A SIMPLE REACTOR MODEL FOR A COMPLICATEDREACTION SYSTEM- CHLORINATION OF PHENOL IN A BUBBLE COLUMN*-

KATSUMI NAKAO, KOICHI HASHIMOTO** AND TSUTAO OTAKE

Faculty of Engineering Science, Osaka University, Toyonaka, JapanA simple reactor model for a complicated gas-liquid reaction system is developed by

taking into account the influence of both gas- and liquid-phase mass transfer, and theanalytical expressions predicting reactor performance at various reaction conditions arederived.

The validity of this model is examined by using the chlorination of phenol in a bubblecolumn. The experimental results are in good agreement with the model predictions.

Prior to the heterogeneous chlorination, homogeneous chlorinations of phenol and thechlorinated phenols were carried out, and the intrinsic reaction rate constants were ob-tained.

Introduction

Recently a number of problems on complicatedheterogeneous gas-liquid reactions have been ex-tensively discussed. In the previous investigations,

however, primary attention has been paid to the in-fluence of the concentration gradients near the gas-liquid interface on the selectivity as well as the overall

rate2«3'5'17~19). The selectivity is affected by the

operational conditions and characteristics of the re-

actor used, but there have been a few papers presentedon this problem for the case of no diffusion limita-

tion9'12'16).

For reactor design and analysis ofa multicomponentsystem, a simple reactor model that can be readilyadapted is particularly useful.

In the present report we develop sets of simplemodel equations representing a gas-sparged reactor

performance for typical rate-controlling processes suchas the reactions predominant in the liquid film and

those in the liquid bulk. Based on the reactionkinetics in the homogeneous liquid phase, the validityof the theory is examined by using the chlorination of

phenol in a bubble column.

1. Kinetics of Homogeneous Chlorination of Phenol

There are a few published data on the kinetics ofthe chlorination of phenol. In aqueous buffer solu-tions8), the results show a strong dependency of the

Received on October 29, 1971

Presented at the 36th Annual and the 5th AutumnMeetings of the Soc. of Chem. Engrs., Japan,

April and October, 1971Takeda Chemical Industries Ltd.

rate constants on pH. On the other hand, in the

kinetic study of the chlorination of pure liquid phenolthrough which chlorine was bubbled15), the rate con-stants were determined from the analysis of maximumconcentrations of the chlorophenols formed. Butthe results are questionable since the kinetics wereinterpreted in terms of homogeneous rate equationswithout considering mass transfer rates.

Although there is wide discrepancy among the

published rate constants, the reaction maybe repre-sented by the scheme shown in Fig. 1. Here eachchlorination step (1) to (7) is second-order, that is,

first-order with respect to both chlorine G and phenoliccompounds A to E. The rate equations are then

å ^^ (ki+k2)AG (1)

å 4JL= klAG-(kt+kt)BG (2)at

-^-= kiAG-kfiG (3)

dD =hBG-hDG (4)dt

å ^-= ktBG+k£G-k,EG (5)

Since it would be difficult to determine the kineticsfrom the experimental data for the overall reaction,the rates of the reaction steps involved were individual-ly measured, with each intermediate product asstarting material.

The glass reaction vessel was devised to eliminatemass transfer effect. It had a volume of 200m/n).Phenol (or chlorophenols) solution diluted by carbontetrachloride was introduced into the reactor in athermostat and stirred magnetically. Chlorine dis-solved in carbon tetrachloride maintained at the

reaction temperature was fed into the reactor to start264 (50) JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

OH O H

k3

B ¥ i %

A F

k5

C I C lC E

A : phenol B : o-ch lorophenol

C : jfr-chlorophenol D : 2,6-dichlorophenolE : 2 ,4 -d ich lo ropheno l F : 2 ,4 ,6 - t r i ch lo ropheno l

Fig . 1 Reac t ion scheme for ch lo r ina t ion of pheno l

the reaction. Chlorine was detected by the iodinedisplacement technique. Grganics were analyzed bythe gas chromatographicmethod7}.A typical kinetic curve of the chlorination ofphenolis shown in Fig.2. The rapid reaction steps (1)and (2) were analyzedfrom the amountsof the re-actants consumed during any given react ion t ime.The rate constants , kx and k2, can be obtained asfol lows.

Theconcentrationof 0-chlorophenolB is expressedas a function of the concentration of phenol A byeliminating t from Eqs.(l) and (2).The result is

~A^=h+^-lh+kJlVAi) ~VA^)\ (6)

In the same way, Eqs.(l) and (3) give the followingexpression for p-chlorophenol C:

. /A \_ k+h ln (CIA)+{k2l(k l+k2-k , )}\A0J h+h-h {CtiAj+'ihKh+h-h)}

(7)

where Aoand Co, respectively, denote the initial con-centrations of phenol and p-chlorophenol.In the case of Jc1+k2^>h+h, Eq.(6) i s reduced asfol lows :

B

1+a1 - A( 8 )

Under the condition that C0IA0, ClA^faHh+h-h]Eq.(7) is simplified as below:

I n IA A o1 + a1 + a - l nc / c 0( I I A 0 ( 9 )

where a=kjk2 and p=k5/k2.

Rearrangementsof the experimentaldata based onEqs.(8) and (9), respect ively, give Figs. 3(a) and 3(b). With the values of k5 obtained separately, kiand k2 were obtained from the slopes of the twostraight l ines .

Steps (3) and (4), the chlorinat ion of o-chlorophe-

nol, are parallel reactions. Thus ks and k4 are deter-minedby the usual method.The rate constants, k5,

0 .1 0

c ? 0 .0 8¥

._牀_

o｣ ｩ 2 ,4 ,6 - t r ic h lo r o -

0 . 0 6 c a l c u l a t e d f r o mco E q s . ( i W 5 )

Vr j~ 0 . 0 4c

^ N ^ & z z z = ｣ ^ I i ｣ ｮ ^

<L>oao

f < K -'A- -/' s. TY

0 . 0 2

0

f ¥ > . - - - -_

5 0 10 0 1 5 0 2 0 0

R e a c t io n t i m e f m in )

Fig. 2 Course of homogeneous chlorination of phenol

w B ^ ^ ^ s ^ - s m ^ m m ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ K K m m m ^ ^ ^ m m ^ ^ ^ m m a ^ ^ m

^ p * = i J h

1.2

1.0

I I

0

2

? 0 .1 < 0 . 8

< 6

L

<

�" 0 .6

0 .4

( b )

s l o p e * i j ｣

0.02 1-

( a )

4 6 8 1 0 2 0 .2 0 .4 0 .6 0 .8 1

(C / C o )/ ( A /A o) [- ] b /a o r- j

D e t e r m in a t i o n o f D e te r m i n a ti o n o f

a = k l l k 2 j 9 = & 5 / & 2

Fig. 3 Determination of kx and k2

kQ and k7, are obtained from the individual chlorina-tions of steps (5), (6) and (7).

The rate constants kx to k7 obtained at different

temperatures are presented in the form of an Arrhe-nius plot in Fig. 4.

The product distribution calculated by integrationof Eqs.(l) to (5) with the rate constants obtainedabove is shown as dotted lines in Fig. 2. Agreementwith the experimental data is satisfactory, taking ac-count of the experimental errors and the relativeproduct distribution calculated based on the observedconcentration of o-chlorophenol.

Amongthe rate constants the following relation isfound to hold.

"'I? *^2^'^5xv>'^3? ^4? ^6) *^7

Consequently, until phenol disappears, the reactionscheme in Fig. 1 may be simplified as follows.

A

B

C

2. Reactor Model

2.1 Basic equationsThe reactor considered is a semibatch bubble col-

umn. Assumptions are made as follows:

VOL. 5 NO. 3 1972 :5i: 265

102i-I 1 1 -i 1-110'38_ I I I I ' -8

6-J^X^^ /k3 ~6

2 7 rV4 7^

iio- \ -10"41£ 8~ \ -8 i-i

5 !- \ \^1O52u) 8- X -8 mo 6- \ -6.g

a- 4" V X "4 à"

o _^ ^

^ 6- |< \ X. "6 ^

2II I I I "Il23.2 3.3 3.4 3.5 3.6

(1/T)x103 [1/°K]

Fig. 4 Reaction rate constants forchlorination of phenol

1. The gas phase passes through the reactor in plugflow. The liquid phase is well mixed.

2. Mass transport process near the gas-liquid in-

terface is described in terms of the two-film theory.3. Properties of liquid such as density and diffu-

sivity remain constant during the reactions.

The rate of decrease in PG, the partial pressure ofthe gas-phase reactant G in the bubble, is equal to

that of mass transfer across the gas-liquid interface.The following equation holds :

-(-^r\^f-)=kaa'(Po-HGi)=Noa' (10)

where vb is bubble rising velocity, a! ratio of surface

area to volume of a single bubble, G%local inter facialconcentration of G, and NGlocal rate of absorption perunit inter facial area.

The rates of change of the bulk concentrations of

liquid-phase reactants Au Bh Ct and EL are expressedas the sum of the mass transfer rate across the surfaceat the outer edge of the liquid film and the reactionrate in the liquid bulk on the assumption of thepseudo-steady state. Thus the four basic equationsare derived for the liquid-phase components. Since

Bt and Et are dependent on At and Ct from thematerial balances mentioned below, however, the

process in the liquid phase can be represented by thefollowing two equations for components A and C,

u o_* r ue à"=^

ll .1§2(llf I I

Xg 0 Xf K{

(a-1) Diffusion-controlled processwith appreciable degradation of

C, case (1-1)

co

: T: r* =5:;å 

j G\i^já"~" i c;qXg 0 Xf XT" Xg 0 Xi

(a-2) Diffusion-controlled (b) Reaction-controlledprocess with no degrada- process, case (2)

tion of C, case (1-2)Fig. 5 Concentration gradients near gas-liquid interface

respectively :-(«-*«)4j7L= dX^-) +(ki+h)AlGl{v-xl)at \ax /x=xt

(id

v u dt V<ix/i=x,+{KAlGl-KClGl)(v-xl) (12)

where v is liquid volume per unit inter facial area.The products B and C are produced in parallel, andthese two reactions are of the sameorder. Hencetheratio of the amounts of the starting material A con-sumed for B to that for C (including that convertedto E) is equal to that of the rate constants h and k2,regardless of the concentration gradients of thereactants in the liquid phase. Also, the amount of

A reacted is equal to the total of products B, C andE. From these material balances, the bulk concen-trations of the final products Bt and Et are related to

At and Ch as follows.

E^AI-iAt+BM)The initial and boundary conditions are

2=0 : PG=P%(13)(14)

2.2 Approximate analytical solutionFor solving the design equations (10) to (12) it is

266 [52) JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

Table 1 Solutions describing the effects of the operating variables on the progressive change of the gasand liquid compositions for various rate-controlling processes

Case 1 The reactions predominant in the liquid film(1-1) Appreciable degradation of C(gas and liquid compositions)

3 - "-'-"WXft) <>à">

I ^otX1-^) (22)a? =i^i(rB-rt')+|t1-å "à"') (23)

I --{(|W5|)+&)} («)(absorption rate)

Eq.(19)

[1-2) No degradation of C(gas and liquid compositions)Expressions for P&, Ah Bt and Eh are the same

equations as in the case (1-1)Ci

At=k +h

('-% (25)

(absorption rate)Eq.(19) with ft?=1

Where

Case 2 The reactions predominant in the liquid bulk(gas and liquid compositions)Eo_ = (i- hgi)it+(HGi) (28)Pg { Pg/ +VP£/ {Z*}

HGi J7F

+t/F ln (^|)-(l+S2) (30)^_=f ^i )(l-Ai) (22)

f - -{(^)-(Sf HP «24>(absorption rate)

Eq.(27)

p_PS M_(HKG\(DA\rj N_/ A:L yZ)0\ ^_ fc2 fJf/ ^ V^U{l+ P I

a/ _/ &2 V *£ \p y- ^g s-^i+A?_ s- ki

necessary to evaluate the mass fluxes across the surfaceat the end of the liquid film. In general, a solutionfor diffusion equations with multiple reactions in theliquid film would be extremely tedious even numerical-ly. Here the mass fluxes are evaluated based on thechemical absorption theory for a single reaction, pos-tulating the concentration distribution near the gas-liquid interface. The following two cases are discus-sed:

(1) The process controlled by the reactions in theliquid film, shown in Fig. 5 (a).

(2) The process controlled by the reactions in theliquid bulk, shown in Fig. 5 (b).The conditions for case (1) to prevail are

r^ifa+kz)AlDGlkL^>l and q^D^IDoG^T andthat for case (2) is r<Cllll3).

Therefore, in the basic equations (ll) and (12) the

terms representing reaction rates in the liquid bulk canbe neglected for case (1), and the diffusion rate termsmay be neglected for case (2).(1) The case of reactions predominant in the

liquid film.

Products B and C are formed in the reaction front(x=xf) and diffuse into the region xf<x<xu whereno reaction occurs since dissolved gas G is zero.This case is classified into two situations as shown inFigs. 5 (a-1) and 5 (a-2) according to the ratio of therate of reaction step (5) to that of diffusion. Theconditions ^dDa/&z>l and -JUJCiDq Ih^l, re-

spectively, are employed approximately as the criteriafor the two cases. Thus these two cases give thelowest and the highest possible yields of C for the

same conversion of A.

(1-1) The case of appreciable degradation of CFor simplicity it was assumed that the position of

the reaction front xf and the inter facial concentra-tion of G, Gi, are governed by the instantaneous firststep of the reaction. Thus, from the theory of ab-sorption with a single instantaneous reaction1), Gtis expressed as follows.

Gi K+ koH {15)Integration of Eq.(lO) with the above equation givesthe spatially average partial pressure PG for an instan-

taneous reaction :po=(^_J^Padz=UP°e-(l-U)(^)HAl (16)

where Q=Koa'RTL\vb, K0=\\{{\\kG)+(H\kL)\ and

C7= (l-e-«)/Q.The terms representing the diffusion rates in the

basic equations (ll) and (12), DA{dA\dx)x=Xl and

Dc(dC/dx)x=Xl, denoted by NA and Nc, respectively,are obtained from the following material balances inthe liquid film. The amount of C formed at thereaction front is equal to the sum of the amounts

physically diffused into the liquid bulk and consumedin theregion 0<x<xf, and the average rate of ab-

sorption of G, NGis equal to the rate at whichGreacts with A and Cin the liquid film. Thus NA andNcare

^(m.,,= M^+(-2t\dx /*=*, Xi-xf

à"At(17)

(18)

VOL. 5 NO. 3 1972 (53; 267

T1-°f^I I I 1 1 1T l(vO*:^- oC=2,33 rvpicas!(1)i ,

<1°< ni\\\ ^ ~"^ UX0.52.56.0- o.8ln\\ * ^ "^^ -0^._®__®_^_ -

^ IV\\\ ^^^ ^""^* |0-9l@1©1©I

.1 0.2-\\T \^®\ \^ ^[1.010.2L

S I I I xI | ^10 05 10 15 20 25 30

Dimensionless reaction time kLat [-]

(a) Effect on conversion

,.o _,- , ! , _,C}/A°forcase(1-1) ^-233 /

[lT^I0.5 1 2.5 16.01 /

|o-9|®I®I®| /<* C1/A1forcase(2) / >$/

cT °-6r"(p=u=o.5) / -n0^' ~~

> |\K|1-O|O.2| / ^X^ Q-1I(Z) (D / ^c(>''

0 0.2 0.4 0.6 0.8 1.0

Conversion of A 1-(A[/A°i) [-)

(b) Effect on yeildFig. 6 Effect of P and U on conversion andyield

where Gt is the inter facial concentration of G cor-responding to PG, given by Eq.(15) with PG in placeof PG.The absorption rate NGis expressed as follows:

NG=^ckL\Gi+(^)Al\ =^cNA (19)^a~~ r>/^ ~ ' nn-un a

DGGi UGhri-f- UA/ii

where fic is the ratio of the absorption rate with thereaction step (5) to that without it. Eq.(20) assumes

that Cf, the concentration of C at x=Xf, may beregarded as the bulk concentration13).

Thus, NAand NGcan be expressed as a function ofthe bulk concentrations of the liquid-phase reactants

A, C and the average partial pressure of the gas-phasereactant G. These two mass fluxes are substitutedinto the basic equations without the reaction rateterms. The resultant equations can be integratedanalytically under the given initial condition. Theresults are presented in Table 1, and they describethe influence of the operating variables on the prog-ress of the reaction.(1-2) The case of no degradation of CIn this case all of the C formed at the reaction front

is transferred into the liquid bulk, and apparently theprocess is regarded as parallel reactions. Therefore

the bulk concentrations of B and C are as shown inTable 1.

The progressive change of the bulk concentrationofA is also given by Eq.(21).

As no reaction of C with G in the region 0<x<xfoccurs (^=1), the rate of absorption is equal to

the rate of change of its bulk concentration.(2) The case of the reactions predominant in the

liquid bulk.Since the dissolved gas exists in the liquid bulk,

Eq.(lO) can be written in the following form:-Mc£i-> K^p° -HGt

(26)

where GLis the bulk concentration of the dissolved gasG.

When diffusion-reaction processes are consecutive,the rate of diffusion of the dissolved gas is equal tothat of disappearance in the liquid bulk. Hencethe absorption rate per unit liquid volume NGa is

expressed as

Naa=KLa [-^-Gl )= {(kl+ks)Al+ksCl]Gl(27)

where a is inter facial area per unit liquid volume.By solving the simplified basic equations with Eq.

(27), Eqs.(28) to (31) shown in Table 1 are obtained,and they represent the course of the reactions.2.3 Influence of reaction conditions on conversion

and yieldThe model developed above certainly has some

limitations because of simplification. However, a

simple reactor model is a powerful tool for design pur-poses. The cases considered are a few rate-control-

ling processes, but a number of situations of practicalinterest are included in them.

For given values of system properties such as kx\k^k2/k5, DAjDGand DC/DG, the influence of the param-eters concerned with the reaction conditions, P=P%jHA°i and Q=KGafRTL/vb,on the conversion of Aand the yield of C, respectively, are shown in Figs. 6

(a) and 6 (b).(1) Effect of the ratio of the initial gas and liquid

concentrations, P{= P°GIHA°l)In Fig. 6 (a) it is seen that the larger the value ofP the shorter is the reaction time required.In the case where C formed is degraded by reactionstep (5) Fig. 6 (b) shows that the yield of C is higherfor larger values of P. This is because the reactionfront moves toward the bulk liquid as P increases.Whenthe reactions in the liquid bulk are predomi-nant, furthermore, the relation between yield and con-version is uniquely determined by the ratio of the rateconstants of reaction steps (2) and (5) independently

268 (54) JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

of reaction conditions, and is the same as that for thehomogeneous reaction. When the reactions occur

appreciably in the liquid film, the yield of C has an in-termediate between the two limiting values dependenton reaction systems and conditions, and sometimes ishigher than that under homogeneousconditions.(2) Effect of dimensionless residence time of thegas-phase Q(= KG arRTLh^)

This parameter governs mainly the average partialpressure of bubble PG as is evident from Eqs.(16) and

(28).

In Fig. 6 is shown the influence of U=(l-e~Q)IQon conversion and yield. With an increase in U, PG

increases, and therefore shorter reaction time is

required and the yield of C is higher, since the reac-tion front moves toward the bulk liquid.

When the reactions in the liquid bulk are rate-determining, Fig. 6 (a) shows that with decrease in

the value of V, representing the ratio of diffusion toreaction rates, the curves approach that for the diffu-sion-controlled process, case (1).

3. Chlorination of Phenol in Bubble Column

3ol Experimental details

The reactor was a bubble column made of glass, 4cm in diameter and 60 cm in height. The gas distri-butor, made of Teflon, was a perforated plate with19 holes of 0.05cm diameter. The chlorine gas ofa given partial pressure was prepared by mixing chlo-rine and nitrogen streams.

Phenol solution diluted by carbon tetrachloride wascharged in the reactor into which nitrogen gas wasbeing introduced. When the solution temperature

had reached the desired level, the chlorine and nitrogengas mixture was introduced into the reactor to start the

reaction.Liquid samples were withdrawn and analyzed by

gas chromatography at the same conditions as that inthe homogeneous runs.

Experiments were carried out at 20°C. The rise inreaction temperature was at most 3°C, and hence itsinfluence was negligible. The average bubble diame-ter dB was measured by the photographic method,and at the end of a run the chlorine concentration inthe saturator was determined to obtain Henry's lawconstant H. The results were as follows. dB= 0.3cm, H= 0.7 atm-Z/mol at 20°C.

The physical absorption of chlorine into carbontetrachloride were performed to determine the overallmass transfer coefficient KG.

The scope of this experiment was as follows: Initialchlorine gas partial pressure P& = 0.2 to 1.0atm.,Initial phenol concentration A\ = 0.2 to 4.3 mol//,

Superficial chlorine gas velocity uG=l to 2 cm/sec,Height,of clear liquid Lo= 20 and 40 cm.3.2 Results and discussion(1) Overall mass transfer coefficientThe change of the bulk concentration of dissolvedgas Gi with time is represented as

_, i i i t i i i i I i ' ' '""å 

02 - PGO.5atm,Ai=0.37mol/l O phenol= å ' <> t = 20°C , uG=1.5cm/s _®_o-chloro-phenol^ V U=40cm ଠp-chloro-phenol-E ^\ I ® 12,4-dichloro- 1_

)jr " Ck calculated from2. _ \. Eqs(21)(22)C^> -

^ir~-¥"j i^l i%i fr i ^ i $-.i 5

0 ' 5 10 15

Reaction time t [min]

Fig. 7 Typical kinetic curves for heterogeneous chlorina-tion of phenol in a bubble column

dG>-= KLa(-%--G:dtH

(32)

Integration of the above equation with Eq.(26) gives

(33)

where W= KLaU= HKGaUThe semilogarithmic plot of {l-{HGijP%)} vs. t

gave a straight line, and from its slope, KGwas deter-mined. KG obtained (0.5 to 1.2 X10~6mol/atm-cm2-sec) were much smaller than the gas-phase masstransfer coefficient kG, i.e. usually an order of magni-tude of 10~4 to 10"5 mol/atm-cm2'sec9). Hence the

gas-phase mass transfer resistance is negligible, andthe liquid-phase mass transfer coefficient, kL arecalculated from the relation l/KG-H/kL. The ex-

perimental value of kL with the deep liquid pool (Lo= 40 cm) was found to be smaller than that with theshallow one (Lo = 20 cm). This is probably becausethe liquid agitation is more intense in the latter. kLobtained (3.3 to 8.4X 10~4 cm/sec) are small comparedwith that usually encountered in aqueous solutions,i.e. ^10~2cm/sec. This may be true in such anorganic system. For example, the data for the chlori-nations of benzene14} and p-cresol5) give kL on theorder of 10~~3 so 10~4 cm/sec.

(2) Determination of rate-controlling processA typical conversion is shown in Fig. 7. Becausek5,the reaction rate constant of chlorination step (5), issmall compared to kL, the liquid-phase mass transfercoefficient, no appreciable final product, 2,4-dichloro-phenol was formed, and apparently the reaction wasparallel.

From the values of kl9 k2 and kL obtained above itwas found that the following conditions for theinstantaneous reaction regime were fulfilled except

near the complete conversion of phenol. Under thepresent experimental conditions,

r=10to 50and T/q=l5to 70

From these facts the process is considered to be inthe instantaneous regime where a reaction front exists

VOL. 5 NO. 3 1972 !55; 269

rr¥j; 1.0

< |-<r

0 .8JZa .

oc�"E 0 .6c*

c(L)<J

0.4uinl/>CD

l^ v 1

ft

¥ X ¥ o

¥ ^ ｮ

R u nP ｣

Cat m l

A i-Cm o i/|]

E xpe ri

m en ta l

C atcu-

a te d1 0 .2 0.812 o ｩ

2 0 .5 0 .3 68 m ｩ

3 0 .6 7 0 .18 7 (ft <D

u 0 .5 0.81 2 牀 ｩ

c a lcu la te d fo r

c a s e (2 ) u n d e r t h e

c o n d itio n o f R u n (2

ｮ

ｩ

ca lcu la te d fo r

c a s e (1- 2 )

I l ^ 1 I

)

.2 0 2 ｮ . <O

if) ¥cCD｣

Q

0

¥

n

0 .2 0 .4 0 .6 0.8 1.0 1.2 1.4

D im e ns io le s s r e a c t io n t im e k La t C-0

a ) E ff e c t o n c o n v e rsio n

c aJ ,

R u n E xperim enta lc| /A-t lB i /A-[ Calc'dss EfL

0.8 O -+ jQ _ _H 2

0

����������������������������������������������������������������������������������������������������������������������������������������

- -- " - ^ _

/ & 蝣 ^ < ki& r -2ｧ & =* r ^ 9

CM (Q (｣ )

r ^ ^ s r-i I ^ ^ B M ^ B^ ^ ^ IMHM ^-S-i M- i li W ^ ^ - i^^ - - PP M ^iP l iM ^ -0. 2 0.4 0.6 0.8

C o nv e rsio n o f p h e n o1 1- (A i/A i) H

(b) E ff ect o n y ield

Fig. 8 Effect of operating variables on conversion and yield in the chlorination of phenol

5.

4. 0

v 3 .0

CNJ2 .0

o from h om ogen eous ch lorina tion�"

�"

�"

I I

�" from h eterog ene ous ch lo rina tion

o o -2 ^ < ¥ -

>｣

1 . 0

�" ^i * I I I

1 .0 2 .0 3 .0 4 0 5 .0

P = P g / H A ? C - J

Fig. 9 Dependenc/ of ki/k2 on P

in the liquid film, with no degradation of C, that is,case (1-2). Thus Eqs.(21), (22) and (25) can be ap-plied to an analysis of the experimental data.

Eq.(21) is transformed as follows.

In-^4T

+

DaIDq)_=-Mt

Based on the above equation the semilogarithmicplots gave straight lines, and from slope M, KGwasdetermined. The diffusivities employed were esti-mated20). It was found that KG obtained (0.4to 1.3X 10~6 mol/atm-cm2'sec) from chemical absorptionagree well with those from physical absorption.

4. Comparison of Experimental Results with Theoreti-cal Calculations

To compare the progress of the reaction with thatcalculated from Eqs.(21), (22) and (25), the ex-perimental data in dimensionless form are plotted inFig. 8 (a), (b).

Under the present experimental conditions the termMin Eq.(21) is much less than unity, and henceEq.(21) is simplified as follows:

ij= {l<ij^)Yl ~Mt) <-Dji^)

This represents the linear relation between conversion

a

nd time as shown in Fig. 8 (a).In Fig. 8 (b) the yield ofCis found to be affected not

by Q, but by P. However, according to the modeldeveloped here the yield should not depend on bothP and Q. This phenomenon suggests that the ratio

of rate constants, k1jk2 is a function ofP. On theother hand, in the parallel reaction system composed

of the same order reactions, the ratio of the rateconstants, kx\k2^ is equal to that of the amounts of

the two products formed, regardless of mass transfereffect. Thus k1/k2 is obtained from the ratio of thetangents at t=0 to the curves representing the pro-

gressive change in the amounts of products B and C.As is shown in Fig. 9, k1/k2 obtained from the productdistribution were well correlated linearly by P for

both homogeneous and heterogeneous chlorinations.This is compared with the reported complicatedfeatures of the chlorinations of phenol derivatives,

such as the strong dependency of the rate constant ofeach chlorination step on the value of pH8) and the

influence of the hydrogen chloride formed duringthe reaction5). These phenomena may be ascribedto the ionic reaction mechanism.

Using kijk2 determined above, the results calculatedfromEqs.(21), (22) and (25) areshowninFig. 8. Theexperimental data are in good agreement with the

theoreticalcalculations. Exceptionally, near the com-

plete conversion of phenol the course of the reactionand the yield deviate from the theoretical predictions.

This is because in this stage of the reaction the chlo-rination of p-chlorophenol and the reaction in the

270 :56: J O U R N A L O F C H E M IC A L E N G IN E E R IN G O F JA PA N

T1.0|, |_ i ,, I, -I A

o _1 3.25mol/i_Q_ ^^g0.8-~T~3:oo ~à¬~ -

9- I5 14.66 IoIoJy* ;\P n r calc'd for yy^^15^^0O.6- case(M) ^^^ ^»2 --calc^d for .rf^^^^v^

g -calc'd for ,^^^O0.4- case(2)j^^ -

X?0.2- *fT ^ ^-*-"' ~~

~ >^ ^^ ' lfg=1atmyN=300rpm.,2^clL^^i i i - i

0 0.2 0A 0.6 0.8 1.0

Conversion of p-cresol H(a) In a stirred vessel with a constant gas-liquidcontacting area

à"5 l^qtmJJ3-cres(4=^.66moi/l,t=35LCrcl ^/^

in Qfi- °bs'd forMargebubbles',^' _

fi (dB=4 2to6.1 mm) X'V obs'dfor 'small >?

9- bubbles' (db=Q34 ^§0.6- to0.58mm) ;'/

u /y

c O.A~ /,'''---calc'd for -§ / case(H)

t ^' _,__calc'd for*02- /" CQSe(K) -^

° 0.2 0.4 0.6 as 1.0Conversion of p~cresol (-)

(b) In a bubble column

bulk liquid become predominant. In Fig. 8(b) theyields for the other rate-determining processes areshown for comparison.

The influence of the various operating conditions,Pg, A°ly LQ and uG on the chlorine absorption rate,Nq agreed well with those predicted from Eq.(19)with pc=l>

5. Interpretation of Published Data inTermsof PresentModel

The data obtained from the consecutive chlori-

nation of p-cresol in a stirred vessel with a constantgas-liquid contacting area17) and in a bubble column18)are shown in Fig. 10. InFig. 10 (a) it is seen thatas the initial concentration of p-cresol increases, theyield of intermediate decreases. An increase in the

viscosity of the reaction mixture, resulting from anincrease in the initial concentration of p-cresol, di-minishes the liquid-phase mass transfer coefficient.Hence the intermediate product is transferred into

the liquid bulk with less degradation by the chlorina-tion in the lower initial concentration. Therefore, asthe initial concentration increases, the yield changesbetween the highest value and the lowest one, both

predicted by the present model. The data in thebubble column except near the complete conversionof p-cresol show that because of the higher valuesof kL in a bubble column, the yield is nearly equalto the highest value almost regardless of the size ofgas bubbles.

It is reported for the chlorination of benzene thatthe selectivity of monochloro-benzene decreases asthe partial pressure of the absorbed gas increases43.

This is partly because with an increase in the partialpressure the gas-phase mass transfer resistance, whichimproves the selectivity, decreases and the reaction ofthe intermediate with the dissolved gas near the gas-liquid interface is enhanced.

Conclusion

A model was presented to predict the reactor per-formance for a complicated gas-liquid reaction. Thevalidity of the model was examined by the chlorina-tion of phenol.For solving the basic equations, the mass fluxes at

the end of the liquid film were evaluated based onthe chemical absorption theory for a single reaction,postulating the concentration distribution near thegas-liquid interface instead of solving the diffusion

equations with a complex reaction. Thus analyticalexpressions were derived describing the influence of

the operating variables on the progress of the reaction.The chlorination ofphenol was carried out in a semi-batch bubble column. On the basis of the reaction

rate constants and the liquid-phase mass transfer coef-ficients determined separately, it was found that thegas-phase mass transfer resistance is negligible, and

that all of the intermediate, p-chlorophenol, formedat the reaction front is transferred into the liquid bulk.Apparently the process may be regarded as a parallelreaction except near the complete conversion ofphenol.

The conversion of phenol, the yields of o- and30-chlorophenols and the chlorine absorption rateunder the various reaction conditions were well

explained by the present model.

Acknowledgement

This work was supported by the Science Research Founda-tion of Educational Ministry, Japan, Grant No. 50201.The authors appreciate the support leading to the publica-tion of this article.

Nomenclature

A, B, C, [etc. = concentrations of phenol, o-chloro-phenol, p-chlorophenol, etc.

[mol/qa, d = gas-liquid inter facial areas per unit liquid volume

and per unit gas volume of a single bubble,

Fig. 10 Chlorination of p-cresol in a stirred vessel17) and in a bubble column18)

VOL. 5 NO. 3972 (57; 271

respectively [ 1 /cm]D = diffusivity in liquid phase [cm2/sec]dB = bubble diameter [cm]G = concentration of chlorine in liquid phase

[mol//]H = Henry's law constant [atm-//mol]

k\,^2,k3, etc. = reaction rate constants shown in Fig. 1[mol//-sec]

kg = individual gas-phase mass transfer coefficient[mol/atm- cm2 -sec]

Kg = overall gas-phase mass transfer coefficient[mol/atm- cm2 à"sec]

kL = individual liquid-phase mass transfer coefficient[cm/sec]

KL = overall liquid-phase mass transfer coefficient[cm/sec]

L = height of gas-liquid fluidized bed [cm]Lo - height of clear liquid [cm]M ^ {HKGl{v-x{) } {DAJDG)U [1/sec]

Na, Nc =å  spatially average mass fluxes of A and C,respectively, across the surface at the end of the_liquid film [mol/cm2'sec]

No = average rate of chemical absorption ofG(chlorine) per unit inter facial area

[mol/cm2 à" sec]Nt = {kL/{v- xi).} (Dc/DG) [1/sec]N2 = {k2/(k1+k2) }lM^ {kL/(v-xl) }(DAJDG)]

{ 1 +P/(Da/Dg) } à" [1/sec]A^s = {h/fa+kjnkLKv-XMP [1/sec]P = P°GIHA<1 [-]

Pq = average partial pressure of G in reactor[atm]

P%= partial pressure ofG in feed gas [atm]Q = KGdRTL\vh [-]q ^ DAAJDoGi [-]

R = universal gas constant [atm-//mol'°K]y = volumetric rate of reaction [mol// sec]

51 - (k.+k^/k, [_]52 = kz/fa+kz) [-]T = absolute temperature [°K]t = time [sec]U = (!-«-«)/« [-]

V = XLa/(^1+fc2)A? [_]v = liquid volume per unit inter facial area [cm]vb = rising velocity of bubble [cm/sec]W = KLaU = HKGaU [1/sec]x = distance from gas-liquid interface [cm]%/ = distance from interface to reaction front [cm]xt = liquid film thickness [cm]z = vertical distance through liquid phase [cm]a = kx\k2 [-]P = h/k2 [-]

fie - ratio of absorption rate with a consecutive

reaction to that without it [-]T = ^Ik1+k2)AlDolkL [-]§G = gas hold-up [-]<^Subscript)>

A, B, C, etc. == components A, B, C, etc. (phenol orchlorophenols)

G = component G (chlorine)/ = reaction fronti = gas-liquid interface/ = bulk liquid

0 = initial value

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