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Consecutive reactions: role of mass transfer factors
Chemical
Engineering
Science,
1974, Vol. 29, pp. 561-569.
Pergamon
Press.
Printed
in Great Britain
CONSECUTIVE REACTIONS: ROLE OF MASS TRANSFER FACTORS V. G. PANGARKAR?
and M. M. SHARMA
Department of Chemical Technology, Matunga Road, Bombay 19, India (Received 12 June 1973) Abstract-The effect of mass transfer factors on the selectivity of a consecutive reaction was studied. A theoretical analysis, based on the film model, was made for different cases to bring out the effect of mass transfer on the selectivity with respect to the intermediate product. The experimental work was concerned with the chlorination of p-cresol dissolved in 1,2,4-trichlorobenzene. A good agreement be-
tween the experimental and the predicted values was observed. INTRODUCTION
accompanied by consecutive reaction is commonly encountered in the organic process industry. A large number of chemical reactions such as, substitution chlorination of aromatics, alkylation of aromatic compounds etc, fall in this category. In most of these cases, selectivity with respect to a particular product is desired. Since two or more reactions are involved the problem becomes complicated and a detailed analysis taking into consideration the interaction between the diffusional and kinetic factors, is required. Several workers have shown that diffusional factors play a significant role in affecting the selectivity of consecutive reactions (van de Vusse[ll, Teramoto et a1.[2]). However, very limited work has been done to verify the theoretical predictions. Further, very little attention has been paid to the cases where the first step involves depletion of the reactive species and where the reaction is instantaneous. It was thought desirable to study a consecutive reaction scheme under a variety of carefully controlled conditions so that the various regimes of mass transfer with chemical reaction could be covered. It was decided to study the chlorination of p -cresol dissolved in 1,2,4-trichlorobenzene at a temperature of about 100°C. Gas absorption
The intermediate product, C, is also capable of reacting with species A. The reaction may be represented as: A+C%D.
Both the reactant, B, and the intermediate product, C, are considered as non-volatile. The reactions (1) and (2) are considered to be irreversible and first order in the solute as well as the reactive species B and C. It is assumed that the resistance to mass transfer is confined to the liquid phase. The following cases will be considered: (i) First step fast pseudo first order and second step slow
Figure la shows the typical concentration profiles for this case. The first step can be considered to be fast when all the dissolved gas reacts in the liquid film adjacent to the interface and the following condition is satisfied: (3)
where: D, = liquid phase diffusion coefficient of species A, cm?/sec k2 = reaction rate constant for the first step
THEORETICAL CONSIDERATIONS
The scheme considered is as follows: Gaseous species A dissolves into the liquid phase and reacts with the liquid phase reactant B according to the reaction:
reaction,
cm’/g mole set
B. = bulk liquid phase concentration of the reactant, B, g mole/cm3 kL = liquid side mass transfer coefficient
without chemical reaction, A+B&C. tPresent address: Department ing, L.I.T., Nagpur, India.
Vol. 29 No. 2-P
cmlsec.
(1) of Chemical Engineer-
In addition the following inequality should be satisfied to ensure that the interfacial concentration of the reactant, B,, is nearly the same as the bulk 561
CES
(2)
V. G. PANGARKAR and M. M. SHARMA
562
43
---EL A*
Ci
c
8
x=0
(a)
(b)
(cl
j&q-j-/j-k& x=0
x=0x
6
8
Fig. 1. Concentration profiles for the various regimes
in consecutive reactions: (a) first step fast pseudo first order and second step slow, (b) both steps fast second order, (c) first step instantaneous.
liquid concentration
Ba:
of the reactant,
X@zz,& kL
(4)
A*
where : A * = interfacial concentration A, g mole/cm3.
of the species
The second step reaction may be considered to be slow when the condition given by the following expression is satisfied: Vi%EQl
ible. Consequently a very high selectivity with respect to the intermediate product, C, can be achieved. Under these conditions mass transfer has no effect on the selectivity. (ii) Both steps fast and second order Here the reactions between A and B, and A and C occur in the film but the concentration of species B at the interface is less than that in the bulk liquid phase. The typical concentration profiles for this case are shown in Fig. lb. The basic equations describing the steady state diffusion of the various species are as follows:
(5)
k,
DA $$
= k>AB +&AC
(6)
d2BckAB
(7)
where : ki = reaction
rate constant for the second step reaction, cm3/g mole set
CO = bulk liquid concentration mediate species
D
‘dx’
’
of the inter-
C, g mole/cm’.
The condition given by expression (3) ensures that the first step reaction occurs mainly in the liquid film and no free solute A exists in the bulk liquid phase. By contrast the condition given by expression (5) implies that the second step reaction occurs chiefly in the bulk liquid phase. Thus, the contribution of the second step reaction is neglig-
D
d2C cdX2 = - k2AB + k;AC.
(8)
The boundary conditions for the above differential equations are as follows: .=O,A=A*,B=Bi,C=Ci,@=g)=O
(9)
563
Consecutive reactions x=S,A=O,B=B,,C=Co
(10)
Equation (6) can be solved by the method of van Krevelen and Hoftijzer [3]. It has been shown[3] that the zero interfacial flux conditions for species B and C given in boundary conditions (9) imply constant interfacial concentrations, Bi and Ci of species B and C, respectively. Thus, for this particular case of non-volatile reactive species the variable concentration terms B and C in Eq. (6) can be replaced by Bi and Ci respectively. With this consideration Eq. (6) reduces to an ordinary second order differential equation that can be readily solved for the prescribed boundary conditions. The solution is:
for B and Ci for C and then subtract Eq. (7) from (6) to get: D d2A_Wd’B dX2 + k;C;A. *dX2-
(15)
In Eq. (15) the concentration profile of A given by Eq. (11) is substituted to yield: D
d2A=DdZB ‘dx’ Adx* k:CiA*sinh[dy(8-x)] + .
sinh [ JT.81
(16)
A =A*sinh[dF(S-x)] .
sinh[Jy.S]
The rate of absorption
(11)
of the solute A, is given by: A*d/DA(k~Bifk;Ci)
x=o=
tanh
VDa (kzBi +k;C) kL 3
Similar operations with Eqs. (6) and (8) yield the following equation : d2A d2C DA-Q = Dcp
(12)
2krBiA*sinh[dF.(S-x)]
+ .
sinh [JT.8]
and for the case when: (17) VDA(k2F+k:C); L
, 3
RA = A * IiDAkzBi +k;G
(13)
The selectivity index, S, is defined as the ratio of the rate of formation of species C to the rate of formation of D. Inoue and Kobayashi [4] have indicated that the selectivity with respect to the intermediate product C, can be represented by the ratio of the pseudo first order rate constants when the reaction (1) and (2) are pseudo first order with respect to the solute gas A. For the present case of second order reactions, a similar definition, with the interfacial concentrations replacing the bulk liquid concentrations is proposed. The selectivity index, S, is then given by: DAkzBi Mi, ’ = DAk;Ci = sb
(14)
The problem is now reduced to the prediction of the interfacial concentrations Bi and Ci. Equations (6) to (8) can be used to obtain the values of Bi and Ci. Thus, in Eqs. (6) and (7) we substitute Bi
Equations (16) and (17) are integrated using the boundary conditions (9) and (10) (Pangarkar[5]). The final equations are as follows:
M, _
1
MO, 4, - 1
+mh
Mi,
_A%_ Mi,+ M-,I
(“I
and
Nz
1
MO, k-1
Mi, - M,
&+ I/-
2Mi,
I
M,,+ M-,
(19)
564
V.G.PANGARKAR
and M. M. SHARMA
Substituting
and
Eq. (22) into Eq. (20) we obtain: (23)
for D,
= Ds = D,. The above equations
can be solved by a trial and error procedure to obtain Mi, and M-,. The selectivity index, S, can then be calculated from Eq. (14). (iii) First step instantaneous and second step fast pseudo first or second order Here the reaction between A and B is so fast that both the species are consumed by the reaction at a plane very close to the interface. The rate of absorption is then controlled by the diffusion of A from the interface and of B from the bulk to the reaction plane. Jhaveri[6] has discussed a similar problem for the case of gas absorption in a medium containing two reactants. However, in the present case the intermediate species, C, is generated in the film. Typical concentration profiles for this case are shown in Fig. lc. The rate of absorption of the gas, A, is given by (Jhaveri [6]): AVIZEE
Ra =
tanh
[
-(h/a)]
ta;fql
,o,
tanh
(24)
of generation =Rate of transport from the reaction plane into the bulk
kdo = A (s _ (21)
kl also increases
decreases.
xmzc
A”’
or
D.4
result (v)
k;
C20) Rate
where kt is defined as:
Now as &,, increases,
vimc
The second step reaction, can thus, be treated as pseudo first order and Ci can be replaced by CA,the concentration of species C at x = A. C, is obtained as follows: A mass balance for species C gives:
or
RA=
The above equation gives the rate of absorption for the case when only species B is present in the liquid phase and when the first step reaction is instantaneous. Thus when & is very much greater than unity, almost complete selectivity with respect to the intermediate product can be realised. For a quantitative estimate of the selectivity index, S, for the general case, (A/S) and C, must be known. From the above discussion it is evident that because of the high kt values, the second step is likely to be pseudo first order as m/kL is substantially reduced. The parameter m/k; may become so low that no reaction occurs in the film. The concentration of the species C, in the film increases due to the generation of C according to the first step reaction. However, the concentration term causes a much more significant increase in C;/A* than in mi/kL. As a result, the condition given by the following expression is likely to be valid for the region 0 < x < A :
and as a
A)
[CA-- Cd
(25)
Therefore: CA = C,+Bo
(26)
when: A*6
In the limit as:
(A/6) is obtained by taking reaction plane. Thus:
(T)+F
a mass balance at the
kt
or tanh
(F)
+p.
noting that:
(27) (22)
or sinh
kt = k&a, (Eq. 21).
v5jEQS)] L
=fi.
Consecutive
The above equation
on simplification
1 -(A/6) sinh [a(~/@]
yields:
=- d&-l a
(28)
where: a=mk,. The rate of formation
of species C is given by: DsBo
R’=(s-A) or kJ% Rc=(l-h/S)’ The rate of formation reaction, D, is:
(29)
of the product of the second
RD= R.,-Rc The selectivity
(30)
index, S, is then obtained
as:
56.5
reactions
the published work of Teramoto et al. [2], carbon tetrachloride was used as the solvent. The solubility of chlorine in this solvent at 25°C is approximately 3.5 x lo-’ g mole/cm’ atm. This value of solubility of chlorine in carbon tetrachloride is relatively very high and will probably introduce a significant gas side resistance in the case of absorption from lean mixtures. The value of the second order rate constant for the first step at 25°C is only 17 l/g mole set (Inoue and Kobayashi[4]). It was, therefore, thought desirable to work at a relatively high temperature so that much higher values of the rate constants can be realized and at the same time the solubility of chlorine can be substantially reduced. This procedure should allow a wider range of variables to be covered. The solvent and the reactant should preferably have negligible vapour pressures at the temperature of operation. It was decided to use TCB as the solvent. The temperature used was 100°C. At lOO”C, the vapour pressure of both TCB and p -cresol are only about 15 mm Hg. ANALYSIS
RC ‘=RA-Rc
The analysis of the feed and product solutions containing mixtures of p -cresol, monochloro-p cresol and dichloro-p -cresol, dissolved in TCB was DISCUSSION OF THE CHEMICAL SYSTEM carried out on an F and M Model 720, dual column programmed temperature gas chromatograph with The experimental studies involved the chlorinathermal conductivity detector. In the present work tion of mixtures of p-cresol and monochloro-pcresol dissolved in 1,2,Ctrichlorobenzene (TYCB). a 3.3 m long, 6 mm i.d. copper column packed with The chlorination of p-cresol occurs according to 20 per cent diethylene glycol succinate supported on Chromosorb W (45-60 mesh) and modified with the following scheme: 3 per cent o-phosphoric acid was used (Teramoto et OH OH al. [2].)
(31)
EXPERIMENTAL
OH
CH,
CH,
The above system has been used by Inoue and Kobayashi [4], and Teramoto et al. [2]. The reactions are specific and no other isomers are formed in the first as well as the second step. Both these reactions are first order in the solute and the reactants and are therefore well suited for the present studies, In
A laminar jet apparatus was used to obtain the diffusivity of chlorine in 1,2,4-trichlorobenzene (hereafter referred to as TCB) and for the reaction between chlorine and p-cresol to give monochloro-p -cresol. The principal design features of the apparatus used were akin to those employed by Sharma and Danckwerts[7]. The diameter and length of the jet used were 0.097 and 6*76cm, respectively. A 5.5 cm i.d. glass stirred cell was used for obtaining the rate constant for the reaction between chlorine and monochloro-p-cresol and for testing the models for the depletion and instantaneous reaction regimes. The stirred cell was provided with a glass cruciform type stirrer and the speed of agitation was varied between 40 to lOOrev/min. A 2.3 cm i.d. jacketed bubble column was used
V. G. PANGARKAR and M. M. SHARMA
566
for testing the model proposed for the case when the first reaction step is pseudo first order and the second step is slow. In all the experiments conducted the gas and liquid phases were brought up to the desired temperature by passing through glass coils immersed in a thermostat. The stirred cell was placed in a similar constant temperature bath. In the case of jacketed bubble column, the column was maintained at the desired temperature by circulating glycerine-water mixture from a constant temperature bath through the jacket. With these arrangements the apparatus could be operated at within ?O.S’C of the desired temperature. RESULTS
AND DISCUSSION
Solubility of chlorine in TCB The solubility of chlorine in the solvent was experimentally determined by saturating the solvent at 100°C and estimating the dissolved chlorine. The Henry’s law constant at this temperature was found to be 2.7 x 10m4g mole/cm’ atm. Difiusivity of chlorine in the solvent
Pure chlorine was absorbed in laminar jets of TCB at 100°C. The diffusivity was found by employing the following equation (Danckwerts 181) which holds for a laminar jet apparatus R:,=4A*fi
m
where: R; = rate of absorption, g mole/set L = liquid flow rate, cm’/sec
kL, = kL,
(33)
where, subscript 1 refers to pure TCB and subscript 2 refers to the reaction mixture. The reaction rate constant for the first step reaction, k2, was determined by absorbing pure chlorine into laminar jets of p-cresol dissolved in TCB. Since hydrogen chloride is evolved during the absorption of chlorine, the normal procedure for measuring the rate of absorption by the gas up-take method could not be used. In the present case the rates of absorption were based on the analysis of the outlet liquid. The second step reaction is relatively slow. A preliminary estimate of the rate constant based on the data of Inoue and Kobayashi[4] indicated that the reaction is likely to fall in the fast pseudo first order reaction regime when dilute chlorine is absorbed in a stirred cell. Accordingly chlorine (approximate 50 mole per cent in a mixture with nitrogen) was absorbed into monochloro-p- cresol dissolved in TCB. The rate of absorption for a pseudo first order reaction is given by: Rn = A * vDnk
[reactantI
(34)
The values of the reaction rate constants for the first and second step reaction can be calculated (32) from the observed values of Rn and a knowledge of A* and DA. The following values were obtained at lOO”c!:k2 = 190 l/g mole set k; = 15 l/g mole sec.
I = length of the jet, cm. The value of the diffusivity of dissolved chlorine was found to be 5.4 x lo-’ cm*/sec. The value of the diffusivity of dissolved chlorine in the reacting mixture was determined by employing the Stokes-Einstein relation, (DAbIT) = constant. Preliminary experiments
In order to calculate the values of the parameter, fi, for ascertaining the regime of absorption for both the steps, data on k,, kZ and k; are required. Chlorine was absorbed into pure TCB at 100°C in the stirred cell and the values of kL were experimentally determined for the various speeds of agitation. The reacting system had a somewhat higher viscosity as compared to the pure solvent. Therefore, the values of k, for the reacting systems was obtained by using the following equation:
The necessary conditions under which Eq. (34) is valid were satisfied. The above values agree reasonably well with the extrapolated data of Inoue and Kobayashi[4] Chlorination of mixtures of p-cresol and monochloro-p-cresol in the stirred cell : fast second order reactions In the stirred cell the kL values are of the order of 3 x lo-’ cm/set. Thus, for instance, at a speed of agitation of 60 revlmin the kL value was 3.5 x
lo-’ cm/set. Consider the following case: [BJ.. = 4 g mole/l DQ = 3 x 1O-5cm’/sec.
Therefore,
567
Consecutive reactions
m
= d3x wx4x 190 OI =43 3.5 x 10-3
and &=1+$=31.
It is evident that a and I&.,are comparable and the first reaction step occurs under conditions of depletion of the reactant B. For the second reaction step the relevant values are: For [Cd., = 1*7gmole/l. ~‘?i&=8
and
C,214.
Therefore, for the second reaction step conditions for a fast pseudo first order reaction are nearly satisfied. However, because of the generation of the species C in the film, the concentration of species C varies from point to point (Fig. lb) in the film. Therefore, a constant concentration equal to C, cannot be assumed as in the case of a pseudo first order reaction. Thus, the second reaction step must be treated as second order. Figure 2 shows a plot of the selectivity index, S, against the liquid side mass transfer coefficient, k,, for A, equal to 31 and & equal to 14. The predicted values are based on Eqs. (14), (18) and (19). The agreement between the experimental and predicted values can be considered as reasonably good. In correlating the experimental data with the theoretical predictions it was assumed that the gas phase was completely mixed. This assumption is likely to be valid as the gas phase was properly stirred by a stirrer located in the gas phase. I
-
I
/,
2.5 3-
2.5
1 Predicted
0
,
o
30
3.5 kL x
4 -0
103.
4.5
, 5.0
cm /set
Fig. 2. Plot of the selectivity index, S, against k, for second order reactions.
The diffusivities of all the species were also assumed to be equal for the purpose of calculating the theoretical values. This assumption is unlikely to cause an error of more than 20 per cent in the predicted S values. The ditB.tsivities of p-cresol and monochloro-p-cresol in TCB are not available in the literature. These were, however, estimated by using the Wilke-Chang equation. The estimated values are: 4..A
: 3.9 X lo-’ cm’/sec
D monochloro-p-crero~ : 3.3 x 1O-5cm%ec When these values are used the diffusivity ratios of p-cresol to chlorine, and monochloro-p-cresol to chlorine are found to be 0.72 and 0.62, respectively. These values are different from unity. Thus, the values of & and I& calculated on the basis of unequal diffusivities, that is from the following equations:
and
4*==++
&Co
(36)
are lower. It has been pointed out that for the case when the diffusivities are not equal the predictions based on the penetration model are more realistic than those based on the film model. However, when the film model analysis is available, the agreement can be improved by using the square roots of the diffusivity ratios in Eqs. (35) and (36)[9]. When these corrections are incorporated, it is found that the A values obtained are 15-20 per cent lower than those obtained on the basis of equal diffusivities. The decrease in & causes more depletion of the reactant B and as a consequence the selectivity decreases. Calculations for a typical case showed that the modified S values were about 15-20 per cent lower than those obtained by assuming equal diffusivities, From Fig. 2 it is seen that the selectivity increases with an increase in the value of k,. This observation is in agreement with the theory. Thus, with an increase in kL the rate of diffusion of the intermediate product, C, from the film into the bulk, and that of the reactant B from the bulk into the film increases, and consequently the concentration of species B in the film increases and that of species C decreases. Thus, more of B is available for reaction in the film and the selectivity increases.
V. G. PANGARKAR and M. M. SHAR%A
568
First step fast pseudo first order and second step
slow As explained in the preceding section the selectivity increases with an increase in k,. At relatively high kL values the conditions given by expressions (4) and (5) are likely to be satisfied. Thus, the first reaction step shifts towards the fast pseudo first order regime whereas the second reaction step becomes slow. In this case, only the first step reaction occurs in the film and since the first step reaction is fast no solute reaches the bulk liquid phase. Thus, highest selectivity can be realized when the conditions given by expressions (4) and (5) are satisfied. It was first thought that a laminar jet apparatus may be useful. However, this idea was abandoned as the change in the concentration of monochlorop-cresol would be too small to be measured accurately particularly when the feed itself contains dissolved monochloro-p -cresol. It has already been explained that the usual up-take method for measuring the rate of absorption cannot be employed as the product of reaction is a gas. It was therefore decided to employ the 2.3 cm i.d. bubble column. In a bubble column the conditions given by expressions (3)-(5) are likely to be satisfied for the set of operating conditions given in Table 1. The selectivity index values are given in Table 1 along with
Thus, G
= 55 and &., = 16.75. Since a is far greater than &.,, the first step occurs in the instantaneous reaction regime. For the second step the relevant values are: (for [CO].. : 1.4 g mole/l):
a
= 8.75
and &=6.
2.5
1
V, - 2.0 4 .’ f 4 2 1,5-
I.0
6
Predicted
0
Experimental
I
I
I
I
I
6
IO
12
14
16
40, Fig. 3. Plot of the selectivity index, S against &I,, for instantaneous reaction regime.
Table 1. Absorption of pure chlorine into solutions of p-cresol and monochloro-p-cresol in the 2.3 cm i.d. jacketed bubble column. Inlet gas velocity = 20 cmlsec lp-CresoM.. CM)
[Monochloro-p-cresol&. (M>
4.2 4.45
[Dichloro-p-cresol,].. 09
l-5 1.34
0.038 0.021
the other relevant data. It can be seen that these values of the selectivity index are approximately two times those obtained under second order conditions (Fig. 2). First step instantaneous and pseudo first or second order
second
step fast
For this study the 5.5 cmi.d. stirred cell was used. Pure chlorine was absorbed into solutions of p-cresol and monochloro-p-cresol in TCB. For a typical case: speed of agitation:
40 rev/min
kL : 2.8 x lo-’ cm/set
[&I.~: 4 g mole/l.
CAP hmcu
(atm) 0.83 0.82
Selectivity Index, S 11.6 12.4
Since, a = I$~ the second reaction step should take place in the fast second order reaction regime. However, as pointed out under the theoretical considerations section, the relevant value of a to be used is that at the reaction plane, x = A, that is -a. Since a = a. (A/S) and (A/S) = l/&, we have V&&0.5. From the above discussion it is clear that the second step reaction apparently satisfies second order reaction conditions. However, as the first reaction step is instantaneous the dissolved gas A does not exist beyond x = A. Thus, the bulk liquid phase for
Consecutive
569
reactions
the species C shifts from x = 6 to x = A. The relevant value of kL is then kl or kt = D/A.
Since kL is far greater than kL the second reaction step becomes slow as the condition given by expression (5) is satisfied. Figure 3 shows a plot of the selectivity index, S, against &.,. The agreement between the predicted and experimental values is within 10 per cent. Thus, it appears that the experimental data can be satisfactorily correlated by the proposed model. CONCLUSIONS
From the above discussion it can be concluded that under certain circumstances mass transfer has a significant effect on the selectivity of consecutive gas-liquid reactions. The agreement between the experimental and predicted values for a variety of cases was found to be reasonably good. NOTATION
A A* B
Bi ’
C
D
DJ kz k; kL
gas A or the concentration of the gas A at any point in the liquid film, g mole/cm3 inter-facial concentration of the gas A, g mole/cm’ liquid phase reactant or the concentration of the reactant at any point in the liquid film, g mole/cm3 interfacial concentration of the reactant B, g mole/cm’ intermediate species formed in the consecutive reaction scheme or the concentration of species C at any point in the liquid film, g mole/cm’ species formed in the second step reaction or the concentration of the species D at any point in the film, g mole/cm3 liquid phase diffusion coefficient of species .I, cm’/sec reaction rate constant for the first step reaction [i.e., reaction 11, cm3/g mole set reaction rate constant for the second step reaction [i.e., reaction 21, cm’/g mole set liquid side mass transfer coefficient in the absence of a chemical reaction. cmlsec
k, specific rate of absorption of the gas A, g mole/cm* set rate of absorption of the gas A, g molelsec selectivity index distance in the direction of diffusion, cm
R.4 Rk
s X
Greek symbols 6 liquid film thickness,
cm +A enhancement factor for the gas A = Rnl k,A * 4il, asymptotic enhancement factor for the first step reaction = 1
47
+$
asymptotic enhancement ond step reaction = 1
factor for the sec-
+$
A reaction mane, cm EL liquid viscosity, cp Subscripts A
species C species i denotes A denotes 0 denotes
A
C interfacial properties properties at the reaction plane bulk liquid properties
Supe,.scti,,t
* denotes interfacial
properties
REFERENCES
[l] g:N
DE VUSSE J. G., Chem. Engng Sci. 1966 21
[2] TERAMOTO M., NAGAYASU T., MATSUI T., HASHIMOTO K. and NAGATA S., J. Chem. Engng (Japan) 1969 2 186. [31 VAN KREVELEN D. W. and HOFTIJZER P. J., Rec. Trao. Chim. 1948 67 563. [4] INOUE H. and KOBAYASHI T., Chemical Reaction Engineering, Proceedings of the Fourth European Symnosium. Brussels: Sunulement to Chem. Ennnn II _Sk. i%S 2j 147. [5] PANGARKAR V. G., Ph.D. Thesis, University of Bombay 1972. [6] JHAVERI A. S., Chem. Engng Sci. 1969 24 1738. [7] SHARMA M. M. and DANCKWERTS P. V., Chem. Engng Sci. 1%3 18 729. [81 DANCKWERTS P. V., Gas-Liquid Reactions, McGraw-Hill, London 1970. [91 HIKITA H. AND ASAI S., J. Chem. Engng (Japan), (English translation) 1964 2 77.
Engineering
Science,
1974, Vol. 29, pp. 561-569.
Pergamon
Press.
Printed
in Great Britain
CONSECUTIVE REACTIONS: ROLE OF MASS TRANSFER FACTORS V. G. PANGARKAR?
and M. M. SHARMA
Department of Chemical Technology, Matunga Road, Bombay 19, India (Received 12 June 1973) Abstract-The effect of mass transfer factors on the selectivity of a consecutive reaction was studied. A theoretical analysis, based on the film model, was made for different cases to bring out the effect of mass transfer on the selectivity with respect to the intermediate product. The experimental work was concerned with the chlorination of p-cresol dissolved in 1,2,4-trichlorobenzene. A good agreement be-
tween the experimental and the predicted values was observed. INTRODUCTION
accompanied by consecutive reaction is commonly encountered in the organic process industry. A large number of chemical reactions such as, substitution chlorination of aromatics, alkylation of aromatic compounds etc, fall in this category. In most of these cases, selectivity with respect to a particular product is desired. Since two or more reactions are involved the problem becomes complicated and a detailed analysis taking into consideration the interaction between the diffusional and kinetic factors, is required. Several workers have shown that diffusional factors play a significant role in affecting the selectivity of consecutive reactions (van de Vusse[ll, Teramoto et a1.[2]). However, very limited work has been done to verify the theoretical predictions. Further, very little attention has been paid to the cases where the first step involves depletion of the reactive species and where the reaction is instantaneous. It was thought desirable to study a consecutive reaction scheme under a variety of carefully controlled conditions so that the various regimes of mass transfer with chemical reaction could be covered. It was decided to study the chlorination of p -cresol dissolved in 1,2,4-trichlorobenzene at a temperature of about 100°C. Gas absorption
The intermediate product, C, is also capable of reacting with species A. The reaction may be represented as: A+C%D.
Both the reactant, B, and the intermediate product, C, are considered as non-volatile. The reactions (1) and (2) are considered to be irreversible and first order in the solute as well as the reactive species B and C. It is assumed that the resistance to mass transfer is confined to the liquid phase. The following cases will be considered: (i) First step fast pseudo first order and second step slow
Figure la shows the typical concentration profiles for this case. The first step can be considered to be fast when all the dissolved gas reacts in the liquid film adjacent to the interface and the following condition is satisfied: (3)
where: D, = liquid phase diffusion coefficient of species A, cm?/sec k2 = reaction rate constant for the first step
THEORETICAL CONSIDERATIONS
The scheme considered is as follows: Gaseous species A dissolves into the liquid phase and reacts with the liquid phase reactant B according to the reaction:
reaction,
cm’/g mole set
B. = bulk liquid phase concentration of the reactant, B, g mole/cm3 kL = liquid side mass transfer coefficient
without chemical reaction, A+B&C. tPresent address: Department ing, L.I.T., Nagpur, India.
Vol. 29 No. 2-P
cmlsec.
(1) of Chemical Engineer-
In addition the following inequality should be satisfied to ensure that the interfacial concentration of the reactant, B,, is nearly the same as the bulk 561
CES
(2)
V. G. PANGARKAR and M. M. SHARMA
562
43
---EL A*
Ci
c
8
x=0
(a)
(b)
(cl
j&q-j-/j-k& x=0
x=0x
6
8
Fig. 1. Concentration profiles for the various regimes
in consecutive reactions: (a) first step fast pseudo first order and second step slow, (b) both steps fast second order, (c) first step instantaneous.
liquid concentration
Ba:
of the reactant,
X@zz,& kL
(4)
A*
where : A * = interfacial concentration A, g mole/cm3.
of the species
The second step reaction may be considered to be slow when the condition given by the following expression is satisfied: Vi%EQl
ible. Consequently a very high selectivity with respect to the intermediate product, C, can be achieved. Under these conditions mass transfer has no effect on the selectivity. (ii) Both steps fast and second order Here the reactions between A and B, and A and C occur in the film but the concentration of species B at the interface is less than that in the bulk liquid phase. The typical concentration profiles for this case are shown in Fig. lb. The basic equations describing the steady state diffusion of the various species are as follows:
(5)
k,
DA $$
= k>AB +&AC
(6)
d2BckAB
(7)
where : ki = reaction
rate constant for the second step reaction, cm3/g mole set
CO = bulk liquid concentration mediate species
D
‘dx’
’
of the inter-
C, g mole/cm’.
The condition given by expression (3) ensures that the first step reaction occurs mainly in the liquid film and no free solute A exists in the bulk liquid phase. By contrast the condition given by expression (5) implies that the second step reaction occurs chiefly in the bulk liquid phase. Thus, the contribution of the second step reaction is neglig-
D
d2C cdX2 = - k2AB + k;AC.
(8)
The boundary conditions for the above differential equations are as follows: .=O,A=A*,B=Bi,C=Ci,@=g)=O
(9)
563
Consecutive reactions x=S,A=O,B=B,,C=Co
(10)
Equation (6) can be solved by the method of van Krevelen and Hoftijzer [3]. It has been shown[3] that the zero interfacial flux conditions for species B and C given in boundary conditions (9) imply constant interfacial concentrations, Bi and Ci of species B and C, respectively. Thus, for this particular case of non-volatile reactive species the variable concentration terms B and C in Eq. (6) can be replaced by Bi and Ci respectively. With this consideration Eq. (6) reduces to an ordinary second order differential equation that can be readily solved for the prescribed boundary conditions. The solution is:
for B and Ci for C and then subtract Eq. (7) from (6) to get: D d2A_Wd’B dX2 + k;C;A. *dX2-
(15)
In Eq. (15) the concentration profile of A given by Eq. (11) is substituted to yield: D
d2A=DdZB ‘dx’ Adx* k:CiA*sinh[dy(8-x)] + .
sinh [ JT.81
(16)
A =A*sinh[dF(S-x)] .
sinh[Jy.S]
The rate of absorption
(11)
of the solute A, is given by: A*d/DA(k~Bifk;Ci)
x=o=
tanh
VDa (kzBi +k;C) kL 3
Similar operations with Eqs. (6) and (8) yield the following equation : d2A d2C DA-Q = Dcp
(12)
2krBiA*sinh[dF.(S-x)]
+ .
sinh [JT.8]
and for the case when: (17) VDA(k2F+k:C); L
, 3
RA = A * IiDAkzBi +k;G
(13)
The selectivity index, S, is defined as the ratio of the rate of formation of species C to the rate of formation of D. Inoue and Kobayashi [4] have indicated that the selectivity with respect to the intermediate product C, can be represented by the ratio of the pseudo first order rate constants when the reaction (1) and (2) are pseudo first order with respect to the solute gas A. For the present case of second order reactions, a similar definition, with the interfacial concentrations replacing the bulk liquid concentrations is proposed. The selectivity index, S, is then given by: DAkzBi Mi, ’ = DAk;Ci = sb
(14)
The problem is now reduced to the prediction of the interfacial concentrations Bi and Ci. Equations (6) to (8) can be used to obtain the values of Bi and Ci. Thus, in Eqs. (6) and (7) we substitute Bi
Equations (16) and (17) are integrated using the boundary conditions (9) and (10) (Pangarkar[5]). The final equations are as follows:
M, _
1
MO, 4, - 1
+mh
Mi,
_A%_ Mi,+ M-,I
(“I
and
Nz
1
MO, k-1
Mi, - M,
&+ I/-
2Mi,
I
M,,+ M-,
(19)
564
V.G.PANGARKAR
and M. M. SHARMA
Substituting
and
Eq. (22) into Eq. (20) we obtain: (23)
for D,
= Ds = D,. The above equations
can be solved by a trial and error procedure to obtain Mi, and M-,. The selectivity index, S, can then be calculated from Eq. (14). (iii) First step instantaneous and second step fast pseudo first or second order Here the reaction between A and B is so fast that both the species are consumed by the reaction at a plane very close to the interface. The rate of absorption is then controlled by the diffusion of A from the interface and of B from the bulk to the reaction plane. Jhaveri[6] has discussed a similar problem for the case of gas absorption in a medium containing two reactants. However, in the present case the intermediate species, C, is generated in the film. Typical concentration profiles for this case are shown in Fig. lc. The rate of absorption of the gas, A, is given by (Jhaveri [6]): AVIZEE
Ra =
tanh
[
-(h/a)]
ta;fql
,o,
tanh
(24)
of generation =Rate of transport from the reaction plane into the bulk
kdo = A (s _ (21)
kl also increases
decreases.
xmzc
A”’
or
D.4
result (v)
k;
C20) Rate
where kt is defined as:
Now as &,, increases,
vimc
The second step reaction, can thus, be treated as pseudo first order and Ci can be replaced by CA,the concentration of species C at x = A. C, is obtained as follows: A mass balance for species C gives:
or
RA=
The above equation gives the rate of absorption for the case when only species B is present in the liquid phase and when the first step reaction is instantaneous. Thus when & is very much greater than unity, almost complete selectivity with respect to the intermediate product can be realised. For a quantitative estimate of the selectivity index, S, for the general case, (A/S) and C, must be known. From the above discussion it is evident that because of the high kt values, the second step is likely to be pseudo first order as m/kL is substantially reduced. The parameter m/k; may become so low that no reaction occurs in the film. The concentration of the species C, in the film increases due to the generation of C according to the first step reaction. However, the concentration term causes a much more significant increase in C;/A* than in mi/kL. As a result, the condition given by the following expression is likely to be valid for the region 0 < x < A :
and as a
A)
[CA-- Cd
(25)
Therefore: CA = C,+Bo
(26)
when: A*6
In the limit as:
(A/6) is obtained by taking reaction plane. Thus:
(T)+F
a mass balance at the
kt
or tanh
(F)
+p.
noting that:
(27) (22)
or sinh
kt = k&a, (Eq. 21).
v5jEQS)] L
=fi.
Consecutive
The above equation
on simplification
1 -(A/6) sinh [a(~/@]
yields:
=- d&-l a
(28)
where: a=mk,. The rate of formation
of species C is given by: DsBo
R’=(s-A) or kJ% Rc=(l-h/S)’ The rate of formation reaction, D, is:
(29)
of the product of the second
RD= R.,-Rc The selectivity
(30)
index, S, is then obtained
as:
56.5
reactions
the published work of Teramoto et al. [2], carbon tetrachloride was used as the solvent. The solubility of chlorine in this solvent at 25°C is approximately 3.5 x lo-’ g mole/cm’ atm. This value of solubility of chlorine in carbon tetrachloride is relatively very high and will probably introduce a significant gas side resistance in the case of absorption from lean mixtures. The value of the second order rate constant for the first step at 25°C is only 17 l/g mole set (Inoue and Kobayashi[4]). It was, therefore, thought desirable to work at a relatively high temperature so that much higher values of the rate constants can be realized and at the same time the solubility of chlorine can be substantially reduced. This procedure should allow a wider range of variables to be covered. The solvent and the reactant should preferably have negligible vapour pressures at the temperature of operation. It was decided to use TCB as the solvent. The temperature used was 100°C. At lOO”C, the vapour pressure of both TCB and p -cresol are only about 15 mm Hg. ANALYSIS
RC ‘=RA-Rc
The analysis of the feed and product solutions containing mixtures of p -cresol, monochloro-p cresol and dichloro-p -cresol, dissolved in TCB was DISCUSSION OF THE CHEMICAL SYSTEM carried out on an F and M Model 720, dual column programmed temperature gas chromatograph with The experimental studies involved the chlorinathermal conductivity detector. In the present work tion of mixtures of p-cresol and monochloro-pcresol dissolved in 1,2,Ctrichlorobenzene (TYCB). a 3.3 m long, 6 mm i.d. copper column packed with The chlorination of p-cresol occurs according to 20 per cent diethylene glycol succinate supported on Chromosorb W (45-60 mesh) and modified with the following scheme: 3 per cent o-phosphoric acid was used (Teramoto et OH OH al. [2].)
(31)
EXPERIMENTAL
OH
CH,
CH,
The above system has been used by Inoue and Kobayashi [4], and Teramoto et al. [2]. The reactions are specific and no other isomers are formed in the first as well as the second step. Both these reactions are first order in the solute and the reactants and are therefore well suited for the present studies, In
A laminar jet apparatus was used to obtain the diffusivity of chlorine in 1,2,4-trichlorobenzene (hereafter referred to as TCB) and for the reaction between chlorine and p-cresol to give monochloro-p -cresol. The principal design features of the apparatus used were akin to those employed by Sharma and Danckwerts[7]. The diameter and length of the jet used were 0.097 and 6*76cm, respectively. A 5.5 cm i.d. glass stirred cell was used for obtaining the rate constant for the reaction between chlorine and monochloro-p-cresol and for testing the models for the depletion and instantaneous reaction regimes. The stirred cell was provided with a glass cruciform type stirrer and the speed of agitation was varied between 40 to lOOrev/min. A 2.3 cm i.d. jacketed bubble column was used
V. G. PANGARKAR and M. M. SHARMA
566
for testing the model proposed for the case when the first reaction step is pseudo first order and the second step is slow. In all the experiments conducted the gas and liquid phases were brought up to the desired temperature by passing through glass coils immersed in a thermostat. The stirred cell was placed in a similar constant temperature bath. In the case of jacketed bubble column, the column was maintained at the desired temperature by circulating glycerine-water mixture from a constant temperature bath through the jacket. With these arrangements the apparatus could be operated at within ?O.S’C of the desired temperature. RESULTS
AND DISCUSSION
Solubility of chlorine in TCB The solubility of chlorine in the solvent was experimentally determined by saturating the solvent at 100°C and estimating the dissolved chlorine. The Henry’s law constant at this temperature was found to be 2.7 x 10m4g mole/cm’ atm. Difiusivity of chlorine in the solvent
Pure chlorine was absorbed in laminar jets of TCB at 100°C. The diffusivity was found by employing the following equation (Danckwerts 181) which holds for a laminar jet apparatus R:,=4A*fi
m
where: R; = rate of absorption, g mole/set L = liquid flow rate, cm’/sec
kL, = kL,
(33)
where, subscript 1 refers to pure TCB and subscript 2 refers to the reaction mixture. The reaction rate constant for the first step reaction, k2, was determined by absorbing pure chlorine into laminar jets of p-cresol dissolved in TCB. Since hydrogen chloride is evolved during the absorption of chlorine, the normal procedure for measuring the rate of absorption by the gas up-take method could not be used. In the present case the rates of absorption were based on the analysis of the outlet liquid. The second step reaction is relatively slow. A preliminary estimate of the rate constant based on the data of Inoue and Kobayashi[4] indicated that the reaction is likely to fall in the fast pseudo first order reaction regime when dilute chlorine is absorbed in a stirred cell. Accordingly chlorine (approximate 50 mole per cent in a mixture with nitrogen) was absorbed into monochloro-p- cresol dissolved in TCB. The rate of absorption for a pseudo first order reaction is given by: Rn = A * vDnk
[reactantI
(34)
The values of the reaction rate constants for the first and second step reaction can be calculated (32) from the observed values of Rn and a knowledge of A* and DA. The following values were obtained at lOO”c!:k2 = 190 l/g mole set k; = 15 l/g mole sec.
I = length of the jet, cm. The value of the diffusivity of dissolved chlorine was found to be 5.4 x lo-’ cm*/sec. The value of the diffusivity of dissolved chlorine in the reacting mixture was determined by employing the Stokes-Einstein relation, (DAbIT) = constant. Preliminary experiments
In order to calculate the values of the parameter, fi, for ascertaining the regime of absorption for both the steps, data on k,, kZ and k; are required. Chlorine was absorbed into pure TCB at 100°C in the stirred cell and the values of kL were experimentally determined for the various speeds of agitation. The reacting system had a somewhat higher viscosity as compared to the pure solvent. Therefore, the values of k, for the reacting systems was obtained by using the following equation:
The necessary conditions under which Eq. (34) is valid were satisfied. The above values agree reasonably well with the extrapolated data of Inoue and Kobayashi[4] Chlorination of mixtures of p-cresol and monochloro-p-cresol in the stirred cell : fast second order reactions In the stirred cell the kL values are of the order of 3 x lo-’ cm/set. Thus, for instance, at a speed of agitation of 60 revlmin the kL value was 3.5 x
lo-’ cm/set. Consider the following case: [BJ.. = 4 g mole/l DQ = 3 x 1O-5cm’/sec.
Therefore,
567
Consecutive reactions
m
= d3x wx4x 190 OI =43 3.5 x 10-3
and &=1+$=31.
It is evident that a and I&.,are comparable and the first reaction step occurs under conditions of depletion of the reactant B. For the second reaction step the relevant values are: For [Cd., = 1*7gmole/l. ~‘?i&=8
and
C,214.
Therefore, for the second reaction step conditions for a fast pseudo first order reaction are nearly satisfied. However, because of the generation of the species C in the film, the concentration of species C varies from point to point (Fig. lb) in the film. Therefore, a constant concentration equal to C, cannot be assumed as in the case of a pseudo first order reaction. Thus, the second reaction step must be treated as second order. Figure 2 shows a plot of the selectivity index, S, against the liquid side mass transfer coefficient, k,, for A, equal to 31 and & equal to 14. The predicted values are based on Eqs. (14), (18) and (19). The agreement between the experimental and predicted values can be considered as reasonably good. In correlating the experimental data with the theoretical predictions it was assumed that the gas phase was completely mixed. This assumption is likely to be valid as the gas phase was properly stirred by a stirrer located in the gas phase. I
-
I
/,
2.5 3-
2.5
1 Predicted
0
,
o
30
3.5 kL x
4 -0
103.
4.5
, 5.0
cm /set
Fig. 2. Plot of the selectivity index, S, against k, for second order reactions.
The diffusivities of all the species were also assumed to be equal for the purpose of calculating the theoretical values. This assumption is unlikely to cause an error of more than 20 per cent in the predicted S values. The ditB.tsivities of p-cresol and monochloro-p-cresol in TCB are not available in the literature. These were, however, estimated by using the Wilke-Chang equation. The estimated values are: 4..A
: 3.9 X lo-’ cm’/sec
D monochloro-p-crero~ : 3.3 x 1O-5cm%ec When these values are used the diffusivity ratios of p-cresol to chlorine, and monochloro-p-cresol to chlorine are found to be 0.72 and 0.62, respectively. These values are different from unity. Thus, the values of & and I& calculated on the basis of unequal diffusivities, that is from the following equations:
and
4*==++
&Co
(36)
are lower. It has been pointed out that for the case when the diffusivities are not equal the predictions based on the penetration model are more realistic than those based on the film model. However, when the film model analysis is available, the agreement can be improved by using the square roots of the diffusivity ratios in Eqs. (35) and (36)[9]. When these corrections are incorporated, it is found that the A values obtained are 15-20 per cent lower than those obtained on the basis of equal diffusivities. The decrease in & causes more depletion of the reactant B and as a consequence the selectivity decreases. Calculations for a typical case showed that the modified S values were about 15-20 per cent lower than those obtained by assuming equal diffusivities, From Fig. 2 it is seen that the selectivity increases with an increase in the value of k,. This observation is in agreement with the theory. Thus, with an increase in kL the rate of diffusion of the intermediate product, C, from the film into the bulk, and that of the reactant B from the bulk into the film increases, and consequently the concentration of species B in the film increases and that of species C decreases. Thus, more of B is available for reaction in the film and the selectivity increases.
V. G. PANGARKAR and M. M. SHAR%A
568
First step fast pseudo first order and second step
slow As explained in the preceding section the selectivity increases with an increase in k,. At relatively high kL values the conditions given by expressions (4) and (5) are likely to be satisfied. Thus, the first reaction step shifts towards the fast pseudo first order regime whereas the second reaction step becomes slow. In this case, only the first step reaction occurs in the film and since the first step reaction is fast no solute reaches the bulk liquid phase. Thus, highest selectivity can be realized when the conditions given by expressions (4) and (5) are satisfied. It was first thought that a laminar jet apparatus may be useful. However, this idea was abandoned as the change in the concentration of monochlorop-cresol would be too small to be measured accurately particularly when the feed itself contains dissolved monochloro-p -cresol. It has already been explained that the usual up-take method for measuring the rate of absorption cannot be employed as the product of reaction is a gas. It was therefore decided to employ the 2.3 cm i.d. bubble column. In a bubble column the conditions given by expressions (3)-(5) are likely to be satisfied for the set of operating conditions given in Table 1. The selectivity index values are given in Table 1 along with
Thus, G
= 55 and &., = 16.75. Since a is far greater than &.,, the first step occurs in the instantaneous reaction regime. For the second step the relevant values are: (for [CO].. : 1.4 g mole/l):
a
= 8.75
and &=6.
2.5
1
V, - 2.0 4 .’ f 4 2 1,5-
I.0
6
Predicted
0
Experimental
I
I
I
I
I
6
IO
12
14
16
40, Fig. 3. Plot of the selectivity index, S against &I,, for instantaneous reaction regime.
Table 1. Absorption of pure chlorine into solutions of p-cresol and monochloro-p-cresol in the 2.3 cm i.d. jacketed bubble column. Inlet gas velocity = 20 cmlsec lp-CresoM.. CM)
[Monochloro-p-cresol&. (M>
4.2 4.45
[Dichloro-p-cresol,].. 09
l-5 1.34
0.038 0.021
the other relevant data. It can be seen that these values of the selectivity index are approximately two times those obtained under second order conditions (Fig. 2). First step instantaneous and pseudo first or second order
second
step fast
For this study the 5.5 cmi.d. stirred cell was used. Pure chlorine was absorbed into solutions of p-cresol and monochloro-p-cresol in TCB. For a typical case: speed of agitation:
40 rev/min
kL : 2.8 x lo-’ cm/set
[&I.~: 4 g mole/l.
CAP hmcu
(atm) 0.83 0.82
Selectivity Index, S 11.6 12.4
Since, a = I$~ the second reaction step should take place in the fast second order reaction regime. However, as pointed out under the theoretical considerations section, the relevant value of a to be used is that at the reaction plane, x = A, that is -a. Since a = a. (A/S) and (A/S) = l/&, we have V&&0.5. From the above discussion it is clear that the second step reaction apparently satisfies second order reaction conditions. However, as the first reaction step is instantaneous the dissolved gas A does not exist beyond x = A. Thus, the bulk liquid phase for
Consecutive
569
reactions
the species C shifts from x = 6 to x = A. The relevant value of kL is then kl or kt = D/A.
Since kL is far greater than kL the second reaction step becomes slow as the condition given by expression (5) is satisfied. Figure 3 shows a plot of the selectivity index, S, against &.,. The agreement between the predicted and experimental values is within 10 per cent. Thus, it appears that the experimental data can be satisfactorily correlated by the proposed model. CONCLUSIONS
From the above discussion it can be concluded that under certain circumstances mass transfer has a significant effect on the selectivity of consecutive gas-liquid reactions. The agreement between the experimental and predicted values for a variety of cases was found to be reasonably good. NOTATION
A A* B
Bi ’
C
D
DJ kz k; kL
gas A or the concentration of the gas A at any point in the liquid film, g mole/cm3 inter-facial concentration of the gas A, g mole/cm’ liquid phase reactant or the concentration of the reactant at any point in the liquid film, g mole/cm3 interfacial concentration of the reactant B, g mole/cm’ intermediate species formed in the consecutive reaction scheme or the concentration of species C at any point in the liquid film, g mole/cm’ species formed in the second step reaction or the concentration of the species D at any point in the film, g mole/cm3 liquid phase diffusion coefficient of species .I, cm’/sec reaction rate constant for the first step reaction [i.e., reaction 11, cm3/g mole set reaction rate constant for the second step reaction [i.e., reaction 21, cm’/g mole set liquid side mass transfer coefficient in the absence of a chemical reaction. cmlsec
k, specific rate of absorption of the gas A, g mole/cm* set rate of absorption of the gas A, g molelsec selectivity index distance in the direction of diffusion, cm
R.4 Rk
s X
Greek symbols 6 liquid film thickness,
cm +A enhancement factor for the gas A = Rnl k,A * 4il, asymptotic enhancement factor for the first step reaction = 1
47
+$
asymptotic enhancement ond step reaction = 1
factor for the sec-
+$
A reaction mane, cm EL liquid viscosity, cp Subscripts A
species C species i denotes A denotes 0 denotes
A
C interfacial properties properties at the reaction plane bulk liquid properties
Supe,.scti,,t
* denotes interfacial
properties
REFERENCES
[l] g:N
DE VUSSE J. G., Chem. Engng Sci. 1966 21
[2] TERAMOTO M., NAGAYASU T., MATSUI T., HASHIMOTO K. and NAGATA S., J. Chem. Engng (Japan) 1969 2 186. [31 VAN KREVELEN D. W. and HOFTIJZER P. J., Rec. Trao. Chim. 1948 67 563. [4] INOUE H. and KOBAYASHI T., Chemical Reaction Engineering, Proceedings of the Fourth European Symnosium. Brussels: Sunulement to Chem. Ennnn II _Sk. i%S 2j 147. [5] PANGARKAR V. G., Ph.D. Thesis, University of Bombay 1972. [6] JHAVERI A. S., Chem. Engng Sci. 1969 24 1738. [7] SHARMA M. M. and DANCKWERTS P. V., Chem. Engng Sci. 1%3 18 729. [81 DANCKWERTS P. V., Gas-Liquid Reactions, McGraw-Hill, London 1970. [91 HIKITA H. AND ASAI S., J. Chem. Engng (Japan), (English translation) 1964 2 77.