Mass-Transfer Rate-limitation Effects in liquid-Phase Oxidation Charles C. Hobbs,’ Ernest H. Drew, Hendrik A. Van’t Hof, Frank G. Mesich, and Michael J. Onore Celanese Chemical Co. Technical Center, P.O. Box 9077, Corpus Christi, T X 78408
The liquid-phase oxidation of organic compounds with air or oxygen as the oxidant is a complex process. The intricate mechanisms are further complicated by the mass-transfer processes involved in the movement of oxygen from the gas phase to the zone of reaction as well as by the transfer of volatile components from the liquid to the gas phase. When oxygen transfer becomes the rate-limiting step, the rate of the overall process is no longer controlled by the chemical mechanisms. Furthermore, it is possible under these conditions for the chemical mechanisms to be significantly altered by the phenomenon of oxygen starvation in the liquid. This complex interplay of physical and chemical parameters has led to much confusion in the interpretation of oxidation mechanisms. Our work indicates that these effects are separable in principle, and the relative contributions are subject to a t least crude quantitative approximation. This resolution has led to rational explanations for some rather puzzling observations. It is fairly well accepted that when the concentration of oxygen in a solution exceeds that in equilibrium with a partial pressure of oxygen of about 10-100 mm of Hg, the rates of many free-radical chain oxidations in such a solvent are essentially independent of the partial pressure (or concentration) of oxygen (Lundberg, 1961). The chain-propagation steps of many oxidations can be represented by the equations:
As the partial pressure of oxygen in the bubbles decreases, a point is reached where Reaction 1 becomes the rate-limiting chemical step. This step is in series with the mass-transfer process which becomes rate controlling. The rate will now be first order with respect to oxygen concentration. If we postulate that the oxygen mass-transfer rate per unit interfacial area is proportional to the concentration gradient of oxygen across the bubble interface, then: (3) where
- dOz _ dt
k A Po2B
- rate of consumption of oxygen =
- dPozB at
proportionality constant interfacial area = partial pressure of oxygen in bubble (assumed to be effectively backmixed) POzEauil= partial pressure of oxygen in equilibrium with the oxygen concentration in solution near the bubble interface Under mass-transfer rate-limited conditions, is negligible. Equation 3 can be rewritten: = =
--do’ = kAPozB dt
(4)
Consider an individual bubble rising through solution.
If it remains constant in size (a reasonable approximation for air, which contains -80% Nz), it will have a constant The value of kl is usually much higher than kz (Walling, 1969), so that above some minimal oxygen concentration, the R. radicals are effectively scavenged. Under these conditions, Reaction 2 (or some other step in cases where a simple peroxide chain may not apply) (Kalling, 1969) becomes rate limiting. Thus, over some range the reaction rate (particularly the rate of consumption of oxygen) is independent of the partial pressure of oxygen in the bubble and the related concentration of oxygen in solution. We may speak of such a system as being “chemically rate limited.” I n such a chemically rate-limited system, the observed overall apparent energy of activation is frequently in the range of 20-30 kcal/mol (Walling, 1969). The roles of the individual contributors to this overall value are complex and perhaps not well understood. It is sufficient for the present purpose t o note that the value is high enough to distinguish the chemical process from most physical processes, which typically have energies of activation of about 3-5 kcal. To whom correspondence should be addressed. 220 Ind. Eng. Chem. Prod. Res. Develop., Vol. 1 1 , No. 2, 1972
rate of rise or dh -= dt
c
(5)
where rate of rise of bubble through the height of the liquid column C = a constant determined by viscosity, density, bubble size Further, if the bubble size remains constant, interfacial area ( A in Equation 4) will remain constant. If we divide Equation 4 by Equation 5, then
dhldt
=
where K = lumped constant characteristic of the system. Integrating over the limits
(7)
where
POphl= partial pressure of O2in the bubble at height hl Po:’ = partial pressure of 0 2 in the bubble at height h2 PO hl In 2 = K(h2 - hl) PO,”‘
Equation 6 is analogous to a first-order kinetic equation in which time has been replaced by height (h). There will, therefore, be a characteristic “half-height” (h1l2)over which the partial pressure of oxygen in the bubble will fall to half its initial value. From Equation 8: In 2 hi/%= K So far we have been considering individual bubbles only. As long as the air-feed rate per unit cross-sectional area of liquid column (or superficial bubble velocity) is low enough (Llitchell and Baxley, 1968), individual bubbles will have little effect on one another and will behave essentially independently. Each bubble should have its own half-height. The swarm of bubbles characteristic of a specific sparger under specific conditions will have a n average effective half-height. The lumped constant for this case a i l l also be a function of sparger performance. R h e n bubble density does become sufficiently great (high superficial bubble velocity), bubble coalescence and/or interference will result in greater halfheights which a i l l no longer be independent of height. These simple concepts will suffice to develop a workable qualitative and even semiquantitative concept of the effect of mass-transfer rate limitations on many liquid-phase oxidations. One must, of course, remain aware that quantitative variations will occur which are not adequately accounted for in this simple scheme. For illustration, consider the liquid-phase oxidation of methylethylketone (MEK) in acetic acid solvent (apparatus shown in Figure 1). I n this and several other systems, we have observed what was a t first a puzzling phenomenon. The rate of uptake of oxygen b y the system appeared to be almost independent of temperature under a given set of conditions. Figure 2 shows the observed response for a particular case. I n other oxidations we have observed another strange pattern of response which was not a t first realized to be related to the first phenomenon. T h a t is, in some oxidations, as temperature was lowered and oxygen concentration in the vent began to rise (air was the oxidizing agent), a critical set of conditions was reached under which the reaction became unstable. If the oxygen concentration in the vent rose above a value characteristic of this critical set of conditions (and the temperature dropped below its characteristic value), the reaction would quickly die. Usually, it could not be restored unless the start-up procedure was reinstituted. This involved heating to a temperature significantly above the “critical” temperature. As the reaction started, the oxygen concentration in the vent became low. Temperature could then be gradually reduced toward the critical value. We have found no straightforlvvard discussion of these phenomena in the literature although related observations have been apparently made. One sometimes finds, for exampl?, statements such as “in some instances oxygen en-
u
Recycle
Pump
Product
M
Figure
1 . MEK oxidation apparatus
4.0
3.0
-
iII
Mole Percent 02 in Vent G a s
0
2.0
02 Consumption Rote,
/ o
I
0
1.0
0
yo-
Mole
Percent
CO in Vent G a s
n 110
125 Temperature,
140
I55
C
Figure 2. Effect of temperature on reaction rate and ventgas composition in MEK oxidation Reaction conditions: pressure, 80 psig; liquid volume, 5 3 0 ml; rousing factor, 1.1 ; liquid-column height, 51 cm; reactor i.d., 1.5 in.; air rote, 2.3 I. (STP)/min; catalyst, 1 0 0 0 p p m Co ion (as acetate); solvent, acetic acid; MEK concentration, 5-7 w t %; liquid-recycle rate, 1.5 I./min
hances the rate of reaction while in others it inhibits the rate” (Pringle and Barona, 1970). I n seeking a n explanation for these results, we performed several series of experiments on the oxidation of N E K in acetic acid solvent with cobaltous acetate as a catalyst. I n one series we would establish a vigorous oxidation of RlEK at an elevated temperature. The concentration of oxygen in Ind. Eng. Chem. Prod. Res. Develop., Vol. 1 1 , No. 2, 1 9 7 2
221
=
f
,,
0 90%
0
0 0
IOOOC
4
A 85T
I
1
I
I
5
IO
15
20
P e r c e n t Oxygen in Vent G a s
Figure 5. Oxygen consumption rates as function of oxygen partial pressure
75
IO0
Temperature,
125
C
Figure 3. Effect of temperature on oxygen concentration in vent gas
Air Rate Liquid n-‘i.i ters (ST Pl/mn Column Height, c m .
,n @ 0
A A 0
5.4 5.4 5.4 5.4 4.5 3. I 1.8
25 38 46 71 71 71 71 1
I
2.5
2.7 I/T
X IO3
A 2.9 ( O K 1
Figure 4. Arrhenius plot of oxygen consumption rates
the vent gas would be low. We would then lower the temperature in small increments and observe the response of the oxygen concentration in the vent gas. Similar runs were made a t a variety of air-feed rates. The results are plotted in Figure 3. I n each case, the concentration of oxygen in the vent gas increases slowly a t first as the temperature is reduced. Finally, a point is reached when the oxygen in the vent gas 222 Ind. Eng. Chem. Prod. Res. Develop., Vol. 1 1 , No. 2, 1972
rises rapidly as the temperature is further reduced. The temperature a t which this change becomes evident increases as the air-feed rate is increased. Figure 3 contains a wealth of information which can be made more evident in several ways. I n Figure 4 the data are shown in a typical Arrhenius plot. The oxygen consumption rate used for the ordinate was calculated from a knowledge of the liquid volume (allowing for rousing: rousing factor is defined as roused volume/quiescent volume), the air-feed rate, the vent-gas rate, and the concentration of oxygen in the vent gas. All the curves have a common portion with a steep slope. Each curve exhibits a low slope portion; the point a t which the transition occurs is a function of the airfeed rate. The high slope portion of the curve corresponds to an apparent energy of activation of -25 kcal/mol. This fits the previous discussion about the chemically rate-limited zone and offers a n explanation for the instability of a liquid-phase oxidation system which is observed a t the time the concentration of oxj’gen in the vent gas increases beyond some critical value. I n a system operating entirely in the chemically ratelimited zone, any minor upset which causes a small lowering of the temperature would cause a relatively large decrease in the reaction rate and thus a decrease in the heat-evolution rate. This mould cause a further decrease in temperature, especially in large systems, and the effect would “snowball.” We did have some difficulty maintaining the stability of our small reactor. R e could operate in the chemically ratelimited region with fair success, however, because heat losses were so high in the unit that the heat of reaction was a relatively small part of the total heat flux. The data in Figure 3 can be plotted in other ways to give further insight into the system. If we take a vertical isotherm a t a given temperature, a knowledge of the air-feed rate, the concentration of oxygen in the vent gas, and the liquid volume will enable us to calculate the specific reaction rate in terms of moles of oxygen consumed per liter of solvent per unit time. Such a plot is presented in Figure 5 . Within experimental error the reaction rate is independent of oxygen partial pressure in the bubble in the region described above as the “chemically rate-limited zone.” This is in accord with the previous discussion. The rate does, of course, vary with temperature. As mass-transfer rate limitation becomes important, the rate a t a given temperature will fall. We should note that in a self-sustaining liquid-phase oxida-
tion system, the rate can be a complicated function of composition, particularly when products as well as feed are oxidizing (Walling, 1969). The runs being discussed were made with 25y0MEK in acetic acid solvent (1000 ppm cobalt catalyst) a t low conversion of the MEK ( ~ 5 - 1 0 % ) in an attempt to minimize this problem. An alternate way of illustrating the above conclusion can be developed from the plots in Figure 6. Here, approximations of the ratio of the concentration of oxygen in the bubble ( P o 2 B ) a t various heights above the sparger to the concentration of oxygen in the feed gas ( P o , F ) are plotted at several air rates. These approximations were made b y measuring the concentration of oxygen in the vent gas a t various liquid levels. Other conditions were kept as nearly constant as possible. We must at this point emphasize that the reported measurements lack a high degree of precision. One significant complication is that there is apparently some relatively ineffective zone above t h e sparger (a single hole capillary in this case) in n-hich the bubbles are forming from the cone of highvelocity gas issuing into the liquid. We have neglected this zone and assumed that the bubbles become effective a t a distance above the sparger corresponding to the visual disappearance of the cone. There is no obvious way to eliminate subjective bias from this estimate. We have, however, used the same value (7.5 cm) for all cases. This value was not visibly affected b y flow rate over the ranges studied. This is believed to be a maximum value. If i t were decreased by a factor of 2, the critical values discussed below would be changed about 15y0 or less. If the specific rate of consuniption of oxygen in the chemically rate-limited zone is constant as indicated above, then the slope of a line from the initial point (7.5 cm above sparger) t o t h e first reliably measurable point (minimum stably operable liquid height), together with the air rate for that particular experiment, will permit the calculation of a minimum specific rate for that set of conditions. A t constant temperature, such rates should be independent of air rate and oxygen concentration in the gas (but will, of course, vary with temperature). This is not to say that the overall rates for the total reactor will be constant. Results from such calculations are shown in Table I. Kote that the predicted constancy is observed well within a factor of 2. I n view of the large measurement errors, this must be regarded as satisfactory. There is no reason to expect such constancy if the specific reaction rate in the zone is a function of oxygen concentration. You will note in Figure 6 that the line for the 7.8 l./min flow rate has not been drawn through the “first measurable
Table 1.
.oo
I
I
I
I
Air Rote, Liters (STPVmin. 0
3.6
A
5.2 7.0 0.7
0 0
25
0
Liquid
50
100
75
C o l u m n Height,
cm
Figure 6. Determination of minimum rates in chemically ratelimited zones
point.” This arbitrary action was taken because the system was highly unstable during this run (low liquid level, high air rate), and the resulting point is not believed to represent steady-state conditions. A simple examination of the other curves indicates that the line shown is much more likely. If, however, one does draw the line through the questionable first point, the slope is changed from 0.0246 to 0.0420 (Table I). This gives a value for the oxygen consumption rate of 11.9 mol/l./hr (vs. 7.0). One could certainly argue that this detracts somewhat from the strength of the conclusions based on this particular graph, but this is only one of several independent indications summarized in the next paragraph. We have presented several observations to support the idea that the initial zone in a liquid-phase oxidation may be chemically rate limited, that the rate in such a zone is independent of oxygen concentration in the liquid and oxygen partial pressure in the bubble, and that the overall effective energy of activation in such a zone is on the order of 25 kcal/mol. Although none of the individual observations can be regarded as conclusive, the sum of them seems impressive. The next question to resolve is whether there is any evidence for the postulated first-order response of the specific reaction rate with respect to oxygen partial pressure in the mass-
Determination of Specific Oxygen Consumption Rate ‘in MEK Oxidation
Temp, 130°C R u n no. 1 2 3.63 5.22 (1) Air rate, 1. (STP)/min (2) Slope from Figure 6, fract,ional oxygen consumption/cm 0.0406 0.0406 (3) Rousing factor. 1.10 1.17 (4) Vol, l./cm 0.02027 0.02027 Mol O2 consumed/l./hr, (1) X 60 X 0.2095 X (2) X (3) 4.5 6.9 22.413 X (4) a Data courtesy A . L. Baxley, Celanese Chemical Co. Technical Center.
3 7.80
4 8.69
5 9.63
0.0246 1.32 0.02027
0.0179 1.37 0.02027
0.0141 1.43 0.02027
7.0
5.9
5.4
Ind. Eng. Chem. Prod. Res. Develop., Vol. 1 1 , No. 2, 1972
223
E 0
100-
0
9.6 8.7
A
7.0
i
r
.-0, W
I c
-f 0
0
-
50-
0
.-0. J
0
0
I 0.4
I
0.8
I
I.2
I
I. 6
2.0
L o g ( 2 0 . 9 5 / % O2 in Vent)
Figure 7. Determination of “half-heights” in mass-transfer rate-limited zones
-0
0.4 0.8 1.2 Log ( 2 0 . 9 5 / % O p in V e n t )
1.6
2.0
Figure 8. Comparison of theoretical zero-order oxygen response to actual response in MEK oxidation Air r a t e = 5.2 I. (STP)/min, temperature = 1 3OoC. Zero-order o x y g e n consumption r a t e is 6.9 mol OQ/l./hr. Theoretical curve approaches 3 2 cm asymptotically
transfer rate-limited zone. Evidence for this can be obtained by consideration of Equation 8. I n the mass-transfer ratelimited zone, a plot of the log of the ratio of oxygen concentration in the gas feed to the concentration in the gas a t a particular height vs. the height should be a straight line. 4 s shown in Equation 10, the slope of this line is inversely related to the half-height. The plot would not, of course, give a straight line for the chemically rate-limited zone. I n this case, the rate of rise of the plot would continually decrease. If zero-order conditions could be maintained until all of the oxygen is consumed (an apparent impossibility), the zero-order plot would approach the height of complete oxygen consumption in an asymptotic manner. Figure 7 shows several typical plots a t a variety of air rates. In general, the plots in the lower height zones show the expected zero-order deviation from a straight line. At the higher column heights, however, all the curves turn upward and can be represented (within experimental error) by a family of parallel lines. The theoretical zero-order response is compared with the actual response in a particular case in Figure 8. From these data, there is a t least a strong indication that after an initial zero-order relationship, a transition to something approaching a first-order relationship occurs. 224
Ind. Eng. Chem. Prod. Res. Develop., Vol. 1 1 , No. 2 , 1972
Assuming the approximate validity of this simple picture, we are now in a position to understand how low apparent energies of activation may be observed. I n Figure 2 and in portions of the curves presented in Figure 4, the apparent energy of activation appears to be less than 1 kcal/mol (actually negative in Figure 2). On first thought, one i s tempted to believe that this is because the system is severely mass-transfer rate limited. However, one would expect that a completely mass-transfer rate-limited system should show some apparent energy of activation energy, perhaps 3-5 kcal/mol. Unknown changes in solvent composition might obscure the measurement of such small values, but in a severely mass-transfer rate-limited system, one would also expect to see corresponding chemical changes, particularly increased production of carbon monoxide. As shown in Figure 2, the onset of high carbon monoxide production does not correspond to the low apparent energy of activation condition. Another possibility is that both chemically rate-limited and mass-transfer rate-limited zones are present in the systems which exhibit low apparent energy of activation and that the low value may be the result of the interrelationships of the zones. One is tempted to dismiss this concept out of hand since i t seems intuitively probable that the two zones would interact to give an overall apparent energy of activation intermediate between the ones characteristic of the individual zones. A little further consideration of this point, however, leads to some interesting insights. I n Figure 9, an idealized theoretical plot of the expected relationships in a mixed zone system is presented. The ratio of the concentration of oxygen in the vent gas to the concentration in the feed gas vs. the height of the liquid column is plotted. The straight line from Po?B/Po,F = 1.0 at zero height to Po9B/Po2F= 0 a t 18 cm represents the expected behavior in the chemically rate-limited zone (zero-order oxygen dependence) a t 125OC (arbitrary) if the zone could exist to the point where oxygen is completely consumed. This does not happen of course. At some point, in this case say P o ~ ~ / P ~ ~ a = o-0.3,
1.00
0.75
\
N
L O
q 0N. 5 0
mo
a 0.25
0
0
25
50
75
L i q u i d C o l u m n Height,
cm.
Figure 9. Theoretical dependence of oxygen concentration in bubble on liquid-column height in mixed-zone system at two temperatures
transition to a mass-transfer rate-limited zone will occur. On the assumption that the transition zone is negligible and that the mass-transfer rate-limited zone exhibits a “halfheight” of 25 cm (a typical value), the curve shown should be obtained. The value of Po2B/Po2Ffalls to half its original value for each 25-cm increase in liquid column height. h t this point we should note t h a t the transition zone is probably not negligible in a real syst’em.The assumption of negligibility will introduce some quantitative error in our interpretation but should not seriously impair the qualitative picture. S o w consider what would occur if the system temperature is increased 10°C. The reaction rate in the chemically ratelimited zone (energy of activation = 25 kcal/mol) would be increased by a factor of 2.17. The zero-order zone would now be represented by the dashed straight line. The transition to mass-transfer rate limitation would no longer occur a t Po2B/Po,F = 0.3, however. The chemically rate-limited zone would now be demanding oxygen a t 2.17 times the original rate, but the mass-transfer mechanism (energy of activation = -5 kcal/mol) could supply i t a t only 1.17 times the original rate. The transition to the mass-transfer rate-limited zone should therefore occur a t Po,B/Po2F = 0.3 X 2.17/1.17 = 0.56. The half-height characteristic of this zone will be 25 c m / l . l i = -21.4 cm. The two curves will cross somewhere between 60 arid 75-cm column height’. In the above instance, if the reactor column height happened to be between 50 and 100 cm (a convenient range), the overall apparent energy of activation would be extremely small. One might even be led to conclude that nothing much happened when the temperature was raised, when in reality profound changes occurred. Additional support for these concepts is available in Figure 2. h’ote that as the temperature continues to rise, a point is a t last reached (>-145OC) where the reaction rate does seem to increase (a crude value of the energy of activation is about 5 kcal/mol). At this point i t was observed that the green-colored zone in the reactor (related to the presence of higher valence cobaltic catalyst ions) had shrunk to the immediate neighborhood of the sparger, the concentration of carbon monoxide in the vent gas increased suddenly and significantly, and the presence of one-carbon compounds (methanol and formic acid) in the liquid product increased sharply. These observations are consistent with the decarbonylation of acetyl radicals taking place in an oxygenstarved system. 0
/I
CHa-C-00. 0
CHeCOOH
o z f
4
101 CHBOH3 HCOOH Formic acid, once formed, is less readily oxidized in such a system because of the relative scarcity of cobaltic ions: CO+ 3
HCOOH +H20 [OI
+ COn
Conclusions
The general picture emerges of two zones interacting in most liquid-phase autosidations using air. I n one of these zones the overall rate is limited by the chemical reactions;
this zone exhibits a n energy of activation of about 25 kcal/ mol. In the other zone the overall rate is limited by the masstransfer rate of oxygen into the liquid; this zone exhibits a n energy of activation of about 5 kcal/mol. Mrhen the two zones coexist, their interrelations are such that the overall energy of activation is usually near zero. Although minor temperature fluctuations will cause the relative volumes of these zones to change, the overall reaction rate and total heat-release rate will vary little. .!my tendency of a temperature drop to induce a further temperature drop is severely attenuated. Such systems are, therefore, quite stable. If the chemically rate-limited zone expands to fill the reactor, the system will be unstable. This comes about because any temperature drop will cause a decrease in overall reaction rate and, thus, in the rate of overall heat release. This will induce a further temperature drop. The effect will build, especially in large systems where the temperature is a rather direct function of the heat-evolution rate. The reaction usually stops abruptly. K i t h some care small systems, where the heat release from the reaction is a relatively small part of the total heat flux, can be maintained in the chemically rate-limited zone. Even so, such systems are much less stable than when the two zones are present simultaneously. It is desirable, therefore, to have a mass-transfer ratelimited zone present in liquid-phase oxidations to insure stability. Since oxygen starvation and consequent lowered efficiencies can occur in such zones, it is also desirable t h a t the mass-transfer rate-limited zone be relatively small. The concepts discussed can be usefully employed in the investigation of a variety of liquid-phase-oxidation reactions. Once one has obtained a series of curves such as those in Figure 4, for example, it is a simple matter to predict the maximum potential rate of a n oxidation a t that particular solvent composition as pressure is increased. By observing the points a t which the various curves depart from the chemically rate-limited curve, one can make at least a rough estimate of the pressure required to approach a chemically rate-limited system under various conditions. One may approach pressure requirements in another way. At a given temperature, one may determine the partial pressure of oxygen in the vent required to obtain the desired rate with the desired stability and chemical efficiency. The total pressure required is then determined by the allowable concentration of oxygen in the vent gas. This technique also gives a utilitarian approach to determining the relative mass-transfer resistances of various solvents. One might compare, for instance, half-heights in the mass-transfer rate-limited zones by use of a standard air-dispersion system. Sufficient refinement of the method could perhaps even yield absolute values. Real chemical rates of liquid-phase-oxidation systems can also be compared by determining rates in the chemically rate-limited regions only. Our experience indicates that both chemical rates and oxygen mass-transfer capabilities of solvents vary over quite broad ranges. literature Cited
Lundberg, W. O., “Autoxidation and Antioxidants,” 5’01 I, Riley, New York, XY, 1961, pp 66, 110. lIitchel1, T., Baxley, 4. L., Celanese Chemical Co. Technical Center, Corpus Christi, TX, private communication, 1968. Process.. 159-75 Prinde. H. W.. Barona. X.., Hudrocarbon ” (Tovember 1970). Walling, C., J . Amer. Chem. Sac., 91, 7590-4 (1969). I
Presented at the Division of Petroleum Chemistry, 162nd Meeting, ACS, Washington, DC, September 1971. Ind. Eng. Chem. Prod. Res. Develop,, Vol. 11, No. 2, 1972
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