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Ind. Eng. Chem. Fundam., Vol. 18, No. 3, 1979
Interactions between Kinetics and Mass Transfer in the Liquid Phase Chlorination of n-Dodecane Michael P. Ramage and Roger E. Eckert” School of Chemical Engineering, Purdue University, West Lafayette, Indiana 4 7907
The effect of mass transferlimitations on product selectivity in the liquid phase chlorination of ndodecane is presented. Surface renewal theory is used to show that selectivity is determined by the values of two dimensionless parameters which represent the interaction between mass transfer and kinetics in the reaction system. Experimental data show that the yield ratio of nlsec-monochlorides is increased 70% as mass transfer limitations increase.
n-Monochlorides obtained from the liquid phase chlorination of C8-C18 n-paraffins are valuable intermediates in the production of fatty acids, sulfonates, esters, alcohols, and amines for use as detergents, fabric softeners, lubricant additives, plasticizers, etc. (Asinger, 1968). In the liquid phase process chlorine, which is bubbled through the liquid paraffin, is transported from the gas phase into the liquid hydrocarbon. There both parallel chlorination of n-paraffin to n- and sec-monochloroparaffins and series chlorination of the monochlorides to dichlorides take place. Since a mixture of chloroparaffins is produced, the process conditions must be optimized in order to maximize the yield of the desired isomer, n-monochloride. A mathematical model of the process could be used to define process conditions which would give maximum yield of the n-isomer. However, development of such a model is an ambitious project since both the intrinsic kinetic and mass transport effects must be taken into account. Ramage and Eckert (1975) have reported intrinsic kinetics for the photoinitiated liquid phase chlorination of n-dodecane. Two investigations of the effect of interphase mass transfer on product selectivity in liquid phase chlorination have been reported: van de Vusse (1966) and Ramage and Eckert (1973). Van de Vusse considered the liquid phase chlorination of n-decane in a semi-batch reactor. He found that the selectivity to total monochlorides in a “nonstirred” reactor was decreased by diluting the hydrocarbons with o-dichlorobenzene. Ramage and Eckert studied the effects of agitation, temperature, and chlorine flow rate on product distribution in the liquid phase chlorination of n-dodecane in a semi-batch reactor. The results of this study show that these three process variables through a very complex interaction significantly affect both the yield of total monochlorides and the yield ratio of nksec-monochlorides. In this paper we will further explore the effect of the mass transfer-kinetic interaction on product selectivity in the photoinitiated liquid phase chlorination of n-dodecane. It will be shown that the interaction can be described by two dimensionless parameters derived from surface renewal theory. In addition, data will be presented which establish that mass transfer limitations can increase the ratio of nlsec-monochlorides by 70%. The directional effect of process conditions on selectivity can be determined from these dimensionless parameters. Theory Intrinsic Kinetics. Ramage and Eckert (1975) have experimentally determined the intrinsic kinetics for the
Table I. Rate Constnats for the Photoinitiated Chlorination of n-Dodecane as Determined by Ramage and Eckert (1975)“ h , = 5.95 x 10-I’ k , = 5.29 X kp = 0.61 x 1 0 - 1 7
k d = 5.41 x k d s = 5.18 x kdp = 8.08 x
io-” io-17 io-’’
a Values are for eq 4 with concentrations in g-mol/L, time in min, and light intensity in quanta/L min.
photoinitiated liquid phase chlorination of n-dodecane which proceeds via the following reaction pathways n-Cl2Hz6
k,
C12
-+
HC1 + n-C1zH25C1
kd,
c12
HC1
k,
ClzH24C12 (1)
kdn
n-ClzH26 cl,HC1 + sec-C12Hz5C1cl,HC1 + ClzH24C12 (2) or alternately if all monochlorides are lumped ClzH2s
HCl
+ ClzH&l+
HCl
+ ClzHZ4Cl2 (3)
Formation rates of all dodecyl chlorides and dichlorides in eq 1-3 are given by the following rate equation d(RC1) - k(Clz)O (RH)(I)0.87 -(4) dt where R is n-dodecane or monochloride and k is the appropriate rate constant. Note that the reactions are zero order in chlorine concentration. Rate constants are given in Table I. Several ways in which temperature can affect the intrinsic kinetics of liquid phase chlorination will be noted. At higher temperature if there is sufficient thermal energy for considerable thermal initiation and this step controls the overall chlorination rate, the observed kinetics will have a high activation energy. However, even at high temperature (>lo0 “C) when thermal initiation is fast relative to propagation and termination, it is possible for the highly reactive free radicals to diffuse slowly in the liquid phase, which effectively traps them locally and favors radical recombination. Ramage and Eckert (1975) explain that this trapping of free radicals, called a “cage effect”, will result in a low activation energy for the overall chlorination. At lower temperature a t which thermal energy is insufficient for thermal initiation, as in Ramage and Eckert’s work at 0-32 “C, a very low activation energy is expected
0019-7874/79/1018-0216$01.00/00 1979 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 18, No. 3, 1979
217
to diffusion is not significant in the system (Ramage, 1971) and in their case was experimentally determined to be and therefore it is not included in the model. negligible. It is important that the above-mentioned The two dimensionless parameters which describe the free-radical diffusion control is different from the mass transfer-kinetic interaction in the liquid phase mechanism being studied in the present paper. Here mass chlorination system will now be derived. First the material transfer of molecular chlorine across a gas-liquid interface balance equations (eq 5-8) will be put in dimensionless to the reaction zone is the diffusional resistance which form by defining two transform variables. alters the course of the chlorination reaction. Mass Transfer-Kinetic Interaction. In order to q = x[k,DoC~1(1)o~87/Lc]0~5 (12) determine the dimensionless parameters which represent the mass transfer-kinetic interaction, a mathematical r = kmDoC;1(I)0.87t (13) model for the liquid phase chlorination of n-dodecane will The dimensionless material balance equations are be developed. A surface renewal model of the Higbie (1935) and Danckwerts (1951) type will be used to represent the mass transfer. That is, the gas-liquid interface is assumed to be made up of small rigid surface elements, which are continuously brought to the interface from a R h a2d - - - = (adi ) d perfectly mixed bulk liquid by the motion of the bulk aq2 a 7 liquid itself. When an element is first brought to the interface, the concentrations of C12,C12H26, S ~ C - C ~ ~ H ~ ~ C ~ , a2P aP n-CI2HwCl,and C12H24C12 in the element are the same as (16) Rp aq2 - a 7 = -Kid + Kdp( j ) p those in the bulk liquid. While a t the interface, chlorine absorbs into the element by unsteady-state molecular diffusion and reaction takes place. The average exposure time of the surface elements is a function of the system hydrodynamics and usually has to be determined exwhere perimentally. The surface renewal model was chosen over the classic film theory model because the former allows for transient concentration changes in the surface elements. In regimes where mass transfer can affect selectivity, the yield of total monochloride (y), and the ratio of n/secmonochloride (7)are determined by the concentration profiles in the surface elements (Ramage and Eckert, 1973). Szekely and Bridgwater (1967) have shown theoretically for first-order kinetics that surface renewal and film theory models predict selectivities which can differ by as much as 21%. The following differential material balances for chlorine, dodecane, and monochlorides (n and sec) describe the compositional changes which take place in one surface element during its lifetime (t*) at the gas-liquid interface. Boundary conditions are at
7
= 0, q
> 0; c =
G;d =-;DO p = -;Ci Cb
Db
Pb
Sb
s = -; Ci Mb
e = - (18) Ci
at q
at x
-
-- d S - dM c = c i ,dD - --- dP - -= 0 dx dx dx dx m,
t > 0; C # m, D #
m,
P # m, S #
m,
M #
m
(10) (11)
The concentration profile of dichloride in the element is obtained by mass balance. The derivatives in eq 10 state that C12H26 and C,2H25C1are nonvolatile. This model assumes an isothermal system and that the evolution of HC1 does not affect the transfer of other components in the surface element. It can be shown that bulk flow due
-
m,
r
> 0; c # m;d # m;p # 00;s # ";e #
m
(20)
The boundary conditions are constant for one exposure time. This model contains nine explicit dimensionless parameters (Rh, R,, R,, Kd, K,, K,, Kd,, Kdp, 2). Another parameter which is implicitly contained in the model is the dimensionless exposure time, r*, of the surface element. Since the R's and K's are fixed for a given chemical system, the concentration profiles and thus the product selectivity in the surface element is determined by the values of the two dimensionless parameters T* and 2. If all surface elements have the same exposure time (Higbie, 1935) then r* and 2 determine the selectivity for the overall reaction system. For a gas-liquid reaction system it is more convenient to use the physical mass transfer coefficient (kLo)than the exposure time. Higbie found the following relationship between kLo and t*
218
Ind. Eng. Chem. Fundam., Vol. 18, No. 3, 1979 MANOMETER
kLo = 2 ( ~ , / ~ t * ) 0 , 5 (21) Solving eq 21 for t* and substituting this value into eq 13, one obtains
b
.
LIQUID SAMPLING
I THEYOMETER
~
I t
A mass transfer modulus can be defined as
N = (T/4)T*
(23)
or
N
=
k,DoC~1(I)o~s7L,/(k,o)2 (24)
Also
N = N,
+ N,
(25)
where
N , = k,DoCi-’( I)0’87Lc / (kL” )
(27)
I
,
i
r
N2
c12
I! I-7
ULTRAVIOLET
LIGHT
+
since k, = k, k,. Therefore, it is concluded that for the liquid phase chlorination of n-dodecane, the product selectivity is fixed by the values of N and 2. The directional relationship which exists between selectivity and the values of N and 2 can be ascertained from the work of Astarita (1967). Astarita defines three reaction regimes (“slow”, “fast”, and “instantaneous”) for a gasliquid reaction system in terms of an equivalent diffusion time (tD)and a reaction time (tJ. For the liquid phase chlorination of n-dodecane
Note that
N = tD/t,
(30)
Thus we can apply Astarita’s criteria to the chlorination system is terms of the parameters N and 2. A reaction system is in the slow regime when (NO.5
