Ind. Eng. Chem. Res. 1988,27, 212-213
212
Response to Comments on “Catalytic Gasification of Coke during the Pyrolysis of n -Hexane” Sir: This is in response to the comments made by Lekshminarayanan (1988) on our recent paper (Mandal and Kunzru, 1986). Our conclusion that the presence of steam is necessary for the formation of catalytic carbon was made for K2C03-coatedsurfaces. Our results of uncoated surfaces are in agreement with the findings of the other researchers mentioned by Lekshminarayanan. Coke deposition on potassium carbonate coated surfaces was not studied by the other investigators. As pointed out, our discussion is based on the assumption that all the coke formed is deposited on the surface. In all our runs, the presence of coke particles in the gas phase was negligible. We do not agree with the conclusion that the asymptotic coking rate will be the same on a quartz reactor, Le., independent of the material of construction. Since this investigation, we have obtained more data on coke formation during naphtha pyrolysis on uncoated and K,C03-coated stainless steel 304, stainless steel 316, and Inconel 600 surfaces (Sahu and Kunzru, 1988; Bahadur et al., 1987). For both coated and uncoated surfaces, the asymptotic coking rates were found to depend on the material of construction. Similarly, in a study by Frech et al. (1986) for Goodyear, the asymptotic coking rate during methylpentene pyrolysis was found to be lower on Alonized 5% Cr/0.5% Mo carbon steel than on the nonAlonized surface. It is possible that the different asymptotic rates result due to the different morphological properties of the coke. More likely, depending on the material of construction, different metals are incorporated on top of the growing carbon chain. Heat- and masstransfer resistances, if any, would be identical for the various surfaces. Another point raised by Lekshminarayanan is the possibility of coke deposition being a mass-transfer-controlled process. The specific runs of Figure 3 in our study (Mandal and Kunzru, 1986) were taken a t a high space time, and the results could have been affected by mass transfer.
However, all the other runs were at a much lower space time, and mass transfer control is unlikely. The value of the activation energy for coke formation would have been much lower if the process was limited by mass transfer. Although Fernandez-Baujin and Solomon (1975) report that, in an industrial cracker, coil coking is a mass-transfer-controlled process, Newsome and Leftin (1979) found that coke formation during naphtha pyrolysis in a bench-scale reactor was not mass transfer controlled. Registry No. Hexane, 110-54-3,
Literature Cited Bahadur, N. P.; Sahu, D.; Kunzru, D. “Reduction of Coke Formation During Naphtha Pyrolysis”. Presented at the Fourth Asian Pacific Confederation of Chemical Engineering Congress, Singapore, May 13-15, 1987. Fernandez-Baujin, J. M.; Solomon, S. M. “An Industrial Application of Pyrolysis Technology: Lummus SRT I11 Module”. Presented at the First Chemical Congress of the North American Continent, Mexico City, Nov 30-Dec 5, 1975. Frech, K. J.; Hoppstock, F. H.; Hutching, D. A. “Factors Affecting Methyl-Pentene Pyrolysis”. Goodyear Tire and Rubber Co. Report, 1986; Goodyear Akron, OH. Lekshminarayanan, H. Ind. Eng. Chem. Res. 1988, preceding paper in this issue. Mandal, T. K.; Kunzru, D. Ind. Eng. Chem. Process Des. Deu. 1986, 25, 794. Newsome, D. S.; Leftin, H. F. “Coking Rates in a Laboratory Pyrolysis Furnace”. Paper presented at the 72nd Annual AIChE Meeting, San Francisco, Nov 25-29, 1979. Sahu, D.; Kunzru, D. “Effect of Benzene and Thiophene on Rate of Coke Formation During Naphtha Pyrolysis”. Can. J . Chem. Eng. 1988, in press.
D. Kunzru Department of Chemical Engineering Indian Institute of Technology Kanpur, India
Comments on “Optimization of Consecutive Reactions with Recovery and Reuse of Unconverted Reactant” Sir: Liu et al. (1987) developed a set of equations to describe the maximum yield of intermediate for simple consecutive reactions taking place in both plug flow and mixed flow reactors followed by separation and recycle of unused reactant. The purpose of this note is to present the results for plug flow with separation and recycle in two compact and convenient design charts and to extend the analysis to the more practical case where separation of A from R is not perfect; i.e., R is also recycled. First, the equations in Liu et al.’s paper for the PFR can be summarized by the design charts of Figures 1 and 2. Second, one can generalize these findings to the more practical situation where some R accompanies the recycled A. The equations for the yield of R for this situation were developed by Kambitsis (1987) and, using the notation shown in Figure 3, can be expressed as
_ --
FR3
FA0
or
(1 - N)(Z - Zk) for h # 1 ( k - 1)(1- NZk)(l - M Z )
F _R-~ ( N - 1)zIn for k = 1 FA0 (1 - N Z ) ( l - M Z )
IO
09
08 07
0.6 05
04 03
02
01 0
(1)
0
01
02
03
04
05
06
one pass conversion of A ot ,,R,
(2)
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08
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-zap+ = I -
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Figure 1. Chart showing the conversion of A which maximizes the formation of R.
0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 1, 1988 213 I.o
0.9
g
Fs3
Plug flow reactor
0.8
a
t
o 0.7
4
X-
0.6
a
Figure 3. Flow diagram for first-order reactions in series in a plug flow reactor followed by a separator and recycle stream.
0.5
c
'2
0.4
0
5
0.3
g
0.2
-
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::
Plug flow with separation and recycle of unreacted A
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!
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!
.+ 0.8 .+ 0
2
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one pass conversion of A at:,,R,
0.9
- zap,= I - !$
-
0.6
5
0.5
0
Figure 2. Chart relating conversions of A a t conditions where formation of R is maximized.
where M and N are the separation ratios for A and R, and Z is the one-pass fraction of A unconverted through the reactor. The maximum yield of R is found from
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2
0.4
= 0.2 5
.E
0.1
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0
.-
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kZop;'
+ LMNZ,,,
- MNZop,k= (k - 1)(M + N ) for k # 1 (3)
0.1
02
03
04
- Z,,~'
or
( M + N)Zop,- In Z,,, - MNZo,,2(1 - In ZopJ = 1 for k = 1 (4) and this maximum yield occurs a t an overall conversion given by (5) These equations reduce to those of Liu et al. when N = 0; thus no R in the recycle stream, as represented by Figures 1 and 2. Separation and recycle of A increases the yield of R, but separation and recycle of R decreases the yield. Figure 4, from Kambitsis (1987),shows when separation and recycle is helpful and when it is not. An illustrative example follows to show the use of these charts.
=
For the first-order reactions
08
09
IO
KK/ll-Kl
FAO
Figure 4. Values of the separation factors M and N which make separation and recycle increase the production rate of R above straight plug flow.
Solution (a) From the lowest curve of Figure 1, we find for the PFR that the yield of R = 25%, at XA= 0.5. (b) From the M = 0.9 curves of Figures 1 and 2, we find that the yield of R = 58% at Xkonepaas = 0.24, and XA,oved = 0.76. (c) For MIN = 0.910.7 and kk/(l-')= 0.25, Figure 4 shows that the yield of R can be raised above the straight plug flow value if M > 59%. Since M = 0.9 here, recycle will help. Thus, solving eq 3 gives the optimum one-pass conversion, Zopt= 87.5%. Then eq 1 gives the maximum yield of R = 33.3% at an overall conversion XA3= 59%.
Literature Cited Liu, D.-2.; Xu, H.-S.; Wang, A . 3 . Ind. Eng. Chem. Res. 1987,26,376.
t Oregon
1
0.6 07
Kambitsis, C. M.S.Thesis, Department of Chemical Engineering, Oregon State University, Corvallis, 1987.
Example
A-R-S
05
2
k = kz/k1 = 2 fiid the conditions which maximize the formation of R (a) in a once-through plug flow reactor (PFR); (b) in a PFR if one can recycle 90% of the unreacted A, or M = 0.9 and N = 0; and (c) in a PFR when some R accompanies A in the recycle stream such that M = 0.9 and N = 0.7.
State University.
* West Virginia University. C. Kambitsis,' R. Turton,t 0. Levenspiel*+
Department of Chemical Engineering Oregon State University Corvallis, Oregon 97331 and Department of Chemical Engineering West Virginia.University Morgantown, West Virginia 26506-6101
