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COMMENTARIES Chemical Reaction Engineering In 1956 a group of European chemical engineers came together in Amsterdam for a symposium1 to exchange ideas on a wide range of topics, all dealing with chemical reactors. Professor van Krevelen suggested that they name the theme of their conference chemical reaction engineering, CRE. This name has taken hold, and today CRE takes its place as one of the key branches of chemical engineering. Let me briefly tell what the thinking was before this development, what was distinctive about the CRE approach, and finally what has happened since. The petroleum processing industry blossomed early in this century, and engineers were needed to serve its goals. To meet this demand, the profession of chemical engineering was founded and chemical engineering departments were created to teach and prepare these engineers. Although this may seem to be an overly simplistic view, still, it is true that the petroleum industry was the most important force driving the creation of our profession. In the first half of our century studies in chemical engineering focused on physical operations. New design methods were developed for flow systems, heat exchangers, absorbers, extractors, distillation columns and the like, and many textbooks were devoted to these subjects. This approach was called unit operations. At that time no general methods had been developed to guide the design of reactors. Instead, a subject called unit processes was created as a means for the orderly classification of processes involving chemical reactions. However, these chemical processes seemed so different, group from group (hydrogenations, thermal cracking, sulfonations, chlorinations, and so on) and even from reaction to reaction within a group, that each process had to be treated uniquely. Intuition and past practices were the prime guides for the practitioner in his quest for a good and efficient design for his particular reaction.
Here is an example of a catalytic rate equation derived from the LHHW theory. For a first-order reversible reaction A a R, dual-site mechanism, surface reaction controlling, no product R in the feed, the rate equation, from H&W2
-rA )
ksLKA (1 + CAKA + CRKR + CIKI + ‚‚‚)
The year 1947 was a momentous year, for it was then that the first book on the engineering of chemical reactors appeared. It was Hougen and Watson’s Chemical Process Principles: Part III, Kinetics and Catalysis. I refer to this book as H&W. This book guided the study of the subject in the petroleum processing and chemical industries and in universities in the United States. In part, its methods and philosophy are still evident today. I call this the petrotech approach. Its unique feature is that it is based exclusively on Eyring’s theory of absolute reaction rates. This was applied by Langmuir-Hinshelwood and Hougen-Watson to reactions of all types: homogeneous, solid-catalyzed gas phase, gas/solid, and fluid/fluid. I designate this theory as LHHW.
CA -
)
CR K
(1) The corresponding conversion expression for a plug flow reactor, from H&W3 is
[
1 +K n +Kn ) ( CW π ) + π( F ) (1 + K1 ) 1 2( + K n + K n )(K π (1 + K1 ) 2
A A0
I I0
A A0
I I0
R
- KA)nA0
2
](
)
+
(KR - KA)2x2 (KR - KA)nA02 nA0 ln 13 1 1 1+ nA0 - 1 + x 21+ K K K 1 2 + KAnA0 + KInI0 (KR - KA)x (K - K )2n x π R A A0 1 12 1+ 1+ K K (2)
( (
)
(
(
)
)
)
(
)
(
)
If we bypass the LHHW model, and instead use a simple first-order kinetic model, we get the following equation in place of eq 1: 1
The Petrotech Approach
(
2
R, ‚‚‚ -r′A ) k′1CA - k′2CR, ‚‚‚ K ) Aa 2
k′1 CR,eq ) k′2 CA,eq (3)
In addition, in place of the cumbersome expression of eq 2, this model gives
k′t′ )
(
xA,eq k′CA0W ) xA,eq ln FA0 xA,eq - xA
)
(4)
Compare the simplicity of eq 3 with eq 1 and eq 4 with eq 2. Also note that the above H&W equations are written without spelling out the meaning of the symbols, but only to show their comparative complexity. As mentioned earlier, the theory of absolute reaction rates was used, not just for solid-catalyzed systems but for all reaction types. As another example, consider a
10.1021/ie990488g CCC: $18.00 © 1999 American Chemical Society Published on Web 09/11/1999
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particle which shrinks as it reacts with gas:
A(g) + B(s) a R(g) + S(g) With slow surface reaction controlling, the LHHW model gives the following rate equation, from H&W:4
-rA )
Area(L′1)2k′1
× (1 + CAKA + CRKR + CIKI + ‚‚‚)2 CRCSKRKS CAKA (5) Ksurf
(
)
which represents the rate of shrinkage of a particle. Alternatively, the shrinking core model gives the following conversion vs time performance expression:
t ) 1 - (1 - xB)1/3 ttotal
(6)
I suggest that the adventurous reader try to develop the equivalent conversion-time expression from the LHHW rate equation, eq 5. A second and much more serious criticism on the use of the LHHW model by engineers is illustrated with the following detailed example laid out by H&W5 on the hydrogenation of iso-octenes (called codimers):
C8H16 + H2 a C8H18 codimer To find a rate equation, 40 experimental runs were made to test 18 possible LHHW mechanisms. These were as follows: (a) adsorption of codimer controlling (b) adsorption of hydrogen controlling (c) desorption of octane controlling (d) surface reaction controlling (e)-(r) ... 14 additional mechanisms By least-squares analysis H&W concluded that only one mechanism, mechanism (h), fit the data. However, Chou6 by a statistical analysis showed that other mechanisms fitted the data equally well. Now, to tell that one of these specific mechanisms represents reality, one must show that 17 of the 18 mechanisms tested do not fit the data. This was not done in this example and has never been done for any example since. This fact shows that choosing one of these 18 mechanisms simply represents a curve-fitting procedure. With this in mind the engineer should pick the simplest model to fit the data. This is the CRE approach, and this often leads to the use of an nth order rate equation. Reactor Design from CRE In approaching the design of a reactor system the engineer has to answer a number of important preliminary questions before embarking on his detailed calculations. These questions are as follows: (1) Do I have the right reactor type in mind: should it be plug flow, mixed flow, recycle, multistage, or what? (2) What temperature progression should I aim for: constant, rising, falling, etc., and would this require heat exchange, maybe multistaged? (3) For a catalytic reaction, what size of particle should be used? This tells what type of reactor should be used: packed bed, fluidized, etc.
(4) Does the catalyst deactivate, and if so, does it deactivate rapidly or slowly? All these questions require dealing with flow and contacting and heat-transfer and mass-transfer factors. Unfortunately, the LHHW rate expressions, such as eqs 1, 2, or 5, cannot in practice incorporate these physical rate phenomena. On the contrary, CRE does deal with the overall problem with a kinetic model appropriate for each class of system (fluid/fluid, fluid/solid, biochemical, solid catalytic, etc.) In many cases the nth order rate model is chosen because it can account in a simple way for all the physical factors. For example, an nth order rate form can account for the following: (1) Nonideal flow of fluid in the reactor by the axial dispersion model (Danckwerts, Wilhelm), by the tanksin-series model (MacMullin, Denbigh), or by combined models. (2) Fluid/fluid systems in which the two-film masstransfer model is combined with nth order kinetics (Hatta, van Krevelen, Sharma). (3) Pore diffusion in catalysts (Damkohler, Thiele, Zeldovich, Wagner, Weisz, Prater, Wheeler). (4) Deactivation of catalysts, and also tell which temperature-time progression is best to use (Szepe, Aris). Let me illustrate this approach by considering the combined effect of pore diffusion and deactivation on reactor behavior. For an nth order reaction, mth order deactivation, and strong pore diffusional resistance (effectiveness factor ) ), we write
{
A f R with -r′A ) k′CAna [mol reacted/kg of cat.‚s] da [1/s] )kdam dt where t is the reactor run time and a is the catalyst activity, with the fresh catalyst having an activity of a ) 1. You may think that this is too simple a model to be of any practical use. Not so. Actually, it is the only model which has been able to account for reaction with both pore diffusion and deactivation effects. To illustrate, for first-order kinetics this model gives the following performance equations for plug flow of gas through a bed of catalyst.
For no pore resistance, ) 1 kd ) 0 and no deactivation,
}
ln
CA0 ) k′τ′, CA
where τ′ )
CA0W FA0
}
For no pore resistance, )1 but first-order deactivation, kd * 0, m ) 1 CA0 ln ) k′τ′ exp(kdt) CA For strong pore resistance, ) 1/MT kd ) 0 and no deactivation,
} ln
CA0 k′τ′ ) CA MT
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}
For strong pore resistance, ) 1/MT and first-order deactivation, kd * 0, m ) 1 CA0 k′τ′ kdt ln ) exp CA MT 2
( )
where
x
MT ) Thiele modulus ) L
k′Fs Deff
These simple performance expressions have been shown by Levenspiel7 to fit the reported data. There is no way to get any useful analytical expressions such as the above by using the LHHW model. And, without an analytical expression, you have no insight to guide you to different and better operating conditions. Reactor behavior is governed by four interrelated quantities. These are shown in Figure 1. For laboratory research, you choose the type of your experimental reactor, hence the flow pattern; you measure the input and the output and from this you can evaluate the kinetics. In process design, you specify the input, you know the kinetics and flow pattern, and from this you can predict the output. Today, many researchers use physical chemistry and quantum thermodynamics to come up with very detailed kinetics: for example, some have used as many as 60 000 individual elementary reaction steps, while at the same time completely ignoring the question of looking for the best contacting or flow model. They just assume that the plug flow model should be used. They should realize that their reactor predictions are only as good as the cruder of the two above-mentioned factors, as illustrated in Figure 2. Often, the lack of knowledge of the expected flow pattern in the reactor is the main cause of uncertainty in the design of reactors, not the kinetics. CRE Today Today, nearly every chemical engineering department in the world includes in its curriculum an undergraduate course devoted to the study of reactors. However, an AIChE survey has shown that, just before the introduction of the CRE approach, only 18% of all departments in the United States taught the subject at all. The simplicity of the CRE approach made this subject teachable. Because of its prestige, some chemical engineering departments have changed their names to departments of CRE. Also, the name has been embraced by all sorts of related and not so related subjects. However, at its core CRE aims to bring together the study of reaction kinetics and the transport phenomena so that the practioner can tell what kind of process to focus upon, so as to end up with a well-behaved reactor setup which operates economically and stably while producing most of what is wanted and least of what is not wanted. Recapitulation The first step in reactor design came in 1947 with the petrotech approach which used the theory of absolute reaction rates as its kinetic model for all reaction types. This was a mechanistic model and was so complex that
Figure 1.
Figure 2.
it was not practical to incorporate into its equations any of the transport resistances. The second step came in 1958 with the CRE approach, which was designed to account for all the physical and chemical rate factors. To do this, it set aside the theory of absolute reaction rates, and in its place adopted simple kinetic rate expressions appropriate for this or that system. This approach gave tractable conversion expressions. Today, at the end of the century, the computer enables the researcher to try the most complicated models that he desires, those involving multiple elementary reactions and/or computational fluid dynamics. But we must be wary when we wield the impressive power of the computer. The findings from such analyses will usually be of little generality and will only apply to the system actually studied. Also, the researcher is able to incorporate into his model many more factors (for example, 60 000 rate expressions) than he has reliable experimental values for. What does that say for his predictions? This type of study is fine for simulation exercises, but when it comes to reactor design the predictions of such analyses should be viewed with caution. Acknowledgment I thank Professors Ken Bischoff, Mike Dudukovic, Steve Szepe, and Richard Turton who have read this paper and have made useful comments. Literature Cited (1) Chemical Reaction Engineering, the First Symposium of the European Federation of Chemical Engineers; in Chem. Eng. Sci. 1958, 8, 1-200.
Ind. Eng. Chem. Res., Vol. 38, No. 11, 1999 4143 (2) Hougen, O. A.; Watson, K. M. Chemical Process Principles, Part III; Wiley: New York, 1947; p 919, eq 37. (3) Hougen, O. A.; Watson, K. M. Chemical Process Principles, Part III; Wiley: New York, 1947; p 929, eq b. (4) Hougen, O. A.; Watson, K. M. Chemical Process Principles, Part III; Wiley: New York, 1947; p 1065, eqs 17 and 22.
(5) Hougen, O. A.; Watson, K. M. Chemical Process Principles, Part III; Wiley: New York, 1947; pp 943-958. (6) Chou, C. H. Least Squares. Ind. Eng. Chem. 1958, 50, 789. (7) Levenspiel, O. The Chemical Reactor Omnibook; OSU Bookstores: Corvallis, OR, 1996; Chapter 31.
Octave Levenspiel Chemical Engineering Department Oregon State University Corvallis, Oregon 97331 IE990488G
