I n d . Eng. Chem. Res. 1990, 29, 920-924
920
Ramshaw, C.; Mallinson, R. H. US. Patent, 4,283,255, Aug 1981, cited in Tung and Mah (1985). Sharma, M. M.iDankwerts, P. V. Chemical Methods of Measuring Interfacial Area and Mass Transfer Coefficients in Two-fluid systems. Br. Chem. Eng. 1970, 15, 522-527. Tung, H. H.; Mah, R. S. H. Modelling liquid Mass-transfer in Higee Separation Process. Chem. Eng. Commun. 1985,39, 147-153. Vivian, J. E.; Brian, P. L. T.; Krukonis, V. J. The Influence of Gravitational Force on Gas Absorption in a Packed Column. AIChE J . 1965, 11, 1088-1091.
* To whom correspondence should be addressed. M. Praveen Kumar, D. Prahlada Rao* Department of Chemical Engineering Indian Institute of Technology, Kanpur Kanpur 208 016, India Received f o r review July 25, 1989 Accepted January 17, 1990
Phase-Transfer Alkylation of Phenylacetonitrile in Prototype Reactors under Magnetic or Ultrasound Mixing Conditions. 2. Kinetic Modeling In a previous paper reporting on the monoalkylation of phenylacetonitrile (PAN) under heterophase conditions, it was observed that the reaction kinetics in prototype reactors could not be accurately interpreted by a first-order rate equation with respect to PAN. T h e experimental profiles of the PAN conversion within the timeframe of interest were influenced to a great extent by the catalyst preconditioning. In the present paper, a general kinetic model that includes the reactions both on the catalyst and on PAN has been developed. A rationalization of the reported findings is also offered on the basis of a mathematical model elaborated for this purpose. The positive effects of ultrasound mixing on the rate of PAN monobutylation reactions, performed either in the presence of soluble and insoluble catalysts or without any added catalyst, are stressed. 1. Introduction In a previous paper (Ragaini et al., 1988), we presented a comparative study of a series of phase-transfer catalysts (PTC), characterized by low molecular mass or polymeric structure. These catalysts were employed in the monoalkylation of phenylacetonitrile (PAN) with butyl bromide (BuBr), using different prototype reactors assembled for both continuous flow and batch-type reactions. Different stirring and mixing conditions for the multiphase reaction systems were also used. One noteworthy finding was that the PAN molar conversion Cy) followed only roughly a first-order rate equation, and y was in any case very much affected by the catalyst preconditioning procedures. Typically when a soluble catalyst such as triethylbenzylammonium chloride (TEBA) was added directly to the mixture constituted by PAN, BuBr, and NaOH,,,, (C, mode), the PAN conversion vs time plot had a concave/ convex shape (Figure la). When an analogous insoluble polymer catalyst containing tributylbenzylammonium chloride and benzyltetraethylene glycol groups bonded to the polymer matrix (TBBA-TEG-PB) was used after an overnight preconditioning with either PAN/NaOH(, (C, mode) or BuBr/NaOH(,,, (C, mode), very distinct FAN conversion vs time plots were obtained (Figure 1, b and c, respectively). Moreover, it was previously observed (Solaro et al., 1980) that heterophase PAN alkylation under strong basic conditions could take place without the addition of any PT catalyst. This fact has been confirmed in the present study, where it is also shown that by using an ultrasound mixer (UM) the PAN conversion, in catalyst-free monoalkylation, can reach very high values (up to 90% at 80 "C), in keeping with the positive effects already observed in PAN monoalkylation in fixed bed reactors. Reactions promoted by ultrasound have been receiving increasing attention, because of their versatility and potential uses in synthetic organic chemistry (Ley and Low, 1989; Mason and Lorimer, 1988; Riaz, 1988; Suslick, 1986, 1988). With the aim of providing a more satisfactory explanation of previous and more recent experimental findings, regarding PAN monoalkylation under heterophase conditions, a mathematical elaboration of a kinetic
,
0888-5885/9Q/2S29-0920$02.~0/0
model was undertaken, and the results constitute the body of the present contribution. 2. Experimental Procedure Details on both the catalysts (including the relevant nomenclature) and the experimental apparatus have been reported in a previous paper (Ragaini et al., 1988) together with a description of the experimental procedures adopted for PAN monoalkylation. A description of the procedures used for the preconditioning of the catalyst (C,, C4, and C5 modes) was provided in the previous section. Experimental examples of the first-order rate equation, viz., -(ln (1- y)) vs time Cy being the relative conversion of PAN), are reported in Figures 2-4; they reproduce the typical shape already represented in Figure 1,parts a, b, and c, respectively. Figure 5 shows the PAN conversion vs time for runs carried out without any added catalyst and under different stirring conditions (curves 1-4). One run was made with ultrasonic mixing and some drops of aqueous ammonia added to the reaction system at 82 " C (curve 1). The results demonstrate that ammonia is not completely desorbed and that it can react with BuBr to form the quaternary catalytic salt Bu4N+Br-. Some further runs with PAN + NaOH were made at 70 "C to verify the possibility of a hydrolytical decomposition of PAN, especially under ultrasonic irradiation. It was demonstrated that, under such conditions, traces of ammonia are formed and can be detected in the vapor phase. This result agrees with a previous paper by Solaro et al. (1980). The observation that PAN alkylation may take place even without any added catalyst (Figure 5) can be explained by the above-mentioned phenomenon (see also section 3). 3. Kinetic Model
The overall PAN monoalkylation reaction, as represented by the equation C6H5CH,CN + BuBr
NaOH,a,, (50%) cat. (R,N+X-)
C6H5CH(Bu)CN + NaBr
+ HzO (1)
can be analyzed in two sets of reactions involving specif1990 American Chemical Society
'k'
Ind. Eng. Chem. Res., Vol. 29, No. 5, 1990 921
1
Cond. C, Cat. Soluble
(last added)
--c
' - ' - ' - ' -
I
time
C d . c* PAN+IyIoH
Tknc (min)
Figure 2. First-order rate equation of PAN molar conversion (y) vs time for TEBA-soluble catalyst and ultrasound mixing a t different temperatures; C5 preconditioning.
time
Cond. C4 ButBr+NaOH
24
t
i 8
time
Figure 1. Qualitative plot of the first-order rate equation of the PAN conversion (y) vs time for different preconditioning procedures.
ically (i) the catalyst and (ii) the PAN. However, this analysis does not take into account the fact that the "transfer process", Le., the mass transfer of the N+R3Xgroup from the organic to the aqueous phase, cannot be considered as the rate-controlling step (Dehmlow and Dehmlow, 1980). (i) Reactions Related to the Catalyst.
-
R4N+ + OHR3N + R(-H) R3N + BuBr
-
+ H20
(Hoffman reaction) (2)
R3N+BuBr- (quaternization reaction) (3) (ii) Reactions Related to PAN. C6H,CHzCN
NH,
NaOH y C6H5CHzCOONa + NH,
+ 4BuBr + 30H-
-
+
Bu4N+Br- 3H20
Time (min)
Figure 3. First-order rate equation of PAN molar conversion Q vs time at 70 OC for TBBA-TEGPB insoluble catalyst and ultrasound mixing: (A) C2preconditioning mode; (B)C4preconditioning mode.
(4a)
+ 3Br(4b)
The series of reactions 2-5 accounts for the initial low reactivity of PAN when either the C2 or the C4 preconditioning mode of the catalyst has been used. In the case of C2 preconditioning (i.e., no BuBr added), the catalyst is partially consumed in accordance with reaction 2, with the formation of a quaternary salt as sketched in reaction 3. With C4 preconditioning (i.e., in the presence of BuBr and NaOH,,,, reactions 2 and 3 have already reached equilibrium at the beginning of the overall reaction, (1). In the case of a soluble catalyst used without any preconditioning procedure, the concave/convex shape (Figure la) of the PAN conversion/time plot can be explained by
Reaction Time (min.)
Figure 4. PAN molar conversion (y) vs time; runs using different Ultrasonic mixing with stirring apparatus and no added catalyst. (0) some drops of NH,(,, added: curve 1, a t 82 O C . (A) Ultrasonic mixing: curve 2, a t 80 O C . (0)Magnetic stirring: curve 3, a t 80 OC. ( 0 )Turbine stirring (about 7000 rpm): curve 4, a t 80 O C .
assuming that the catalyst, added as the last component to the reaction mixture, gives rise contemporaneously to the PAN alkylation and to both reactions 2 and 3. The
922 Ind. Eng. Chem. Res., Vol. 29, No. 5 , 1990
ratios [OH-]/[PAN] >> 10 and [BuBr]/[PAN] > 5: furthermore, if one introduces the total concentration of the quaternary species, [NO], generated by the catalyst, one has [No] = [R,N] + [R,N+], i.e., [R,N] = [NO] - [R,N+/ LJnder these conditions, eq 13 can be rewritten as d[R,N+]/dt = k5([No] - [R4N+]) - k*[R,N+] 1141 where
k, = k,’[OH-j
h , = h,’[BuBr] Equation 14 can then be analytically integrated, giving [R,N+] = E + Fe-‘;‘ (15) where kS“1 E=---
k, + k5
,k-L--
30
90
60
120
F = E - [NO] G = k , 6 ti,
150
Time ( m i d
Figure 5 . Calculated and experimental molar conversions of PAN (y) vs time at 70 “ C , using eqs 22a-c with five parameters, TEBAsoluble catalyst, and a C5 preconditioning mode. ( A ) ultrasonic mixing, (B) magnetic stirring.
former is responsible for the concave part of the plot, Le., a slowing down of the reaction rate, while the second one helps to increase the overall reaction rate. Reactions 4 and 5 also account for the alkylation of PAN in the absence of catalyst. In fact, we have noticed the formation of NH,, especially when using the UM stirring mode, (Figure 51, and this NH, can generate tetrabutylammonium bromide by exhaustive alkylation with BuBr. 3.1. Kinetic Equations. To develop mathematical equations suitable for the rationalization of the kinetic model, it is better to rewrite eqs 1-5, taking into consideration the overall reaction deriving from the sum of eqs 4a and 4b but without the stoichiometric coefficients. The series of reactions can be summarized as follows, where MA is the monoalkylated product of PAN [Le., C6H,CH(Bu)CN] : PAN
+ BuBr
k I‘
OH
C6H5COO-+ Bu4N+Rr-
PAN t BuBr PAN
+ BuBr
k2
OH-:R&+
*
OH-:BU,N+
MA MA
+ NaOH 5 R,N + R(-H) + H,O k5 R,N + BuBr R3BuN+Br-
R4N+
(6)
-
(9) (10)
From reactions 6-10, the following kinetic equations can be derived, where the molar concentrations (moles/liter) of the different species are indicated in square brackets: -d[PAN]/dt = k,’[PAN][BuBr][OH-] + k,’[PAN] [BuBr] [R,N+] + k,‘[PAN] [BuBr][Bu,N+] (11)
d[Bu,N+]/dt = k,’[PAN][BuBr][OH-]
(12)
Then, considering all the quaternary species arising from the original catalyst (R,N+), one may derive (13) d[R,N+]/dt = k,’[R,N][BuBr] - k,’[R,N+][OH-] The concentrations of NaOH and BuBr can be considered as constant, since they still reflect the initial concentration
(17, (18)
Also eqs 11 and 13 can be rewritten using k , = k,’[BuBr][OH-] (19; h, = k2’[RuBr] (20, k 3 = k,’[BuBr] (211 On the basis of eqs 15 and 19-21, the original system of eqs 11-13 can be rewritten as follows: -d[PAN]/dt = h,[PAN] + h,[PAN][R,N+] + h3[PAN][Bu4N+](22a) d[Bu,N+]/dt = k,[PAN]
(2%)
+ Fe-Gt
[K,N+] = E
122c; These equations, with five parameters, constitute the general model. 3.2. Simplification of t h e Model. The general model (eqs 22a, 22b, and 22c) can be simplified if the catalyst (R,N+) has been preconditioned overnight with BuBr and NaOH (C, mode). In fact, in this case the concentration [R,N+] can be assumed to be equivalent to E (eq 16). Le., the value derived from eq 15 at t = a. Thus, the system of eqs 22a-c may be reduced to eqs 22a and 22b, replacing k2[R4N+]in eq 22a with ii,” = k2E. This model has just three parameters. Moreover, for the uncatalyzed reaction, only eqs 6 and 8 have to be considered, and the system of eqs 22a-c i s reduced to eqs 22a and 22b without the second term on the right side of eq 22a, since k , = 0. This model has two parameters. This last simplification of the model can be applied to runs in which soluble TBA (tetrabutylammonium chloride, Bu,N+Cl-) catalyst is used as the last component added to the reaction mixture. In that case, eqs 7 and 8 are the same, and only one need be considered; in addition, the amount of Bu,N+ formed in reaction 6 can be neglected since Bu,N+ salt is added as catalyst. On the other hand, the reaction rate of the first step is so much accelerated by the addition of TBA that it is possible to assume that [Bu,N+] is a constant. Therefore, eq 22a, with k , = 0 &e.. ignoring eq 7 ) and kg” = k3[Bu,N+], becomes -d[PAN]/dt = ( k , + ha”)[PAN] = KIPAN] (23 where k = k , + k,”. The integration of eq 23 produces -(ln (1 = kt (24 where y, the moiar conversion of PAN, is defined as = 1 - ([PAN]/[PAN],-,) ~
8
)
)
Ind. Eng. Chem. Res., Vol. 29, No. 5, 1990 923 Table I. Kinetic Constant and Related Activation Energies for Monoalkylation of Magnetic Stirrer (MS) catalyst stirring mode T,"C k2', min-' m o r 2 Lz 70 4.52 x 10-3 TBBA-TEG-PB UM 80 9.39 x 10-3 85 1.45 X 70 1.69 x 10-3 MS 80 3.78 x 10-3 TBBA-TEG-PB 85 5.55 x 10-3 40 2.11 x 10-1 TEBA UM 60 5.58 X lo-' 70 1.14 40 6.60 X TEBA MS 60 2.97 X lo-' 70 4.68 X lo-' N, number of constants in the model.
PAN Using an Ultrasonic Mixer (UM) or No
E , kcal/mol
rb
3
18.2
0.9995
3
19.3
0.9999
5
11.7
0.9923
5
14.2
0.9962
* r, Arrhenius correlation coefficient. ,
[PAN], being the initial concentration of PAN at t = 0. 4. Calculation Results The general model (eqs 22a-c) is effective in the C5mode (soluble catalyst added last) and has five constants (k&. A drastic simplification of the general model, which still generates very good results, is possible with TBA-soluble catalyst in the C5mode (eq 24). The runs using the C4 preconditioning mode for the catalyst (overnight with BuBr + NaOH, )) may be interpreted by a model with three constants (&, ki' = k2E,k3),whereas those with no catalyst can be interpreted by a model with two constants (kl,k3). In the C2 preconditioning mode, reaction 10 does not hold any longer, and the model is formally the same as that represented by the general system of eqs 22a-c, although only four of the constants (kl,kp,k,, k4) are operative, since k5 = 0. In our study, the system of eqs 22a-c and the relevant derived equations for the simplfied models were integrated by the four-order Runge-Kutta method, and then a nonlinear routine (Buzzi Ferraris, 1968) was applied to optimize the integrated values with respect to the experimental ones. For eq 24, a simple straight-line analysis was utilized. In Figures 5-7, we present some examples that compare the experimental profiles of the PAN conversion to those calculated by the appropriate theoretical model. In a previous paper (Ragaini et al., 1988) where we used a pseudo-first-order kinetic to analyze our experimental results, we found that the activation energies for the runs carried out with ultrasound mixing were about 10% lower than those obtained for analogous runs performed under conventional stirring modes. These results were also confirmed by the application of the more complete kinetic model reported in this paper (Table I).
5. Conclusions The kinetics of the PAN monoalkylation reaction involving BuBr in the presence of different PT catalysts and different preconditioning modes are well represented by the general system of eqs 22a-c, consisting of three equations, the first two of which are first-order differential equations. Such a system, which holds when catalyst is added as the last component to the reaction mixture (C, mode), can be simplified when the catalyst is preconditioned overnight with BuBr and NaOH(,, (C, mode) or with PAN and NaOH, ) (C,mode) or in the absence of any catalyst. If the butylation of PAN is performed in the presence of soluble TBA catalyst (Bu,N+X-) in the C5 mode, a very simple first-order rate equation gives a good interpretation of the experimental results (eq 24). The use of ultrasound mixing noticeably increases the reaction rate (Ragaini et al., 1988) and a t the same time
o
0.6
0.5 Calcd
04
03
.5 0.4
f6
Yr
0.2
0.2 0.1
0
C Time (min)
Figure 6. Calculated and experimental molar conversions of PAN (y) vs time: (A) a t 70 "C according to the model using three parameters (C, preconditioning mode); (B) a t 85 "C according to the model using two parameters for runs with magnetic stirring and no added catalyst.
0.2
./ /
0
A 1
0
30
I
60 90 Time (min)
120
150
Figure 7. Calculated and experimental molar conversions of PAN (y) vs time at 70 "C, using TEBA-soluble catalyst, the C6 preconditioning mode, and ultrasound mixing.
can provide high PAN conversions even in the absence of any catalyst, especially if some drops of aqueous ammonia
Ind. Eng. Chem. Res. 1990,29, 924-927
924
are added. This last result can be taken as further evidence of the utility of ultrasound effects in the preparative organic chemistry, including those cases where the reactions are performed under heterophase conditions and in fixed-bed reactors (Ragaini et al.. 1986, 1988). Nomenclature PTC = phase-transfer catalysis or phase-transfer catalyst(s) PAN = phenylacetonitrile BuBr = butyl bromide TEBA = triethylbenzylammonium chloride (solublecatalyst) TBBA-TEG-PB = tributylbenzylammonium chloride-benzyltetraethylene glycol-polymer bonded (insoluble catalyst) TBA = tetrabutylammonium chloride (soluble catalyst) C5 = no preconditioning of the catalyst, Le., the catalyst is the last component added to the reaction mixture C2 = preconditioning of the catalyst overnight at the reaction temperature with a mixture of PAN + NaOH(,,, (BuBr is added as the last component at the beginning of kinetic run) C, = preconditioning of the catalyst overnight at the reaction temperature with a mixture of BuBr + NaOH,q, (PAN is added as the last component at the beginning of kinetic run) UM = ultrasonic mixer (20 kHz) MS = magnetic stirring (about 1000 rpm) FB = fixed bed Registry N o . TEBA, 56-37-1; TBBA, 23616-79-7; TEG, 86259-87-2; C6H5CH2CN,140-29-4; BuBr, 109-65-9; NaOH, 1310-77-2: C,H,CH(Bu)CN. 5798-79-8
L i t e r a t u r e Cited Buzzi Ferraris, G. Quad. Ing. Chim. Ital. 1968,4, 171; 1968,4, 180. Dehmlow, E. V.; Dehmlow, S. S. Phase Transfer Catalysis; Verlag Chemie: Weinheim, 1980. Ley, S. V.; Loa, C. M. R. Ultrasound i n Synthesis; Springer-Veriag: Berlin, 1989. Mason, T. J.; Lorimer, J. P. Sonochemistry; Ellis Horwood: ChiChester, U.K. 1988. Ragaini, V.; Verzella, G.; Ghignone, A.; Colombo, G. Ind. Eng. Chem. Process Des. Deu. 1986, 25, 878. Ragaini, V.; Chiellini, E.; D’Antone, S.; Colombo, G.; Barzaghi, P. Ind. Eng. Chem. Res. 1988, 27, 1382. Riaz, S.A. Aldrichimica Acta 1988, 21, 31. Solaro, R.; D‘Antone, S.;Chiellini, E. J . Org. Chem. 1980,45, 4179. Suslick, K. S. Mod. Synth. Methods 1986, 4, 1. Suslick, K. S. Ultrasound. Its Chemical, Physical, and Biological Effects;VCH: New York, 1988.
* To whom correspondence should be addressed. Vittorio Ragaini,* Giovanni Colombo, Paolo Barzaghi Dipartimento di Chimica Fisica ed Elettrochimica Universitci di Milano, via Golgi 19 20133 Milano, I t a l y
Emo Chiellini, Salvatore D’Antone Dipartimento di Chimica e Chimica Industriale Universitci di Pisa, via Risorgimento 35 56100 Pisa, I t a l y Received for review April 5 , 1989 Accepted February 7 , 1990
A Method for the Determination of Dahlin’s Algorithm Parameters Equations for use in tuning the first-order Dahlin control algorithm are presented in this paper. T h e algorithm contains only one adjustable or tuning parameter (A) t h a t must be specified once the sampling interval and process parameters are determined. To obtain a n optimum value of A, tuning equations relating A t o t h e process time constant and sampling rate were developed. Over the years, several digital algorithms have been developed and are becoming popular in control systems. One of these control algorithms is the one developed by Dahlin (1968). This algorithm was developed to be used in processes with significant deadtime. Chiu et al. (1973) have studied the first- and second-order Dahlin algorithms by using a model of a jacketed backmix reactor. Condon and Smith (1977a) compared the Dahlin algorithm to continuous and discrete PID controllers. In another study, Condon and Smith (1977b) performed a sensitivity analysis on the algorithm. Development of t h e Control Algorithm A basic digital control loop is shown in Figure 1. Figure 2 is a simplified version of this control loop, which was used in the study presented here. The control element and the transmitter are incorporated in the process-transfer function. The process block diagram shown in Figure 2 can be analyzed (using z transforms) following a procedure analogous to the one used to study continuous systems. The analysis starts by relating Y ( z )and R ( z ) through the closed-loop pulse-transfer function: -Y (-z ) - D ( z ) H G k ) (1) R ( z ) 1 + D(z)HG(z) where Y ( z )is the z transform of the sampled function of the controlled variable, R ( z ) is the z transform of the sampled function of the controller’s set point, D ( z ) is the 0888-5885/90/2629-0924$02.50/0
controller’s pulse-transfer function, and HG(z) is the pulse-transfer function of the zero-order hold and process. Solving eq 1 for D ( z ) results in 1 Y(z)/R(z) (z) = D(z) = M E ( z ) HG(z) 1 - Y ( z ) / R ( z )
(2)
where M ( z ) is the z transform of the discrete controller’s output function and E ( z ) is the z transform of sampled error function. To completely develop the above control algorithm, the function HG(z) must be known and the functions Y(z)and R ( z ) must be specified. Equation 2 is referred to as the synthesis equation for a digital controller design. The basis of the Dahlin algorithm is that the closed-loop response to a step change in set point should be that of a first-order-plus deadtime (FOPDT). This closed-loop response in the Laplace domain is given by e-w
1
Y ( s ) = -Xs+ls
(3)
where to, is the deadtime of the closed-loop system and X is the time constant of the closed-loop system. In Dahlin’s article, to, is assumed to be an integer which is the approach number of the sampling time (T), used in this presentation. T o obtain HG(z), the process-transfer function G(s) must be determined; the form of G(s) used is that of a FOPDT. This transfer may be obtained from the openloop step response of the process (Smith, 1972). The step 1990 American Chemical Society
