Periodic Operation of Chemical Reactors || Chromatographic Reactors

C H A P T E R

20

Chromatographic ReactorsPeter Lewis Silveston*, Kenji Hashimotoy, Motoaki Kawasey

*Waterloo, Ontario, Canada and yKyoto, Japan

P

h

O U T L I N E

20.1 Introduction 5
69
20.2 Concept and Types 5
70
20.3 General Models 5
7320.3.1 Distributed Systems 573 20.3.2 Lumped Models 578
20.4 Cyclic Steady State 5
79
20.5 Pulse Chromatographic Reactor 5
80
20.6 Countercurrent Moving BedChromatographic Reactor 5
87
eriodic Operation of Reactors

ttp://dx.doi.org/10.1016/B978-0-12-391854-3.00020-6 569

20.7 Continuous Rotating AnnularChromatographic Reactor 5
90
20.8 Stepwise, Countercurrent Multi-StageFluidized Bed ChromatographicReactor 5
91
20.9 Fixed Bed Chromatographic ReactorWith Flow Direction Switching 5
92
20.10 Extractive Reactor Systems 5
93
20.11 Centrifugal PartitionChromatographic Reactor 5
93
20.1 INTRODUCTION

With this chapter and the two that follow,a discussion of separating reactors begins.Such reactors draw together a solid catalystand an adsorbent, a solid that traps one of thereaction products. The adsorbent serves toprevent a reverse reaction or a further reactionof that product, and to initiate its separation

from the reaction mixture. Chromatographicreactors employ such a mixture of catalyst andadsorbent. Swing reactors, considered inChapter 22, do so as well. Using an adsorbentrequires regeneration to release the productand to re-use the solid, thus mandating periodicoperation. Separating reactors differ from oneanother only in the way regeneration isaccomplished.

Copyright � 2013 Elsevier Inc. All rights reserved.

http://dx.doi.org/10.1016/B978-0-12-391854-3.00020-6

20. CHROMATOGRAPHIC REACTORS570

Mathematical models for these systems arevirtually the same and their initial conditionsand boundary conditions are often similar.Consequently, modeling and calculationalconsiderations for both chromatographic andswing reactors will be discussed in this chapter.Aida and Silveston (2005) discuss chromato-graphic and swing reactors in much moredetail. These authors also examine other typesof separation that have been tested in combina-tion with chemical reaction such as extraction,vaporization (catalytic distillation), and sedi-mentation. Separation of the second phase insuch systems is simple and continuous opera-tion is routine.

The chromatographic reactor is the oldest ofthe reaction and separation combinations. Notlong after the introduction of chromatographyas a separation technique, Roginskii et al. (1962)observed that an equilibrium-limited reactioncould be forced toward completion by carryingout the reaction in a chromatographic column.Shortly thereafter, Magee (1963) proposed a sim-plified model for a reaction in such a column.Promoting reaction through separating productsfrom reactants is an even older concept.Glueckaufand Kitt (1957) and Thomas and Smith (1959)described a pulse reactor in which productadsorption shifted the reaction towards comple-tion. Hattori and Murakami (1968) theoreticallyderived the conversion and yield in a chromato-graphic reactor and compared them with thosein a tubular reactor at steady state, while in a suc-ceeding paper (Murakami et al., 1968) they studiedthe cracking of cumene over a silica-alumina cata-lyst using a rectangular pulse. The effect of pulsewidth on the conversion predicted in their firstpaperwasverified. Shortly beforeMurakami,Mat-sen et al. (1965), using the dehydrogenation ofcyclohexane, experimentally verified that conver-sion in a chromatographic reactor was greaterthan that in a continuous tubular reactor underthe same temperature and pressure. Langer et al.(1969) discussed the overall potential of the gaschromatographic column as a chemical reactor

PERIODIC OPERATIO

and derived a simple equation for estimating theirreversible first-order rate constant from chro-matographic measurements. Disadvantages andlimitations of chromatographic reactors werealso discussed.

Since these exploratory efforts, a large litera-ture on versions of chromatographic reactors,models for such reactors, and their applicationto chemical systems have appeared. Reviewsof work prior to 1990 have been published byBarker et al. (1987a,b), Barker and Ganetsos(1988), Barker et al. (1992a, 1990b) and by Carta(1991). Unfortunately, the emphasis of thesereviews is on biotechnology applications.A comprehensive review of the published liter-ature up to 2005 is contained in a book by Aidaand Silveston (2005).

20.2 CONCEPT AND TYPES

Figure 20-1 illustrates the principle of a chro-matographic reactor (CR) using as an examplethe catalytic dehydrogenation of cyclohexane.A pulse of C6H12 (A) in a nitrogen carrier gasis introduced into a fixed bed of mixed catalystand adsorbent in (a). Above 200�C, C6H12

chemisorbs on the catalyst and breaks downto benzene (B) and atomic hydrogen. The latterrapidly combines to form H2 and desorbs.C6H6 is strongly adsorbed. The adsorptiondifference inaugurates separation betweenproducts as well as reactant. Weakly adsorbed,H2 moves through the reactor at almost thevelocity of the carrier gas. C6H12, morestrongly adsorbed, moves more slowly throughthe reactor and continues to break down. Thisis the situation shown in (b). The sequencecontinues as the C6H12 pulse moves throughthe reactor causing spreading of the C6H6

and H2 peaks evident in (c). Once C6H6 rea-ches the end of the bed, a new pulse ofC6H12 is introduced at the entrance (Figure 20-1d).Nearly complete conversion may be obtainedin pulse operation provided the bed is long

N OF REACTORS

REACTOR ZONE

CO

NC

ENTR

ATIO

N

AXIAL POSITION

A

A

A

A

A

N

B

B

B

C

C

C

L0

L0

L0

L0

N2

N2

N2

N2

(a)

(b)

(c)

(d)

FIGURE 20-1 Concentrations of the C6H12 reactant (A), C6H6 product (B) and H2 product (C) in successive times as

a pulse of C6H12 in an N2 carrier gas moves through a mixed bed of catalyst and adsorbent and undergoes catalytic

dehydrogenation. (Figure reproduced from Aida and Silveston (2005) with permission. � 2005 by Blackwell Publ. Ltd.)

20.2. CONCEPT AND TYPES 571

enough. However, there is a throughputpenalty because reactant is not fed continu-ously to the reactor.

Increasing throughput is made possible bymaintaining a constant feed rate and physicallymoving the catalyst and adsorbent bed past thefeed point. This is the countercurrent movingbed chromatographic reactor (CMCR) operationshown in Figure 20-2. Gaseous reactant ina carrier gas moves upward, while the solidbed of catalyst and adsorbent moves down-ward. Dehydrogenation of C6H12 again serves

PERIODIC OPERATIO

as the example. C6H12 is fed at the middle ofthe reactor, while a carrier gas enters from thebottom. Reaction products, H2 and C6H6 areseparated by adsorption differences. Weaklyadsorbing H2 is driven upward through thefalling bed of catalyst and adsorbent by thecarrier gas and emerges in the effluent at thetop of the reactor. Catalyst and adsorbent parti-cles are fed at the top and are withdrawn fromthe bottom. C6H12 and C6H6 adsorb on the cata-lyst and are carried downward. If the bed isdeep enough, cyclohexane is fully converted

N OF REACTORS

Solid

x = L

x = 0

H2

C6 H12

C6 H6

GaseousProductH2

GaseousReactantC6H12,N2

Solid &Adsorbed Product (C6H6)

(a)

Solid

x = L

x = 0

H2

C6 H12

C6 H6

GaseousProductH2

Solid &Adsorbed Product (C6H6)

(b)

ReactantC6H12

Carrier GasN2

FIGURE 20-2 Steady-state concen-

tration profiles in a countercurrent

moving bed chromatographic reactor

(CMCR) packed with a homoge-

neously mixed bed of catalyst and

adsorbent. (Figure reproduced from

Aida and Silveston (2005) with permis-

sion. � 2005 by Blackwell Publ. Ltd.)


and only C6H6 adsorbed on the catalyst emergesfrom the bottom of the bed.

A variation of this contacting technique is thecontinuous rotating annular chromatographicreactor (CRAC). The principle is the same, but inthe rotating bed the catalyst/adsorbent particlesare motionless relative to the bed. The bed itselfis carried past the feed inlet and product outlet.

In these systems, all flows are continuous.A countercurrent moving bed of catalyst andadsorbent converts the reactor system from anunsteady state to steady state. Of course, cata-lyst and adsorbent circulating through thereactor encounter periodically varying fluidenvironments.

A third version is the simulated countercur-rent moving bed chromatographic reactor

PERIODIC OPERATIO

(SCMCR) in which the bed is stationary butthe feed entrance and product exits shift withtime. Fluid flow through the bed is continuousas well. Chapter 21 is devoted to simulatedmoving bed systems, so we reserve furtherdiscussion until that chapter.

A great many reaction systems, such as hydro-genation, chlorination or oxidation, involve morethan a single reactant. For these systems, periodicflow reversal can be introduced into the chro-matographic reactor. Called reverse-flow chro-matographic reactors, such systems can eitherimprove performance if the size of a mixed bedof catalyst and adsorbent is restricted, or reducebed size for a specified conversion. Reverseflow chromatographic reactors will be consid-ered at the end of this chapter.

N OF REACTORS

20.3. GENERAL MODELS 573

In chromatographic reactors, a fluid desor-bent, called an eluent, strips adsorbed productand residual reactant from the adsorbent. It isalsopossible to use pressure reduction or a highertemperature to force desorption. Reactors usingpressure change are referred to as pressure swingsystems, while those employing a temperatureincrease are called temperature swing ones.Chapter 22 deals with both reactor types.

There are important constraints on the choiceof adsorbent. Weak adsorption of the keyproduct increases bed length and thus capitalexpense, while strong adsorption raises thecarrier gas or solvent requirement per unit ofreactant processed and results, also, in a moredilute product. This increases the cost of productconcentration and recovery. A further constraintarises for single reactions with multiple reac-tants. Significantly different affinities of theadsorbent for the reactants can cause their sepa-ration and a retardation of the reaction rate. Thisis not a problem when one reactant serves as thecarrier or solvent. Screening of candidate adsor-bents is an important step in development ofchromatographic reactor systems. The topic isdiscussed by Aida and Silveston (2005).

20.3 GENERAL MODELS

20.3.1 Distributed Systems

The purpose of Figure 20-3 is to define thevariables used in the model presented in this

C0,T0,F0 Ci,ni,T

qi,Tssolids

A

Lx

Nb t

ρ ε

FIGURE 20-3 Schematic of the catalyst-adsorbent bed of cr

bed parameters, inlet and bed variables. (Figure reproducedBlackwell Publ. Ltd.)

PERIODIC OPERATIO

section. The separating reactor shown schemat-ically in the figure could be any one of a CR,a swing reactor, or a section between ports ofa CMCR or a SCMCR. In the first two casesthe solid phase is stationary and the bottomline representing flow of solids should beremoved. The variables qi and Ts now refer toconditions at a fixed plane in the bed. Fora SCMCR, the solid phase is stationary and Us

represents virtual motion. The schematic isbroken into parts to indicate internal variablesin the bed. Symbols at the ends indicate inputvariables, some of which will be functions oftime. Reactor parameters, treated as constantin the model, are the symbols shown in theboxes. A single solid phase serving as catalystand adsorbent is assumed. Dispersive fluxesresulting from concentration or temperaturegradients are not shown in the schematic.

Because isotropic beds of catalyst and adsor-bent are generally used, separating reactors,chromatographic as well as swing, aredescribed by the same set of heat and materialbalances. A momentum balance should be partof the set, but in practice it is replaced bya phenomenological equation. Table 20-1 statesthe pseudo-homogeneous, one-dimensionalmodel for a separating reactor containinga packed bed made up of a single solid func-tioning as both adsorbent and catalyst ora homogeneous, fully mixed solids bed of sepa-rate adsorbent and catalyst. The modeldoes vary with the application as indicated in

fluid

Us,T0,

oss-section A and length L for a separating reactor showing

from Aida and Silveston (2005) with permission. � 2005 by

N OF REACTORS

TABLE 20-1 Partial Differential Equations of Pseudo-Homogeneous Models for Chromatographic and Swing Reactors

Mass balance for component i

εtvCi

vtþ rb

vqivt

¼ Dxv2Ci

vx2� 1

A

vnivx

þUsrbvqivx

þ rbnir: (20-1)

Overall mass balance for components

εtvC

vtþ rb

XNC

i¼ 1

vqivt

¼ Dxv2C

vx2� 1

A

vn

vxþUs rb

XNC

i¼ 1

vqivx

þ rb

XNC

i¼ 1

nir: (20-2)

In both equations: Us¼ 0 for a CR, SCMCR, PSR, or TSR; while

εtvC

vtþ rb

XNC

i¼ 1

vqivt

¼ 0 for a CMCR at steady state;

energy balance

�εt CpgCþ rbCps

� vTvt

¼ kxv2T

vx2� Cpg

n

A

vT

vxþUs rb Cps

vT

vx� P

A

v

vx

�nC

�� rb

XNC

i¼ 1

Haivqivt

þrbDHRr� 4h0dc

�T � Ta

�:

(20-3)

In this equation: Us¼ 0 for a CR, SCMCR, PSR or TSR;

v

vx

�nC

�¼ 0 for a CR;CMCR or SCMCR;

�εtCpgCþ rbCps

� vTvt

¼ 0 for a CMCR at steady state:

Flow model: Ergun correlation (instead of momentum balance)

d P

d x¼ �Jv u� Jku

2 (20-4)

where

Jv ¼ amg½lsð1� εbÞ�2

d2p ε3b

(20-5)

Jk ¼ lsð1� εbÞrgdp ε3b

: (20-6)


Table 20-1. These changes arise in the case ofa CR or SCMCR or the swing reactors becausethe solids are stationary. For a CMCR, thechanges occur because this reactor operates at

PERIODIC OPERATIO

steady state. Assumptions of the model arethat: 1) The bed is isotropic, 2) intraparticlediffusion proceeds so rapidly that it can beneglected, 3) only a single reaction occurs,

N OF REACTORS


4) particles are isothermal and uniformlybathed by the fluid phase, 5) the bed has noradial gradients, 6) all motion in the bed isplug flow, 7) fluids, simple or mixtures, exhibitideal behavior, 8) all transport and thermody-namic properties do not vary as pressure ortemperature change, 9) mass and heat transferbetween fluid and solid is fast enough so thatconcentration and temperature differencesbetween the phases are negligible and, finally,10) both adsorption and desorption are rapidso that the adsorbate is at equilibrium withthe fluid phase.

The pseudo-homogeneous model is thesimplest model for chromatographic and swingreactors, but it presents a dilemma: the rateconstant, k, in the rate term, r, can be extractedonly with difficulty from independent ratemeasurements on the catalyst itself because theterm in the model is formulated in terms ofthe bulk density of a combined catalyst andadsorbent. It is preferable to evaluate the rateconstant from measurements with the catalyst-adsorbent mixture employing the samepseudo-homogeneous model.

In Table 20-1, the total void fractionεt ¼ εb þ ð1� εbÞεp, where εb and εp are the bedor bulk and particle porosity respectively.Usually, an intimate mixture of catalyst andadsorbent, two solid phases, will be used.When this is the case, rb modifying the adsor-bate density qi terms must be replaced by (rb)adsand the rbmodifying the reaction rate termmustbe replaced by (rb)cat. These “bulk” densitiesare the product of a volume fraction and theparticle density. Thus, (rb)ads¼ εads (rp)ads. Thetotal void fraction term changes too:εt ¼ εb þ εadsεpads þ εcatεpcat . The dispersion termin Table 20-1 is based on the fluid volume. Itmay also be based on the reactor volume.When this definition is used Dx should bereplaced by εtDx. In Eq. (20-3), specific heatand density may not be the same for catalystand adsorbent. Thus, rb(Cp)s should be replacedby rads(Cp)ads þ rcat(Cp)cat. The two other rb terms

PERIODIC OPERATIO

also change because they become specific toeither catalyst or adsorbent.

If Eqs (20-1) and (20-2) are broken into sepa-rate balances for the fluid and solid phases,a heterogeneous model results. When this isdone, the balances must be coupled by rate oftransport and/or rate of adsorption terms. Ofcourse, separate balances for each phase arenecessary when transport between phasesand/or adsorption is rate controlling andwhen measurements of the transport or adsorp-tion steps are to be made. When the solid phaseis stationary, the adsorbate flux terms disap-pears from all models, including Eqs (20-1)and (20-2) in the pseudo-homogeneous model.

The heterogeneous model is presented inTable 20-2. This model assumes that fluid-particle transport is slow compared withadsorption rates. The Ergun relation, Eqs(20-4) to (20-6), is used to determine the pressuredrop for the heterogeneous model, just as it iswith the homogeneous model.

Heat and material balances in Table 20-2again assume a single solid phase serving bothas catalyst and adsorbent. As discussed forTable 20-1, different materials are normallyused. The versions presented were chosenbecause they offer a reduced set of dimensionlessgroups. Generally, heat transfer between phasesis rapid so that the pseudo-homogeneousassumption is appropriate for the energybalance. Lumping catalyst and adsorbent causesproblems in defining a rate of reaction term, asmentioned above, because the surface concentra-tion, qi, represents an adsorbate concentrationrather than the concentration on the surface ofthe catalyst. A similar problem arises with theflux terms. Although the mass and heat transfercoefficients for catalyst and adsorbent will besimilar, the driving forces will not be. An advan-tage of distinguishing between catalyst andadsorbent is that the rate expression andconstants for r can be taken from independentrate measurements on the catalyst. Lumpingboth materials into a single solid phase means

N OF REACTORS

TABLE 20-2 Partial Differential Equations of Heterogeneous Models for Chromatographic and Swing Reactors

Mass balance for component i in the fluid phase

εtvCi

vt¼ Dxi

v2Ci

vx2� 1

A

vnivx

� kmiam rb

Ci �

qiKi

!: (20-7)

Overall mass balance for components in the fluid phase

εtvC

vt¼ Dx

v2C

vx2� 1

A

vn

vx� amrb

XNc

1¼ 1

kmi

�Ci � qi

Ki

�: (20-8)

In both equations,vCi

vt¼ 0 for a CMCR at steady state.

Mass balance for component i in the solid phase

rbvqivt

¼ Us rbvqivx

þ kmiam rb

�Ci �

qiKi

�þ rbnir: (20-9)

Overall mass balance equation for components in the solid phase

rb

XNC

i¼ 1

vqivt

¼ Us rb

XNC

i¼ 1

vqivx

þ amrbXNc

i¼ 1

kmi

�Ci �

qiKi

�� rb

XNC

i¼ 1

nir: (20-10)

In both equations, Us¼ 0 for a CR, SCMCR, PSR or TSR;

vqivt

¼ 0 for a CMCR at steady state;

Energy balance for the fluid phase

�εtCpgC

� vTvt

¼ kxv2T

vx2� Cpg

n

A

vT

vx� P

A

v

vx

�nC

�þ am h rb

Ts � T

!: (20-11)

In this equation,v

vx

�nC

�¼ 0 for a CR, CMCR and SCMCR;

vT

vt¼ 0 for a CMCR at steady state:

Energy balance for the solid phase

rbCpsvTs

vt¼ ks

v2Ts

vx2þUs rb Cps

vTs

vx� am h rb

Ts � T

!� rb

XNC

i¼ 1

Haivqivt

� rb DHRr: (20-12)

In this equation, Us¼ 0 for a CR, SCMCR, PSR, or TSR;

vTs

vt¼ 0 for a CMCR at steady state:


PERIODIC OPERATION OF REACTORS


that the rate constants must be extracted frommeasurements on the adsorbent-catalyst mixtureusing an appropriate model.

Instead of being listed in another table, theequations are amended below assuming cata-lyst and adsorbent are different materials.Volume fractions and particle densities areused in place of “bulk” densities.

Fluid phase material on component i:

εtvCi

vt¼ Dxi

v2Ci

vx2� 1

A

vnivx

� kmiamðεadsrpadsÞ

Ci �qiKi

!þ εcatrpcatnir:

(20-13)

Solid phase material balance on component i:

εadsrpadsvqivt

¼ Usεadsrpadsvqivx

þ kmiamεadsrpads�

Ci �qiKi

�(20-14)

considers just the adsorbent because adsorptionon the catalyst has been assumed to be negli-gible. Changes to the total mass balances, Eqs(20-9) and (20-10) must also be made. Thesechanges may be readily seen from the amendedcomponent material balances above. Thepseudo-homogeneous assumption for theenergy balance is made by simple changes inEq. (20-3). Thus,

�εtCpgCþ εcatrpcatCpcat þ εadsrpadsCpads

� vTvt

¼ kxv2T

vx2� Cpg

n

A

vT

vxþUs

�εadsrpadsCpads

þεcatrpcatCpcat

� vT

vx� P

A

v

vx

�nC

�� εadsrpads

PNC

i¼ 1

Haivqivt

þ εcatrpcatDHRr� 4h0dc

ðT � TaÞ:

(20-15)

PERIODIC OPERATIO

Eqs (20-1 to 20-3), (20-7), (20-9) and (20-11)represent the fluid velocity by the total molarflow rate for the fluid, n. Velocity is affected bytemperature and pressure. If isothermal andisobaric conditions are assumed and the fluidphase is dilute, fluid velocity, u, can replacethe molar flow rate.

For many years, the balances given in Tables20-1 and 20-2 were used in normalized ordimensionless form for calculations. This prac-tice has lost favor in recent years. Nonetheless,dimensionless groups that arise from normali-zation are important for correlated experi-mental data. These groups are summarizedin Table 20-3. Dimensionless forms of thepseudo-homogeneous and heterogeneousseparating reactor models are given by Aidaand Silveston (2005) and their applicationdiscussed. Model variables in those sets ofequations have been rendered dimensionlessby characteristic length, space time, meanvelocity and adsorbent capacity. In the energybalance the temperature departure (T-T0) isused and made dimensionless by the inlettemperature (T0). The normalized modelscontinue to assume a single solid acting asboth catalyst and adsorbent.

Table 20-3 defines the dimensionless vari-ables that arise from normalization. Followingthe suggestion of Aida and Silveston (2005), thesolid-fluid velocity ratio, so important in charac-terizing moving bed chromatographic reactors,is called the Aris Number (NAr) to honor hisimportant contributions to the theory of chro-matographic reactors. Use of the Damkohlernumber is well-established. However thefirst form shown in Table 20-3 is stronglytemperature-dependent. Frequently the rateterms in dimensionless models are representedby a dimensionless Damkohler number, N’Da,containing b, the Prater number.

For simulated moving bed chromatographicreactors, the Danckwerts boundary conditionsare used and apply to a segment of the bedbetween j and jþ1 or j-1 and j in Figure 21-1.

N OF REACTORS

TABLE 20-3 Definition of Dimensionless Groups Used with Chromatographic and Swing Reactors

Bodenstein number for mass : Nd ¼ DxA

LF0:

Bodenstein number for heat ðgasÞ : ðNhÞg ¼ kxCpgrb N

A

LF0:

Bodenstein number for heat ðsolidÞ : ðNhÞs ¼ ksCpsrbN

A

LF0or

¼ ksCpcatεcatrpcat þ Cpadsεadsrpads

A

NLF0:

Damkoehler number for component i assuming an irreversible; 1storder rate model : NDa i ¼εtALkri

F0or kgi

�t:

Temperature independent Damkoehler number : NDa i ¼εtALkiF0

:

Prater number : b ¼ E

RT0:

Aris NumberðNArÞ or the velocity ratio of solid and fluid : s ¼ εtAUs

F0:

Boundary conditions characterize the different types of chromatographic reactors andwill be set forth, if necessary, when each type of reactor is

discussed in this chapter.


Fluid flows downward in the figure so atj where fluid enters the j-1 to j segment,

Dxid

dxðCiÞ

��j¼0�

¼ 1

A

�ðniÞjj¼0� � ðniÞjj¼0þ

�(20-16)

kxdT

dx

��j¼0�

¼ Cpg

A

�ðnTÞjj¼0� � ðnTÞjj¼0þ

�:

(20-17)

At j-1 where fluid leaves the segment,

dT

dx

�� ¼ dCi

dx

�� ¼ 0: (20-18)

PERIODIC OPERATIO

If the boundary, j, between two segments isa junction, the flow, ni, in Eqs (20-16) and (21-17)must be augmented by (ni)f if it is a feed point ordiminished by (ni)p if it is a product withdrawalpoint. The position atwhich the boundary condi-tions apply varies with time.

20.3.2 Lumped Models

A cell model can be a useful, alternativerepresentation of a packed bed of mixed adsor-bent and catalyst. In such models, a cascade ofcells, each with a uniform temperature and

N OF REACTORS

20.4. CYCLIC STEADY STATE 579

composition, is assumed. Thus, each cell can bedescribed by a lumped model. Cascade modelsare best suited to fixed bed CRs and SCMCRs.Isothermal operation is usually assumed asa representation of heat dispersion wouldrequire the use of pseudo-heat transfer coeffi-cients to represent conductive flows betweencells. Variables in a cascade model are shownin given by Figure 20-4. In this figure, the boxesare cells, j-1, j and jþ1. There are junctionsaround each cell denoted by j-1 and j that allowthe model to be applied to a SCMCR.

Cell models are used mainly with dilutesystems under isothermal and isobaric condi-tions. Assuming a pseudo-homogeneoussystem and using the assumption listed forTable 20-1, the material balance for the ith

component is:

V

εt

dCji

dtþ rbads

dqji

dt

!¼ FðCj�1

i � CjiÞ þ rbcatniVr:

(20-19)

Superscripts identify the cell or junction. Theoverall material balance is:

V

εtdCj

dtþ rbads

XNc

i¼ 1

dqidt

!¼ FðCj�1 � CjÞ

� rbcatVrXNc

i¼ 1

ni:

(20-20)

Mass balances at junctions between cells, j-1,j, jþ1, in Figure 20-4 are algebraic relations.

j – 1

j – 1 j +j

j

Cj, F

v

qj, Us

PERIODIC OPERATIO

It is necessary to estimate the number of cellsto apply the cell model. This number, Ncell, canbe estimated from the chromatographic peakcharacteristic using the following relationship(Falk and Seidel-Morgenstern, 1999):

Ncell ¼ 5:54ðtR=w0:5Þ2 (20-21)

where tR is the retention time, andw0.5 is the cor-responding peak width at half-height.

20.4 CYCLIC STEADY STATE

With the exception of the simple, pulseversion, chromatographic reactors run contin-uously and eventually reach what can becalled a cyclic steady state. In this state,concentration of any component, Ci, tempera-ture, T, velocity, u, quantity of an adsorbateon a surface, qi, are constant at identical timesmeasured from the start of the cycle ata specific position in the reactor. That condi-tion can be written for a cycle of period,s, for ns � t � (nþ1)s as:

Ci

�x; t� ¼ Ci

�x; tþ s

�; qi

�x; s� ¼ qi

�x; tþ s

�;

uðx; sÞ ¼ uðx; tþ sÞ; Tðx; tÞ ¼ Tðx; tþ sÞ;(20-22)

where n is a large integer. Of course, the con-dition applies as well to the reaction, adsorp-tion and transport rates and thus it implies theabsence of fouling and deactivation processes.Figure 20-5 illustrates the cyclic steady statewith respect to a reactant concentration.

1

FIGURE 20-4 Cascade representa-

tion of a separating reactor. Each cell,

(j -1), j, (j D 1), is assumed to have

a uniform concentration and temper-

ature. Junctions on either side of all

but the first and final cells permit

fluid addition or withdrawal. (Figure

reproduced from Aida and Silveston(2005). � 2005 by Blackwell Publ. Ltd.)

N OF REACTORS

C Reactant

C Reactant AT AXIAL

For n < t < sn

t t +

For sn < t < s(n+1)

AXIAL POSITION

1 100

(n+1) τ

(n-1) τ (n+1) τs (n+1) τsn τ n τ

(b)

(a)

TIME t

POSITION λ

τ

τ

τ

τ τ

FIGURE 20-5 Schematic repre-

sentation of the cyclic steady state

for a reactant at an axial point l

within the reactor. Two cycles are

shown. (Figure reproduced from Aidaand Silveston (2005) with permission. �Blackwell Publ. Ltd.)


20.5 PULSE CHROMATOGRAPHICREACTOR

Of the various types of chromatographicreactors, the simplest introduces a pulse ofreactant into a bed of intimately mixed catalystand adsorbent in a continuously flowing carrierfluid. The principle of the pulse chromato-graphic reactor (CR) was illustrated in Figure20-1. The operation was the first to be proposed(Roginskii et al., 1962) as well as the first to bemodeled (Magee, 1963) and studied experimen-tally by several research teams (Bassett and

PERIODIC OPERATIO

Habgood, 1960; Gaziev et al., 1963; Roginskiiet al., 1962; Matsen et al., 1965). Pulse chromato-graphic reactors are now used for analyzingthe reaction kinetics and testing adsorbentsand catalysts. Aida and Silveston (2005) offera thorough discussion of modeling as well asapplication of pulse chromatographic reactors.Table 20-4 summarizes many of the theoreticaland experimental contributions for this type ofreactor.

The pulse chromatographic reactor was firstapplied to kinetic studies of heterogeneouscatalytic reactions because this device uses

N OF REACTORS

TABLE 20-4 The Pulse Chromatographic Reactor (CR) Literature

Investigators Type of Study Reaction Observations

Klinkenberg (1961) Calculational General Reaction effect onchromatographic band width

Gaziev et al. (1963) Experimental Dehydrogenation of C6H12

Demonstrated C6H6 yield inexcess of equilibrium

Roginskii et al. (1961) Calculational General Interpretation of peak shape

Roginskii et al. (1962) Experimental As above As above

Roginskii and Rozental (1962) Calculational General Model development

Magee (1963) Simulation Generalreversiblereaction

Proposed simplified model

Semenenko et al. (1964) Simulation Dehydrogenation of n-C4H10

Yields in excess of equilibrium

Roginskii and Rozental (1964) Calculational General Derivation of kinetic models

Matsen et al. (1965) Experimental C6H12 DehydrogenationConversion in excess ofequilibrium

Saito et al. (1965) Calculational General Model development

Gore (1967) Calculational General Represented operation of a CR interms of sine and error functionwaves

Kocirik (1967) Simulation General Analysis of CR using moments ofchromatographic curves

Hattori and Murakami (1968) Calculational General Analysis of pulse reactors andCRs

Chu and Tsang (1971) Simulation General Effect of operating parameters onCR performance

Wetherold et al. (1974) Experimental &Simulation

Hydrolysis ofmethyl formate

Conversion in excess ofequilibrium; model validation

Unger and Rinker (1976) Experimental Ammoniasynthesis

Demonstrated increasedconversion

Schweich and Villermaux (1978) Experimental &Simulation

C6H12 DehydrogenationModel development andvalidation

Sardin and Villermaux (1979) Experimental Esterification Increased conversion with noseparation of reactants

Schweich et al. (1980) Calculational General Calculation method

(Continued)

20.5. PULSE CHROMATOGRAPHIC REACTOR 581


TABLE 20-4 The Pulse Chromatographic Reactor (CR) Literature (cont’d)


Schweich and Villermaux (1982a, b, c) Simulation C6H12 DehydrogenationAssumption of local reactionequilibrium questionable

Antonucci et al. (1978) Experimental C2H6 DehydrogenationConversion in excess ofequilibrium

Cho and West (1986) Experimental CO oxidation Chromatographic effects withina catalyst pellet

Zafar and Barker (1988) Experimental &Simulation

Enzymaticsucrosepolymerization

Validation of a plug flow model

Liden and Vamling (1989) Simulation Consecutivereactions

Improved selectivity over PFR

Sad et al. (1996) Experimental Dehydroisomerization of n-C4

Use of composite catalysts anddifferentadsorbents

Mazzotti et al. (1997a) Experimental &Simulation

Esterification ofalcohol withHAc

Back-mixing due to densitydifferences in displacement front

Wu (1998) Experimental Enantioselectiveesterification

Analytical method of measuringenantioselectivity

Falk and Seidel-Morgenstern (1999) Simulation Hydrolysis ofmethyl formate

Conversion improvement due toa dilution effect

Wu and Liu (1999) Experimental Esterification ofracemicnaproxen

Analytical method of measuringenantioselectivity

Migliorini et al. (2000) Experimental &Simulation

Enzymatic diolesterification

Importance of water content;model validation

Silva and Rodrigues (2002) Experimental &Simulation

Diethyl acetalsynthesis

Model validation and parametermeasurement

Falk and Seidel-Morgenstern (2002) Experimental &Simulation

Hydrolysis ofmethyl formate

Product separation and recoverymore important than conversion

Gelosa et al. (2003) Experimental &Simulation

Triacetinesynthesis

Conversion greatly in excess ofequilibrium

Yu et al. (2004) Experimental &Simulation

MeOH - HAcesterification

Measurement of adsorption andkinetic parameters

Vu et al. (2005) Simulation Hydrolysis ofmethyl formateand acetate

Model for equilibrium andreaction transformed into anequivalent equilibrium system

Note: Calculational¼ theoretical study, usually a simulation.




only a small amount of reactants and requiresless experimental time than classical steady-state procedures. Since the reactor operatesunder unsteady state, to obtain the kineticdata for reactor design, it was necessary torelate conversion and yield in the two systems.This was done by Saito et al. (1965) and Hattoriand Murakami (1968). They found that in thecase of linear reactions, the results from a pulsechromatographic reactor are in agreement withthose from a steady-state reactor, while fornonlinear reactions there is a remarkabledisagreement.

In pulse chromatographic reactors, the reac-tants are fed periodically to the reactor inlet ina carrier fluid. The shape of the pulse, theamount of injection, the cycle time and theinterval between injected pulses are importantoperating variables. Matsen et al. (1965) experi-mentally examined the performance of thepulse chromatographic reactor for the dehy-drogenation of cyclohexane to benzene andhydrogen with a Pt/Al2O3 catalyst, wherealumina acted as the adsorbent. Rectangularpulses of C6H12 were fed into the reactor ina helium carrier gas. The thermal conductivityof the effluent gas was recorded potentiometri-cally. Using single pulses in a relatively long

OPTIMUM REPETITIVE PULSING

BENZENE RECONVERTEDCYCLOHEXANE

UNCONVERTEDCYCLOHEXANE

HYDROGEN

REC

OR

DER

RES

PON

SE

CC OF CARRIER GAS

Seco

nd P

ulse

Inje

cted

Third

Pul

se In

ject

ed(C

hrom

atog

ram

Sha

pe is

Con

stan

t Bey

ond

This

Poin

t)

4

3

2

1

0

-10 20 40 60 80

PERIODIC OPERATIO

reactor, Matsen et al. observed well-separated,fairly sharp peaks of H2 and C6H6 with a smallreactant sample. As the sample size increased,these peaks tailed toward each other. Witha sufficiently large sample, a sharp peak ofunreacted cyclohexane appeared between H2

and C6H6. Since the effect of carrier gas flowrate on conversion was not significant, adsorp-tion, reaction and desorption were rapid underthe conditions studied so dehydrogenation wasequilibrium-limited. As the pulse frequencyincreases, the H2 peak from a fresh pulsecatches up with the C6H6 peak from theprevious pulse and a reconverted C6H12 peakappears in the product chromatogram. Thus,the optimum pulsing operation is to usea sample pulse as large as possible and to pulseas frequently as possible without allowinga peak of unconverted C6H12 to arise in theexit stream. Figure 20-6 demonstrates such anoptimum mode of operation. The experimentalconditions are given in the figure caption.Conversion in the pulse chromatographicreactor was 96.4%. This was about 30% greaterthan that under equilibrium for the reactoroperating conditions.

Schweich and Villermaux (1982b) also dealtwith the dehydrogenation of cyclohexane in

100

FIGURE 20-6 Product chromatogram for

an optimal repetitive pulsing. Measurement

conditions: TReactor[ 225�C, LReactor[ 50 cm.

Catalyst Wt.[ 8 g, UCarrier[ 10 cm3/min,

pulse volume[ 12 mL, pulse separation

[ 3.5 min. (Figure adapted from Matsen et al.(1965) with permission. � 1965 by the American

Chemical Society.)

N OF REACTORS

treg

tinj

tcyc

FIGURE 20-7 Illustration of injection, regeneration

and cycle time for a pulse chromatographic reactor. (Figurereproduced from Falk and Seidel-Morgenstern (2002). � 2002

by Elsevier Publishing Co.)


the pulse chromatographic reactor. ConversionX was measured as a function of the period ofthe injections. The authors observed an optimalsequence of injections that depended on thereaction temperature. At TReactor¼ 220�C, theoptimal time between injections was aboutfiveminutes. Experimental results showed thatconversion in the pulsed chromatographicreactor exceeded the equilibrium conversion.

A mixed cell model was used by Falk andSeidel-Morgenstern (1999) to simulate the perfor-mance of the pulse chromatographic reactor.Porosity of the bed, the number of cells andequilibrium constants were estimated from theelution profiles for the hydrolysis of methylformate over an acidic ion exchange resin. Reac-tion kinetics were assumed to be reversible andsecond-order; kinetic parameters were deter-mined from batch experiments. Simulatedelution profiles agreed well with separate exper-imental measurements. The authors addressedthe question of whether a chromatographicreactor provides a higher conversion thana continuously operated fixed bed reactor underthe same operating conditions. Thus, theycompared the performance of both reactors forthe same amount of reactant per unit time andthe same volumetric flow rate. The authorsfound that, in the range of the conditionsconsidered, the conversion for the fixed bedreactor with the diluted reactant exceeded thatof the pulsed chromatographic reactor. How-ever, as the injection is extended, the tworeactors perform similarly. Of course, the chro-matographic reactor has the advantage ofdirectly collecting separated products.

Falk and Seidel-Morgenstern (2002) extendedthis earlier work introducing a dilution ratio,4, which specifies the rectangular pulse illus-trated in Figure 20-7:

4 ¼ 1� t inj=s cyc ¼ t reg=scyc; (20-23)

where inj scyc and treg represent, respectively, theinjection duration, the cycle period and theregeneration time between successive injections.

PERIODIC OPERATIO

When the cycle period is only slightly less thantinj the dilution ratio is small and the operationof the chromatographic reactor functions likea conventional fixed bed reactor. Longer regen-eration times lead to larger values of 4. Falkand Seidel-Morgenstern (2002) discussed theperformance of chromatographic reactors interms of three performance parameters: Produc-tivity of the desired product, conversion of reac-tant and recovery of injected reactant in the pureproduct. The production rate showedmaximumvalues of 4¼ 0.8. An increase of 4 increasedconversion and product separation. Recoverydecreased as the dilution ratio drops and feedflow rate increases.

In the pulse chromatographic reactor, thecatalyst is continuously regenerated by thecarrier fluid between successive pulses.However, when one of the products is stronglyadsorbed, regeneration is difficult for short

N OF REACTORS


treg between pulses. An example arises in ester-ification using a cationic exchange resin as bothcatalyst and adsorbent because water is stronglyadsorbed on the resin. Reactive chromatog-raphy is a solution of such a problem. In thisoperation the solute reacts with the adsorbateto regenerate the adsorbent. A reactive chro-matographic reactor is also referred to as a fixedbed adsorptive reactor.

Mazzotti et al. (1997a) demonstrated experi-mentally the operation of reactive chromatog-raphy for the synthesis of ethyl acetate (EtAc)from ethanol (EtOH) and acetic acid (HAc)over an Amberlyst 15 resin. At start-upa mixture of reactants is continuously fed tothe resin bed initially saturated with the EtOHsolvent. As reaction occurs, water is trappedby the resin, whereas EtAc is carried by the fluidstream along the column. Since a product (EtAc)is removed from the resin surface, esterificationproceeds until the limiting reactant (HAc) isconsumed. At each location in the bed, thisprocess continues until water saturates theresin. Thereafter, the composition remainsconstant and at equilibrium. Figure 20-8 illus-trates the time evolution of the outlet composi-tion. First, EtAc breaks through together with

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

0 1.2 1.4Dimensionless Time

Volu

me

Frac

tions

PERIODIC OPERATIO

ethanol. After water saturates the bed of resin,water and acetic acid break through togetherand the steady-state equilibrium compositionis attained. In between these breakthroughs,a solution of EtAc in alcohol can be collected.Before a new feed pulse can be introduced, theresin must be regenerated. This can be accom-plished using EtOH as the desorbent, as illus-trated in Figure 20-9. The weakly adsorbedcomponents, EtAc and HAc, are quickly des-orbed resulting in a rather sharp transition. Onthe other hand, water elutes much more slowly.In both figures the curves were calculated byusing a pseudo-homogeneous dispersion modelwith a rate term employing component activi-ties rather than concentrations. Agreementbetween model and experimental and theoryis satisfactory.

Silva and Rodrigues (2002) discussed in moredetail the dynamic behavior of a fixed bedadsorptive reactor for the synthesis of diethyla-cetal from EtOH and acetaldehyde overa cationic resin catalyst (Amberlyst 18) withwater as a byproduct. For a simulation theyemployed a mathematical model allowing foraxial dispersion as well as external and internalmass transfer resistances. Adsorption was

1.6 1.8

FIGURE 20-8 Reaction experiment with

upflow through the bed; the plot shows the

measured composition as volume fraction

of species exiting the reactor: (C) acetic

acid; (3) ethanol; (D) water; (B) ethyl

acetate. All curves are calculated by the

simulation model. (Figure reproduced from

Mazzotti et al. (1997a). � 1997 AmericanChemical Society.)

N OF REACTORS

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

0 1.2 1.4 1.6 1.8Dimensionless Time

Volu

me

Frac

tions

FIGURE 20-9 Regeneration exper-

iment with downflow through the

bed; the plot shows the measured

composition as volume fraction of

species exiting the reactor: (C) acetic

acid; (3) ethanol; (D)water; (B) ethyl

acetate; all curves are calculated by

the simulation model. (Figure repro-duced from Mazzotti et al. (1997a). �1997 American Chemical Society.)


described by a multi-component Langmuirisotherm and an experimental reaction rateexpression was used. The experimental concen-tration vs. time profiles in their reactor for thereaction and the regeneration steps were similarto those shown in Figures 20-8 and 20-9. Inorder to better understand the behavior of theconcentration-time profiles, the internal concen-tration profiles of each species in the fluid phaseinside the reactor at different times were deter-mined through simulation.

Gelosa et al. (2003) investigated the synthesisof a commercial product glycerol triacetate (tri-acetine) by esterification of glycerol with aceticacid using reactive chromatography and theapproach of Mazzotti et al. (1997a). A chromato-graphic reactor can produce high-purity triace-tine at high conversions, but the presence ofwater in the resin at the end of the regenerationstep has a detrimental effect on the final triace-tine purity. The reaction proceeds consecutivelythrough a series of three esterification steps,each producing water, with glycerol monoace-tate and glycerol as intermediate products. Theexperimental apparatus consisted of a singlecolumn with an internal diameter of about1.5 cm and a length of 44 cm that was packed

PERIODIC OPERATIO

with the resin Amberlyst 15. Transient changesin the concentrations of components at thereactor outlet in both reaction and regenerationexperiments were compared with predictionsof a mathematical model, the kinetics and equi-librium parameters of which were estimatedfrom batch experiments. Agreement was con-sidered to be good.

In addition to being used as a screening tool,pulse chromatographic reactors have been usedto examine the behavior of catalysts that swellin the presence of reactants or products sothat the trapping capacity of the solid changeswith fluid composition. This behavior isobserved with polymer-based ion exchangeresins such as Amberlyst 15. Researchers inZurich developed a model for the esterificationof ethanol by acetic acid over a cationicexchange resin that allowed for a variation ofthe resin void fraction and in this way itsadsorption capacity. For this reaction, the rateof diffusion in the resin is affected by swelling.However, the effect on reactor performance issmall (Mazzotti et al., 1997a).

Extraction of rate of reaction and adsorptionequilibrium constants was demonstrated byYu et al. (2004). Good agreement was found

N OF REACTORS

20.6. COUNTERCURRENT MOVING BED CHROMATOGRAPHIC REACTOR 587

with constants obtained through other tech-niques. In a new development, Seidel-Morgen-stern and colleagues use matrix-basedadsorptionmodeling assuming adsorptive equi-libria whose behavior in a fixed bed is well-known and show how a reactive system can betransformed into an adsorptive one providedthe reactions are linear. This approach wasapplied to hydrolysis reactions of differentstoichiometries to determine whether completeconversion and product separation is possible(Vu et al., 2005). In addition, these investigatorspresent a predictive model that introducesdispersion and is not restricted to linear kinetics.

20.6 COUNTERCURRENT MOVINGBED CHROMATOGRAPHIC

REACTOR

Production limitations of pulse operation canbe overcome by allowing the catalyst and adsor-bent solids to flow through the reactor counter-current to the flow of reactants and products.When this is done, the feed to the reactor andwithdrawal of products are continuous ratherthan periodic. The reactor operates at steadystate and only ordinary differential equationsdescribe the reactor performance. Catalyst andadsorbent, however, are not at steady state asthey move through the reactor space and comeinto contact with different fluid environments.These solids experience cyclically changingenvironments.

The throughput of a chromatographic reactormay be substantially increased by using a coun-tercurrent moving bed. Product yield perweight of catalyst or adsorbent, however, maynot change greatly because a much largerweight of solids will be needed when they circu-late through the reactor. The moving bed alter-native exchanges the complexities andproblems of periodic operation for those ofmoving solids. These problems are nonuniformflow and attrition of the solids. Attrition means

PERIODIC OPERATIO

solids replacement and the continuous removalof fines.

The countercurrent moving bed chromato-graphic reactor (CMCR) is often associatedwith the University of Minnesota researchgroup directed initially by Aris and later byCarr. However, the concept was proposed atabout the same time by a Japanese team (Takeu-chi and Uraguchi, 1976a) who studied separationspossible with moving beds and demonstratedthroughput advantages. Table 20-5, redrawnfrom Aida and Silveston (2005), summarizes thecountercurrent moving bed chromatographicliterature.

There appears to be little current interest inthe type of countercurrent moving bed chro-matographic reactors shown in Figure 20-2with downward cascading solid catalyst andadsorbent because of the well-known problemsencountered with flowing solids. However,past work, summarized in Table 20-5, hasbeen useful for understanding concentrationdistributions in practical reactive chromato-graphic systems.

Tables 20-1 and 20-2 contain pseudo-homo-geneous and heterogeneous models for CMCRs.Danckwert’s boundary conditions are used forthis type of reactor.

Using a pseudo-homogeneous model andassuming plug flow, Aris and co-workerssearched for concentration discontinuities(shock fronts) that arise in CMCRs. They didso using various mathematical procedures:1) Method of characteristic where results areplotted as phase planes or as hodographs(Viswanathan and Aris, 1974; Cho et al., 1982;Fish and Carr, 1989) and 2) stability analysis (Pet-roulas et al., 1985a,b). Top discontinuities wherethe solid phase enters the CMCR, as well asfeed point and bottom discontinuities wherefluids enter, are always present and internaldiscontinuities can occur if the fixed bed of cata-lyst and adsorbent is long enough. The criticalparameters for discontinuity location are k, therelative adsorptivities of product and reactant,

N OF REACTORS

TABLE 20-5 Countercurrent Moving Bed Chromatographic Reactor Literature


Viswanathan andAris (1974)

Calculation andsimulation

General irreversiblereaction

No improvement in conversion was found, butexistence of shock fronts was observed.

Takeuchi and Uraguchi(1976a, b)

Calculation General Calculation of separation based on moments.

Takeuchi and Uraguchi(1977a, b)

Experimentaland simulation

General, CO oxidation No improvement in conversion was observed.Model validation undertaken

Takeuchi et al. (1978) Simulation General consecutivereactions

Selectivity improvement over a PFR was found.

Cho et al. (1982) Simulation General reversiblereaction

Discontinuity identified and discussed.

Altshuller (1983) Simulation General Undertook treatment of a complex isotherm.

Petroulas et al.(1985a, b)

Experimentaland simulation

Hydrogenation ofmesitylene

Improved product purity and conversion overequivalent PFR.

Fish et al. (1986) Experimentaland simulation

As above Description of reactor design and troubleshootingof operational problems.

Fish and Carr (1989) Experimentaland simulation

As above Model validation.

Lode et al. (2003a) Simulation General Comparison of CMCR and SCMCR design.


and the Aris Number, s, the ratio of solidvelocity to fluid velocity in the CMCR. Thisterm arises in the dimensionless mass balancesand is defined in Table 20-3. To describe themovement of a reaction species i, another formof the Aris No. can be used,

si ¼Us

uf

1� εb

εb

NKA

1þ KACA þ KBCB(20-24)

where a binary reaction A % B and adsorptiveequilibrium given by a Langmuir isotherm isassumed. The presence of an internal disconti-nuity is essential to performance of theCMCR. In the region of the bed below thediscontinuity, CMCR performance is given bythe reaction system, namely reaction equilib-rium, whereas, above the discontinuity, adsorp-tive equilibria determine the overheadcomposition. Figure 20-10 illustrates disconti-nuities in a CMCR with a stripping section

PERIODIC OPERATIO

for an A % B isomerization in which A is themore strongly adsorbed component. Therecycled adsorbent contains neither A nor B.The feed contains just A, but adsorbed B iscarried past the feed point by the adsorbent.A is trapped by the adsorbent and convertedto B so it does not leave in the product stream.The reaction system is isothermal and the equi-librium relation is given in the hodograph, (c)in the figure.

Mixing cannot be avoided in flow througha porous media. Thus, more accurate mass andheat balance models must contain dispersion

terms, such as the Dxi

v2Ci

vx2term in Eq. (20-1)

and the kxv2T

vx2term in Eq. (20-3) for the

pseudo-homogeneous model of Table 20-1 orin Eqs (20-7), (20-8), (20-11) and (20-12) for theheterogeneous model in Table 20-2. Allowing

N OF REACTORS

FIGURE 20-10 Discontinuities in a simulation of an A 4 B equilibrium controlled reaction in a countercurrent

moving bed chromatographic reactor: (a) Schematic of the CMCR with a side feed point and stripping gas fed at the

bottom, (b) reactant “A” and product (B) trajectories within the reactor bed and (c) hodographic representation showing

discontinuities. (Figure copied from Petroulas et al. (1985a) with permission. � 1985 Pergamon Press Ltd.)

20.6. COUNTERCURRENT MOVING BED CHROMATOGRAPHIC REACTOR 589


Stationary Feed InletEnzyme Solution

Mobile Phase FlowMobile Phase Flow


for dispersion replaces the discontinuities bysteep concentration and temperature gradients.Their steepness depends on the magnitude ofthe dispersion coefficient. Indeed, steep gradi-ents are predicted in models for simulatedmoving bed chromatographic reactors. Exam-ples of measured or predicted steep gradientsin SCMCRs may be seen, for example, inFigures 21-4, 21-7, or 21-19.

ROTATION

Products

FIGURE 20-11 Operating principle of a CRAC reactor

for an enzyme-catalyzed reaction. The rotating annular

volume is packed with a mixture of catalyst and adsorbent

while the mobile phase is the eluent. The reaction species

carried furthest from the feed point in the angular direc-

tion is the species most strongly adsorbed.

(Figure reproduced from Sarmidi and Barker (1993a) withpermission. � 1993 by the Society for the Chemical Industry.)

20.7 CONTINUOUS ROTATINGANNULAR CHROMATOGRAPHIC

REACTOR

Moving the bed instead of individual cata-lyst/adsorbent particles solves the attritionand nonuniform flow problems of movingbeds mentioned earlier. Such a moving bedcan be realized by rotating an annular bed ofcatalyst and adsorbent past feed and carrierfluid injection points in a top plane and productand carrier fluid removal points along a bottomplane as shown in Figure 20-11. Although thefigure shows a biochemical application, thecontinuous rotating annular chromatographicreactor (CRAC) can be used for any reactionwith a small heat. Passing fluids through rotat-ing packed beds of solids is a well-establishedtechnology in energy conservation. Rotatingbeds are commercially available in various sizesfor recovering heat continuously from hotexhausts and transferring the captured heat tocombustion air. They are described and theirperformance analyzed in the regenerative heat-ing literature.

CRAC systems have been used in prepara-tive chromatography and are being exploredfor reactive chromatography as indicated inTable 20-6. Interest seems to have lapsed since1995 despite their simple operation anddemonstrated performance. CRAC is perhapsthe only moving bed chromatographic reactorthat is ready for commercial application. Theonly limitation at the present state of

PERIODIC OPERATIO

development is throughput, arising frommechanical limitations on rotating a heavybody of solids in the form of an annulus. Labo-ratory scale devices are discussed by Aida andSilveston (2005).

With the exception of an early paper(Wardwell et al., 1982), CRAC reactors havebeen used for liquid systems. These systems,particularly biochemical ones, are isothermalso they can be described by just materialbalances. They are also continuous so the timederivative disappears. Their geometry, however,requires modification of their model equations;the position variable, x, from the material

N OF REACTORS

3

2

1

00 100 200 300 400

GlucoseFructoseSimulated

DEGREES FROM FEED POINT

GLUCOSE

FRUCTOSE

CO

NC

ENTR

ATIO

N (%

w/v

)

Experimental;

FIGURE 20-12 Comparison of a CRAC reactor simu-

lation with experimental measurements for the enzymatic

inversion of sucrose at 100�C. Eluent flow rate[ 8000 cm3/

h, liquid feed rate[ 230 cm3/h containing 25 wt% sucrose;

u[ 240�/h. (Figure reproduced from Sarmidi and Barker(1993b) with permission. � 1993 by Pergamon Press Ltd.)

TABLE 20-6 Continuous Rotating Annular Chromatographic Reactor Literature


Cho et al. (1980a, b) Simulation andexperiment

Catalytic hydrolysis ofmethyl formate

Complete conversion was obtained; modelpredicted experiments closely.

Wardwell et al. (1982) Simulation andexperiment

Catalytic dehydrogenationof C6H12

Conversion greatly exceeded equilibriumlimit. Simulation predicted separation poorly.

Sarmidi & Barker (1993a) Experiment Enzymatic saccharificationof starch

Conversion to maltose very much higher thanin a batch reactor.

Sarmidi & Barker (1993b) Simulation andexperiment

Enzymatic inversion ofsucrose

Complete conversion of sucrose; simulationclosely predicted experimental performance.

Herbsthofer & Bart (2003) Simulation andexperiment

Fe3þ reduction by Ir4þ CRAC reactor gave 5 x higher conversion thana PFR. Model verified experimentally.

20.8. STEPWISE, COUNTERCURRENT MULTI-STAGE FLUIDIZED BED CHROMATOGRAPHIC REACTOR 591

balances in Tables 20-1 and 20-2 is retained, buta second variable, z, reflecting angular positionfrom the point of feed injection, must be intro-duced. Thus,

εuvCi

v2þ rads

vqiv2

þ 1

A

vnivx

�Dxiv2Ci

vx2¼ rcatnir;

(20-25)

where u is the angular velocity and A is thex-section of the mixed bed of catalyst and adsor-bent. Molecular diffusion in the direction ofrotation is neglected.

Sarmidi and Barker’s experiments arecompared with a simulation using Eq. (20-25)in Figure 20-12. Data were obtained froma 1.2 � 135 cm X-section annular bed packedwith a Dowex 50W-X4 adsorbent and an a-amylase maltogenase. The enzyme was bledinto the eluent stream. It can be seen that thesimulation slightly overestimated the productconcentrations in the take-off streams.

Herbsthofer and Bart (2003) using the reduc-tion of ferric ion by an iridium ion as their testsystem also observed good agreement of simu-lation and experiments at 50�C. They also foundan optimal angular velocity for Fe3þ reduction.Aida and Silveston (2005) provide a furtherdiscussion of this contribution as well as someearlier work.

PERIODIC OPERATIO

20.8 STEPWISE,COUNTERCURRENT MULTI-

STAGE FLUIDIZED BEDCHROMATOGRAPHIC REACTOR

Dutch investigators (van der Wielen et al.,1990,1998; Vos et al., 1990a,b,c) have investigateda true moving bed chromatographic reactoremploying periodic fluidization of a mixed

N OF REACTORS


catalyst and adsorbent bed. By using particles ofa different size and density for adsorbent andcatalyst, these researchers caused the catalystparticles to be held stationary in the reactorvessel, while the adsorbent particles separatedfrom the mixed bed and flowed under gravitydownward to a lower stage. Thus the adsorbentmoved countercurrent to the reactant. Themeans for accomplishing segregation anddownflow was adjustment of the fluid upflowvelocity and periodic flow direction reversal.Operation of the Vos-van der Wielen system isdepicted in Figure 20-13. Van der Wielen et al.(1998) discuss the application of this system tothe preparation of 6-aminopenicillanic acidfrom penicillin G. Research on this novelmoving bed system appears to have ended.Aida and Silveston (2005) provide a lengthierdiscussion of the van der Wielen work.

20.9 FIXED BEDCHROMATOGRAPHIC REACTOR

WITH FLOW DIRECTIONSWITCHING

A strongly adsorbed reactant or product canbe carried out of the bottom of a countercurrent

FIGURE 20-13 Sequence of fluid flow operations in a liqu

countercurrent flow of liquid phase reactant and adsorbent. F

particles. (Figure reproduced from van der Wielen et al. (1998) w

PERIODIC OPERATIO

moving bed chromatographic reactor if theeluent flow is too small, diminishing the yieldor product separation. Raising the eluent flowcorrects this difficulty but with the penalty ofa diluted overhead product and the extraeluent cost. Caram and Viecco (2004) demon-strate that periodically switching the flowdirection through the catalyst-adsorbent bedcan trap the strongly adsorbed component toensure its complete conversion. This rearrange-ment avoids higher eluent consumption andproduct dilution. Figure 20-14 illustrates theoperation of the flow reversal alternative. Theauthors investigated the performance of theirsystem for first-order, reversible and irrevers-ible isomerization reactions, for an irreversibleconsecutive reaction using cell (lumped)models (see Section 20.2.2). They also under-took a simulation of the hydrogenation ofmesitylene in order to compare performanceto that of a CMCR (Petroulas et al. 1985a,b; Fish& Carr, 1989) and observed that conversionand product purity achieved by the reverseflow chromatographic reactors are lower thanthose achieved in a CMCR for the sameassumptions.

Reverse flow operation is the subject ofChapter 18.

id flow pulsed, fluidized bed chromatographic reactor with

illed circles[ adsorbent particles; open circles[ catalyst

ith permission. � 1998 by the AIChE.)

N OF REACTORS

Carrier

Reactant

Carrier &Products

Carrier

Reactant

Carrier &Products

First half of cycle Second half of cycle

FIGURE 20-14 Schematic of the operation of

a reversing flow chromatographic reactor showing the two

parts of a cycle. (Figure reproduced from Caram and Viecco(2004) with permission. � 2004 AIChE.)

20.11. CENTRIFUGAL PARTITION CHROMATOGRAPHIC REACTOR 593

20.10 EXTRACTIVE REACTORSYSTEMS

Extractive reactors are liquid-liquid systemsthat can function as separating reactors for reac-tants available as liquids. Likewise absorberscan also perform both reaction and separationfor gas phase reactants. We do not considerthese operations in this book because they aregenerally operated continuously. Furthermore,contacting immiscible streams of liquids orgases and liquids are well-developed operationsin industry.

There are exceptions for several processesemploying reactive extraction and absorption.For these, periodic operation is either advanta-geous or simply necessary. One of theseprocesses is the air oxidation of SO2 over anactivated carbon catalyst. Several activatedcarbons function at room temperature, butthey strongly adsorb the SO3 product. In thepast, investigators have shown that theadsorbed SO3 can be quantitatively strippedfrom the carbon surface by water to formsulfuric acid. Oxidation can be performed ina trickle bed packed with carbon granuleswith a continuous, co-current feed of air, SO2

and water (Hartman and Coughlin, 1972; Mataand Smith, 1981); however, considerably higheroxidation rates are attained by periodicallyswitching between liquid and gas flow (Haure

PERIODIC OPERATIO

et al., 1989; Metzinger et al., 1994; Lee et al.1996b). Chapter 17 deals with periodic opera-tion of three phase reactors and SO2 oxidationis discussed there in some detail.

A similar technique was used by Yamada andGoto (1997) for the hydrogenolysis of carboben-zophenylalanine to phenylalanine over aPd/carbon catalyst employing a dichloroethanesolvent. Phenylalanine is insoluble in thissolvent and deactivates the catalyst by crystal-lizing on its surface. Water, however, dissolvesphenylalanine so these researchers carried outthe hydrogenolysis in a countercurrent tricklebed by periodically switching the liquid feedat the top of the bed between the reactant dis-solved in dichloroethane and water. The latterstream contained the product. Aida and Silveston(2005) discuss the Yamada and Goto experimentalwork.

20.11 CENTRIFUGAL PARTITIONCHROMATOGRAPHIC REACTOR

We end this chapter with a brief discussion ofthe application of a centrifugal partition chro-matographic reactor (CPCR) for a liquid phasereaction. The CPCR employs reactant pulsesand operates with two liquid phases, one ofwhich is held stationary at the centrifuge outerwall by the vessel design and a density differ-ence between it and the second, circulatingliquid. The stationary phase contains a catalyst,generally an enzyme, as applications have beento biochemical systems. Products of the reactionmust have different partition coefficients for thetwo liquid phases.

When a pulse is carried into contact with thestationary liquid, a reactant enters that phase.Products are formed and diffuse back intothe circulating phase, partially separated bydiffering partition coefficients. The mobilephase is moved through the centrifuge forrepeated interchange with a different portionof the stationary phase, thus affecting reactant

N OF REACTORS


conversion and separation of the reaction prod-ucts as may be seen by separate peaks in thecirculating liquid. DenHollander et al. (1998)describe the application of CPCR to the chirallyselective enzymatic hydrolysis of N-acetyl-L-methionine into L-methionine and by-productacetic acid. A second paper dealt with hydro-lysis of a racemic mixture of N-acetyl-methio-nine.

Notation

A
= bed or reactor cross sectional area (cm2) A = component a = specific surface area am = specific surface area for mass transfer
(cm2/gsolid)
B = component CMCR = continuous moving bed chromatographic
reactor
CPCR = centrifugal partitioning chromatographic
reactor
CR = chromatographic reactor CRAC = continuous rotating annular-bed chromato-
graphic reactor
CSTR = continuous stirred tank reactor C = concentration (mol/cm3)component Ci = concentration of i Cp = specific heat (cal/mol$K) Dxi = axial dispersion or diffusivity of species i d = diameter (cm) dc = vessel diameter (cm) dp = particle diameter (mm) E = activation energy (various units) EtAc = ethyl acetate EtOH = ethanol F = volumetric flow rate (m3/h) F0 = entering volumetric flow rate Ha = heat of adsorption (kJ/mol) HAc = acetic acid DHR = heat of reaction (kJ/mol) h = heat transfer coefficient (various units) h0 = heat transfer coefficient i = chemical species indicator Jk = kinetic coefficient in the Ergun Eq. Jv = viscous coefficient in the Ergun Eq. j = position, stage or step indicator, cell number K = equilibrium constant Ki = adsorption equilibrium constant for species
i (L/g)

PERIODIC OPERATIO

k

N OF RE

= position, stage or step indicatorspecies or component indicator

k
= rate constant (various units) k’ = temperature independent rate constant
(coefficient in the Arrhenius term)
km = mass transfer coefficient (mol/cm2$s) kr = rate constant ks = conductivity of the solid phase (J/cm2$s) kx = axial conductivity (J/cm2$s) kg = defined in Table 20-3
L
= bed or column length (m) MeOH = methanol m = position, stage, step indicator N = adsorption capacity, number of adsorption
sites (1/g adsorbent)
NAr = Aris number defined in Table 20-3
Nc
= Number of components Ncell = number of cell NDa = Damkohler No. N’Da = temperature independent Damkohler No. Nd = Bodenstein No. for mass Nh = Bodenstein No. for heat Nm = ratio of volumetric mass transfer coefficient
to space velocity
n = integer n = molar flow rate (mol/h) ni = molar flux of component I, molar flow rate
for species I (mol/h)
ns = number of segments or stages in a column
or bed
PDE = partial differential equation PFR = plug flow reactor PSR = pressure swing reactor P = pressure (kPa) qi = adsorbate loading (mol/g adsorbent) r = rate of reaction (various units) SCMCR = simulated continuous moving bed
chromatographic reactor
s = counting integer TSR = temperature swing reactor T = temperature (K) Ta = ambient temperature Ts = solid or surface temperature t = time (s, h) tinj = injection time (s) tR = retention time (s, min) treg = regeneration duration (s, min) t = residence time (h) Us = solids velocity u = superficial velocity (cm/s) uf = fluid superficial velocity (cm/s) VOC = volatile organic compound
ACTORS

20.11. CENTRIFUGAL PARTITION CHROMATOGRAPHIC REACTOR 595

V
= volume, usually of bed or reactor (m3) Vj = volume of jth bed or column w0.5 = width at half height Xi = conversion of reactant i x = axial position, also stage no. counting from
top or bottom of a column

Greek S
ymbols
a
= coefficient in the Ergun Eq. b = Prater No. ε = void fraction ( ) εads = adsorbent volume fraction εb = void fraction in bulk of solid, also bed void
fraction
εbed = void fraction in bed εcat = catalyst volume fraction εp = particle (adsorbent) void fraction εt = total void fraction, usually referred to the bed
volume, but also to particle volume
4 = dilution ratio k = ratio of adsorptivities l = parameter in Ergun relation mg = gas viscosity (various units) n = dimensionless total molar flow rate nI = stoichiometric coefficient for component i
dimensionless molar flow rate forcomponent i

q
= dimensionless time r = density rads = adsorbent density (g/cm3) rb = bulk density of adsorbent or catalyst-
adsorbent (g/cm3)
rcat = bulk density of catalyst rg = gas density rs = solid density s = Aris No. or flow ratio of solid and fluid s = period (s, h) scycle = cycle time or period (s, h) ss = switching time, duration between movement
of inlet/outlet location (s, h)
u = angular velocity (rad/s)
= ratio of solid to fluid heat capacities
j = ratio of pressure and thermal energies zv = normalized viscous pressure drop
contribution in the Ergun Eq.

PERIODIC OPERATIO

zk

N OF RE

= normalized kinetic pressure dropcontribution in the Ergun Eq.

Superscripts

f
= feed j = cell or position or step indicator k = position or step indicator m = time-step indicator t = top * = flow ratio, equilibrium quantity
Subscripts

A, B
= chemical species a = ambient, adsorbent adsorption ads = adsorbent b = bulk cat = catalyst cyc = cycle Da = Damkohler f = feed g = gas i = reaction component or species inj = injection j = jth section, zone or bed, also reaction species
or reaction number
k = kth section, zone or bed, also reaction species
indicator
L = outlet or exit m = mass n = stage number ns = number of top stage p = particle, bead, pellet or withdrawal point R = reaction reg = regeneration s = solid, or switch (switching) t = total x = axial 0 = feed or inlet 0L = just before inlet 0D = just after inlet 0.5 = half height 1,2 = position or time indicators
ACTORS

Periodic Operation of Chemical Reactors || Chromatographic Reactors

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