(Firse reccived 14 June 1995; revised manuscripr recei,ed and acceprqd 21 A"guse 1995)

EFFECT OF INTRAPARTICLE DIFFUSION ON CATALYSTDECAY

1..

(2)

(1)

al r = O, dCcoídr = O

1 d ( dCco)D· - - r -- = rcoa(r e)

CIco r dr dr . 1

CJrf!mic{l/ Eflgi~urinq SciE'nr.e. Vol. SI, No. 5. pp. 633-61;;', J?96CQPyright '"ti 1996 EI:;c'Iicr Scicncc Ud

Prin(:::d in Grea¡ 8rilain. AlJ righl.'.> ro::scrvcd

OC<)9 -2509j96 SI S.C;O .;. 0.00

wirh rhe following boundary conditions:

gas-shifi reaction (WGSR):

MATHE:'vlATICAL MODEL

For an isothermal, cyJindrical catalyst particle with

constant properties and ignoring the externaI diffu­sional effects, the mass conservation equarion ,for the

reacrant (CO) is

for which a Langrnuir-Hinshelwood-type kinetics is

assumed to apply. These catalysts have good low­

temperature activity and are tberefore attractive since

the e.quilibrium is favored at low temperarure. In

addition to higher activiry, another advantage claim­

ed for the low-remperature shift catalysts is higher

seJectivity and fewer side reaclions at elevated

pressures (van Herwijnen and de long, 1980; Salmi

and Hakkarainen, 1989). However. copper-based

Iaw-temperature shif, cataIysts are being irreversibly

poisoned by even smalJ quantities of cblorine in thefeed (Young and Clark, 1974).

With respect to WGSR, Elnashaie and Alhabdan

(1989) analyzed the jEtraparticle effecls on an indus­trial reactor operating at steady srate. Gonzalez

Velasco er al. (1992) proposed optimal policies in

a WGS industrial reactor wirh catalyst decay but

disregarding the diffusional efÍects.

0009 - 2509 (95)00299- 5

~ Pergnmon

Absrract~ The inrerreiation between interna! diffusion and deactiV:ltion is ex;;mi"ed. The stud'! is centered

On the copper cat:llysl used in the warer-gas-shifl reacrion ('NGSR). This caralys[ is deacti',:ared by the

presence of chlorine in the feed. A Langmuir-Hinshelwood model for the react,on kinerics is considered.

Wirh a high diffusional resistance, the poison is e1iminated inside rhe peilel, and this aplains ¡he observedinhomogeneous deacriva¡ion of the industrial bed. The !ife of the catalyst increases when diffusional

resistance for the poison increases. A genera! equation foe the efíectiveness factor. which includes thecata1ysl decay. is defined.

M. CHOCRÓNL\ M.e RAFFO CALDERÓN], N. AMADEO: and M. LABORDEt

: Department of Chemical Engineering (FI) - PINMATE (FCEyN). Universily of Buenos Aires, P:lbelJónde Indusrri:ls. Ciud:ld Universitari:l, 1428 Buenos Aires. Argentina .

!Depanment of Chemical Reactors, eNEA, Buenos Aires, Argentina

t Cürrespoodi!1g :.luthor.

INTRODüCTION

Reactor models for catalytic reactions overlaid with

transport restriction and with simultaneous:catalysr

deactivation are as yet not develope'd to a satisfactoryleve!.

Masamune and Smith (1966) solved the mass con­

servarion equations numerically for a single, isother­mal cataIyst pellet with first-order reaction and de­

activation. They analyzed tbe tbree different types of

deactivation: series, independent and paralle!.

The analysis of Masamune and Smith (1966) bas

been extended to a complex first-order reaction sys­

tem by Murakami ei al. (1968) and ro Langmuir­

Hinshelwood kinetics by Chu (1968). Chu introducedtbe concept of a reJative effectiveness factor.

Hegedus (1974) studied the general case of com­bined external and interna] mass transfer resistances

and the effect of the pellet geometry.

The concept of activity, as defined by Levenspiel

(1972) was introduced by Krishnaswamy and Kittrell

(1981) in arder to study the diffusional effecrs in

a catalyst wirh deactivation. They developed analyti­cal procedures for nrh-order irreversible reaclÍons anddefined a deactivatian effectiveness factor.

More recently, Grzesik ei al. (1992a, b) applied rbe

rime-on-stream rheory (TOST) for a first-order reac­tion system to solve a fixed-bed reactor model consid­

ering borh the intraparticle diffusion restriclion andcatalyst decay_

lo'The aim af this work is-to analyze tbe effects of the

internal diffusion in a catalyst pellet in the presence ofa slow decay of the catalyst activiry. The st~dy has

been applied to a coppér catalysl used in ¡he warer-

-\'.

(10)

(i1)

I I I50 60 70 30

Li:ngrh %

[ a(r)dVaM = V .

J: reoa(r) d V'7=----­TCOQ.HV

Fig. 1. .-\cli:;ity liS re:lCCOr le!1gth.

°

0.2

1 Yoar 2Year JYear

1.0¡

0.3

fO.Ó< OA,

The solution of equation sys¡em [l)-(3) is de{ailed

in the ";ppendi.~.The effectiveness factOr of eo is defined as

where

In eq. (10) the surface reaction rate, which remains

constant during the operation time, is affeeted by the

average activity instead of the surface activity, anintuitively more attracci'le definition, as wil! be ex­

plained in the following.

(8)

RESULTS

In a previous paper, González Velasco e¡ al. (1992)

proved that the indumial catalyric bed is deactiva¡edinhomogeneously, wirh a fronr of de3.ctivation mov-

(5) ing forward in the bed wi(h rime as indicated in Fig. 1.The bed is clearly divided into two zones: the first with ,

(he ca¡aiyst completely deactivated (a = O) and the

second wirh fresh catalyst (a = 1). Therefore, [he anal-

ysis for a pellet placéd atehe inl¡:t of rhe bed wili be ( O(ó) also valid for al! other pellets in the bed unit shifted in

__ time acco.rriing to the position relative to rhe front.)Then, for a pelle¡ placed in a zone of the bed where

T = 2300e and cgo = ~.7 x 10 - 3 moll- 1, the effectof the poisoning rate on ¡he caralysr decay was investi-

gated in order to obtain ¡he k1 values which can

reproduce rhe situacion showed in Fig. 1.

In Fig. 2(a)-(c) poison profiles in the pellet for three

values of k¡ (0.2.2000 and 8000 moll-' h - ') ar differ­

en¡ times of operation are shown. Ir can be seen that

the profiles become sharper when k L in~es, and(9) (hus for high values of k i the poison will be exhausred

inside the pe1k(.

, The activiry profiles for ¡he same values 01' k 1 and

times of operario n are presented in Fig. ~(a)-(c). As

for ¡he cO[JcentrJtion. a¡ ~ given time the pr~files ~

sh:lrper ~hen k 1 inc~ªses: nevenhcless. ¡he averaaeJ.c[ivicy lnCr~:lScS wit~ ~n(r~:.lSlr.g k ~ sinc~ Ihe YJ.lue

Cl,

2.2ex~(iOI5/T)

O." ex;;! 15:3.3,'T)

O (})~ 7 ~:(p(27H.9. T¡0.05 ex DI i 596.·I/T)

dC;;7dr = O

Cp = cg

CO

rcoa=---(rco), = O

r-- - -:O;:.-;.-~ -: -.:;::.....,ain ;:::ac~¡I)n3.:_

1 1-=-+--D"" D",,' DK'

a¡ r = R,

H,

at r = O,

r,0198 O.f)O~J2 O.C03i O.eD5ll 0.003

Kco ia:::> - )K.!.o atm-·,:··e!;. tat;-r - IJ

/\.-1;. dL . -:,

The reaction rate of the poison is

The deactivation ra[e is

kCcoCH,o(l - (J)

(1 + KcoCeo +- KH:OCH,O + Kco,Cco, + KH,CHY

(3)

The kinetic expression for the mQ.in reactlon is

given by (.\m,!deo ec ,,1.,1995):

rco =

Compound

óS.!

1 d ( dC,)D.· - - r -- = r alr ¡).(, r dr \ dr / a ,

wirh the following boundary conditions:

wirh par2.merer values given in Table i

The conc~ntration of the ¡th species is re!a¡ed to ¡he

ea concentration by the fo!lowing expressi,0r.:

(C;- C?) = 7., D"co (Cco - C~o) (4)CLeo D::f;

The Wheeler equation (Wheeier, 1955) was' used inorder to e'lalu2.te the effecrive diffusion coemcient of

each component and of the poison (see Table 2):

where the activlty is d~fined Q.s

The m2.SS conserva¡ion equarion for ¡he pOIson(chlorine) is given by

wirh a = 1 a[ ¡ = O for all r.

The kineric eoefficient of ea. (8) was evalu::w::d from

experimental data of ::In industria! reactor applying

(he one-dimensional pscudohomogeneous rT',odd

(Gonzi!ez V~!J.seo ¿¡ al., ,9921.

\

I,!

I¡¡1

¡¡"

II¡.~I .:-: ....::.f" ..: ~_._.:.> ..

1

1

I.íIr

1:::.:,::::;:'r·- .

I. I

I

I

II

------,---_._---~~_._.•...-_.. . --- -.=_-'~' --~-

685

1.00.8

rIR

rfR

t=O

t=O

0 ..\ 0.6r/R

0.2

O

o

(b)LO'

0.9

Ó.8

0.7

~ 0.6>

;:¡ 0.3-< 0.4

0.3

0.2

0.1

(a) I.0t0.9

0.3

'" 0.7> 0.6

u 0.5

< 0.4

O.} 1st month0.2F--------- _0.\ 2nd month

(e)

fig. 3. Aetivity ·vs dimensionless radius al diíferenl timesofoperation: (a) k, = 0.2moll-¡ h-l, (b) k, = 1ooomoll-1

h-', (e) k, = 8000 moll-' b-l

increases. when k 1 deereases; it means that the deae­tivation rate decréases when th;;-Qise-a-- d1ffusional

resistance increases. Ot.."lerwise, for the highestk, va!ue seleeted, the effectiveness factor initial!y de­creases with the time of operation, but thereafter itfollows the general lrend of r¡ to approach 1 as timeincreases. This can be explained by consideringeq. (10) while making a sírnultaneous analysis of theactivity and eo profiJes (Figs 3 and 4). Al srnal!values o'f time lhe activity is seen to decrease abruptlyin the externa! zone of tbe pellet while rco rernainsapproxirnately constant. On the other hand, in thecenter of lhe pellet even though the activity is signifi­cant, ¡he eo concentration, and consequently rco, areexuemely srna!!.

It may be noted tba[, :,¡ ¡ = O, the diffusional effectin lhe main reJctioo i5 signiilcant. -.

1.0

I1.0

I0.8

I0.8

Effeet or inlrapartiek diffusion on eatalysl decay

I

0.6r/R

rfR

I I004 0.6

rfR

0.4

I0.2

0.2

4th month

3rd month

2nd month

r m

o

0.99994O

0.99995

0.99999

(a)\.0??oo

(b)1.0

0.9

0.8

0.7

oÜ 0.6S::! 03

~ 0.4

U 0.30.2

0.1

(e)1.0

0.90.80.7Ü0.6

'"

o>U 0.3Ñ ;:¡

Ü0.4 -<

U0.3

Ü 0.99998oS( 0.99997

ÜU 099996

of kz (0.002 h - ') remains the same (slow deactivationrate)o

The eo profiJes are shown in Fig. 4. 1t can beappreciated that the profiles depart more slowly fromthe initial profile (at r = O) when k¡ is increased. Thismeans that the catalyst deactivates more slowly. ifk, increases. .

The effect of k¡ on the effectiveness factor for eaconversion is indicated in Fig. 5. It approaches 1 at¡arge values of time for al! k, values. The fact that theeffectiveness factor, ~s defined in eq. (10), approaches1 indicates that the catalyst js completel .deactivated.This situation only arises if the average activity is zeroand not if the surface activity is zero. Thus the defini­tion of effectiveness factor as in eq. (10) is juslified. Ina'ddition, at a given time, Ibe effectiveness fae.ter

Fig. 2. Dimensionless poison eonecnlratión vs dimen­sionless radius al diíferent times of operation: (al k, =0.2 moll-' h-1: (b) k, = 2ooomoll-' h-', (e) k, = 8000

moll-' h-,.

i'lOTATlOi'i'

a

acrivity

a,lr

average activity

C;

concenrration of i component, mo11-3

Cp

concentration oi poison, mol 1- 3

C~o

dimensionless concentration of eoDd';

effective diffusion coefficient of i-

component, 12 t-1D<;ip

eFfective diffusion coefficient of poison,12 r - I

1D,\(;

molecular diffusion coefficient oi itcomponent, 12 t-1 DK

Knudsen diffusion codficient, 12 t - 1,.\E

variable defined in eq_ (lOA)

k

kinetic coefficient of main reaction

[eq. (3)J, moI1-3t-'atm

-'kt

kpC~, lpoll-3 t-1

1:2

kdq, t-1 ..K

equilibrium constant

K;

adsorption constant ai i component,atm-'kd

kinetic coefficienr of deactivation rate

[eq. (8)J, 13 t-I mol-I1:

kinetic coefficient of poisoning ratep [eq. (7)J, t-1radial coordinate, 1r'

dimensionless radius,

R

pellet radius, 1

rco

main reaction rate, moll- 3 t - 1

*dimensionless main reaction raterco

r p

poisoning reaction rateo moll- 3 t - I

Y, value in the center oi tbe pellet'!une

10

M. CHOeRÓN el al.

It is proved lhat lhe life of ¡he catalyst increascs

",hen diffusional resislance (high values of k 1) for the

poison incre:lses. [n ¡his case, lhe average activitYaiSQincreases. Masamune and Smi[h (1966) and Grzesik .

el al. (l992a) arrived e¡ rhe same conclusion for anirreversible firsl-order reaction.

High values of k" ior ",hich the poison can beeliminared inside the pellet, exolains the In­

bomogeneous deac¡iva[ion or the ind'ust[ial b~d, such

as il can be observed in Fig. 1. 1t also means lhat lhe

analysis made ror a pe!let placed in a gjven zone or the

bed is valid ror al! the peIlets in [he bed.

Al t = O, a diFfusional resistance ror the main reac­

tant exists (/¡ < 0.2).

The definirion or ¡he eFfecti'leness faclor given by

eq, (10) predicls lhal r¡ tends to 1 ror large limes of

operation, al any Thiele modulus value. This con­

clusion agrees wilh thal of Grzesik er al. (1992a), whoused irreversible first-order kínerics and the TOST

lheory, Equa¡jon (10) is lhe generalized definition of

the effectiveness iacwr and it is v:llid for any type ofkinencs. In addition, chis equarion includes rhe deacti­

vation. Consequently it may be concluded that

r¡ tends to 1 ior large times oi ogerarion regaLdless_oJ_the kineiics and [he assumed mechanism oi deactiva-_tion.

t=O .

0.6 0,8

4th month

r/R0,4

,0.2

2ndmonth/

.-..- ....- .•.

~.~~.\.• ~.~ o

• k,=O.2mol/lh \ ¿\\• k¡=2000mol/lh \ ".

+ ,~(8000mOlllh , \ ./).1 I O~I 2 :\" 100 1 :; J 10'

Thiele modulus*Caverage activity)'~

4th month

- k,=O.2 mollh-k,=2000 mol/h

"k,=8000 mol/h _4th

monlh.

°

oü~~~"c:">ü~ I.jUJ

'0-'g

2

/0---:7·-·-· /+~ o / •

; / ¿ /~ . / .~ I./¿ /.~=o.2mOl/lh;:: J.5 ¿ I/lhtlJ............. + ¿ k=2000mo

10.1 +__ ._ • ..-/ • k=8000mol/lha ! I j I r

O 2 3 4 5

Time months

1.0

0,9

0.8

0,7

8 06'"

So! 0,5

8 04U 0.3

0,2

O.,

SUMlYIARY AND CONCLUSIONS

Diffusional effects are studied for a catal)'.>t used in

the WGSR which suffers an independent deactivationdue to chlorine in the feed. -

Fig. 5. Effectiveness factor of eo vs operation time 1:, = 0.2,2000, 8000 moll- I h - 1

Fig. 6. Effectiveness factor of eo vs Thiele modulus of COmodified by"the average activiry (C!>~o:<Dco,a~') k, = 0.2,

2000, 8000 mol ¡- 1 h - l.

Fig, 4, DimensionJess eo concentration vs dimensionlessradius al different times ofoperation and diñerent k, vaJues,

686

A plot oi the effectiveness factor oi CO vs rhe Thiele

modulus modified by the average activity (<!>éo), is

shown in Fig. 6 ior three different values of 1:t. Each

( curve represents the evolution of both parameters) during the time of operation. it is norewortny that

) these plots have the same shape as that corresponding,to a non-deactivated catalystThat leastd fOIr lOhwkt values. Final!y, at a given !ele mo u us, t e

effectiveness factor in creases when k, decreases.

687

(A2)

(Al)

(A4)

(A7)

(A6)

C, = C~(I - X,l

r, = d Y,/ds.

1 ,

- ~ Y, - lv;a(r*, e)(1 - Y,)

(A5)

dX, d Y,-=-=Y,dr- dr- -

d(dY,\ dY, ,- -1=-=1"ds dr' / es

~('~\=dYJ=y"dr'" \ cs) dr"

YJ = d Y,jds.

I d ( . dC 20) ,.--,- ---,- r- -- = <1>corcoa(r', ejr" dr" dr" .

1 d ('. dX,\ ,- - r' -) = 'v;(1 - X la(r' t)r" dr" dr· " . ;J ,

rJ¡c = r/ R,

with Y, = S ar r* = O and Y, = O ar r- = l

ae e = O, a(r", t) = I for all r'

al r" = O, dC20/dr" = dX ,/dr" = O

at r" = 1, C¿o = 1 and X, = O.

da(r", e)

- -d-e - = k,( 1- X ,)a(r', t) (A3)

wirh Y, = O at r- = O.

The following auxiliar)' vari:lbles are del1.ned:

..\PPE"DIX

lo order to obtain lhc dimensiQnless íorm of the difTercn­

tiai eqs (l). (5) and (8), {he follo'.ving defini¡jons must be gi ....en

\Virh lhe following boundary and inirial conditions:

lt must be ·nored rhat r20 is only J function of rhe CO

concentration ir ~q. (-\.)is considered. Then, (he dimension­less dilTerential eqs (1), (5) and (8) are

Differenrialing eqs (4A) and (5A) wirh eespect to s andcrossing derivati ....es:

Taking into account rhat an independent deacrivarion isconsidered and that rhe deacrivation is relarivelv slow

(k, -G k,), eqs (2."1) and (3"\) can be solvecI sequentiallY. Con­

sidering a(r') = I ar e = O, a profile of X,(r') is oblainedfrom eq. (lA). The nexr step is to eeplace ¡bis prolile in

eq. (3A) and integrate until a time e + 61. Ihe new activityprofile [a(r*, r + "'e)] is used to evaluate :l new poison pro­file from eq. (2.A). This procedure is repeated until

a(r', e + /(r) has become negligible.

The activity profiles seored al intervals of l month (thewhoJe period considered \Vas 3 years (Gonzalez Velasco ee

al .. 1991)) are used to obtain lhe CO profiies from eq. (lA).Concentrarion values in the center cith~ pellet were evalu­

ated using ¡he shooting ,echnique (Hlavacek and Kubichek,

1983). This method. applied to [he CO and chiorine mass

balances, implies rhal for e:lch of eOs (2,1,.) and (3A) twoordinary differential equations are obtained. For instance,for eq. (2A):

Efíoct oí intraparticlc difTusion on cHal}'st doeay

iniria!

surface

REFERENCES

Atnadeo, N., Cerrella, E., Pennella. F. and Laborde, M.,

1995, Kinetics oí rhe low-temperature water-gas shift reac­tion on a copper/zinc o.~ide/alumina catalyst. Larin Am.Appl. Res. 25, 21. .

Chu, c., 1968, Effect oí adsorption on the fouliog oí caralysrpellets. lEC Fundam. 7, 509.

Elnasahie, S. S. E. H. and Alhabdan, F. M., 1989, Mathemal­

ieal modelling and computer simulation oí industrial

water-gas sbifr converters. ¡vIaeh. Compue. :'vfodel/ing 12,1017.

González Velasco, 1., Gutiérrez Ortiz, M., Goozález Marcos,

l ..Amadeo, N., Laborde, M. and Paz, M., 1992, Optimal

inlet temperature trajectories íoe adiabatic packed reac­tors witb catalyst decay. Chem. Engng Sei. 47, 1495.

Grzesik, M .• Skrzypek, l. and Wojciechowski, B.. 1992a.Modelling of inlraparticle diffusion affecred by [he time­

on-stream catalyst decay. Chem. Engng Sci. 47, 2805.Grzesik, M., Skrzypek. 1. and Wojciechowski, B., 1992b,

Time-on-srream catalysr decay behavior in a fixed-bedcatal)'ric reactor under rhe innuence oí inr,aparticle diffu­

sion: intraparticle diffusion aÍfects only c:ltal)'tic ,e:lctions.Chem. Engng Sei. 47, 4049.

Hegedus, L L, 1974, On the poisoning of porous caralystsby an impurit)' in the feed. lnd. Engng Citem. F,mdam. 13,190.

Hlavacek, M. and Kubicek, V., 1983, Numerical So/ueions o/

Non-linear Boundary Val"e Problems wirh Appliearions.Prentice-Hall, EngJewood Cliffs, N1.

Krishnaswamy, &-attd Kittrell, J R., 1981, Diffusional in­

fluences on deactiyation rates. A.LCb.E. 1. 27, 120.

Levenspiel. O., 1972, Citemica/ Reacror Engineering, 2nd.Edition. Wiley, New York.

Masamune, S. and Smitb, l. M., 1966, Performance of fouledcatalyst pellers, A.LCh.E. 1. 12, 384.

Murakami, Y .. Kobayashi. T., Hanori, T. and Masuda, M.

1968, Effect of intraparticle diffusion on catalyst fouling.lEC Fundam. 7,599.

Sal mi, T. and Hakkarainen, R., 1989, Kioetic 5<udv oí the

Jow-temperature water-gas sbift reaction oyer a éu-ZnOcatalyst. Appl. Cara/. 49, 285.

van Herwijnen, T. and de long. W.. 1980, Kinetics and

mechanism of the CO shifr on Cu/ZnO: L Kinerics ofthe forward and reverse CO shirt reactions. 1. Caca/. 63,83.

Wheeler, A., 1955, Caealysis, Vol. n, Chap 2 (Edited byP. H. Emmer). Reinhold Pub. Corp., New York.

Young, P. W and Clark, C. ª', 1974. \Vhy shiit ca'<ll)'stsde:lctivJ.t~. CJ¡em. Enqng Prog. 5"2, SlO.

r¡

Sl'perscriprO

x p conversion of lhe poison

Y" 1'2, Y), auxiliary variables

1'~

Greek letrers

'1., stoichiometric coefficient of i component

$ lenn of equilibrium in eq. (3)toler~nce

effectiveness factor of eonllmber of iteralions

Thjele modulus of eo<Dco' a~;'Tbiele modlllus of poison

M. CHOCR6N el al.

s'" =SK_~.

(A9) dE(SK)jds(All)

(A12)sl(';- 1 = S¡'; _ y! ,.'"L~.

Y':\'''l.J" .

The equations are solved using a fourth-order Runge Kuttamethod.

Then, in function 01 Y 1 and Y 3:

whcec o is the tolerancc admitted. Ir this condition is not

satistjed, a new value 01 s (SK+ ') must be employed. In arder

la estim:lte the new value equation (lOA) must be expandcdin Taylor series, rrom which:

(A8)

(.'1.10)

~(dY2)=dY"= _~ Y.+'D;a('*,i)Y)d,' ds d,· ,*with y" = O al r· = O.

A value ór SK at ,* = O is assumed and the eqs (4A), (5.'1.),

(7.'1.) and (9A) are integrated up to r' = 1. At chis point thefollowing condition must be satisned:

688