I
F.
DeMARIA, J. E. LONGFIELD, and G. BUTLER
Engineering Research Section, Central Research Division, American Cyanamid Co., Stamford, Conn.
Catalytic Reactor Reaction kinetics and a gas flow model are combined to give a method for scale-up of fluid bed data for the oxidation of naphthalene to phthaJic anhydride
T H E CATALYTIC OXIDATION of naphthalene to phthalic anhydride represents one of the larger applications of oxidation as a unit process. Traditionally, phthalic anhydride has been manufactured by the catalytic oxidation of naphthalene in fixed bed reactors using a supported vanadium oxide catalyst. However, fixed bed reactors have certain unavoidable deficiencies. Tube diameters must be kept small in order to avoid excessive radial temperature gradients, and the charging of catalyst can be an exacting and tedious task. Feed concentrations of naphthalene in air must normally be maintained below about 1 mole yo in order to avoid an excessive exotherm leading to low yields of phthalic anhydride and excessively rapid catalyst deterioration. Efficient heat recovery from fixed bed reactors is difficult and frequently not achieved. The advent of the fluidized bed technique for carrying out catalytic reactions has offered a solution to several of these problems, but has raised others peculiar to fluidized bed processing. Catalyst charging problems are eliminated; temperatures within the bed are very uniform and heat transfer coefficients are such as to permit efficient recovery of the heat of reaction. Because of these advantages, several phthalic anhydride producers-in U.S.A. and England-are currently using the fluid bed process. However, problems associated with the scale-up of the fluid process are much greater than with fixed beds. These problems arise largely from the fact that the gases flowing through a fluid bed do not proceed in plug flow from the inlet to the outlet, but rather undergo varying degrees of backmixing and/or bypassing. As a result, the gases leaving the fluid bed have a broad distribution of residence times rather than a single residence time. T o predict the effects of scale-up in such a system, one must have a de-‘
scription of the gas flow patterns within the fluid beds and their changes with scale-up; know the kinetics of the pertinent chemical reactions; and be able to combine these two pieces of information to yield a description of the overall reactor performance. The substance of this paper will be a consideration of the latter two of these steps. First, the state of our knowledge concerning the kinetics of the principal reactions involved in naphthalene oxidation will be reviewed. Based on this review, a simplified scheme for the reaction system has been adopted. This kinetic scheme is combined with the eddy diffusivity model for gas mixing in fluid beds to show the types of interactions which may occur among the reactor design characteristics. For maximum phthalic anhydride yield and virtual elimination of naphthalene and naphthoquinone in the product, the unit should be operated a t temperatures slightly above the optimum and, depending upon the details of reactor design and oxidation kinetics, possibly with some intermediate feed injection point above the bottom of the bed. Kinetics Most workers who have studied the catalytic oxidation of naphthalene agree that the principal reactions to be considered are those indicated below (3, 4). k/
Naphti~:“”:
Naphthalene Phthajlc Anhydride
/
Maleic Anhydride,
C0,COe
The recent work of Shelsrad, Downie, and Graydon (72) indicates that, for 1,2 naphthoquinone completeness, should be shown as an intermediate in reaction 2. However, its rate of oxidation to phthalic anhydride is very rapid and for design purposes it may safely be neglected. I n order to make this kinetic scheme more tractable for use in reactor design considerations, the reaction sequence outlined above has been simplified somewhat and kinetics have been assigned to the important reactions. I n this analysis, the authors have drawn primarily on the results reported by Mars and van Krevelen (9),Calderbank ( Z ) , Ioffe and Sherman (7), and
-
Shelstad, Downie, and Graydon (72), along with data obtained in the authors’ laboratories. All of these workers used catalysts of more or less similar composition-namely, VZOSand K & 0 7 or K2S04 supported on SiOz. Naphthalene Disappearance One may consider first the kinetics of naphthalene disappearance, that is, the sum of reaction 1, 2, and 5 without asking as to their relative rates. The situation is best summarized by the data of Mars and van Krevelen ( 9 ) showing the effect of naphthalene and oxygen concentrations on the rate of naphthalene oxidation. They observed that a t naphthalene partial pressures below about 4 mm. of Hg the rate is roughly first order in naphthalene concentration, while a t partial pressures greater than about 8 mm. of Hg, it is almost independent of naphthalene concentration. The data of Calderbank (2) in the range of naphthalene concentrations from 15 to 76 mm. of H g and those of Ioffe and Sherman (7) in the range of 5 to 11 mm. of Hg tend to support these observations. The results reported by Shelstad, Downie, and Grandon (72) show a similar trend but the transition to nearly zero order kinetics appeared to occur a t a somewhat lower naphthalene level. In the region of oxygen partial pressures below 300 to 400 mm. of Hg, the rate was found to vary almost linearly with 0 2 concentration. This observation is also supported by the data of Calderbank and of Ioffe and Sherman. Relative Rates of Reactions Information as to the relative rates of reactions 1, 2, and 5-i.e., the oxidation to naphthoquinone, phthalic anhydride, and C O CO2-may be obtained by measuring the yields of the various products a t low conversion levels. Figure 1 shows the yields of 1,4-naphthoquinone and phthalic anhydride as a function of total naphthalene conversion. Both curves are seen to extrapolate to about 50yo a t zero total conversion indicating that in the initial attack, about 50y0 of the naphthalene goes to naphthoquinone and 50% to phthalic anhydride with little or no complete combustion to C O and COz. Calderbank reported that during the initial stages of the oxidation approx-
+
VOL. 53,
NO.
4
APRIL 1961
259
Y
1
l
i
64
4
2 1 s o
0
->
_I
I
10
I
20
I
I
30
40
,
50
,
60
I
70
I 80
90
TOTAL NAPMHALENE CONVERSION (MOLE % )
Figure 1 . Yields of naphthoquinone and phthalic anhydride are compared as a function of total naphthalene conversion s ’
3 Figure 2. Conversion to naphthoquinone decreased as temperature and contact time increased
imately 65% of the naphthalene oxidized is converted to 1,4-naphthoquinone, the remainder going directly to phthalic anhydride. He found little or no direct oxidation to CO and COz. The initial split between naphthoquinone and phthalic anhydride was independent of the naphthalene and oxygen concentrations, indicating that both reactions had the same kinetics. Ioffe and Sherman reported that the initial attack on naphthalene yielded about 40y0 naphthoquinone and 6070 phthalic anhydride, with little or no direct oxidation to CO and COz.
%=
c,
ka
+
kl kg
-
2k1
In deriving Equation 1, the effect on the rate of the changes in the oxygen concentration through the catalyst bed has been neglected. The significance of this fact will he considered later. Using the values of k l determined from the rate of naphthalcne disappearance, one may find by trial and error, values of k3 kg which when substituted in Equation 1 yield plots of C,/C.$ us. t which best fit one’s experimental data. This procedure has been followed for the current data with the results shown in Figurc 2. The solid lines are calculated on the basis of Equation l for ks; the points selected values of k3 are experimental. For most of the points the agreement is seen to be fair11 goodperhaps lending some support to the use of Equation 1 with the implicit assumption that quinone oxidation is a first order reaction. In considering the oxidation of naphthoquinone. one must also ask as to the relative rates of reactions 3 and 6i.e., the reactions to phthalic anhydride COz, respectively. By and to CO direct measurements of the oxidation of naphthoquinone, Ioffe and Sherman obtained yields of phthalic anhydride of 50 to 7070, with 30 to 50% of the naphthoquinone reacted going to COz. However. a portion of the C O Zmay have come from the secondary oxidation of phthalic anhydride. The authors’ results indicate relatively little direct oxidation of either naphthalene or naphthoquinone to COz. Consider again the curves in Figure 2 in which mole fraction of naphthalene COz is plotted converted to CO
+
The Oxidation of Naphthoquinone-Reactions 3 and 6 Much less has been published on the kinetics of naphthoquinone oxidation than on naphthalene oxidation. The only data from which direct conclusions can be drawn are those of Mars and van Krevelen (9). They indicate that at naphthoquinone partial pressures belolv 1 to 2 mm. the rate of naphthoquinone oxidation varies directly with its partial pressure while at higher partial pressures, the rate is somewhat less dependent on naphthoquinone concentration. Less direct evidence may be obtained by following the changes in naphthoquinone concentration with contact time during the oxidation of naphthalene. The data presented so far indicate that the principal reactions involved in the formation and oxidation of naphthoquinone are as follows : 2 7 Phthalic Anhydride Naphthalene 1 Naphthoquinone -+ 3 + 6
Products
If one assumes that reactions 1, 2, 3, and 6 are all first order with respect to the organic reactant, and further that kl = kz as indicated by the data of Booth and Fugate, then the fraction of
260
the initial naphthalene converted to quinone at any time, t is, given by
INDUSTRIAL AND ENGINEERING CHEMISTRY
+
4[
t .
o
h
b
I
1 ’ 2 ’ CONTACT TI
along with the naphthoquinone data. Total conversions to C O ? are seen to be small and practically constant from 9 seconds to 15 seconds even though the total naphthalene conversions and conversions to phthalic anhydride increased considerably during this rime interval. These data indicate that relatively little CO and COZ are formed by parallel reactions during the oxidation of naphthalene and naphthoquinone to phthalic anhydride but that most of that which is formed results from the oxidation of phthalic anhydride.
The Oxidation of Phthalic An hydride
W . T . Booth and Fugate, in the authors’ laboratories, studied the effect of initial oxygen concentrations over the range 10 to 20 mole 70on the initial rate of phthalic anhydride oxidation. Their data are summarized in Figure 3 in which log (initial rate) is plotted os. log (initial 0 2 concentration) for the three temperatures studied. All three lines have very nearly the same slope and indicate
+
+
I
I
-1 7
15
/I
LOG
I
02
2 13 30hCEhTQAT10N-MO-iFT3
14
1
Figure 3. Oxygen concentration affects the initial rate of phthalic anhydride oxidation uniformly
CATALYTIC REACTOR D E S I G N that the rate varies with approximately the 0.8 power of the oxygen concentration. Unfortunately, only integral conversion curves are available from which to draw conclusions concerning the kinetics with respect to phthalic anhydride. Since the order with respect to oxygen was not far from first, the available data have been fitted to the integrated form for a second order reaction.
Table I.
Kinetics of Phthalic Anhydride Oxidation
Time, Sec.
PCP, G. Mole/Ft.a
4 9 15
0.0038 0.0017 0.0009
4
0.0045 0.0026 0.0019
ha,
PCozr
Cu. Ft./G. Mole, Sec.
G. Mole/Ft.3 Temperature = 400' C.
0.80 1.32 1.27
0.106 0.091 0.084
Temperature = 385' C. 9
15
0.54 0.80 0.71
0.112 0.098 0.092
Temperature = 375' C.
or, assuming constant pressure throughout the bed
By assuming that complete oxidation occurs, one may write the oxygen concentration in terms of the phthalic anhydride concentration and thus obtain by integration
The values of kd calculated in this manner are listed in Table I. The rate constants calculated from the data a t 9 and 15 seconds contact times are in reasonable agreement. Those calculated from the 4-second data are substantially lower, perhaps indicating a kinetic order less than one at the higher phthalic anhydride concentrations.
Summary of Kinetics A summary of the kinetics of the major reactions in naphthalene oxidation is presented in Table 11. Reactions 1 and 2, the direct oxidation of naphthalene to naphthoquinone and phthalic anhydride, respectively, appear to be of about equal rate. The rates of both seem to depend on the naphthalene cnncentration to an order intermediate between 1.0 and 0.5 or even lower depending upon the concentration level and on the oxygen partial pressure to roughly, the first power. There appears to be very little direct oxidation of naphthalene to CO and COZ; in other words, ks is small relative to kl and kz and for the purpose of further considerations here it will be neglected. What little evidence is available indicates that, at least in the region of low naphthoquinone concentrations, the oxidation of naphthoquinone to phthalic anhydride is roughly first order in naphthoquinone. Its dependence on oxygen concentration is completely unknown. The current data indicate relatively little direct oxidation of naphthoquinone to CO and C02, while those of Ioffe and Sherman would indicate somewhat more. In subsequent reactor design considerations, reaction G has been purposely neglected.
4
0.0048 0.0030 0.0025
9
15
0.114 0.100 0.096
0.37 0.64 0.52
of equations shown above for reactor design purposes-namely, that the oxygen concentration is constant during the course of the reaction. T h a t the oxygen concentration dependence is the same in all three rate expressions does not completely validate this approximation, since the oxygen concentration may be lower near the exit of the reactor where reaction 4 predominates than near the Naphthoquinone inlet where reactions 1 and 2 predominate. I t may be instructive then to consider the magnitude of the apNaphthalene proximation. Consider the case in which one is operating with a feed gas consisting of 1.O mole yo naphthalene in air, under Phthalic Anhydride + conditions leading to virtually complete 4 Maleic Anhydrid? oxidation of all naphthalene and naphco, coz thoquinone, and with 85 mole 7 0 of the feed converted to phthalic anhydride O n assuming that each of the reactions and 15 mole yo to COz. Under such involved is first order with respect to conditions, the oxygen concentration both the organic reactant and the oxygen would decrease from 21 mole % in the concentrations the following kinetic feed to 15.4 mole Yo in the product, repequations are obtained : resenting a decrease of 27yo or a variation of +1570 from the mean. Such d - dt- ( P C N )= ( k l ky)p2CivCox a variation is certainly larger than is desirable in computations of this sort, and for inlet naphthalene concentrations much greater than 1 mole 7 0 the approximation must be considered quite unacceptable. For this reason, as well ~ ~ P ' C Q C O ~~ ~ P ' C P C O as ~ that discussed in the preceding paragraph, the subsequent calculations can be considered valid only for relatively low This scheme is probably quite good for naphthalene feed concentrations. relatively low naphthalene feed conAssuming that the reaction scheme outcentrations, but not at all valid a t higher feed concentrations. lined above adequately describes the situation, and further that the approxOne further approximation is made, imation of constant oxygen concentrato permit more ready use of the system
The rate of oxidation of phthalic anhydride to CO and C O S appears to depend on roughly the first power of the phthalic anhydride concentration. The dependence on oxygen concentration seems to be slightly less than first order. Based on the foregoing analysis, one may simplify the kinetic scheme originally advanced to that shown below:
i3
+
+
Table II.
Major Reactions in the Catalytic Oxidation of Naphthalene Kinetic Order Reaction
Naphthalene + Naphthoquinone ( k ~ ) Naphthalens -+ Phthalic Anhydride ( k ~ ) Naphthoquinone +. Phthalic Anhydride (ks) Phthalic Anhydride +. MAA, CO, COz, (k4)
Organic 0.5-1.0
-1.0
0.5-1.0 -1.0 -1.0
-1.0
(or less) Naphthalene + MAA, CO, COZ, (ks) Naphthoquinone -+ MAA, CO, Con, (k6)
0 2
... ...
...
-0.8
... ...
VOL. 53, NO. 4
Relative Rate Importantk,zm Important Important Important (k4 < k l , kz, and ha) Small Small
APRIL 1961
261
tion throughout the reactor is adequate, psuedo-first order reaction rate constants for reactions 1 through 4 have been evaluated for several catalysts from conversion data obtained a t different temperatures and contact time in small 2inch diameter fluidized beds. Gas mixing measurements made under conditions similar to those used in the kinetic studies indicated that the fluid beds could neither be characterized as completely mixed reactors nor as plug flow reactors, but were perhaps closer to the latter. Accordingly, the data were interpreted on the assumption that the reactors behaved as integral convertors. The pseudo rate constants thus obtained are symbolized with capitals to distinguish them from the true constants. The values obtained for two such sets of rate constants are shown in Figure 4 as functions of temperature. For both catalysts Ks is seen to be somewhat greater than K1 and Kz. O n the other hand, K4 is substantially smaller than any of the other three rate constants. A significant difference between catalysts A and B may be noted, however, for catalyst A , K1, K z , and K3 all have considerably higher activation energies than does Ka, indicating that this catalyst might be expected to perform most satisfactorily a t high temperatures and short contact times. With catalyst B, Kd has a higher activation energy than do K1, Kz, and K3 indicating that it might perform better a t relatively longer contact times and lower temperatures. Reactor Design Considerations A demonstration is given below of the interactions which may occur among the microkinetics in a system, the gas mixing characteristics within a fluid bed, and the reactor design itself in terms of its effect on product yield and purity. In particular, the kinetic scheme for naphthalene oxidation, which has just been outlined, will be combined with the equations for the eddy diffusivity model for gas mixing within a fluid bed to obtain predictions of product yield and purity as functions of mean residence time, temperature, and the degree of gas mixing and for the two sets of reaction rate constants just presented. Initially, only the situation in which the naphthalene feed is introduced a t the reactor inlet will be consideredlater, the effects of introducing the naphthalene a t various axial levels along the length of the reactor will be studied. The back mixing of gases in a fluid bed has been investigated by various authors ( I , 5, 6, 8, 70, 7 7 , 73). The simplest method of representing the over-all gas transport is to superimpose on the bulk flow of gas an axial diffusional transport according to Fick’s law: rate of diffusional transport =
- E grad
262
pck
!lf-7 0
\
eo
Figure 4. Pseudo reaction rate constants in the catalytic oxidation of naphthalene
I 360
DO01
370
I 350
I
I 330
340
I
320
TEMPERATURE ‘C
where pC, represents concentratioa of component K in moles per unit volume. If the fluid bed is assumed to be homogeneous-that is, the solid-gas dispersion is uniform with no localized areas where only gas bubbles or dense catalyst clouds exist-a material balance about an infinitesimal fluid bed element a t steady state gives : +
div ( E grad
pCk
+
- upC~)
pl7k
= 0
(2)
Here the first term represents the mass outflow, and pI’k the rate of formation of component K per unit of time. For an actual fluidization system, the well recognized presence of gas bubbles may produce marked departure from a uniform and random dispersion of the solid within the gas. May (70), Van Demter (73), and Kaup (8) have proposed various twophase representations of fluidized systems. One model (70) considers a bubble phase proceeding at a higher velocity than the average where no back mixing occurs. Mass transfer takes place between the bubble phase and the dense phase laden with solids. The internal mixing in the second phase is described by means of an effective diffusion coefficient. Other representations are simplifications and/or variations of the above but no factual experimental observation is so far available to support one model over another. For this reason and in order to reduce the complexity of the problem, Equation 2 was assumed to give an adequate representation of a fluid bed. For an isothermal reactor having a
INDUSTRIAL AND ENGINEERING CHEMISTRY
uniform cross section, negligible pressure drop ( p = constant), and no volume i
change during reaction (u = constant), Equation 2 can be simplified : div ( E grad
pCk)
-
* u grad pck
+ pI’k = 0 (3)
The change in number of moles due to the formation of phthalic anhydride or complete oxidation of the product is negligible since the amount of carbon monoxide, dioxide, and water formed nearly balances the amount of oxygen consumed. Any small change is minimized by the large nitrogen dilution. O n making the further assumption of uniform radial concentration, Equation 3 can be reduced to a one-dimensional problem :
where x is the axial distance from the bottom of the reactor. The boundary conditions used are : uCr
-E
dCk - = UC;;x dx
0
; x = h
where C”, is the inlet concentration of the Kth component. The first condition is self evident since it is a flux balance at the inlet of the bed. The latter is less obvious, however, as there is no apparent physical reason why the concentration gradient should be zero a t the top of the bed especially for a fluidized reactor where the boundary of
CATALYTIC REACTOR DESIGN 1.0
1
\
Catalyst A gives less naphthoquinone at optimum phthalic anhydride yields
Figure 5.
Catalyst A, left;
the fluidized catalyst powder is fluctuating and rather indefinite. This boundary condition is required, however, in order to obtain a solution which will converge to the performance of a complete mixer when E tends to infinity. In fact, the second boundary condition is a mathematical requirement which excludes any feedback of component K once it has left the fluid bed. Since the extent of mixing in a fluidized bed reactor frequently approaches that of a complete mixer, the outlet boundary condition is considered applicable. The kinetic terms consistent with the previous discussion are :
rN
=
d a = - ( K ~+ dt
rQ
=
2
=
K~)cN
--K,CQ f KlCN
r p = ddCp t --
-KKlCP $. K?CN
contact time, 6 seconds
catalyst B, right;
1 0
,
,
I
I
,
f
CONTACT TIME 6SEC
13
09-
:
z3 b
3
g 08-
07-
?
E
:_---:11--:-:: 0- C A T L I S T L 0
- CbTALIST
B
06mrYP'rIc
,
WXiHr lllX0C
,ooI l ' Y i D
ccm
*(,XLO
PISIO*
i
L
,'OW
[ooB006-
Figure 6. Mixing parameter and contact time affect maxi-
8
OWsol.
oDo
* 005
010
025
050
IO
25
50
100
1 230
(5)
+ K3CQ
Therefore, the combination of the transport model with the appropriate kinetics leads to the following systems of equations: Naphthalene concentration :
E -dzCN -dx2 U
UdCN
dx
CN - E dcN dx
- (KI f K2)CN Uc:;
X
0
= 0
(6)
VOL. 53, NO. 4
0
APRIL 1961
263
I
CONTACT TIME 6 S E C
CONTACT TIME SSEC.
09
$ 1
I
I I
I
!
PECLET NO = u h l 2 E
,
1
0,
1
1
r
,
I
CONTACT TIME IBSEC
03SC
4
Y
Figure 7. Temperature and contact time show this effect on phthalic anhydride yield and purity for catalyst A, left, and catalyst 6, right
Naphthoquinone concentration : d2cQ dx2
E--
u
dC Q -
dx
- KICQ
+ KICN = 0
i
=
1, 2, 3
; x = h
Phthalic anhydride concentration :
dCp - = dx
; x = h
Solution of these three sets of differential equations gives the following expressions for the outlet concentrations:
where : hu Pe = 2E
264
The Peclet number Pe defined as the ratio of the effective diffusion time, h2/2E, to the average residence time, h/u: is a suitable dimensionless quantity expressing the extent of backmixing taking place in the system. A Peclet number of zero corresponds to complete mixing whereas for plug flow the value of Peclet number approaches infinity. Typical yield-temperature plots of phthalic anhydride and naphthoquinone concentrations a t the outlet of the reactor are shown in Figure 5 (left and right) or catalysts A and B, respectively, calculated for a contact time of 6 seconds. Each curve represents a different degree of mixing as indicated by the Peclet number which varies from 0.1 to 50. In commercial fluidized beds the Peclet number is found to vary in the range of 0.2 up to 3.0 depending on the geom-
INDUSTRIAL AND ENGINEERING CHEMISTRY
etry and flow condition in the bed. Small experimental beds may be characterized by much larger Peclet numbers. The main differences in behavior of the two catalysts are already apparent in these plots. One may notice that catalyst A is less sensitive to mixing and that in the temperature range corresponding to maximum yields larger quantities of naphthoquinone are present when catalyst B is used. The locus of maximum yield is plotted us. the Peclet number in Figure 6 for contact times of 6 and 18 seconds. The longer contact time is more favorable to the performance of catalyst B but the relative insensitivity to mixing and lower naphthoquinone concentration characteristics of catalyst .4 are still retained. Figure 7, left, compares temperature and mixing behavior of catalyst A a t two different contact time levels. These figures are obtained by cross plotting the yield temperature curves for given constant temperatures. For a contact time of 6 seconds the optimum temperature is at about 350' C. whereas for a contact time of 18 seconds, the optimum temperature is at about 330' C. depending on the degree of mixing considered. These plots show that in order to reduce rhe naphthoquinone
CATALYTIC REACTOR DESIGN concentration of the product, it may be necessary to operate somewhat above the optimum temperature and, if this course is followed, the degree of mixing has very little influence on the final yield. A large amount of mixing may in some cases increase the yield of product. A similar plot for catalyst B is shown in Figure 7 , right. This helps to emphasize the point that this catalyst is more sensitive to mixing and that naphthoquinone is difficult to suppress unless temperatures in excess of 40' C. above the optimum are used with too great a penalty on phthalic anhydride yields. Another point illustrated by this figure is that in scaling u p from experimental units having a low degree of mixing and operated a t relatively short contact times to production units having a higher degree of mixing but operated a t longer contact times one may achieve substantial improvements in yield, contrary to what one would generally expect. For example, a small test unit having a Peclet number of 10.0 would yield 86 mole yo phthalic anhydride when operated a t a contact time of 6 seconds. A larger unit having a Peclet number of 2.5 would show a yield of 91% when operated at 18 seconds contact time and a corresponding optimum temperature. That is, the detrimental effect of mixing is more than offset by the improved process conditions. The fact that a t temperatures above
the optimum, a large degree of mixing may be even beneficial to product yield while maintaining low quinone concentration led us to examine the possibility of introducing the feed a t some intermediate location above the bottom of the fluid bed.
able to analytical treatment, the assumption was made that the increase in flow rate due to the feed injection is negligible-i.e ,, W
-A(x PA
If one considers a fluid bed in which the fluidizing gas is fed a t the bottom and the reactant feed is injected a t some point xo along the bed, one may write a material balance analogous to the previous one :
-
[u
+W A (x
-
XO)
(10)
PA
G + 1'~+ W __ 6 ( x PA Ok
0
This assumption in the case of naphthalene oxidation is quite justified when one considers that the addition of the naphthalene feed in the carrier gas increases the total linear gas velocity in the bed by a maximum of about 2%. Equation 9 thus becomes
Movable Feed Location
E ! ?
- XO)
- XO)
=0
With the further assumption that the reaction rate constants are not functions of the feed point location, one may combine Equations 5 and 10 and obtain the following differential equations and corresponding boundary conditions for the naphthalene, naphthoquinone, and phthalic anhydride, respectively. Naphthalene concentration :
(9)
W is the mass feed rate and A the cross sectional area of the bed. The term E A ( x - x o ) accounts for the increase in PA
bulk flow due to the feed introduced a t xo and __ wc"k 6 ( x - X O ) is the source of fiA
the Kth component in the feed. This equation may be easily solved when CK is a reactant. For intermediates and products, however, I'k becomes a complicated piecewise function of distance along the bed which makes the solution of Equation 9 above quite difficult. In order to make it more amen0
2t
0.1
-
I
I
t / '
I
-
0.0
0.0-
1.0-
09-
-
0 -330%
n
350.0
0 -370*G.
:090
0
2e
I
0 -330.0
-- 360% 370*0.
1
z
8yo 0
e
20.7-
I
06-
b
006-
;:I
0 02
ow
0 001 FRACTIONAL DISTANCE OF INJECTION POINT UP THE BED
T
I
I
I
I
00 02 04 06 OB 10 FRACTIONAL DISTANCE OF INJECTION POINT UP THE BED
Figure 8. The effect of moving the feed injection point, under certain conditions, is to increase the phthalic anhydride concentration in ihe product without appreciably increasing the naphthalene and naphthoquinone content Catalyst A, left;
catalyst 6, right
VOL. 53. NO. 4
APRIL 1961
265
Naphthoquinone concentration :
; x = 0 ;x = h
(12)
Phthalic anhydride concentration :
_-
dCp
dx
0
;x = h
(13)
Solution of the three sets of differential equations gives the following expressions for the outlet concentrations:
(Figure 8, left) where naphthalene and naphthoquinone concentration are so low as to be negligible, their presence in the product is not appreciably increased. I n those cases where their concentration is appreciable even with the bottom feed injection point, as illustrated by Figure 8, right, movement of the feed increases outlet concentrations of naphthalene and naphthoquinone a t the expense of the phthalic anhydride yield. If the model presented in this paper had taken into consideration the dependence of the reaction rate constants on oxygen concentration, one is led to believe that the effect of moving the feed injection point could be shown to be even more pronounced. Acknowledgment The authors are indebted to their colleagues a t the American Cyanamid Co. for their advice and suggestions, and the use of valuable data furnished by W. T. Booth and W. 0. Fugate. 6 (x
Nomenclature = cross
where:
= = XQ
=
D ,- I 1 i -
(wi
+ wz)epe70w, + 1)s
epew,
x
-
= (1
- (wi
-
wz)epe.row
1)2e--Pew*
=
=
The effect of moving the feed injection point as predicted by the above equations is illustrated in Figure 8 (left and right) for catalysts A and B, respectively. The conditions used are: Flow velocity = 1.O feet per second, bed height = 18 feet, and a Peclet S o . of 1. For catalyst A , some conditions exist in which raising the feed point above the bottom may be beneficial to the phthalic anhydride yield. Thus, for example, by moving the feed point one third of the way u p the column for a temperature of 350’ C. the phthalic anhydride concentration in the product may be increased by about 470 without appreciably increasing the naphthalene and naphthoquinone content of the product. This phenomenon is observable only when the reactor is at conditions above the optimum temperature and contact time for maximum phthalic anhydride yield. Such an effect is obtained from the postulated model because the movable feed point accomplishes two purposes :
=
=
=
=
=
=
=
sectional area of reactor; sq. ft. constant defined in text. concentration of Kth component; mole fraction. concentration of Kth component in the feed; mole fraction. constant defined in text. effective diffusivity; sq. ft ./see. height of fluidized bed; ft * reaction rate constant for the oxidation of naphthalene to naphthoquinone. reaction rate constant for the oxidation of naphthalene to phthalic anhydride. reaction rate constant for the oxidation of naphthoquinone to phthalic anhydride. reaction rate constant for the oxidation of phthalic anhydride to maleic anhydride, CO, and COS. reaction rate constant for the oxidation of naphthalene to maleic anhydride, GO, and C o n . reaction rate constant for the oxidation of naphthoquinone to maleic anhydride, CO, and
cor.
= pseudo first order reac-
I t reduces the effective contact time; therefore, it improves the performance of the catalyst. I t reduces the mean concentrations of the various components in the fluid bed; thus for phthalic anhydride this means less oxidation to C O and COz. I n the range above the optimum conditions
266
INDUSTRIAL AND ENGINEERING CHEMISTRY
tion rate constant for oxidation of naphthalene to naphthoquinone. = pseudo first order reaction rate constant for oxidation of naphthalene to phthalic anhydride.
-
pseudo first order reaction rate constant for oxidation of naphthoquinone to phthalic anhydride. pseudo first order reaction rate constant for the oxidation of phthalic anhydride to maleic anhydride, CO, and C O Z . Peclet number, dimensionless. time, second. true axial velocity in fluid bed, ft./sec. velocity vector in fluid bed, ft./sec. axial distance above grid in fluid bed, f t . axial height of injection point above grid, ft. constant defined in text. feed rate, moles/sec. constant defined in text. constant defined in text. unit step function = 0 when x < x o = 1 when x 2 xo xo) = Dirac delta function, derivative of the unit step function, ft.-’. density of fluidizing gas, gram m o l e ~ , / f t . ~ . dimensionless axial distance in fluid bed above grid. dimensionless axial distance of injection point above grid.
I
Subscript A’. Q, and P used to indicate concentrations are for naphthalene, naphthoquinone, and phthalic anhydride, respectively. literature Cited (1) Askins, J. W., Hinds, G. P., Jr., Kunreuter, F., Chem. Eng. Progr. 47, 401 (1951).
(2) Calderbank, P. H., Znd. Chemist 28, 291 11952). (3) Dikon, J, K., Longfield, J. E., “Catalysis.” Vol. VII, Kew York, 1960. (4) Farkas, A., D’Allesandro, A. F., J . Colloid Sci. 11, 653 (1956). (5) Gilliland, E. R., Mason, E. A., IND. END. CHEM.41, 1191 (1954); 44, 218 (1952). (6) Handlos, A. E., Kunstman, R. W., ~
Schissler, D. O., IND. ENG. CHEM. 49, 25 (1957).
(7) Ioffe, 1. I., Sherman, Y . G., J . Phys. Chem. (U.S.S.R.) 28, 2095 (1954); 29. 692 (1955).
(8) Kaup,‘ Vaientin, Ph.D. thesis, Yale University, 1959. (9) Mars, P., van Krevelen, D. W., Chem. Eng. Sci. 3, Special Supplement, 41 (1954).
(10) May, W. G., Chem. Eng. Progr. 55, 49 (1959). (11) Reman, G. H., Chem. & Znd. (London), 1955, p. 46. (12) Shelstad, K. A , , Downie, J., Graydon, W. F., Can. J. Chem. En
