Catalysis
and Catalytic
Reactors
10
It isn't that they can't see the solution. It is that they
can't see the problem.
G , K. Chesterton
Overview. The objectives of this chapter are to deveIop an understanding of
catalysts, reaction mechanisms, and catalytic reactor desip. Specifically,
after reading this chapter one should be abIe to (1) define a catalyst and
describe its propwties, (2) describe the steps in a catalytic reaction and in
chemical vapor deposition (CVD) and apply the concept of a rate-limiting
step to derive a rate law, (3) develop a rate law and detwmine the rate-law
parameters from a set of gas-solid reaction rate data, (4) describe the different types of catalyst deactivation. determine an equation for cataIytic activity from concentration-time data, define temperature-time trajectories to
maintain a constant reaction fate, and (5) calculate the conversion or c a w
Zyst weight for packed (fixed) M s . moving beds, well-mixed (CSTR) and
straight-through (STTR] ff uid-bed react,ors for t
ring and n
iag catalysts. The various sections of this ch,
$ 1 ~corn
each of these objectives.
10.1 Catalysts
Catalysts have been used by humankind for over 2000 years.' The first
observed uses of catalysts were in the making af wine, cheese, and bread. It
was found that it was always necessary to add small amounts of the previous
batcb to make the current batch. However, it wasn't until 1835 that Benelius
' S.T- Oyama and G.A. Somojai, J. Chem. Educ,, 65,765($986).
646
Catalysis and Catalytic Reactors
Chap. 10
began to tie together observations of earlier chemists by suggesting that small
amounts of a foreign source couId greatly affect the course of chemical reactions. This mysterious force attributed to the substance was called catalytic. In
1894, OstwaId expanded Berzelius' explanation by stating that catalysts were
substances that accelerate the rate of chemical reactions without being consumed. In over 150 years since Berzelius' wark, catalysts have come to play a
major economic role in the world market. In the United States alone, sales of
process catalysts in 2007 will be over $3.5 billion, the major uses being in
petroleum refining and in chernica1 productjoti.
10.1.I Definitions
Summary hlotes
A cafalyst is a substance that affects the rate of a reaction but emerges from
the process unchanged. A catalyst usually changes a reaction rate by pramoting a different molecu!ar path ("mechanism") for the reaction. For example,
gaseous hydrogen and oxygen are virtuaIly inerl at room temperature, bur react
rapidly when exposed to platinum. The reaction coordinate shown in Figure
10-1 is a measure of the progress abng the reaction path as Hz and 0:
approach each other and pass over the activation energy bamer to form H20.
A more exact comparison of the pathways, similar to the margin figure, is
given in the Summary Notes for Chapter 10. Catal~eisis the occurrence, study,
and use of catalysts and catalytic processes. Commercial: chemical catalysts are
immensely important. Approximately one third of the material gross national
product of the United States involves a catalytic process someuphere between
raw material and finished p r ~ d u c t The
. ~ development and use of catalysts is a
major part of the constant search for new ways of increasing product yield and
selectivity from chemical reactions. Because a catalyst makes ~t possible to
obtain an end product by a different pathway with a Iower energy barrier. it
can affect both the yield and the selectivity.
Gas
HZ+ O2
'.
\,
H20
f
, '
.-...-catalyst
p
z
r
Fast
Figure 10-1 Different reaction paths.
Normal1 y when we talk about a catalyst, we mean one that speeds up a
reaction, although strictly speaking, a catalyst can either accelerate or slow?[fie
--
' V. Hacnsel and R. L. Burwell. Jr.. Sci. Am.. 22.5(10). 46.
Catalysts can acceImate the reactlon
rate but cannot change the
equilibrium.
f m a t i o n of a particular product species. A catalysr changes only the mle of o
reaction; it does nor aflecr the equilibrium.
Homogeneous catalysis concerns processes in which a catalyst is in solution with at least one of the reactants. An example of homogeneous catalysis is
the industrial 0 x 0 process for manufacturing normal isobutylaldehyde. It has
propylene, carbon monoxide, and hydrogen as the reactants and a liquid-phase
cobalt complex as the catalyst.
Reactions carried out in supercritical fluids have been found to accelerate
the reactino rate greatly.' By manipulating the properties of the solvent in
which the reaction is taking place, interphase mass transfer limitations can be
eliminated. Application of transition states theory discussed in the Professional
Reference Shelfon the CD-ROMof Chapter 3 has proven useful in the analysis
of these reactions.
A heterogeneous catalytic prncpss involves more than one phase: usually
the catalyst is a solid and the reactants and products are in liquid or gaseouy
form. Much of the benzene produced in this country today is manufactured
from the dehydrogenation of cyclohexane (obtained from the distillation of
crude petroleum) using platinum-on-alumina as the catalyst:
Cyclohexane
Examples nf
hetempeneon4
cata?ytic reactions
Benzene Hydrogen
Sometimes the reacting mixture is in both the liquid and gaseous forms,
as in the hydrodesuEfurization of heavy petroleum fractions. Of these two types
of catalysis, heterogeneous catalysis is the more common type. The simple and
complete separation of the fluid product mixture from the solid catalyst makes
heterogeneous calalysis economically attractive, especially because many catalysts are quire vaIuable and their reuse is demanded. Only heterogeneous catalysts will be considered in this chapter.
A heterogeneous catalytic reaction occurs at or very near the fluid-solid
interface. The principles that govern heterogeneous catalytic reactions can be
applied ro both caralytic and noncatalytic fluid-solid reactions. The two other
types of heterogeneous reactions invoIve gas-Iiquid and gas-liquid-solid systems. Reactions between gases and Iiquids are usually mass-transfer limited.
-
-'
-
Savage, S. Gopalan. T. I. Mizan, C.J. Manino, and E. E. Brmk, AlChE 1.. 41
(7) 1723 (1995). B. Subramanian and M. A. McHugh, IEC Pn7ce.r~Desrgn and
P. E.
Dr~,elopmrrrt,25, I t 1486).
648
Catalysis and Catalytic Reactors
Chap
10.1.2 Catalyst Properties
Because a catalytic reactinn occurs at the fiuid-solid interface, a large inter
cia1 area is almost always essential in attaining a significant reactian rate.
Ten pram$ of this many catalysts, this area is provided by an inner porous structure {i.e., i
cntalyv passes< solid contains many tine pores, and the surface of these pores suppties the a
nlure surface area
than a U.S. needed for the high rate of reaction), The area possessed by some porous ma
fontball held rials is surprisingly large. A typical silica-alumina cracking catalyst has a pc
volume of 0.6 crn3/g and an average pore radius of 4 nm. The correspondi
surface area is 300 m2Jg.
A catalyst that has a Large area resulting from pores is called a porn
c a t ~ l y s t Examples
.
of these include the Raney nickel used in the hydrogenari~
of vegetable and animal oils, the platinum-on-alumina used in the reforming
petroleum naphthas to obtain higher octane ratings, and the promoted in
used in ammonia synthesis. Sometimes pores are so small that they will adn
small molecules but prevent large ones from entering. Materials with this tyl
Catalyst types:
of pore are called molecular sieves, and they may be derived from natural su
Porotls
stances such as certain clays and zeolires, or be totally synthetic, such as son
Molecular sievcs
Monolithic
crystalline aluminosili~ates(see Figure 10-2). These sieves can form the bas
- Supported
Unsupponed
Typical
zeolite catalvst
FaujasiteType Zeolite
0
12 Ring
(a)
Ibl
(a) Framework structures and (b) p r e cross sections of we types of
zeolires. (a) Faujasite-type zeolite has a three-dimensional channel system wrth
pores at least 7.4 A in diamerer. A pore i s formed by 12 oxygen atoms in a ring.
(b) Schematic of reaction CH,and C6HICHy (Note the slze of the pore mouth and
the interior of the zeolite sre nor to scale.) [(a) from N.Y.Chen and T. F. Degnan.
Chem. Eng. Pmg., 8#(2), 33 (1988). Reproduced by permission of the Amencan
Institute of Chemical Engineers. Copyright O I988 AIChE. All rights reserved.]
Figum 10-2
sec. 10.1
High setectivit~to
para xylene
Catalysts
649
for quite selective catalyrts; the pores can control the residence time of various
molecules near the catalytically active surfact to a degree that essentially
allows only the desired molecules to react. One example of the high selectivity
of zeolite cataIysts is the formation of xylene from toluene and methane shown
in Figure 10-2(6).4 Here benzene and toluene enter through the pore of the
zeolite and react on the interior surface to form a mixture of ortho. meta. and
para xylenes. However, the size of the pore mouth is such that only
para-xylene can exit thr~ughthe pore mouth as meta and onho xylene with
their methyl group on the side cannot fit rhrough the pore mouth. There are
interior sites that can isomerize ortho and meta to para-xylene. Hence we have
a very high selectivity to form para-xylene. Another example OF zeolite specificity is controlled placement of the reacting molecules. After the motecules
are inside the zeolite, the configuration of the reacting molecules may be abIe
to be controlled by pPacement of the catalyst atoms at specific sites in the
zeolite. This placement would facilitate cydization reactions, such as orienting
ethane molecutes in a ring on the surface of the catalyst so that they Form
benzene:
Monolithic catalysts
k~ either porous
or nonporous.
Not all catalysts need the extended surface provided by a porous structure, however. Some are sufftciently active so that the effort required to create
a porous catalyst would be wasted. For such situations one type of catalyst is
the monolithic catalyst. Monolithic catalysts are ~omnllyencountered i n processes where pressure drop and heat removal are major considerations. Typical
examples include the platinum gauze reactor used in the ammonia oxidation
portion of nitric acid manufacture and catalytic converters used to oxidize pollutants in automobile exhaust. They can be porous (honeycomb) or nonporous
(wire gauze). A photograph of an automotive catalytic converter is shown in
PRS Figure RIE.1-2. Platinum is a primary catalytic rnateriat in the monolith.
In some cases a catalyst consists of minute particles of an active material
dispersed over a less active substance called a slipport. The active materia[ is
frequently a pure metal or metal alloy. Such catalysts are called supported cntalysts, as distinguished from unsupported catalysts. Catalysts can also have
small amounts of active ingredients added called pmrnorers, which increase
their activity. ExampIes of supported catalysts are the packed-bed catalytic converter automobile, the platinum-on-alumina catalyst used in petroleum reforming, and the vanadium pentoxide on silica used to oxidize sulfur dioxide in
manufacturing suIfuric acid. On the other hand, the platinum gauze for ammonia oxidation, the promoted iron for ammonia synthesis, and the sitica-alumina
dehydrogenation catalyst used in butadiene manufacture typify unsuppolted
catalysts.
R. J. Masel, Chemical Kindics and Caralvsis (New York: Wiley Interscience, 2001).
p. 741.
650
Deactivation by:
-- Aging
Poisoning
. Coking
Chemisorption on
active sites rs what
catalyzes the
reaction
Catalysis and Catalytic Readors
Chap 10
Most catalysts do not maintain their activities at the same levels for
indefinite periods. They are subject to deactivation, which refers to the decline
in a catalyst's activity as time progresses. Catalyst deactivation may be caused
by (1) aging phenomenon, such as a gradual change in surface crystal structure; (2) by poisoning, which is the irreversible deposition of a substance on
the active site; or (3) by fouling or coking, which is the deposit of carbonaceous or other material on the entire surface. Deactivation may occur very
fast, as in the catalytic cracking of petroleum naphthas, where coking an the
catalyst requires that the catalyst be removed after only a couple of minutes in
the reaction zone. In other processes poisoning might be very slow, as in automotive exhausr catalysts, which gradually accumulate minute amounts of lead
even if unleaded gasoline is used because of residual lead in the gas station
storage tanks.
For the moment, let us focus our attention on gas-phase reactions catalyzed by solid surfaces. For a catalytic reaction to occur, at least one and frequently all of the reactants must become attached to the surface. This
attachment is known as adsorprion and takes place by two different processes:
physical adsorption and chemisorption. Physical adsorption is similar to condensation. The process is exothermic, and the heat of adsorption is relatively
small, being on the order of 1 to 15 kcallrnol. The forces of attraction between
the gas molecules and the solid surface are weak. These van der Waals forces
consist of interaction between permanent dipoles, between a permanent dipole
and an induced dipole, andlor between neutral atoms and molecules. The
amount of gas physically adsorbed decreases rapidly with increasing temperature, and above its criticai temperature only very small amounts of a substance
are physically adsorbed.
The type of adsorption that affects the rate of a chemical reaction is
chernisorption. Here, the adsorbed atoms or molecules are held to the surface
by valence forces of the same type as those thar occur between bonded atoms
in rn01ecuIes. As a result the electronic structure of the chemisorbed molecule
is perturbed significanrly, causing it to be extremely reactive. Interaction with
the catalyst causes bonds of the adsorW reactant to be stretched. making
them easier to break.
Figure 10-3 shows the bonding from the adsorption of ethylene on a platinum surface to form chemisorbed ethylidyne. Like physical adsorption.
chemisorption is an exothermic process, but the heats of adsorption are generally of the same magnitude as the heat of a chemical reaction ( i t . . 40 to 400
kTlmol). If a catalytic reaction involves chemisorption, it must be carried out
within the temperature r a n g whek chemisorpfion of the reactants is appreciable+
In a landmark contribution to catalylic theory, Taylofl suggested that a
reaction is not catalyzed over the entire solid surface but only at ceriain actil'f
sires or centers. He visualized these sites as unsaturated atoms in the solids
that resulted from surface irregulatities, dislocations, edges of cqstals. and
cracks along grain boundaries. Other investigalors have taken exception to this
' H. S . Taylor, Proc. R. Sor. k~trdon,A108.
105 (19281.
Sec. 10.1
Cetalysts
651
Figurc 10-3 Ethylidyne as chem~snrbedon platinum. (Adapted from G.A. Somojai.
Intmduction to Sudoce Chemr.rtr?.and Catalysis, U'iley. New Ymk, 1994.)
definition, pointing out that other properties of the solid surface are also important. The active sites can also be thought of as places where highly reactive
intermediates (i.e., chemisorbed species) are stabilized long enough to react.
This stabilization of a reactive intermediate is key in the design of any catalyst.
However, for our purposes we wilI define an active site as a poinr on rhe caralysst surface that can form strong chemical bonds wirh an ad.~nrbedorom or
nrolecule.
One parameter used to quantify the activity of a catalyst is the rurnm!Pr
frequency (TOR. f. It is the number of molecules reacting per active site per
second at the conditions of the experiment. W e n a metal catalyst such as platinum is deposired on a support, the metal atoms are considered active sites.
The dispersion, D,of the catalyst is the fraction of the metal atoms depoqited
that are on the surface,
Example I U-1
Turnover Frequency in Fisther-Trnpsch Synrhesig
The Fischer-Tropsch synthesis was studied using a commercial 0.5 wt 4r Ru on
y-A120~.h
The catalyst d~speisionpercentage uf atoms exposed. determined from
qR.
S. Dixit and L. L. Tavlaiides, Ind. Eng. Chem. Pmcvss DPS.Dei:, 22, 1 (1983).
652
Catatysis and Catalytic Reactors
Char
hydrogen chemisorption. w35 round to br 498. At a pressure of 988 kPa and a t
ptrature of 475 K. a turnover frequency. I;., , of 0.044 s-1 wa5 reported for meth
What i s the rate of formation of methane, r i , in rnoIls.g of catalyst (metal pluc ,
port)?
- 0.044 molecules
I mol CH,
6 . 0 2 10"
~ molecules
-
(surface atom Ru) s
0.49 surface atoms
total atoms RII
6 . 0 2 t~0'' atornL Ru
g atom (mul) Ru
g atoms Ru 0.005 g Ru
101.1gRu
I
= 1.07
x !O-%olls.g
gtotal
catalyst
(EIO-
That is, 1.07 x 1W moles (6.1 x 10" molecules) o f methane are jumping
one gram o f catalyst every second.
Figure 10-4 shows the range of turnover frequencies (rnolecules/site
as a function of temperature and type of reaction. One: notes that the turno
frequency in Example 10-1 is in the same range as the frequencies shown
the box for hydrogenation camlysts.
10.1.3 Classification of Catalysts
While platinum can be used for some of the reactions shown in Figure 1C
we shall also discuss several other classes of reactions and the catalystsn7
Alkylation and Dealkylation Reactions. Alkyletian is the addition of
alkyl group to an organic compound. This type of reaction is commonly c
ried out in the presence of the Friedel-Crafts catalysts. AlC13 along wit1
trace of HCI. One such reaction is
A similar alkylation is the formation of ethyt benzene from benzene and ethyle
' J. W. Sinfelt. Ind. Eng. Chem., 62(2),23 (2970); 62(10).66 (1970). Also, W. B.Inr
in P. H. Emmertt. Eds., Catalysis, Vol. 2 (New York: Reinhold. 1955). p. I, :
R. Masel, Kincrics (New York: Wiley, 2003).
Sec. 10.1
Catalysts
Hydrogenation
7
/-
Dehydrogenation
200
400
Temperature
600
8 00
(Kl
Figure 10-4 Range o f turnover Frequencies as a function for different reactions
and temperatures. (Adapted from 6.A Somorjai. Intmduc!ion lo Srrrfacc
C l ~ e t n i and
~ I ~Catrrlysrs, Wiley, New York. 1994.)
The cracking of petrochemical products is probably the most common
deaikylation reaction. Silica-alumina, silica-magnesia, and a clay (montmorillonite) are common deatkyIation catalysts,
Isomesization Reactions. In petrochemical production, the conversion of
normal hydrocarbon chains to branched chains is important, since !he latter ha.$
a higher gasoIine octane number. When n-pentane is isomerized to i-pentane,
the octane number increases from 62 to 90!! Acid-promoted AIIOBis a catalyst
used in such isomerization reactions. AIthough this and other acid catalysts are
used in isomerization reactions, it has been found that the conversion of normal paraffins to isoparaffins is easiest when both acid sites and hydrogenation
sites are present, such as in the catalyst Pt on A120,.
Hydrogenation and Dehydrogenation Reactions. The bonding strength between hydrogen and metal surfaces increases with an increase in vacant d-orbltals. Maximum catalytic activity will not be realized if the bonding is too strong
and the products are not readily desorbed from the surface. Consequently, this
maxjrnum in catalytic activity occurs when there is approximately one vacant
d-orbital per atom. The most active metals for reactions involving hydrogen are
generally Co, Ni, Rh, Ru, Os, Pd, Ir, and Pt. On the other hand, V, Cr, Nb, Mo,
Ta, and W, each of which has a large number of vacant d-orbitltls, are relatively
inactive as a result of the strong adsorption for the reactants or the products or
both. However, the oxides of Mo (MoOz) and Cr (CrIQ2) are quite active far
most reactions involving hydrogen. Dehydrogenation reactions are favored at
high temperatures (at least 200"C), and hydrogenation reactions are favored at
654
Catalys~sand Catalylrc Reactors
Chap. 10
lower temperatures. Industrial butadiene, which has been used to produce synthetic rubber, can be obtained by the dehydrogenation of buteoes:
"*'"
CH3CH=CHCH3
> CCW2=CHCW=CH2+H2
(possible catalysts: calcium nickeI phosphate, Cr2Q3,etc.)
The same catalysts could also be used in the dehydrogenation of ethyl
benzene to form styrene:
An example of cyclization, which may be considered to be a special type of
dehydrogenation, is the formation of cydohexane from ra-hexane.
Oxidation Reactions. The transition group elements (group VIII) and subgroup I are used extensively in oxidation reactions. Ag, Cu, Pt, Fe, NI, and
their oxides are generally g d oxidation catalysts. In addition, V20s and
M n 4 are frequently used for oxidation reactions. A few of rhe principal types
of catalytic oxidation reactions are:
1. Oxygen addition:
2C,H,c O2
ZSO,+O,
2co+o,
)
v:o3
2C2H40
2SO,
2C0,
2. Oxygenolysis of carbon-hydrogen bonds:
2C,H,OH +O,
2CH,CHO+ZH,O
2CN,OH + 0,
A"
2HCW0 + 2H,O
3. Oxygenation of nitrogen-hydrogen bonds:
4. Complete combustion:
Platinum and nickel can be used for both oxidation reactions and hydrogenation reactions.
Hydration and Dehydration Reactions. Hydration and dehydration catalysts have a strong affinity for water. One such catalyst is AIZO3,which is used
in the dehydration of alcohols to form olefins. In addition to alumina, silica-alumina gels, clays, phosphoric acid, and phosphoric acid salts on inert carriers
have also been used for hydration4ehydration reactions. An example of an
industrial catalytic hydration reaction is the synthesis of ethanol from ethylene:
CH2=CH2+ H 2 0
PCH3CH20H
Sec. 10.2
655
Steps In a Catalytic Reaction
HaIogenation and DehaIogenation Reactions. Usual1y, reactions of this
type take place readily without utilizing catalysts. However, when selectivity
of the desired product is low or it is necessary to run the reaction at a lower
temperature, the use of a catalyst is desirable. Supported copper and silver
halides can be used for the halogenation of hydrocarbons. Hydrochlorination
reactions can be carried out with mercury copper or zinc halides.
Summary. Table 10-1 gives a summary of the representative reactions and
catalysts discussed previously.
TABLE
10- 1.
TYFu OF REACTIONSAND B P R E S ~ A T ~ VCATALYSTS
E
Rcacrion
C~fpI~srs
1. Walogenation-dehalogen~tion
2. Hydration-dehydration
3. Alkylation4ealkylat1on
4. Hydrogenation-dchydragenation
5. Oxidation
6. Isornerization
CUCI,, AgCI. Pd
AI:O~,M ~ O
AICI,. Pd, Zeolites
Co. Pt, Cr,D3. NI
Cu.Ag, Ni, V,OI
AIC13. Pt/A1201. Zeolites
If, for example, we were to form styrene from an equimolar mixture of ethylene and benzene. we could carry out an alkylation reaction to form ethyl benzene, which is then dehydrogenated to form styrene. We need both an
alkylation catalyst and a dehydrogenation catalyst:
10.2 Steps in a Catalytic Reaction
A photograph of different types and sizes of catalyst is shown in Figure 10-5fa).
A schematic diagram of a tubular reactor packed with catalytic pellets is shown
i n Figure 10-5(b). The overalI process by which heterogeneous catalytic reactions proceed can be broken down into the sequence of individual steps shown
in Table 10-2 and pictured in Figure 10-6 for an isornerization reaction.
(a)
Figure 10-5 (a] Different shapes and sizes or catalyst. (Counecy of the Engelhard
Corporat~nn.
I
Catalysis and C ~ f a W i cR e ~ r ! c r r
Pecked catalyst bed
Cataiyst pellet
Chi
Catalyst pellet surface
Pores
(bl
Figure 10.5
( h ) Catalytic pecked-bed reactor-schemaric.
Each step in Table 10-2 is shown schematically in J3gure 10-6.
1. Mass transfer (difhqian) o f the reactantls) (e.g..PpecIes A) fmm the bulk fluid to the exte
surface of the catalyst pellet
2. O~ffusionof the reactant from the pore mouth through the catalyst pores to the irnmedia
vicinity of the internal catalytic surface
3. Adsorption nT reactant A onto the catalyst surface
4. Reaction on the surface of the catalyst (e.g., A d B)
5. Deqorption of the product5 (e.g., 8 ) from the surface
6. Dtffusron of the pmducts from the interior o f she pellet to the pore mouth at the external
surface
7. Mass trancfer of the praducts from the external pellet surface to the bvlk Ruid
Figure 10.6
Steps in r heterogeneous catalytic reacrion.
Sec. 10.2
A reaction takes
place on the surface,
but the species
involved i n rhe
reaction must get ro
and from the surface
In this chapter we
fucus on:
3 Adsorption
4. Surface reaction
5 . Desorption
Steps ~na Catalytic Reaction
657
The overall rate of reaction is equal ra the sate of the slowest step in the
mechanism. When the diffusion sreps ( 1 , 2 , 6 ,and 7 in Table 10-2) are very fast
compared with the reaction sreps (3, 4. and S ) , the concentrations in the immediate vicinity of the active sites are indistinguishable from those in the bulk
fluid. In this situation, the mnspon or diffusion steps do not affect the overall
rate of the reaction. In other situations, if the reaction steps are very fast
compared with the diffusion steps, mass transport does affect the reaction rate.
In systems where diffusion from the bulk gas or liquid to the catalyst surface
or to the mouths of catalyst pores affects the rate, changing the flow conditions
past the catafyst should change the overall reaction rate. In porous catalysrs, on
the other hand, diffusion within the catalyst pores may limit the rate of reaction. Under these circumstances, the overall rate will be unaffected by external
flow conditions even though diffusion affects the overall reaction rate.
There are many variations of the situation described in Table 10-2. Sometimes, of course, two reactants are necessary for a reaction to occur, and both
of these may undergo the steps listed earlier. Other reactions between two substances may have only one of them adsorbed.
With this introduction, we are ready to treat individually the steps
involved in catalytic reactions, In this chapter only the steps of adsorption, surface reaction, and desorption will be considered [i.e.. it is assumed that the diffusion steps (1, 2, 6, and 7) are very fast, such that the overall reaction rate is
not affected by mass transfer in any fashion]. Funher treatment of the effects
involving diffusion Iimitations is provided in Chapters 1I and 12.
Where Are W e Heading? As we saw in Chapter 5, one of the tasks of a
chemical reaction engineer is to analyze rate data and to deveIop a rate law
that can be used in reactor design. Rate laws in heterogeneous catalysis seldom
follow power law models and hence are inherently more difficult to formulate
from the data. To develop an in-depth undemanding and insight as to how the
rate laws are formed from heterogeneous catalytic data, we are going to proceed in somewhat of a reverse manner than what is normally done in industry
when one is asked to develop a rate Iaw. That is, we will postulate catalytic
mechanisms and then derive rate laws for the various mechanisms. The mechanism will typically have an adsorption step, a surface reaction step, and a
desorption step, one of which is usually rate-limiting. Suggesting mechanisms
and rate-limiting steps is not the first thing we normally do when presented
with data. I-lowever, by deriving equations for different mechanisms, we will
observe the various forms of the rare law one can have in heterogeneous catalysis. Knowing the different forms that catalytic rate equations can take, it will
be easier to view the trends in the data and deduce the appropriate rate law.
This deduction is usually what is done first in industry before a mechanism is
proposed. Knowing the form of the rate law, one can then numerically evaluate
the rate law parameters and postulate a reaction mechanism and rate-limiting
step that is consistent with the rate data. Finally, we use the rate law to design
catalytic reactors. This procedure is shown in Figure 10-7. The dashed lines
represent feedback to obtain new data in specific regions le.g., concentrations,
Catalvsis and Catalytic Reactors
Chap. 10
Obtain deta horn
labralory resclm
,'
I
\
An algorithm
Figure 10-7 Collectin,g infnrmarion for catalytic reactor design.
temperature) to evaluate the rate law parameters more precisely or to differentiate between reaction mechanisms.
We will discuss each of the steps shown in Figure 10-6 and Table 10-2.
As mentioned earlier. this chapter focuses on Sreps 3, 4, and 5 (the adsorption.
surface reaction and desorption steps) by assuming Steps 1, 2, 6, and 7 are
very rapid. Consequenrly to understand when this assumption is valid, we shall
give a quick overview of Steps 1, 2, 6. and 7. Steps 1 and 2 involve diffusion
of the reactants to and within the catalyst pellet. While these steps are covered
in detail in Chapters 11 and 12, it is worthwhile to give a brief description of
these two mass transfer steps to better understand the entire sequence of steps.
10.2.1 Step IOverview: Diffusion from tha Bulk to the External
Transport
For the moment let's assume the transport of A from the bulk fluid to the external surface of the catalyst is the slowest step in the sequence. We Pump all the
resistance to transfer from the bulk fluid to the surface in the boundary layer
surrounding the pellet. In this step the reactant A at a bulk concentration CAh
must travel through the boundary layer of thickness 6 to the external surface of
the pellet where the concentration is CAsas shown in Figure 10-8. The rate of
transfer {and hence rate of reaction. -[:) for this slowest step is
Rate A kc (C,, - C,,)
where the mass transfer coefficient, k , is a function of the hydrodynamic conditions. namely fluid velocity, U,and the particle diameter, D,,,
As we will see (Chapter I I I the mass transfer coefficsent is inversely proportional to the boundary layer thickness. 6,
Sec. 10.2
659
Steps in a Catalytic Reaction
Figure 10-8 Diffusion through the external boundary layer. [Also see Figure
Ell-1.1.1
and direct1y proportional to the coefficient diffusion (i-e., the diffusivity DAB).
At low velocities of fluid flow over the pellet, the boundary layer across which
A and B must diffuse is thick, and it takes a long time for A to travel to the
surface, resulting in a small mass transfer coefficjeat kc. As a result, mass
transfer across the boundary layer is slow and limits the rate of the overalE
reaction. As the velocity across the pellet is Increased, the boundary layer
becomes smaller and the mass transfer rate is increased. At very high velocities
the boundary layer is so smalI it no longer offers any resisfance to the diffusion
across the boundary layer. As a result, externat mass transfer na longer limits
the rate of reaction. This external resistance also decreases as the particle size
is decreased. As the fluid veIocity increases andlor the particle diameter
decreases, the mass transfer coefficient increases until a plateau is reached, as
shown in Figure 10-9. On this plateau, CAb= CAs,and one of the other steps in
the sequence is the slowest step and Iirnits the overall rate. Further details on
external mass transfer are discussed in Chapter 1I .
Overall
Rate
longer the slowest step
External diffusion
is ths slowest step
Figure 10-9 Effect nf overall raze on particle size and Ruid velocity.
660
Catalysis and Catalytic Reactors
Char
10.2.2 Step 2 Overview: Internal Diffusion
Now consider that we are operating at a fluid velocity where external diffuz
is no longer the rate-limiting step and that internal diffusion is the slowest sl
In Step 2 the reactant A diffuses from the external surface at a concentral
C,, into the pellet interior where the concentration is C,. As A diffuses E
the interior of the pellet, it reacts with catalyst deposited on the sides of
pore walls.
For large pellets, it takes a long time for the reactant A to diffuse into
interior compared to the time it takes for the reaction to occur on the inte~
pore surface. Under these circumstances, the reactant is only consumed n
the exterior surface of the pellet and the calalyst near the center of the pelle
wasted catalyst. On the other hand, for very ma11 pellets it takes very li
time lo diffuse into and out of she pellet inrerior and, as a result, internal (
fusion no Longer Iirnits the rate of reaction. The rare of reaction can
expressed as
Rate = k, CA,
where CAsis the concentration at the external surface and k, is an overall c
constant and is a function of particle size. The overall rate constant,
increases as the pelIet diameter decreases. In Chapter 12 we show tl
Figure 12-5 can be combined with Equation (12-34) to arrive at the plot of
as a function of Dp shown in Figure 10-lO(b).
We see that at small particle sizes internal diffusion is no longer the slc
step and hat the surface reaction sequence of adsorption, surface reaction. a
desorption (Steps 3, 4, and 5) limit the overall rate of reaction. Consider nc
one more point about internal diffusion and surface reaction. These steps
through 6) are not at all affected by flow conditions external to the pellet.
In the rnateriai that follows, we are going to choose our pelIet size a1
external fluid velocity such that neither external diffusion nor internal diffusid
I
Surface reaction sequence
internal diffusion
k
- -1
OD
Figre 10-10 Effect of particle size on overall reaction rate constant. (a)
Branching of a single pore with deposited metal; (b) Decrease in rate constant
with increasing particle diameter..
Sec. 10.2
Steps
in a Catalytic Reaction
661
is limiting. Inqtead. we assume that either Step 3 adsorption, Step 4 surface
reaction, or Step 5 desorption, or a combination of these steps. limits the overall rate of reaction.
10.2.3 Adsorption Isotherms
Because chemisorption is usually a necessary part of a catalytic process, we
shall discuss i t before tnaring catalytic reaction rates. The letter S will represent an active site; alone it will denote a vacant site, with no atom, molecule,
as complex adsorbed on il. The combination of S with another Iettes
(e.p., A . S ) will mean that one unit of species A will be adsorbed on the site S.
Species A can be an atom, molecule, or some other atomic combination.
depending on the circumstances. Consequently, the adsorption of A on a site S
is represented by
The total rnotar concentration of active sites per unit mass of catalyst is equal
to the number of active sites per unit mass divided by Avogadro's number and
will be labeled C, (rnolig .cat). The molar concentr?ttion of vacant sites, C ,, is
the number of vacant sites per unit mass of catalyst divided by Avogadro's
number, In the absence of catalyst deactivation, we assume that the total concentration of active sites remains constant. Some further definitions include
partial pressure of species i in the gas phase. atm or kPa
p,
surface
concentration of sites occupied by species i, rnollg cat
Cres
A conceptual mode1 depicting species A and B on two sites is shown in Figure
10-11.
Figure 10-11 Vacant and occupied sites
For the system shown, the total concentration of sites is
Site balance
Postulate
mdels: then see
which one(s,
fit(s) the data.
ct
=
c, + c~.s
+ CR.s
(10-1)
This equation is referred to as a ~ i l balance.
e
Now consider the adsorption of a nooreacting gas onto the surface of a
cataryst. Adsorption data are frequently reported in the form of adsorption isotherms. Isotherms portray the amount of a gas adsorbed On a solid at different
pressures but at one temperature.
First, a model system is proposed and then the isotherm obtairled from
the model is compared with the experimental data shown on the curve. If the
curve predicted by the model agrees with the experimental one, the model may
reasonably describe what is occurring physically in the real system. If the predicted curve does not agree with data obtained experimentally. the model fails
662
Catalysis and Catalytic Reactors
Ghap. 71)
to match the physical situation in at least one irnportarrt characteristic and perhaps more.
Two models will be postulated for the adsorption of carbon monoxide on
metal surfaces. In one model, CO is adsorbed as molecules, CO,
as
is the case on nickel
In the other, carbon monoxide is adsorbed as oxygen and carbon atoms instead
of molecular CO.
as i s rhe case on
-Fe-Fe-Fe-
Two models:
I . Adsorption as
CO
2. Adsorption as
C and 0
-Fe-Fe-Fe-
The former is caIled molecular or nondissociared adsorprion (e.g., CO) and
the latter is called dissociative adsorption (e.g., C and 0).Whether a molecule
adsorbs nondi ssociatively or dissociative1y depends on the surface.
The adsorption of carbon monoxide molecules will he considered first.
Because the carbon monoxide does not react further after being adsorbed, we
need only to consider the adsorption process:
See
Reference Shelf
For Adcorption
irong
CO+S (c0.s
(10-2)
In obtaining a rate law for the rate of adsorption, the reaction in Equation (10-2)
can be treated as an e l e m e ~ ~ r ureacrion.
q
The rate of attachment of the carbob
monoxide molecules to the active site on the surface i s proportional to the number of collisions that these molecules make with a surface active site per second. In other words, a specific fraction of the molecules that strike the surface
become adsorbed. The collision rate is, in turn, direc~ly-proportional
to the car.
bon monoxide partial pressure, Pco Because carbon monoxide moiecules
adsorb only an vacant sites and not on sites already occupied by other carbon
monoxide molecufes. the rate of attachment is also directly proportional ro the
concentration of vacant sites, C,. Combining these two facts means that the
v
p
,
,
R. L. Masel, Principles of Adsorption and Reaction on Solid Sutjures (New Y d :
Wiley. 19963.
Set. 10.2
Steps in a Catalytic Reaction
663
rate of attachment of carbon monoxide molecules to the surface is directly proportional to the product of the partial pressure of CO and the concentration of
vacant sites; that is,
A
Rate of attachment = kAPcoC,
A
The rate of detachment of molecules from the surface can be a first-order
process; that is, the detachment of carbon monoxide molecules from the surface is usually directly proportional to the concentradon of sites occupied by
the adsorbed molecules (e.g.,
rate of detachment = k-ACco.s
The net rate of adsorption is equal to the rate of molecular attachment to
the surface minus the rate of detachment from the surface. If k, and k - , are
the constants of proportionality for the attachment and detachment processes.
then
~ d ~ ~ , , , The
~ ~ratio
~ ~ K A = kA/k-, is the adsorprio~equilibrium constanr.
A . S to rearrange Equation (10-3) gives
A+S
The adsorption rate constant, kA, for mofecular adsorption is virtually
independent of temperature. while the desorption constant, k-*, increases
exponentially with increasing temperature. The equilibrium adsorption constant K A decreases exponentially with increasing temperature.
Because carbon monoxide is the only material adsorbed on the catalyst.
the site balance gives
)
- =
k,=
[A.
C,= C[. -t Cco
-
P A =( a m )
Using it
<]
(1 0-5)
At equilibrium. the net rate of adsorption equals zero. Setling the left-hand
side of Equation (10-4) equal to zero and solving for the concentration of CC,
adsorbed on the surface. we get
G o s = K* c,.pro
Using Equation (10-5) to give C, in terms of Cco., and the total number of
sites C,. we can solve for Cm., in terms of constants and the pressure of carbon monoxide:
G o . s = kA C, PCO = KAPCO(CI- CCO. S)
Rearranging gives us
Catalysis and Catalytic Reactors
Chal
This equation thus gives the concentration of carbon monoxide adsor
the surface, C,-o.s, as a function of the partial pressure of carbon monox
and is an equation for the adsorption isotherm. This particular type of isothc
equation is called a Langrnuir iso~herm.~
Figure 10-12(a) shows a plot of
amount of CO adsorbed per unit mass of catalyst as a function of the par
pressure o f CO.
One method of checking whether a model (e.g., molecular adsorpt
versus dissociative adsorption) predicts the behavior of the experimental d
i s to linearize the model's equation and then lot the indicated variab
against one another. For exarnp<e, Equation (10-7)maybe arranged in the fc
od
MolecuIar
adwmtrnn
-0
+ 1
Cc0.s KAC!
Pm
-pco
C,
(10
and the linearity of a plot of P,,ICco.sas a function of Po will determine
the data conform to a Langrnuir single-site isotherm.
Next, the isotherm for carbon monoxide adsorbing as atoms is derivec
Dissmiative
adsorption
co + 25
a Cc.s+ 0 . S
When the carbon monoxide molecule dissociates upon adsorption, it i s referr
to as the dissociative adsorption of carbon monoxide. As In the case of mole
ular adsorption, the rate of adsorption is proportional to the pressure of cxb,
monoxide in the system because this rate is governed by the number of ge
eous collisions with the surface. For a molecule to dissociate as it adsort
however, two adjacent vacant active sites are required rather than the sing
site needed when a substance adsorbs in its moIecular fom. The probability
Linear
Figure 10-12 Langrnuir isotherm for (a) molecular adsorption (b) dissociative
adwrption of CO.
after Irving Langmuir ( t 881-1957). who first proposed it. He received th
Noh1 Prize in 1932 for his discoveries in surface chemistry.
9 Named
5%. 10.2
665
Steps ~na Catalyt~cRsact~on
two vacant sites occurring adjacent to one another is proportional to the square
of the concentration of vacant sites. These two observations mean that the rate
of adsorption is proportional to the product of the carbon monoxide partial
pressure and the square of the vacant-site concentration, P,,Cj.
For desorption ro occur, two occupied sites must be adjacent, meaning that
the rate of desorption is proportional ta the product of the occupied-site concentration. (C - S) X (0S). The net rate of adsorption can then be expressed as
-
Factoring out k,, the equation for dissociative adsorption is
Rate o f diswiative
adsorption
where
For dissociative adsoption both k, and k-, increase exponential1y with
increasing temperature while KA decreases with increasing temperature.
At equilibrium, r,,, = 0, and
kAPcoclf = k-ACc.5Co.s
FOSCc.S = CO.$,
(
~
~
P
~
=~ CO.
~ s" Z ~ v
(10-IO)
Substituting for Cc.sand CoAsin a site balance Equation (10-I),
Solving for C,
I
C, = C, /( 1 + 2 ( ~ ~ $ ~ ~ ) ~ ~ )
This vaIue may be substituted into Equation (10-10) to give an expression that
can be solved for Co.s. The resulting equation for the isotherm shown in Fig-
1
I
Langmuir isotherm
for adsorpt~onas
ure IO-lZ(b} is
atomic carbon
monoxide
Dissociative
adsorption
Taking the inverse of both sides of the equation, then multiplying through
by (PCo)I", yields
2 *' I
p
-=
(PC01
c~S
CF:"
PZ
sus :
:P
I
ct(KA)113
+
2(P,o)"Z
(10-12)
cf
If dissociative adsorption is the correct model, a plot of (ft$C0.,) vershould be linear with slope (2/C,).
666
Catalvsis and Catalytic Reactors
Cheo. 10
When more than one substance is present, the adsorption isotherm equations
somewhat more complex. The principles are the same, though, and the isotherm equations are easily derived. It is left as an exercise to show that the adsorp
tion isotherm of A in the presence of adsofiate B is given by the relationship
ate
Ct-Cv+CS
~B'+~
Note assumptions in
rhe model
and check their
validity
When the adsorption of both A and B are first-order processes. the desorptions
are also first order, and both A and B are adsorbed as molecules. The derivations of other Langrnuir isotherms are relatively easy and are left as an exercise,
In obtaining the Langrnuir isotherm equations, several aspects of the
adsorption system were presupposed in the derivations. The mast important of
these, and the one that has been subject to the greatest doubt, is that a unjfoform
surface is assumed. In other words, any active site has the same artsaction for
an impinging molecule as does any orher site. Isotherms different from the
Langmuir types, such as the Fseundlich isotherm, may be derived based on
various assumptions concerning the adsorption system, including different
types of nonuniform surfaces.
10.2.4 Surface Reaction
The rate of adrorption of species A onto a solid surface,
A+S
A-S
is given by
Surface reaction
After a reactant has been adsorbed onto the surface, it is capable of reacting in
a number of ways to form the reaction product. Three of these ways are:
1. Single sire. The surface reaction may k a single-site mechanism in
which only the site on which the reactant is adsorbed is involved in the
reaction. For example, an adsorbed molecule of A may isomerize (or
perhaps decompose) directly on the site to which it is attached, such as
N = n.p@mene
I= I - p m m
.A
A.S
B-S
5tngle stte
Because in each step the reaction mechanism is elementary, the surface reaction rate law is
667
Steps in a Catalytic Reactbn
Sec. 10.2
where Ks is the surface reaction equilibrium constant Ks = kslk-s
2. Dual site. The surface reaction may be a dual-site mechanism in
which the adsorbed reactant interacts with another site (either unoccupied or occupied) to form the product.
K, = (dimensionless)
Duel site
For example. adsorbed A may react with an adjacent vacant site to
yield a vacant site and a site on which the product is adsorbed, such
as the dehydration of butanol.
For the generic reaction
the corresponding surface reaction rate Eaw is
Dual Sire
(10-16)
Another example of a dual-site mechanism is the reaction between
two adsorbed species, such as reaction CO with 0
K,= (dimensionleas)
For the generic reaction
--
;,. ....,,-A
{ 0.
,TC ,
/.D.,.
/
AaS
+ B.S
C.S
+ D.S
Dual srte
the corresponding surface reaction rate law is
668
Catalysis and Catalytic Reactors
Cha
A third dual-site mechanism is the reaction of two species adso
on different types of sites S and S'. such as reaction of CO with
For the generic reaction
Dual site
the corresponding surface reaction mte law is
Reactions involving either single- or dual-site mechanisms, w
were described earlier are sometimes referred to as following L
muir-Hirsshelwood kinetics.
3. Eiq-Rideal. A third mechanism is the reaction between an adso
molecule and a molecule in the gas phase, such as the reaction of
pylene and benzene
Langmu~rHinshelwocd
kinetics
C3*.*
B
.A:
@.: .
,@-.:
&4&
,'C:
&-&
For the generic reaction
Eley-Rideal rnechan~srn
A . S + B(g)
c-S
the corresponding surface reaction rate law is
(10
This type of mechanism is referred to as an Eley-Rideal mechan,
10.2.5 Desorption
KK = (am)
.
En each of the preceding cases, the products of the surface reaction adso
on the surface are subsequently desorbed into the gas phase. For the desoq
of a species (e.g., C),
C-S
the rate of desorption of C is
C+S
Sec. 10.2
Steps in
a Catalytic Reaction
669
where Koc is the desorption equilibrium constant. We note that the desorption
step for C is just the reverse of the adsorption step for C and that the rate of
desorption of C, r,, is just opposite in sign to the rate of adsorption of C. r,,:
In addition, we see that the desorption equilibrium constant Kw is just the
reciprocal of the adsorption equilibrium constant for C,Kc:
In the material that follows, the form of the equation for the desorption step
that we will use will be similar to Equation (10-2 I).
10.2.6 The Rate-Limiting Step
When heterogeneous reactions are carried out at steady state. the rates of each
of the three reaction steps in series (adsorption. surface reactiorl. and desorption) ate equal to one another:
However, one particular step in the series is usually found to be rare-limiting or mte-controlling.That is, if we could make this particular step go faster,
the entire reaction would proceed at an accelerated rate. Consider the analogy
to the electrical circuit shown in Figure 10-13. A given concentration of reactants is analogous to a given driving force or electromotive force (EMF). The
current I (with units of Cwbmbs/s) is analogous to the rate of reaction, -ri
(rnol/sWgcat), and a resistance R, is associated with each step in the series.
Since the resistances are in series. the total resistance is just the sum of the Endividual resistances, for adsorption (RAD),surface reaction (Rs), add desorption
(RD),and the current, I, for a given voltage, E, 1s
ifowing us
down?
Plgure 10-13 Electrical analog to heterogeneous renctionu.
Catalysis and Catalflic Reactors
he concept of a
nte-limiting step
An alrwithm to
determine the
rate-limtting step
Chap. 10
Since we observe only the total resistance, R,,,.it is our task to find which
resistance is much larger (say, 100 R) than the other two (say. 0.1 0).Thus,if
we could lower the largest resistance, the current I (i.e., -rA) , would be Iarger
for a given voltage, E. Analogously, we want to h o w which step in the adsorption-reaction-desorption series is limiting the overall rate of reaction.
The approach in determining catalyric and heterogeneous mechanisms is
usually termed the Longrnuir-Hinskelwood approach, since it is derived from
ideas proposed by Hinshelwood'O based on Langmuir's principles for adsorption. The Langmuir-Hinshelwood approach was popularized by Hougen and
Watson" and occasionatly inellides their names. I t consists of first assuming a
sequence of steps in the reaction. In writing this sequence. one must choose
among such mechanisms as moiecular or atomic adsorption, and single- or
dual-site reaction. Next, rate Iaws are written for the individual steps as shown
in the preceding section, assuming that all steps are reversible. Finally, a
rate-limiting step is postulated, md steps that are not rate-limiting are used to
eliminate all coverage-dependent terms. The most questionable assumption in
using this technique to obtain a rate law is the hypothesis that the activity of
the surface toward adsorption, desorption, or susface reaction is independent of
coverage; that is, the surface is essentiaIly uniform as far as the various steps
in the reaction are concerned.
An example of an adsorption-limited reaction is the synlhesis of aamrnonia from hydrogen and nitrogen,
over an iron catalyst that proceeds by the following mechanisrn.j2
H2+2S
+ 2H.S
Rapid
Dissociative
adsorption
of N, limits
NH.S+H+S
i
HH,N-S+S
H , N . S + H . S (NNH,S+S
Rapid
I0C. N. H i n s h e l w d , The Kinetics of Chemical Chan~e(Oxford: Clarendon h e s s 1940).
I'O.A. Hougen and K. M. Watson. Ind. E ~ R Chem.,
.
35.529 (1943).
'?From the literature cited in G. A. Sornorjai. lnfmdurrion m S~trjhceC h e m i s t ~atld
Cataljj.~is(NEWYork: W~ley,1994). p. 482.
Sec. 10.3
Synthesiz~nga Rate Law, Mechanism, and Rate-Limiting Step
67 1
The rate-limiting step is believed to be the adsorption of the NZmolecule as an
N atom.
An example of a surface-limited reaction is the reaction of two noxjous
automobile exhaust products. CO and NO,
carried out over copper catalyst to form environmentally acceptable products,
N2 and CO?:
Rapid
Surface reaction
limits
Rapid
Analysis of the rate law suggests that C 0 2 and
Problem P 10-7,).
N, are weakly
adsorbed (see
10.3 Synthesizing a Rate Law, Mechanism,
and Rate-Limiting Step
We now wish to develop rate laws for catalytic reactions that are not diffusion-limited. In developing the procedure to obtain a mechanism. a rate-limiting step, and a rate law consistent with experimental observation, we shall
discuss a particular catalytic reaction, the decomposition of cumene to form
benzene and propylene. The overall reaction is
A conceptual model depicting the sequences of steps in this platinum-catalyzed reaction is shown in Figure 10-14. Figure 10-14 is only a schematic representation of the adsorption of cumene: a more realistic model is the
formation of a complex of the rr orbitals of benrene with the cataIytic surface.
as shown in Figure 10-15.
Adsorption
Suriace
reaction
cab
necorption
Adsorption of
cumens
-Surfoca
react ion
Derwpl~onof
benzene
Catalysis and Catalytic Reacton
Cha
Figure 10-15 n-orbttal complex on surface.
The nomenclature in TabIe 10-3 will be used to denote the various
cies in this reaction: C = cumene, B = benzene. and P = propylene. The I
tion sequence for his decomposition is
C
These three steps
represent the
mechanism for
+S
+& C.S
k*
"
C'S
k4
B.S <
ka
)
Adsorption of cumene on the surface
B .S + P
cumene
decomposition
k,
Ideal Gas
L ~ W
)
B
+S
Surface reaction to form adsorbed
benzene and propylene in the
gas phase
Desorption of benzene from surface
Equations (10-223 through (10-24) represent the mechanism proposed for
reaction.
When writing rate laws for these steps, we treat each step as an eler
tary reaction; the only difference is that the species concentrations in the
phase are replaced by their respective partial pressures:
PC = CcRT
cc
-
PC
There is no theoretical reason for this replacement of the concentration.
with the partial pressure, PC;it is just the convention initiated in the 1930s
used ever since. Fortunately PC can be calculated directly from Cc usini
ideal gas law.
The rate expression for the adsorption of cumene as given in Equi
(10-22) is
C+S
C*S
k - ~
TAD
1-
= kAPcC, - k-ACc.s
Adsorption:
r,, = k, P&,--
Sec 10 3
Syntbesr-rmg a RaZe Law, Mechan~sm,and Rate-Llmrt~ngStep
673
,
I f I.,,,, ha\ unit\ of (tnollg c a t - c ) ;IL~ C, ha\ unit\ nt'(mol cumcnc i ~ c l ~ ~ ~ h c t l / g
cat) typical unitc of k , , X and K( ~woultlhe
,.
[ A , I =(I\P.r.s)-
' or(atrn.h)-'
{ k - % ]= h - I ors-I
The rate Law for the surface reaction step producing adsorbed benzcne
and prnpylene in the gas phase.
with the s u r f ~ ~ crenorion
c
~quilibriiurrconsranr being
Typical units for ks and Ks are s-' and kPa. respectively.
Propylene is not adsorbed on the surface. ConsequentIy, its concentration
on the surface is zero.
Cps=O
The rate o f benzene desorptian [see Equation (10-74)j i s
I
I+D =
kDCR.s- k-DPRCL,
Desarption:
Typical units of kD and XDBate
desorprion of benzene.
rD = k,,
S-'
( )CB s-
1
( lo-27)
[ 10-28)
and kPa, respectively. By viewing the
From right to left. we see that desorption is just the reverse of the adsorption of
benzene. Consequently, it is easily shown that the benzene adsorption equilihrium constant Ks is just the reciprocal of the benzene desorption constant K,,ll:
Catalysis and Catatytic Reactors
Chap. 10
-
K, = 1
KD,
and Equation (10-28) can be written as
Because there is no accvmulation of reacting species on the surface the rates
of each step in the sequence are all equal:
1-
(10-30)
For the mechanism postulated in the sequence given by Equations
(10-22) through (10-24), we wish to determine which step is rate-limiting. We
first assume one of the steps to be rate-limiting (rate-con~olling)and then formulate the reaction rate law in terns of the ~artialpressures of rhe species
present. From this expression we can determine the variation of the initial
reaction rate with the initial total pressure. If the predicted rate varies with
pressure in the same manner as the rate observed experimentally. the implication is that the assumed mechanism and rate-limiting step are correct.
10.3.1 Is the Adsorption of Cumene Rate-Limiting?
To answer this question we shall assume that the adsorption of cumene is
indeed rate-limiting, derive the corresponding rate law, and then check to see
if it is consistent with experimental observation. By assuming that this (or any
other) step is rate-limiting, we are considering that the reaction rate constant of
this step (in this case k,) is small with respect to the specific rates of the other
steps (in this case k , and kD).I3 The rate of adsorption is
Need to express C,,
and Cc,s in terms
of PC. P,, and Pp
Because we can measure neither C, or Cc.s,we must replace these variables
in the rate law with measurable quantities for the equation to be meaningful.
For steady-state operation we have
(10-30)
-~.d==r~,,=r~=r,,
''Strictly speaking one should compare the product k4Pc with k, and k,.
s kg cat
Dividing by KhL,PCIce note
the ratio,
R,>P,
Ls
atm
= @ . The reawn i s that in order to cornpaw terns.
kg car
mol ]
(-3).
):[ and):( mud ali havr the same units r8
~ADPC
result is the same however
;kg c a t
~ h .end
Sec. 10.3
Synthesizing a Rate Law Mechanism, and Rate-Limiting Step
675
For adsorption-limited reactions, k~ is small and ks and kD are large. Consequently. the ratios rslks and r ~ l kare
~ very small (approximately zero),
whereas h e ratio rAD/kAis relatively large. That is, the prduct for h e adsorption step [k,Pc] (s-I) is small with respect te the other rate constants: k, (s-1)
for the surface reaction step and kD (s-I) for the desorption step.
The surface reaction rate law is
Again, for adsorption-limited reactions the surface specific reaction rate
ks is large by comparison, and we can set
r=
ks
'S=
fJ
and solve Equation (10-31) for Cc.s:
To be able to express CC.ssoleIy in terms of the partial pressures of the species present, we must evaluate CB.$.The rate of desorption of benzene 1s
's-(J"yD
to find C, and
Cc 3 in terms of
partial pressures
Hawever, for adsorption-limited reactions, k~ is large by comparison. and we
can set
m=
k,
1 and then solve Equation (10-29) for CB.s:
Ce,s=KepaCv
After combining Equations f 10-33) and
(10-351,we have
Replacing Cc.sin the rate equation by Equation (10-36) and then factoring C,.,
we obtain
( )
K P P
r A ~ = k Ap , - L P
(
~ , = k ,pc--
(10-371
Observe that by setting r,, = 0,the term (KsK c / K B ) is simply the overall partial pressure equilibrium constant. Kp. for the reaction
Catalysis and Catalytic Reactors
Chal
The equilibrium constant can be determined from thermodynamic I
and is d a t e d to the change in the Gibbs free energy, AGO, by the equation I
Appendix C)
where R is the ideal gas constant and T is the absolute temperature.
The concentration of vacant sites, C,, can now be eliminated from Ec
tion (10-37) by utilizing the site balance to give the total concentration of si
C,, which is assumed constant: l4
Total sites = Vacant sites+Occupied sites
Because cumene and benzene are adsorbed on the surface, the concentratior
occupied sites is (Cc., +- CBAS),
and the total concentration of sites Is
Site balance
C, = C,
+ Cc.s+ CB-S
(1@
Substituting Equations (10-35) and (10-36)into Equation (10-401, we h
Solving for C,, we have
Combining Equations (10-41) and (10-371, we find that the rate law for
catalytic decompositon of curnene, assuming hat the adsorptioa of curnene
the rate-limiting step, is
Cumene reaction
sate law if
adsorption were
the limiting step
'JSome prefer to write the surface reaction rate in terms of the fraction of the sud
of sites covered (i.e.. f,? rather than the number of sites CA.Scovered, the differel
being the multiplication factor of the total site concentration. C,. In my event.
final form of the rate law is the same because C,, KA,ks, and so on, are dI lurn~
into the reaction rate constant. k.
Sec 10.3
Synthesizrng a Rate Law. Mechanism, and Rate-Llrniting Step
677
We now wish to sketch a plot of the initial rate as a function of the partial pressure of cumene. PC,,. Initially, no products are present; consequently,
P , = PB = 0. The initial rate is given by
( 10-43)
-rho = C, k,4Pco= kPco
If the cumene decornpostion is adsorption rate limited. then the initial rate will
be linear with the initial parlial pressure of cumene as shown in Figure 10- 16.
If adsorption were
ln~tialpartial pressure of cumene, PCD
rate-limiting. the
data should show
-ri increasing
linearly with
Figure 10-16
CJninhibited adsorption-timited reaction.
Pa,.
Before checking to see if Figure 10-16 is consistent with experimental
observation, we shall derive the carresponding rate laws and initial rate plots
when the surface reaction is rate-limiting and then when the desorption of benzene is rate-limiting.
10.3.2 Is the Surface Reaction Rate-Limiting?
The rate of surface reaction is
Single-site
mechanism
Since we cannot readily measure the concentrations of the adsorbed species,
we must utiEize the adsorption and desorption steps to eliminate Cc and CB.S
,
from this equation.
From the adsorption rate expression in Equation (10-25) and the condition that kA and k, are very large by comparison with ks when surface
reaction is controlling (i.e., rm/kA = 01, we obtain a relationship for the
surface concentration for adsorbed curnene:
cc s = KcPcCu
In a similar manner, the surface concentration of adsorbed benzene can
be evaluated from the desorptjon rate expression [Equation / 10-29)] together
Using
1 with the approximation:
to find CB.sand
Cc.s in terms of
partial pressures
when
-E 0
P~
k,
then C B .=~ K B P B C ,
678
Catalysis and Cataly#c Reactow
Chap. 10
Substituting for Capsand Cc.sin Equation (10-26) gives us
The only variable left to eliminate is C, :
ct = c, + cB.S
+ cc.S
Site balance
Substituting for concentrations of the adsorbed species, CB.S,and Cc.s yields
P
Cumene rate law
for surfacereaction-limiting
The initial rare is
At low partial pressures of curnene
1
+ KcPm
and w e observe that !he initial rate will increase linearly with the initial partial
pressure of cumene:
At high partial pressures
KrP,
I
and Quation I 10-45) becomes
and the rate i s independent of the panial pressure of curnene. Figure 10-17
shows the initial rate of reaction. as a function of initial partial pressure of
cumene for the case of surface reaction controlling.
10.3.3 Is the Desorption of Benzene Rate-Limiting?
Thc rate expression for the desorption of benzene is
D'
= k,
(Cg
s-KBf'BCL
1
Sac. I 0.3
Synthesrz~nga Rate Law, Mechanism, and Rate-Limiting Step
679
If surface
reaction were
rate-limiting, the
data would show
this behavior.
Initial partial pressure of cumene, PCO
Figure 10-17
For desorplionl~rnltedreactiuns.
h t h LAD and I ,
are vet! large
compared wrth AD.
Surface-reaction-limited.
From the rate expression for surface reaction, Equation (10-26). we
set
!Lo
As
a hich i%small.
to obtain
Similarly. for the adsorption step. Equation (10-251, we set
r~
o,
k*
to obtain
Cc s = KcPCC ,
then substitute for Cc.s in Equation (10-46):
K K P C
CB-$=
PP
Combining Equations ( I 0-28) and (10-47) gives us
where Kc i s the cumene adsorption constant. K , is the surface reaction equilibrium constant, and Kp is the gas-phase equilibrium constant for the reaction. To
obtain an expression for C,. we again perfon a site balance:
Site balance:
C, = Cc.s + C,.,
+ C,
After substituting for the respective surface concentrations. we salve the site
bal nnce for C,,:
680
Cata'ysis and Catalytic Reactors
Cl?a
Replacing C,. in Ecluat~on( 10-48) by Equation ( 10-49) and multipl
the nuinerator and denominator by Pp, we vhtain the rate expression
decorption cr~ntrol:
C~~mene
decr>mpn<~t~un
rille
law !f deqorptlun
Ncrc Iiniiting
tf derorprlon
control\. he uliti.11
rdre ic indepcnrlrnt
of p a f l i ~ plrcrltre
l
of ctlrnenr.
To determine the dependence of the initial rate on partial pressur
set P p = PR = 0; and the rate law reduces to
cumene. we again
- I"&, = k,C,
-I+:,,
with the corre~pondingplot of
shown i n Figure IO- 18. If desorpticln
controlling, we would see that the initial rate would be independent of the
rial partial pressure o f cumene.
ln~tialpartial pressure of cumene, PCo
Fipre 10.18
Dewrpt~on-limitedrencrlon.
10.3.4 Summary of the Cumene Decomposition
Cumcnc
decompu'itlon
surface-reaction-
limited
The experimental observations of -r&, as a function of Pco are shown in Fi
10- 19. From the plot in Figure 10- 19. we can clearly see that neither adsoq
nor desorption is rate-limiting. For the reaction and mechanism given by
C-S
I3.S
+P
the rate law derived by assuming that the surface reaction is rate-limiting ai
with the data.
The rate law for the case of no inerts adsorbing on the surface is
See. 10.3
Synthesrzlng a Rate Law. Mechanism, and Rate-Limiting Step
Surt~cvlimited
~ ; 1 ~ t i omechilni=.m
1\
i, consictcnt with
experimeti1;11 data.
Init~aipartial pressure of cumane, PCo
Figure 11)-I9 Actual in~tialrate as a funct~onof partial preqsuw of uunlcne.
The forward curnene decomposition reaction is a single-site mechanism
involving onEy adsorbed curnene while the reverse reaction of propy lene in the
gas phase reacting with adsorbed benzene is an Eley-Rideal mechanism.
tf we were to have an adsorbing inert in the feed, the inert wouId not participate in the reaction but would occupy sites on the catalyst surface:
Our site balance is now
Because the adsorption of the inert is at equilibrium. the concentration of
sites occupied by the inert is
Cl.s= KIPLC,
( t O-51,)
Substituting For the inert sites in the site balance, the rate law For surface reaction control when an adsorbing inert is present is
10.3.5 Reforming Catalysts
We now consider a dual-site mechanism. which is a reforming reaction Found
in petroleum refining to upgrade the octane number of gasoline.
Side Note: Ocbne Number. Fuels with low octane numben can produce
spontaneous combustion in the cylinder before the airlfueI mixture is compressed to its desired value and ignited by the spark plug. The following figure shows-the desired combustion wave front moving down from the spark
plug and the unwanted spontaneous combustion wave in the lower
right-hand corner. This spontaneous combustion produces detonation waves
which constitute engine knock. The lower the octane number the greater the
chance of engine knock.
Catalysis and Catalytic Readors
%-~pontsnwu~
Combustion
I
Calibration Curve
1
Chap 10
t
I
Unknown
100% heptane 100% iso
Octane Number
The octane number of a gasdine is determined from a calibration
curve relating knock intensity to the % iso-octane in a mixture of jso-octane
and heptane, One way to calibrate the octane number is to place a transducer on the side o f the cylinder to measure the knock intensity (K.1,) (pressure pulse) for various mixtures of heptane and iso-octane. The octane
number is the percentage of iso-mtane in this mixture. That is, pure
iso-octanehas an octane number of 100, 808 iso-octanel20% heptane has
an octane number of 80, and so on. The knock intensity is measured for this
80120 mixture and recorded. The relative percentages of iso-octane and heptane are changed (e.g., 901101, and the test is repeated. After a series of
experiments, a calibration curve is constructed. The gasoline to be calibrated is then used in the test engine, where the standard knock intensity is
measured. Knowing the knock intensity, the octane rating of the fuel is read
off the calibration curve. A gasoline with an octane rating of 92 means that
it matches the performance of a mixture of 92% iiso-octane and 870heptane.
Another way to calibrate octane number is to set the knock intensity and
increase the compression ratio. A fixed percentage o f iso-octane and heptane is placed in a test engine and the compression ralio (CR) is increased
continually until spontaneous combustion occurs, producing an engine
knock. The compression ratio and the corresponding composition of the
mixture are then recorded, and the test is repeated to obtain the calibration
curve of compression ratio as a 'function of % iso-octane. After the calibration curve is obtained, the unknown is placed in the cylinder, and the compression ratio (CR)is increased untiI the set knock intensity is exceeded.
The CR is then matched to the calibration curve to find the octane number.
The more compact the hydrocarbon molecule, the less likely it is to
cause spontaneous combustion and engine knock. Consequently, it is
desired to isomerize straight-chain hydrocarbon molecules into more compact molecules through a catalytic process called reforming.
Sec. 10.3
Catalyst
Synthesizing a Rate Law, Mechanism, and Rate-Limiting Step
683
One common reforming catalyst is platinum on alumina. Platinum on
alumina (A1203)(see SEM photo below) is a bifunctional catalyst that can be
prepared by exposing alumina pellets to a chloropSatinic acid solution, drying,
and then heating in air 775 to 875 K for several hours. Next, the material is
exposed to hydrogen at temperatures around 725 to 375 K to produce very
snlaIl clusters of Pt on alumina. These clusters have sizes on the order of 10 A,
while the alumina pore sizes on which the Pt is deposited are on the order of
100 to 10,000 (i.e., 10 ta 1000 nml.
Platinum on alumrna (Ftpuru Irom K I \l.:kc.l.
Ch~~lrrrtrl
Kmeiics ntrd Cutaleris.
N'lley. NCI~York. 2001. p. 7W)
As an example of cataIytic reforming we shall consider the isomerization
of n-pentane to f-pentane:
n-pentane
0 7 5 "I"
A1:0,
<
,i-pentane
Normal penlane has an octane number of 62. whiIe iso-pentane has an octane
number of 90! The 17-pentane adsorbs onto the platinum, where it i s dehydrogenated to fonn I?-penlene. The n-pentene desorbs from the platinum and
20%
25rk adsorbs onto the alumina. where it i s isomerized to i-pentene, which then
20%
desorbs and subsequentIy adsorbs onto platinum. where it is hydrogenated to
10% form i-pentane. That is,
Gasoline
I na
In"
Cr
Cb
C7
,-,
c,
C I ~
.
I
5%
-H2
n-pentane
'H:
AL-01
(
2
n-pentene (i-pentene
PI
(
)
PI
i-pentane
We shaIl focus on the i~orneriza~ion
step to develop the mechanism and the
rate law:
A[-0;
n-pentcne
i-pentene
684
Catalysrs and Catalyt~cReactors
Char
The procedure for formulating a mechanism, rate-limiting step. and co
sponding sate law is given in Table 10-4.
Table 10-5 gives the forms of wte laws For different reaction mechanir
that are irreversible and surface-reaction-limited.
----
-
. .
Single site
A-S
+B.S
Dual site
A.S
+ B*S
-
C.S
+S
-r;
=
~ P P B
( 1 +K,P,+KnPa+
&PC)'
Eley-Rideal
We need a word of caution at this point. Just because the mechanism :
rate-limiting step may fit the rate data does not imply that the mechanisn
co~rect.'~
Usually, spectroscopic measurements are needed to confirm a me
anism absolutely. However, the development of various mechanisms ,
rate-limiting steps can provide insight into the best way to correIate the c
and develop a rate law.
10.3.6 Rate Laws Derived from the Pseudo-SteadyState Hypothesis
In Section 7.1 we discussed the PSSH where the net rate of formation of re
tive intermediates was assumed to be zero. An alternative way to derive a (
alytic rate law rather than setting
is t o assume that each species adsorbed on the surface is a reactive interne
ate. Consequently, the net rate of formation of species i adsorbed on the s
face will be zero:
The PSSH should
be used when
mre than one
step is limiung
I5R. I. Masel, Principles of Adsorprion and Reaction on Solid Surfaces {New Yr
WiEey, 1996). p. 506.http:llwww.uiuc.edu/ph/www/r-masel/
Sec. 10.3
TABLE10-4.
Synthesizing a Rate Law, Mechanism, and Rate-Limfting Step
A~COR~THM
FOR
685
D ~ R M T Y I REACTION
NG
MECHANISM
AND RATE-LIMITIKG
STEP
Isornerization of n-pentene IN) to i-pentene (1) over alumina
Refnrming
reactlon to rncrease
octane number
OF gasoline
I . SeIacr n merhonism. (Mechanism Dual Site)
N S S
Adsorption:
N.3
N-S + S
Surfa~ereaction:
I S+ S
I
Teat each reaction step as an elementary reaction when writing rate laws.
2. Assume a mre-Itmiring step. Choase the surface reaction first. since more than 75% ofoll heremgeneow rencttons rhar are not diesion-limited ow surface+reaction-1Emt1ed.
The rate law
for the surface reaction step is
3. Find the expwssron for concenlmfionof the adsorkd speci6.t CC;
s. Use the other steps that are
not limit~ngto soFw for C,.s(e.g.. CN.S
and C1.5).For this reaction.
From
9 = 0:
CN = PNKGC,
~ A P
Foliowngthe Algorithm
From
9
k,
5
,
Cl =
0:
P;P
= KlP1C,
4. Write a sire balance.
c,= cv+ CN5 f
CT.~
5 . Derive the mte law. Combine Steps 2. 3, and 4 to arrive at the rate law:
6. Cornpure with data. Compare the rate law derived in Step 5 with experimental data. If they
agree, there is a good chance that you have found the correct mechanism and rate-limiting
step. If your derived rate law (i.e., model) does not agree with the data:
a. Assume a different rate-limiting step and repent Steps 2 through 6.
b. If, after assumlng that each step is rate-limiting, none of the derived rate laws agree with
the experimental data. select a different mechanism (e.g.. A Single Site Mechanism):
.
.
N +S
a N-S
NhS
I*S
ITS
14- S
and then pmeed through steps 2 through 6.
The single-site mechanism turns out to be the correct one. For this mechanism the rate law
is
c. If two or more models agree, the statistical tests discussed in Chapter 5 {e.g.. comparison
of residuals\ should be used to discriminate between them (see the Supplemenmy Reading}.
686
Catalysis and Catalyfic Reaclors
Chap. 10
While this method works well for a single rate-limiting step, it also works well
when two w more steps are rate-limiting (e.g., adsorption and surface reaction). To illustrate how the rate laws are derived using the PSSH,we shall consider the isornerization of normal pentene to isn-pentene by the following
mechanism, shown as item 6 of Table 10-4:
The rate Jaw for the irreversible surface reaction is
The ner rate
of the adsorbed
species (i.e.. active
The net rates of generation of N - S sites and 1. S sites are
intermediates)
Solving for CN+S
and C,.sgives
and substituting for CN.Sin the surface reaction rate law gives
From a site balance we obtain
Use the PSSH
method when
.
After substituting for C?;.s and Ci.S.solving for C,, . which we then substitute
in the rate law, we find
pw
Some steps are
irrevers~hlc.
n o ar more
steps are rateltrn~t~ng.
k-, + ks
( 1 0-62 1
Sec. 10.3
Synthesizing a Rate Law, Macbnlsm, and Rate-Limiting Step
687
The adsorption constants are just the ratio of their respective rate constants:
We have taken the surface reaction step to be rate-limiting; therefore, the surface specific reaction constant, ks, is much smaller than the rate constant for
the desorption of normal pentene, LN;
that is,
In-
ks
and the rate law given by Equation (1 0-62) becomes
This rate law [Equation (10-63)] is identical to the one derived assuming that
rADlkAD= 0 and rD/kAD 0. However, this technique is preferred if two or
more steps are rate-limiting or if some of the steps are irreversible or if none
of the steps are rate-limiting.
10.3.7 Temperature Dependence of the ~ a t ' eLaw
Consider a surface-reaction-limited irreversible istlmerization
in which both A and B are adsorbed an the surface, the rate law is
The specific reaction rate, k. will usually follow an Arrhenius temperature
dependence and increase exponentially with temperature. However. the adsorp
tion of all species on the surface is exothermic. Consequently, the higher the
temperature, the smaller the adsorption equilibrium constant. That is, as the
temperature increases, K, and KB decrease resulting in less coverage of the
surface by A and B. Therefore, at high temperatures, the denominator of catalytic rate laws approaches 1. That is. at high temperatures (low coverage)
688
C a t a ? ~ iand
s Catajytic R ~ l a c M r s
ChaF
The rate Inw could then he npproximated nh
Ze:lc.ctin::
the
,dcorhed cptu~esa l
high leinpr.~l~ire~
-1:;
=kfA
or for a reversiblr isomerization we wouId have
stnttgier
ror mudel bu~lduig
Alenrithm
Drrhrcr
Rate law
Ftrrrl
Mcchanr.~m
E~,of~rrrrc
Rate law
paranlttcrr
WPYIS~
PBR
CSTR
The algorithm we cafl use as a ctast in postulating n reaction mechani
and rate-limiting step is shown in Table 10-4. Again, we can never really prc
n mechanism by comparing the derived rate law with experimental data. In'
pendent spectroscopic experiments are usually needed to confirm the mec
nisni. We can. however, prove that a proposed mechanism is inconsistent N
the experimental data by following the algorithm in Table 10-3. Rather than t,
in9 a11 the experitnental data and then trying to build a model from the d:
Box et al.Ih descrrbe techniques of sequential datii ~rtkingand model buildir
10.4 Heterogeneous Data Analysis
for Reactor Design
In this section we focus on four operations that reaction engineers need to
able to accomplish: ( I ) developing an algebraic rate law consistent with exp
irnental observations. (2) analyzing the rare law in such a manner that the ri
law parameters ( e . ~ .k,, K,) can readily be extracted from the experimenfal da
(3) tinding a mechanism and rate-limiting step consistent with the experirnen
data. and 14) designing a caralytic reactor to achieve a specified conversion. 1
shall use the hydrodemethylation of toluene to illustrate these Foi~roperatior
Hydrogen and toluene are reacted over a solid mineral catalyst cantal
ing clinoptilolite la crystalline silica-alumina) to yield methane and benzene
We wish so design a packed-bed reactor and a fluidized CSTR to proce
a feed consisting af 30% toluene, 45% hydrogen, and 25% iinerts. Toluene
fed at a rate of 50 moI/min at a temperature of 6;10°Cand a pressure o f 40 at
(4057, kPa). To design the PBR. we must first determine dle rate law from t,
differential reactor data presented in Table 10-6. Fn this table we find the ra
of reaction of toluene s a function of the partial pressures of hydrogen (H). tc
uene (T), benzene (B), and methane (MI. In the first two runs. methane w
introduced inta the feed together with hydrogen and toluene, while the 0th
product. benzene, was fed to the reactor together with the reactants only in ru~
3.4, and 6. In runs 5 and 16 both methane and benzene were introduced in tl
feed. In the remaining runs, neither of the products was present in the feel
E. P. Box, W. G. Hunter, and I. S. Hunter. Stnristir~for Engi~zeers(New Yor
Wiley. 1978).
l7 J. Papp. D.Kallo. and G.Schay- J. CnraL. 23, 168 ( 1 97 I).
I%.
Sec 10.4
Heterogeneous Data Analysrs lor Reactor Deslgn
689
T,\H[t: 11)-h. DATA
FROLI r\ D T F ~ E R F ~
REA(.IIIK
TIAL
Set A
I
-1
Set B
3
4
5
h
Unwrdmhle the data
to find the
rare law
C
7
8
9
Set D
10
II
12
13
I1
15
16
Set
stream. Because the conversion was less than t % in the difTerential reactor. the
partial pressures of the products. methane and benzene. in these runs were
essentialiy zero, and the reaction rates were equivalent to initial rates of reaction.
10.4.1 Deducing a Rate Law from
the Experimental Data
Assuming that the reaction is essentially irreversible [which is reasonable after
comparing runs 3 and 51, we ask what qualitative c~nclusionscan be drawn
from the data about the dependence of the rate o f disappearance of toluene,
- r ; , on the partial pressures of toluene. hydrogen, methane, and benzene.
I. Dependence on (he product methnne. If the methane were adsorbed
on the surface, the partial pressure of methane would appear in the
denominator of the rate expression and the rate would vnry inversely
with methane concentration:
Catalysis and Cabtytic Reacton
Foltowv7?g
the Algorithm
If i t is in the
denominator. it i s
pmhably on the
surface.
Chap. 10
However, from runs I and 2 we observe that a fourfold increase in the
pressure of methane has little effect on -r;. Consequently, we
assume that methane is either very weakly adsorbed {i-e.,KMPM G 1 )
or g m s directly into the gas phase in a manner similar to propylene in
the cumene decomposition previousIy discussed.
2. Dependence on he producr benzene. In runs 3 and 4, we observe that
for fixed concentrations (panial pressures) of hydrogen and toluene
the rate decreases with increasing concentration of benzene. A rate
expression in which the benzene partial pressure appeass in the
denominator could explain this dependency:
The type of dependence of -r$ on PB given by Equation (10-68)
suggests that benzene is adsorbed on the clinoptiloIite surface.
3. Drpe~~dence
on loluene. At low concentrations of toluene (runs 10
and 1 I), the rate increases with increasing partial pressure of toluene,
while at high toluene concentrations (runs 14 and 151, the rate is
essentially independent of the toluene partial pressure. A form of the
rate expression that would describe this behavior is
A combination of Equations (10-68) and (10-69) suggests that the
rate law may be of the form
4. Dependence on Itydrugen. When we examine runs 7, 8, and 9 in Table
10-6. we see that the rate increases linearly with increasing hydrogen
concentration. and we conclude that the reaction is first order in H:.
In lisht of this fact. hydrogen is either not adsorbed on the surface or
its coverage of the surface is extremely low ( 1 >> K H 7 P H 2for
) the preqsums used. If it were adsorbed, -r; would have a dependence on
PHI analogous to the dependence of -r+ on the partial pressure of
toluene. PT [see Equation (1 0-6911. For first-order dependence on Hz.
'-r;
- PH2
(10-71)
Combining Equations (10-63) through (10-71).we find that the rate law
is in qualitative agreement with the data shown in Table 10-6.
Sec. 10.4
Heterogeneous Data Analysts for Reactor Design
691
10.4.2 Finding a Mechanism Consistent
with Experimental Observations
We now propose a mechanism for the hydrodemethylation of toluene. We
assume that toluene is adsorbed on the surface and then reacts with hydrogen
in the gas phase to produce benzene adsorbed on the surface and methane in
ALTroximatel~ the gas phase. Benzene is then desorbed from the surface. Because approxi75" O r a l '
heterogeneous mately 75% of all heterogeneous reaction mechanisms are surface-reacrmction tion-limited rather than adsorption- or desorption-limited, we begin by
mechanisms are assuming the =action bet ween adsorkd toluene and gaseous hydrogen to be
surface-reactinnreaction-rate-limited. Symbolically, this mechanism and associated rate laws
for each elementary step are
,,,
a T-S
Adsorption: T(g) f S
Prows&
Surface reaction: H2(g)
mechanism
+ T.S
B - S + M(g)
Desorptian: B S (BB(g) + S
r~ = k, ICB s -KBP, Cu)
For surface-reaction-limitedmechanisms,
we see that we need to replace
that we can measure.
CT.sand CR.S
in Equation ( I 0-73) by quantities
For surface-reaction-limited mechanisms, we use the adsorption rate
Equarion (10-72) to obtain CT.S:
Then
and we use the desorptinn rate Equation (10-74) to obtain CB5 :
692
Catalysis and Catalytic Reactors
Chap.
Then
The total concentration of sites is
PMom a site
balance to obtain C,.
Substituting Equations (10-75) and (to-76) into Equation (10-77) and
arranging, we obtain
I
Next, substitute for C,., and C,., and then substitute for C, in Equatic
(10-73) to obtain the rate law for the case of surface-reactioncontrol:
k
Neglecting the reverse reaction we have
Rate law for
surface-reaction-
limited mechanism
Again we note that the adsorption equilibrium constant of a given species ,
exactly the reciprocaI of the desorption equilibrium constant of that species.
10.4.3 Evaluation ol the Rate Law Parameters
In the original work on this reaction by Papp et al.,'s over 25 models wer
tested against experimental data, and it was concluded that the precedin
mechanism w d rate-limiting step (i.e., the surface reaction between adsorbe
toluene and H, gas} is the correct one. Assuming that the reaction is essential1
irreversible, the rate law for the reaction on dinoptilolite is
We now wish to determine how best to analyze the data to evaluate th
rate law parameters, k, KT,and Kg.This analysis is referred to as pamrnere
e s t i m a t i ~ n . 'We
~ now rearrange our rate law to obtain a linear rdationshil
between our measured variables. For the rate law given by Equation (10-80)
bid.
l9
See the Supplementary Reading for a variety
law pnrameters.
of techniques for estimating the rat4
I
Sec. 10.4
693
Heterogeneous Data Analysis lor Reactor Design
we see that if both sides of Eq~~arion
(In-80) are divided by PH,P.I.and the
equation is then inverted,
L~nearizethe rate
equation to extract
the rate law
panmeters.
A linear-leastI
Fquares analys~sof
the data fhown in
h b l e 10-6 is
presented on the
CD-ROM.
The regression techniques described in Chapter 5 could be used to determine
the rate law parameters by using the equation
(R5.1-3)
One can use the linearized least-squares analysis to obtain initial estimates of
the parameters k, KT, KB,in order to obtain convergence in nonlinear regrecsion. However, in many caaes i t is possible to use a nodinear regression analysis directly as described in Section 5.2.3 and in Example 10-4.
Example 10-2
Regression Analysis tn Determine the lWodel Parameters
k, K g , nnd KT
The data from Table 10-6 were entered into the Polymath nonlinear-least-squms
program with the following modification. The rates of reaction in column 3 were
multiplied by 10"'. so that each of the number< in column I was entered directly
(1.e.. 71.0. 71.3, ...). The model equation was
Living Example Problca
Rate =
k P ~ P ~ I
E +KRP,+K,rPT
Following the step-by-step regression procedure in Chapter 5 and the Summary
Notes, we arrive at the following pamrneter valufi shown in Table E 10-2.I.
-
Model: WTE k'PT'PH2lll +KB'PB+WPr)
Nonlimr regrea*on s e l t i q
Max # l t s m h s = E-l
Precbn
R*2
E
0.9999509
O.gB8~0.1128555
variance r 0.2508084
RaZadj
~msd
r
694
I
Catalysis and Catafylic Reactors
Chap. 10
Converting the rate law to kilograms of catalyst and minutes,
we have
Ratio of sites
occupied hy toluene
to those occupied
by benzene
After we have the adsorption constants, KT and K,, we can calcuIaze the
ratio of sites occupied by the various adsorbed species. For example, the ratio
of toluene sites to benzene sites at 40%conversion is
We see that at 40% conversion there
are approximately 12% more sites occu'
pied by toluene than by benzene.
10.4.4 Reactor Design
Our next step is to express the partial pressures P,. PB,and PH1as a function
of X, combine the partial pressures with the rate Iaw, - r i . as a function of
conversion, and carry out the integration of the packed-bed design equation
I
Brample l&3
Fired (i. @,. Packed)-Bed Reactor Design
The hydrodemethylation of roluene is to he carried out in a packed-hed reacror. Plot
the conversion. the pressure ratio, p and the panial pressures of toluene, hydrogen.
and benzene as a function of catalyst weight. The molar feed rare of toluene to the
reactor is 50 rnollmm, and the rt'actor is operated at 40 atm and 640°C. The feed
consists of 30% toluene, 459 hydrogen, and 25% inerts. Hydrogen is used in
excess to help prevent coking. The prewure drop parameter, a. is 9.8 x lov5 kg-'.
Also determine the catalyst welghr tn a CSTR w ~ t ha bulk density of 400 kg/m7
10.4 p l c d ) .
Living Exsmplc Problc
1
1 . Design Equation:
Sec. 10.4
Heterogeneous Data Analysts for Reactor Design
Balance on
loluene (T)
2. Rate Law. From Equation (EIO-2.1) we have
with k = 0.00087 moIJam21kgcatlmin md K, = 1.39 amrl and KT = 1.038 c~m-1.
3. Stoichiometw:
Relating
Toluene (T)
Benzene
(B)
Hydrogen (H,)
Ps
Because
P,,
E
= 0.
=P r I , X ~
I E TO-3.5)
we can use the integrated fortn of the pressure drnp term.
tn!al pressure
at the enlrance
=
Note that P,
designate? the inilia1 partial pressure of toluene. In t h ~ sexample ~ h c
~nit~al
total pressure 1s designated Po to avojd any confi~sjon.The initial mole f r x tion of toluene is 0.3(i.e..!
,
= 0.3). so that the initial partial prewre of toluene i s
Pressure drnp in
PBRn i$ disc'u~scdin
Section 4.5
PI,, = 10..1)(40) = 12 atm
The maximum catalyst weight we can hate and nch fall below I atm 1s found from
Quation (4-33) for an entering pressure of 40 atm and an exit pressure of I atm.
Conwquentll;, we will sct our final \\eight 10.000 kg and deterniinc the cclntel \lc>n
as a fi~nction of catalyst we~ght up to th!r ~altle.Equntions tElO-3.1) through
696
The c:~lculatiuns f ( ~ r
nn 1 P are given url
the CD-ROM.
~ e f e r e n c Shelf
t
Catalysis and Ce!aly?lc Reactcrs
( E 10-3.5) are hewn in the Polymath program in Table E 10-3 I. The conversion
<hewn as a f~nctionof catalyst weight in Figure Et0-3.1, and profiles of the par1
prewures of toluene. hydrogen, and benzene are shown in Figure: E10-3.2. We nj
that the pressure drop causes the partial pressure of benzene 10 go through a ma
mum as one travenes the reactor.
For the case of no pressure drop, the conversion that would have be
achieved with 10.000 kg of catalyst weight would have been 79% compared w
69% when there i s pressure drop in the reactor. For rftefeed mfe given, elilninart
or mitirmi,-i~rgpw.r.wre drop wutrld i n c m s c the pwditcrion of benzene h,v up to
r?rilEinupoimiis per yeor!
Differentialequations as entered by the user
[ 1i d(X)ld(w) = - W T O
Explicit equations as entered by the user
[l] m o = 5 0
[ 2 ] k-.00087
[ I ] KTr1.038
I 4 1 KBz1.39
[ 5 1 alpha = 0.000098
I6; P0=40
Living Example Problcr
Chap.
PTo = 0.3"Po
t 8 l y t (I -afpha*w)"0.5
[7 1
[ 9 J P=y'Po
[ 1a 1 PH2 = FTo'(l.5-X)*y
[ 11 1 PB = PTo'X'y
[I21 PT = PToa(1-X)'y
[?3 1 ti = -k'PT'PHZ(l +KB'PB+KT'PT)
[I41 R A T E = - I ~
Conversion pmtile
down the
packed hed
w (kg)
Figure E10-3.1
Conversion and pressure ratio profiles.
Heterogeneous Oata Analysis for Reactor Design
1
=
Note the partial
prcbsure ot knzenc
goes rhrouph a
n~nximt~rn.
Why?
I
Fluidized
We note in Figure EiR3.2 that the partial pressure o l hcnzenc goes through a rnnximom rs a rewit of the dccma.r in m1.1 presiurc becrlrie of ihc pressure d l v y
We wili now criculvre the fluidized CSTR catalyst we~ght necessary to
achieve the rrme conveninn as in the packed-bed reactor at the sitme operating conditions. The bulk density in the fluidized reactor is 0.4 gicm'. The design equation is
CSTR
A
In
-
Out
+
Gen
=
Accum
Fra
-
FT
+
r;w
=
0
Rearranging
Writing Equation (E10-2.3) in terms of
and P,, = I 2 atm. we have
-rf
conversion
and then substituting X = 0.65
8.7x104prp~4
8.7~10~P?m(l-~)(1.5-~
=2,3x10-~ mo1
I + I.39PBr i . 0 3 8 ~ ~ = I.39PwY+
i+
I038P,(l -R)
kgcat min
W =d
F
-
=
(50 mol .F/min)lO.65)
2 . 3 loLJ
~ mnl T/kg cat-min
W = 1.4x lo4 kg of catalyst