, there is only a limited number of publications dealing with this influence on complex reaction schemes and making comparisons between experimental and calculated results (Inoue and Kobayashi, 1968; Van de Vusse, 1966). In discussing hydrocarbon oxidations, the conclusions put forward are mainly qualitative, usually not very satisfactory and sometimes even contradictory (Burguieu, 1972). A priori, the mass transfer might be expected to influence the overall transformation rate without the nature and intensity of this effect being quite so evident. Since the oxidizability of alcohols and ketones is appreciably greater than that of hydrocarbons themselves, it might be expected, for example, that the concentration gradients generated by mass transfer would modify the selectivity caused by the chemical reaction. If most of the hydrocarbon oxidation occurred near the interface, there 318
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 4, 1974
These equations are accurate for a first-order reaction with respect to oxygen (for hydrocarbon conversions of less than 15% for which the kinetics is degenerate with respect to hydrocarbon). For orders different from the first order, the same equations can be kept with the following definition of Ha (Hikita and Asai, 1964)
The oxygen that has penetrated into the bulk of the liquid phase reacts there according to an m-order reaction. We can thus write
fho, =
kc.(02)Lm
(4)
Since we know the solubility and diffusivity of oxygen and can estimate kI,, we can eliminate k , and ( 0 ~from ) ~ these equations to obtain a function g(Ha,m,a) = 0
(5 )
In addition, experimental measurements with cyclododecane give several values for the oxygen flux such as GO2 = 1.05 X mol/cc sec a t 900 rpm and dO2= 2.5 X 10W7mol/cc sec at 1800 rpm. Equation 5 was solved numerically for different values of m taken between 0 and 1, keeping a as a parameter. The numerical values used were: kL = 6.6 X cm/sec (according to Calderbank, 1967); (02)i = 1.5 x mol/ cc (measured and according to Prausnitz, 1961); and Do2 = 6.25 x 10-5 cmZ/sec (according to Wilke and Chang, 1955). It first became apparent that the solution is not very
sensitive to m. For m = 1, the result of this calculation is given in Figure 2. Furthermore, measurements by a photographic method showed that the interfacial area varies from 2.5 to 12 cmz/cc for stirring rates ranging from 900 to 1800 rpm. Figure 2 thus shows us that, under such conditions, f is always close to 1, the Hatta number is always considerably less than 1 (hence excluding any speeding up of the transfer as the result of the chemical reaction) and ) ~ varies greatly with a. The location of the ( O Z ) L / ( O Zratio the reaction then becomes clear. It takes place inside the liquid with an intervention of the mass transfer to prevent this phase from becoming saturated. Hence the selectivity depends above all on the relations between the chemical kinetics constants, whereas the transformation rate is affected by the oxygen transfer to the extent that the order with regard to oxygen is different from zero order. The only acceptable estimate for this order is actually m = 1. Considering that the reaction takes place inside the liquid, we have
( v ) 1800 r p m (Y) 900 r p m
(02)L at 1800 r p m (02)L at 900 r p m >
=
It should be mentioned that this equation is valid for acceptable values of [ ( O Z ) a~ t. 1800 rpm/(Oz)L at 900 rpm] only if m is near 1. A comparison of the two curves ( O Z ) ~ / ( 0 2 ) i (Figure 2) gives an estimate of the corresponding interfacial areas a. We find 2.5 and 12 cmz/cc for 900 and 1800 rpm, respectively. The value of k , can then be deduced from the values chosen for Ha, Le., k , = 5 x sec-I. We can thus conclude that most of the chemical transformation takes place in the liquid phase. In addition, the order of the reaction with respect to oxygen appears to be in the vicinity of the first order and, although the physical transfer is not slow enough for the oxygen to be entirely consumed in the liquid film near the interface, it nonetheless has enough influence for the liquid phase to be relatively far from saturation, especially for values of a lower than 10. As a result, stirring has negligible influence on the selectivity of the transformation but directly affects the overall reaction rate. This is exactly what was observed experimentally (Burguieu, 1972). Furthermore, a measurement of the apparent activation energy of this transformation shows a very low value (3-4 kcal/mol) and this result supports the interpretation given above (J.C. Burguieu, unpublished results). It should also be pointed out that the oxygen concentration in the bulk of the liquid depends on the values of both kl, and k , . Therefore, the above conclusions can be transposed to apply to cyclohexane oxidation only if consideration is given to the change brought about in these two values as the result of physical (viscosity, density) and chemical properties. This means that the conclusions as to the location of the reaction do not change, but the oxygen saturation of the liquid may well be different; the viscosity of cyclohexane being lower, this will be in favor of the oxygen saturation of the liquid phase. V. Building a Mathematical Model for Cyclohexane Oxidation We have already pointed out that boric acid was used to improve the selectivity of the transformation by esterifying the cyclohexanol formed. These esters are resistant to oxidation, In this case, the reaction scheme becomes scheme 111. Assuming first order with regard t o each reactant and
using a continuous reactor of the perfectly stirred type while assuming that the reactor feed is pure cyclohexane (Figure l), this scheme results in the following mass balances ?LAO
-
HA
= (kl
+
k,)(A)(O2),V =
(kl + ZB
+
ZE
1
(kin,
=
I’ k2)nA(02)L3
(74
1‘
- ~ ~ % B ) ( O ~ ) L F(7b)
V k4ZC ( 0 2 ) L F
(7d)
The liquid-phase oxygen concentratibn can be calculated from the mass balance of the transfer flow from the gas phase to the liquid phase. Oxygen consumptions at each step of oxidation are given in scheme 111 with x being the total number of oxygen moles that disappear per mole of cyclohexane transformed into by-products. The oxygen balance is then written as follows, using symbols such as the ones given in Figure 1
The assumption of a perfectly stirred reactor (This assumption is justified for the liquid phase, due to the high recirculation rate. For the gas phase, this assumption is not completely correct, but the deviation from this ideal situation influences only the numerical value of the transfer coefficient k L a . )enables us to write
Before substituting this eq in eq 7, it should be simplified by comparing the different terms in the denominator. For average operating conditions, the different parameters have the following values: a = about 5 cm2/cc (estimate based on our own experiments); k ~ ,= 0.1 cm/sec (estimate according to Calderbank (1967), dB > 2.5 mm); Q,r = 1400 cc/sec total flow rate recirculating under conditions c g H12 and inerts included; ( 0 ~= ) ~ mol/cc, experimental datum; ( O Z ) , = 6.8 x mol/cc; He = 2.5 (Hildebrand estimate) (Hildebrand and Scott, 1950); V = lo5 cc; and F = 14 cc/sec. Estimating D is a more delicate matter. In the 100-1. reactor, molar flows of absorbed oxygen of 1.5 X mol/sec were measured. Assuming, for a first estimate, ~ , find that ( 0 ~ = ) ~3.6 . X that ( 0 ~= )0 .~9 ( 0 ~ ) we mol/cc. This gives the following estimate of DV/F: DV/F = 1.5 x 10-2/3.6 10-7 = 4.2 x lo4. We easily find that He.Q,r < kLaVandHe.Q.r < DV/F. The first inequality is extremely important. If He. 8 . r can be neglected before kLaV, one recognizes that the liquid-phase oxygen concentration, with our reacting conditions, becomes independent of k L and depends solely on the molar flow rate of injected oxygen. Hence, under these Ind. Eng. Chern., Process Des. Develop., Vol. 13, No. 4 , 1974
319
conditions, the oxygen flow admitted to the reactor is small and, in reality, controls the reaction procedure. Actually, He-Q.r is not entirely negligible, but we still feel that this assumption is justified in compiling a simplified and workable model. Likewise, if we can neglect He.Q.r in front of D V / F , we finally obtain
It should be mentioned that the amount Q,r(Oz), is nothing other than no2, i.e., the molar oxygen flow rate a t the reactor inlet. In an initial approximation, this means that all the oxygen injected into the reactor is consumed. In reality, term He.Qrr is not entirely negligible. Its value is about 10 times less than that of terms D V / F and kLaV. We can then calculate that the oxygen concentration a t the reactor outlet is not entirely nil but is in the vicinity of 5 to 10% of the value a t the reactor inlet. This is confirmed experimentally, with between 1.1 and 1.8% oxygen being found in the off-gas. We then took 96% as our initial oxygen-conversion estimate (1.25% oxygen in the tail gas). Equation 10 can than be written
Since esterification is almost a thermoneutral reaction, we assumed that X was independent of the temperature. To determine PH*, a mass balance had to be determined for the water around the reactor. To do this, water outflows had to be known: 1 mol/mol of cyclohecane, 1 mol/mol of ester, and y mol/mol of by-products. An examination of the overall material balances led to the conclusion that an average of one mole of cyclohexane transformed into by-products results in the formation of 1 mol of CO or COa, Le., one mole of water. In this case, the water balance can easily be calculated around the reactor; water eliminated from the reactor
0 . 2 1 - )l &--(4
+ 1 - 0.79 cp-q
] (164
water produced
Therefore, system (7) finally becomes (0.21 - CP)Q (1
By introducing the following parameters we can substantially simplify the system of eq 7
To complete the model, we must also take into consideration two experimental findings linked to the flow rate variation of the gas circulating inside the reactor. (i) An increase in the flow rate of gases other than oxygen was found to have a favorable influence on both selectivity and the alcoho1:ketone ratio in the effluent from the reactor. (ii) Oxygen consumption per molecule of cyclohexane transformed into by-products was also found to decrease slightly with the same flow rate. We attempted to include these observations in the mathematical model. It appears obvious that the first observation could be linked to the esterification conditions. This reaction is actually very fast around 150-160°C; we shall assume that equilibrium is attained. If we assume further that the boric acid concentration is constant in the liquid phase because there is an excess of this compound in the solid state in the reactor and that the vapor-liquid equilibrium for water is reached, we can write
This equation combined with equations (14) and (7b) enables us to write
*A0
nE =
-
1
1
+
(On2'
Chem., Process
Des. Develop., Vol. 13, No. 4, 1974
- ')'
h P H Z O22,400 X K
(n,
(17a)
- pnB)(17e)
As an initial approximation of u and T , this correlation gave u = 2.64 and T = 15.4. The model thus contains seven parameters (a,@, 7,X, u , T , and c p ) that have to be determined from the 15 experiments available to us. Cyclohexane vapor pressure, which we took as being equal to its partial pressure a t the temperature considered, was calculated from the equation = 1 1 . 4 3 - 0.1826T 0.00095T2
Ind. Eng.
a)nB
At this stage, the only fact not integrated into the model has to do with the correlation we found to exist between x and n.r. By looking a t the oxygen balances that are available, we are able to determine the empirical correlation.
Pc6H12
320
+
= 22,400 X K
nA
+ (150°C
5
T
5
190°C)
VI. Determining the Parameters-Model Results The problem was then to adjust the seven parameters as well as possible so as to recalculate the experimental results of the 15 experiments performed as part of systematic experimentation. The experimental results contained three responses conversion: selectivity:
c
= n~~ - n~
nB
S =
t h e OL/ONE r a t i o :
+
nA 0
??.E
%A0
-
R =
nB
+ nc %A
+
(19)
nE
nC
There were thus considerable data (45 results) available for defining the seven parameters. Considering that this parameter adjustment was to be done by a nonlinear regression using seven variables, the initial estimates were of great importance. We chose: for a, p, and y, values determined in a kinetic analysis by Ser6e de Roch (1965) in the absence of boric acid LY = 0.27, /3 = 24, and y = 18; for u and T , the initial estimates have already been mentioned; for A, a value obtained as follows. From eq 19 it can be calculated that
Figure 3. Comparison of the conversion, selectivity, and ol/one ratio values calculated from the kinetic model with the corresponding experimental values.
Table I Parameters
n,
= n A o C ( l - S ) = (Oo21 - @ ) Q x ync (21) 22,400 X K
Equation 7e can be used to find
Initial estimate 0.27 24 18 0.6
2.64 15.4 0.0125
Using eq 14, we then estimated
nB
Equation 17f can be solved for P H ~ while O taking this value of XPHzointo consideration. We thus obtain the estimate, X = 0.60 f 0.15. The estimate for cp has already been given as cp = 0.0125. Using these values, the seven parameters were adjusted by nonlinear regression, according to Rosenbrock’s method (Rosenbrock and Storey, 1960) to minimize the “deviation’’ function expressed as deviation = YI(Ccalcd ?‘Z(Scalcd - Sexptl)’
cexptl)‘ + +
Y3(Rcalcd
- Rexptl)z (24)
The calculated values of each response were obtained by solving the system of eq 17 after this system had been reduced, by substitution, to two equations with two unknowns. In the “deviation” function (24) we introduced response weighting coefficients yi so as to give each term the same importance, with the values of C, S, and R being respectively around 0.1, 0.8, and 10. This regression provided the parameter values given in Table I. The results obtained with the model thus adjusted are compared with the experimental results in Figure 3. Agreement is sufficiently satisfactory for the model to be used in calculating an industrial reactor, of the staged type if necessary.
End value 0.2 19 32.75 0.60
2.70 14.57 0.015
We can thus conclude that, despite the complexity of the reaction scheme and of the multiple phenomena occurring in this transformation, a relatively satisfactory and simple model can be worked out. This model demonstrated that the flow rate of inerts has great importance on the selectivity. This flow rate influences the water stripping, whose elimination facilitates esterification and influences oxygen consumption during the formation of by-products (eq 18).Thus the influence of mass transfer on selectivity as mentioned by Steeman, et al. (1960), seems to be an indirect one, resulting from the influence on the stripping of water and other volatile compounds. Considering further the values of the Hatta number we obtained, our conclusions are not in conflict with those formulated by Van de Vusse (1966), nor with those proposed by Inoue and Kobayaski (1968).
VII. Simplified Model As we have already said, the mathematical model described above was compiled from experimental data obtained in a continuous pilot plant. This means that any scaling-up could not be attempted until the pilot plant experiments were completed. Nonetheless, before these continuous tests, other discontinuous experiments had been performed for the purpose of exploring the influence of different operational variables and to determine variation areas for building the pilot plant. Upon completion of this discontinuous testing campaign, it had already become apparent that the industrial unit would have to include several perfectly stirred reactors working in series. The result obtained (Figure 4) showed that selectivity decreased as conversion increased. Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 4, 1974
321
1 0.15
I
0.05
0
0.10
I
Figure 4. Calculated curves of selectivities us. conversion. The S and s curves have been calculated for the mentioned operating conditions. The experimental points (batch) were not all obtained with identical operating conditions; most of them correspond to a I)value of 0.04, leading to better selectivities.
The breaking up of the overall reaction volume into a series of reactors should thus have a favorable effect on the selectivity obtained. However, for reasons of cost, there was no question of building a pilot plant with several (3 or 4) reactors in series. Therefore, when deciding to build a continuous pilot plant equipped with a single reactor, there had to be some certainty that the results would be transposable to the case of a unit with several reactors. For this, a very simple analysis of the discontinuous results was made so as to make certain, at least approximately, of this transposition of the pilot plant results. If we simplify reaction scheme I11 to a consecutive scheme A B C, the following magnitudes can be defined - dC, i n s t a n t a n e o u s selectivity: s = dC A
Figure 5. Curves S and s.vs. conversion. The S curve has been obtained from batch experiments and the s curve has been deduced from the preceding one using eq 25.
I
, II
--
i n t e g r a t e d selectivity:
cB
S=
'A0
conversion:
C =
cAO
-
-
-
cBO cA
A '
LAO
The last two quantities above are identical with those used up to now and defined by eq 19. Instantaneous selectivity is the one obtained in a continuous perfectly stirred reactor, while integrated selectivity is the result of the discontinuous process. From the above equations, we can easily derive
dS s = s + c dC (25) This equation can be applied to the case we are interested in, provided that the simple consecutive scheme can be considered as an initial approximation of the more complex scheme already described. In particular, we must admit that selectivity depends solely on conversion, at least for a given set of operating conditions that are kept constant. Figure 4 gives an idea of the approximation thus accepted. From curve S = f( C) (Figure 4), curve s = f ( C ) (eq 25) can thus be plotted. Total conversion can then be broken up into equal fractions to be obtained in each reaction stage. The conversion in each stage is regulated independently by controlling the air make-up, for example. As an illustration, Figure 5 shows curves S = f ( C ) and s = f ( C ) while at the same time visualizing the comparison 322
Ind. Eng. Chern., Process Des. Develop., Vol. 13, No. 4, 1974
Figure 6. Curves showing the influence of the number of reactor stages on the selectivity. The curve corresponding to the simplified model has been calculated from the s curve of Figure 5, while the one corresponding to the kinetic model results from the s curve of Figure 4.
of the selectivities obtained for the same conversion in a single reactor and in a cascade of four reactors. For a discontinuous reactor we have
S =
&sc
sdC
0
whereas for a series of N stages we write
If the conversions achieved in each stage are equal to one another, eq 27 can be reduced to
The shaded rectangles in Figure 5 express eq 21. The influence of the number N of stages can also be figured out, and the variation in the selectivity us. N can be plotted for constant total conversion. Figure 6 gives curves S = g(N) as they can be calculated from the simplified model (eq 27, dotted-line curve) and from the kinetic
model (eq 17, solid-line curve). Both models can be seen to provide for an appreciable gain in selectivity when going from a single reactor to four reactors in series. Although based on a debatable assumption, the simplified model is nonetheless a useful tool for transposing the results obtained with a single reactor to the case of several reactors in series. However, the kinetic model both con: firms the validity of this transposition and enables real optimization to be made of the operating conditions for the construction of the first industrial unit.
VIII. Conclusion This study has resulted in the compiling of a mathematical model for the oxidation of cyclohexane and has served to reveal the following factors. (i) The reactor operates in kinetic conditions, although the mass transfer influences the transformation rate. (ii) As a result, stirring has no direct effect on selectivity. (iii) For the operating conditions chosen, conversion can be controlled by the fresh-air make-up in the reactor. (iv) The favorable influence of a high gas flow rate can be explained by the elimination of reaction water. This thus requires a sufficient gas-liquid transfer coefficient. (v) The selectivity of the transformation can be appreciably increased by using perfectly stirred reactors in series. For the industrial construction of such a unit, we chose reactors of the same type as those illustrated in Figure 1. This choice was motivated by the tendency, observed in the pilot plant, for heavy and sticky by-product to accumulate on the reactor wall at the surface of the liquid. Tangential injections were performed for the purpose of washing the wall at those points, but it is quite obvious that a poor design could result in the formation of a vortex inside the reactor, in which case the gas-liquid contact area would become very small. After gas is injected into the liquid it is very quickly sucked toward this axial channel created by the vortex. To prevent this phenomenon from appearing, turbulence and nonsystematic circulations caused by the gas flow must be relied upon. This phenomenon was analyzed in two scale models 30 and 60 cm in diameter, and a design criterion was worked out. To sum up, the mathematical models and this hydrodynamic criterion were what enabled the two industrial projects to be carried out with full success. Nomenclature a = interfacial area in relation to the liquid volume in the reactor, cmz/cc CI = concentration of compound I, mol/cc 3 0 2 - diffusivity of 0 2 , cm2/sec . F = volumetric liquid flow rate, cc/sec k1, = mass transfer coefficient, cm/sec
kc = kinetic constant, depends on m k l , kz, . . . = kinetic constant of step 1,2, . . . , cc/mol sec m = reactionorder nI = molar flow rate of compound I, mol/sec % = total molar flow rate of gas phase, mol/sec
( O Z ) ~(, 0 ~= )0 ~ 2 concentration in the gas at inlet, outlet of reactor ( O Z ) ~(, 0 2 ) ~= 0 2 concentration a t gas-liquid interphase in the bulk of the liquid, mol/cc P, PI = total pressure, partial pressure of compound I, atm Q, Qrr = total volumetric flow rate of NTP fresh air, of gas in the reactor, cc/sec r = reaction rate, mol/cc sec T = temperature V = liquid volume in the reactor, cc Greek Letters 7 = amount of CO + COz in blowdown gas 0 = liquid residence time, sec cp = amount of oxygen in blowdown gas $ = amount of oxygen in the gas at the inlet to the reactor Literature Cited Astarita, G., "Mass Transfer with Chemical Reaction," Elsevier, Amsterdam, 1967. Bashkirov, A. N., eta/.. Neffekhymia. 1, 527 (1961). Burguieu, J. C., Doctoral Dissertation, Lyon, France, 1972. Busson. C.. dissertation for the Conservatoire National des Arts et MBtiers, Paris, 1966. Calderbank, P. H., Chern. Eng., 45, 209 (1967). Danckwerts, P. V., "Gas-Liquid Reactions," McGraw-Hill, New York, N. Y. ., 1970 .- -. Emanuel, N. M., et a/., "Liquid Phase Oxidation of Hydrocarbons," Plenum Press, New York, N. Y . , 1967. Emanuel, N. M., et ai.. "The Oxidation of Hydrocarbons in the Liquid Phase," Pergamon, Oxford, 1965. Hikita, H., Asai, S., Int. Chem. Eng., 4, 332 (1964). Hildebrand, J. H., Scott, R. L., "The Solubility of Nonelectrolytes," Dover Publications, New York, N. Y., 1950. Inoue, H.. Kobayashi, I . , iVth Europ. Symp. Chern. React. Eng.. Brussels (1968). Prausnitz, J. M.,A/ChEJ., 7, 682 (1961). Reich, L., Stivala, S. S., "Autoxidation of Hydrocarbons and Polyolefins," Marcel Dekker Inc., New York, N. Y., 1969. Rosenbrock. H. H.. Storey, C., ComputerJ., 3, 175 (1960). Rushton, J. H., e t a / . , Chern. Eng. Progr., 46, 467 (1950). Seree de Roch, I., lnstitut Francais du Petrole, Report No. 12, 347 (1965). Spielman, M.,AIChEJ.. 10,497 (1964). Steeman, J. W. M., et ai.. Chem Eng. Sci.. 14, 39 (1960). Van de Vusse, J. G., Chern. Eng. Sci.. 21,631 (1966). Wilke, C. R . , Chang, P., AIChEJ., 1, 264 (1955).
Received for reuieu: J a n u a r y 2 , 1974 Accepted J u n e 11, 1974 Presented a t t h e 3rd I n t e r n a t i o n a l S y m p o s i u m o n C h e m i c a l R e a c t i o n Engineering, Evanston, Ill., Aug 27-29, 1974. O t h e r p a pers presented a t t h e s y m p o s i u m h a v e been p u b l i s h e d in a book entitled, " C h e m i c a l R e a c t i o n Engineering. 11," n o w available as "Advances in C h e m i s t r y Series No. 133."
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