Ind. Eng. Chem. Res. 1992,31,949-958 = chemical potential of component i 4 = dimensionless Gibbs energy of mixing or A,G(x)/RT Q = constant used in the EOS,Table I w = acentric factor, Table I pi
Subscripts
c = critical property e = equilibrium value i , j , 1, 2 = components i, j , 1, 2 k = a dimension in the hyperspace (n > 3) L1,L2,V = phase identification r = property divided by ita critical value, Table I Superscripts a, b = composition identification E = excess function I, 11, 111, IV = phase identification
Literature Cited Ammar, M. N.; Renon, H. The Isothermal Flash Problem: New Methods for Phase Split Calculations. AZChE J. 1987, 33, 926-939. Baker, L. E. Private communication, May, 1989. Baker, L. E.; Pierce, A. C.; Luke, K. D. Gibbs Energy Analysis of Phase Equilibria. SOC.Pet. Eng. J. 1982 (Oct), 731-741. Barrufet, M. A.; Eubank, P. T. New Physical Constraints for Fluid Mixture Equations of State and Mixture Combining Rules. Fluid Phase Equilib. 1987,37,223-240. Cairns, B. P.; Furzer, I. A. Multicomponent Three-phase Azeotropic Distillation. Part 11. Phase-Stability and Phase-Splitting Algorithms. Ind. Eng. Chem. Res. 1990,29,1364-1382. Elhaeean,A. E. New Methods for Phase Equilibria and Critical Point Calculations. Ph.D. dissertation in chemical engineering, Texas A&M University, College Station, TX, May 1991. Eubank, P. T.; Barrufet, M. A. A Simple Algorithm for Calculations of Phase Separation. Chem. Eng. Educ. 1988 (June), 36-41.
949
Fussell, D. D.; Yanosik, J. L. An Iterative Sequence for PhaseEquilibria Calculations Incorporating the Redlich-KwongEquation of State. SOC.Pet. Eng. J. 1978 (June), 173-182. Gautam, R.; Seider, W. D. Computation of Phase and Chemical Equilibrium. Part I. Local and Constrained Minima in Gibbs Free Energy. AZChE J. 1979,25,991-999. Heidemann, R. A. Three-phase Equilibria Using Equations of State. AZChE J. 1974,20,847-855. Michelsen, M. L. The Isothermal Flash Problem. Part I. Stability. Fluid Phase Equilib. 1982a,9,1-19. Michelsen, M. L. The Isothermal Flash Problem. Part 11. PhaseSplit Calculation. Fluid Phase Equilib. 1982b,9,21-40. Nghiem, L. X.; Aziz, K.; Li, Y. K. A Robust Iterative Method for Flash Calculations Using the Soave-Redlich-Kwongor the PengRobinson Equation of State. SOC.Pet. Eng. J. 1983 (June), 521-529. Null, H.R. Phase Equilibrium in Process Design; Wiley: New York, 1970; pp 98-102. Radzyminski, I. F.; Whiting, W. B. Fluid Phase Stability and Equations of State. Fluid Phase Equilib. 1987,34, 101-110. Risnes, R.;Dalen, V. Equilibrium Calculations for Coexisting Liquid Phases. SOC.Pet. Eng. J. 1984 (Feb), 87-96. Sahimi, M.; Davis, H. T.; Scriven, L. E. Thermodynamic Modeling of Phase and Tension Behavior of C02/Hydrocarbon Systems. SOC.Pet. Eng. J. 1985 (Apr), 235-254. Soave, G. Equilibrium Constants from a Modified Redlich-Kwong Equation of State. Chem. Eng. Sci. 1972,27,1197-1203. Swank, D. J.; Mullins, J. C. Evaluation of Methods for Calculating Liquid/Liquid Phase-Splitting. Fluid Phase Equilib. 1986,30, 101-110. Trangenstein, J. A. Minimization of Gibbs Free Energy in Compositional Reservoir Simulation. SOC.Pet. Eng. J. 1985 (Sept), 233-246. Wagner, Z.; Wichterle, I. High Pressure Vapor-Liquid Equilibrium in Systems Containing Carbon Dioxide, 1-Hexene,and n-Hexane. Fluid Phase Equilib. 1987,33,109-123. Received for review June 10,1991 Accepted October 17,1991
An Improved Reaction System To Investigate Micromixing in High-Intensity Mixers John R. Bourne, Oemer M. Kut, and Joachim Lenzner* Technisch-Chemisches Laboratorium, ETH, CH-8092 Zurich, Switzerland
The diazo coupling between 1-naphthol and diazotized sulfanilic acid a t room temperature and pH
9.9 has been widely used to study the influence of mixing on the product distribution of fast chemical reactions. It is sufficiently fast for application in mixers whose rates of turbulent energy dissipation do not exceed 200-400 W-kg-'. Alternative reactions have been screened with a view to studying interactions between mixing and reaction in higher intensity mixers. Extension of the existing system to the simultaneous couplings between 1- and 2-naphthols and sulfanilic acid is recommended. Analpis by spectrophotometry was carried out, and extinction coefficients are tabulated. The kinetics of the five possible reactions have been studied, and second-order rate constants are given. This extended system should be suitable for energy dissipation rates in aqueous solutions up to about lo6 W0kg-l. Both reaction systems were run under semibatch conditions in a stirred tank reactor, and the applicability of the extended reactions was confirmed.
1. Introduction Micromixing exerts usually a strong influence on the product distribution of fast multiple chemical reactions. T h e relative proportions of mono- and bisazo dyes formed *Author to whom correspondence should be addressed. Present address: Department of Chemical Engineering, Swiss Federal Institute of Technology Ziirich, Universitiitsstr. 6, CH-8092Ziirich, Switzerland.
b y coupling 1-naphthol and diazotized sulfanilic acid i n alkaline aqueous solution has been i n use for over a decade as a means of characterizing the micromixing performance of various reactors. The necessary analytical method and the reaction kinetics are available (Bourne et al., 1990). The determination of the energy dissipation rate e i n the mixing and reaction zone-starting from the measured product d i s t r i b u t i o n and a m a t h e m a t i c a l model of micromixing-has been explained, and some limits of resolution of t h i s method have been given (Bourne and 1992 American Chemical Society
950 Ind. Eng. Chem. Res., Vol. 31, No. 3, 1992
Table I. Values of Turbulent Energy Dissipation Rates Detectable with the Former (1-Naphthol/Diazotized Sulfanilic Acid) Test Reaction Wskg-' ~ ~ = 6 0~ , = 5 0 m01.m-3 m01.m-3 511 736 30.8 44.4 367 255 15.1 21.7 219 152 12.8 8.9 t,
xs
iG
0.03 0.03 0.04 0.04 0.05 0.05
3.166 X 2.681 X 4.483 X 3.835 X 5.801 X 4.988 X
C Y
20 100 20 100 20 100
Maire, 1991a). Since a chemical reaction becomes mixing-controlled if its half-life is on the order of or smaller than that of the mixing process, the product distribution of multiple reactions will only depend upon the mixing intensity-here expressed through the rate of dissipation of the kinetic energy of turbulent velocity fluctuations, t-over a particular range of e. At higher t values, product distribution is determined by the reaction kinetics, whereas some other asymptotic product distribution, no longer responding to changes in mixing intensity, results when t is below the useful range. Table I refers to coupling 1-naphthol,Al, and diazotized sulfanilic acid, B, in dilute aqueous solution at 298 K and pH 9.9 (Bourne et al., 1990). The initial stoichiometric ratio of A1 to B was Y~ = 1.2 A semibatch reactor was considered where the feed rate of B is so low that it does not influence the product distribution XS, defined by xs = C0.R + 2% (1) Cp-R + 2cs One part by volume of B-rich feed (concentration cm) was added to a! parts by volume of less concentrated A-rich solution in the reactor. With given operating conditions, the energy dissipation rates, e, and Damkohler numbers, E, corresponding to measured product distributions, XS, were calculated using the engulfment model of micromixing, as explained earlier (Bourne and Maire, 1991a). The analytical error in determining XS spectrophotometrically is approximately i0.005,which implies that XS should be in excess of 0.04 or 0.05 for accurate determination of e. From Table I it follows that the upper limit of resolution of e is about 300 Wnkg-'. Approximate values of the maximum rates of energy dissipation range from 5 W-kg-' in centrifugal pumps and tubular reactors through 50 W*kg-' in stirred tanks to lo00 W-kg-l in static mixers and 5000 W-kg-' in rotor-stator devices. The 1-naphthol coupling is too slow to characterize micromixing in high-intensity devices like certain designs of static mixer (Bourne and Maire, 1991b) and rotor-stator machines. Still higher intensities have been reported in producing emulsions (Davies, 1987) with local t values ranging from 10 to lo9 Wskg-'. Whether rapid contacting of miscible reagents in such emulsifiers would be successful is unknown-e.g., do the locally high t values persist long enough to achieve complete micromixing?but it is clear that high-intensity mixers cannot be adequately investigated with the 1-naphtholJdiazotized sulfanilic acid coupling in aqueous solution. It is the purpose of this contribution to offer the faster chemistry needed to characterize some high-intensity mixers. After discussing various possible reactions, a simple extension of the existing diazo couplings will be recommended. 2. Designing a Suitable Test Reaction System 2.1 General Considerations. Rapid reactions whose product distributions are mixing-controlled require com-
petitive steps. These occur in the following competitiveconsecutive (2) and competitive (or parallel) (3) schemes: kl
A+B-R
kz
R+B-S
(2)
kl
Al+B-P
A2+Bka-Q (3) Characteristics which are sought in test reactions include the following: 1. Rapid, irreversible, second-order kinetics with few (preferably two) products and no side reactions are desirable. 2. Rate constants should not differ too widely if it is required to detect differences in product distribution relative to the chemical regime; e.g., for the 1-naphthol coupling k l / k 2 = 6500 (Bourne et al., 1990), so that XS C 0.001 in the slow regime, which can be approached at high mixing intensities. Such a small XS value is however below the analytical resolution (f0.005). Rate constants differing by approximately 2 orders of magnitude are suitable. 3. A routine, inexpensive, and accurate instrumental analytical method is sought. 4. Low concentrations of highly reactive reagents, which should be directly available on the market and sufficiently pure that they require no further purification, are sought. 5. Water is the preferred solvent, and the solubilities of reagents and products should be known and not exceeded in micromixing measurements. Adequate solubility allows variations in concentrations and volume ratios, CY, which are important experimental variables. The viscosity has been increased through addition of less than 1wt ?A (carboxymethyl)cellulose,although this additive is not ideal (Bourne and Maire, 1991b). 6. Hazards (fire, explosion, toxicity, corrosion, volatility, effluent disposal, etc.) must be considered. A potential test reaction will only be practically useful if its hazards can be reduced to an acceptable level by simple and cheap measures. 23. Screening of Some Potential Reactions. Several aromatic nitrations exhibit mixing-controlling product distributions (Schofield, 1980). The simultaneousnitration of benzene and toluene using a nitronium salt with tetramethylene sulfone as solvent (Tolgyesi, 1965) corresponds to eq 3. These nitrations are too slow for the characterization of high-intensity mixers, and it would be necessary to change its reagents A1 and .42 to mesitylene and durene, for example. Moreover, the solvent- and similar solvents, e.g., nitromethane for single-phase nitrations-and other hazards of nitration would greatly complicate routine use of these reactions in industrial-scale mixing tests. In section 2.1 the points 1,5, and 6 present serious problems with respect to nitrations. The simultaneous reduction of cobalt complexes (A1 and A2) using a limited amount of chromous ion (B) is mixing-controlling at low agitation intensities (Wood and Higginson, 1966). The complexes have to be prepared and must be stored and used in the absence of oxygen, e.g. under N2.The rate constants depend strongly upon ionic strength. Problems with points 1,4 and 6 (effluent disposal) make this system unattractive. The competition between the precipitation of iron hydroxides from ferric sulfate (Al) by sodium hydroxide and the alkaline hydrolysis of ethyl monochloroacetate (A2) is influenced by mixing (Baldyga and Bourne, 1990). The hydrolysis is however too slow (half-life around 0.3 s) to
Ind. Eng. Chem. Res., Vol. 31, No. 3, 1992 951 Table 11. Listing of Possible Reaction Systems reagent 1 reagent 2 crit Dointan 1-naphthol-6-sulfonic acid p-nitroaniline 2-nitro-p-anisidine p-nitroanilinel,&dihydroxynaphthalene sulfanilic acid 2-nitroaniline4-sulfonic acid p-nitroaniline 2,7-dihydroxynaphthalene 2, 4, 5 2-nitroaniline4-sulfonic acid sulfanilic acid l&dihydroxynaphthalene-3,6- p-nitroaniline 1, 2, 5 2-nitro-p-anisidine disulfonic acid sulfanilic acid 1,7-dihydroxynaphthalene 1, 3 2-nitroaniline4-sulfonic acid sulfanilic acid 2,3-dihydroxynaphthalene 5, 6 2-nitroaniline4-sulfonic acid p-nitroaniline 2-hydroxynaphthalene-62-nitro-p-anisidine sulfonic acid sulfanilic acid 2,6-dihydroxynaphthalene sulfanilic acid 1-hydroxy-2-naphthoic acid 2-nitroanilinewith 2-naphthol 4-sulfonic acid sulfanilic acid 3-hydroxy-2-naphthoic acid 1, 6 2-nitroanilinewith 2-naphthol 4-sulfonic acid sulfanilic acid 2-naphthol-6-sulfonic acid 1, 2 with 2-naphthol no crit sulfanilic acid 1-naphthol with 2-naphthol points OCritical points are 1, impurity; 2, rate constants too low; 3,too many isomers/unwanted side reactions; 4, insolubility in water; 5, steric problems with secondary coupling; 6, instability.
achieve competition in a high-intensity mixer. The analysis is not routine and instrumental. Precipitation might influence the fine scale turbulence structure in the reaction zone. Difficulties occur with points 1 , 2 (k,>> kJ, 3, and 5 of section 2.1. Whereas the primary coupling between 1-naphthol (A) and diazotized sulfanilic acid (B) is sufficiently fast (k,in eq 2 = 1.3 X lo4 m3.mol-ld), the secondary coupling is too slow (k, S= 2 m3.mol-'d) for high-intensity mixers (refer to Table I). One modification of this system omitted the deactivating sulfonic acid group on the diazonium ion to give the coupling between 1-naphthol and diazotized aniline (Garcia-Rosa and Petrozzi, 1990). Although this reaction is mixing-controlled a t low agitation intensities, lower solubility and lower primary reaction rates resulted (section 2.1, points 1 and 5). A nitro group in the aromatic diazonium ion would increase its electrophilic property and so raise k, and k2 in eq 2. The simultaneous introduction of a sulfonic acid group in either the diazonium ion (B) or the coupling component (A) would raise the solubility and possibly shorten the half-life of the diazo couplings. Systems such as either 2-nitroaniline-4-sulfonic acid with 1-naphthol or p-nitroaniline with 1-naphthol-6-sulfonic acid could be considered. Unfortunately, only 1-naphthol is available in sufficient purity (section 2.1, point 4). Modifications to the existing diazo coupling to increase k2 without decreasing kl and to raise solubility do not seem to be promising. In the place of naphthol and aniline derivatives, couplings between either naphthyldiazonium ions with naphthol derivatives or phenyldiazonium ions with phenyl derivatives were also considered. Such reactions are associated with large numbers of isomeric products, which would greatly complicate the chemical analysis. Table 11contains diazo couplings, which were considered as possible test reactions to assess high-intensity mixers,
+ A1
A2
B
Figure 1. Representation of the new test reaction system.
and indicates where problems occur: the numbers refer to the six points in section 2.1. The result of this screening was to choose the simultaneous coupling of 1- and 2-naphthols with diazotized sulfanilic acid for detailed evaluation.
3. Characteristics of the Simultaneous Diazo Coupling of 1- and 2-Naphtholswith Diazotized Sulfanilic Acid 3.1. Introduction. Figure 1shows the five reactions which can occur. The first four, referring to 1-naphthol and its derivatives, including the reaction kinetics, have already been studied (Bourne et al., 1990). The fifth, referring to 2-naphthol, exhibits no isomer and no bisazo dye (see section 3.8), and it requires characterization with respect to reaction kinetics (k3) and chemical analysis. Then the capacity of the whole system in Figure 1 to measure high rates of turbulent energy dissipation must be evaluated. 3.2. Solvent. As before (Bourne et al., 1990), the solvent is an aqueous solution at 298 K containing 111.1 rn~l-m-~ each of sodium carbonate and sodium bicarbonate. The ionic strength is 444.4 m ~ l * r nand - ~ the pH is 9.9. 3.3. pK Values. The pK values of the compounds in Figure 1are Al, 9.36; A2, 9.54; B, 10.48 ((pK1+ pK2)/2); o-R,9.17; p R , 8.26; S, 7.57; and Q, 11.3. Further details, including experimental results, are available (Lenzner, 1991). 3.4. Extinction Coefficients of 1-and 2-Naphthols. 1-and 2-Naphthols (Merck 6223 and 6234) were dissolved in turn, and their extinction coefficients were determined and stored in a diode array spectrophotometer (HewlettPackard 8452 A with Workstation 9153 C). Table I11 contains these results, which enable mixtures of these two reagents to be analyzed prior to reaction. Although the shift between these spectra is relatively small, a two-component analysis allowed initial concentrations of A1 and A2 to be checked.
952 Ind, Eng. Chem. Res., Vol. 31, No. 3, 1992 Table 111. Molar Extinction Coefficients of the Naphthols at T = 25 O C , I = 444.4 mol*mJ, and pH 9.9 m2.mo1-' nm 2-naphthol 1-naphthol 1314.20 250 908.24 1107.30 252 624.25 737.66 254 462.03 424.20 256 378.58 240.58 258 345.05 153.72 260 340.80 118.55 262 349.03 106.47 264 359.37 104.64 266 373.00 107.82 268 397.25 113.71 270 429.34 121.59 272 454.32 131.09 274 462.15 142.19 276 462.17 154.77 278 469.56 168.19 280 492.90 181.96 282 508.96 284 486.76 195.96 210.35 438.32 286 226.18 387.79 288 243.50 356.75 290 261.64 292 348.41 280.44 319.22 294 298.26 252.98 296 313.76 179.54 298 330.27 123.77 300 348.81 302 90.94 368.00 304 76.16 390.91 306 72.77 417.14 308 76.20 437.16 310 83.36 454.73 312 93.33 475.27 314 103.82 496.60 316 113.44 A,
c,
A,
nm 318 320 322 324 326 328 330 332 334 336 338 340 342 344 346 348 350 352 354 356 358 360 362 364 366 368 370 372 374 376 378 380 390 400
m2.mo1-l 2-naphthol 1-naphthol 517.02 122.35 131.81 541.99 142,55 566.14 568.80 155.22 563.24 169.71 566.46 183.18 191.52 577.51 586.75 193.94 193.63 581.45 554.98 193.64 510.28 194.87 456.27 196.93 198.95 400.89 200.34 348.74 200.38 301.46 259.16 198.63 221.25 194.01 187.67 185.80 157.86 173.62 131.49 157.84 108.23 138.85 88.15 118.31 72.22 98.57 56.62 78.78 61.33 44.84 35.12 46.51 27.23 34.31 21.06 24.81 16.23 17.53 12.42 12.35 9.60 8.66 7.25 6.02 2.23 1.25 1.01 0.70 c,
Table IV. Molar Extinction Coefficients of 2-Naphthol Monoazo Dyestuff at T = 25 "C,I = 444.4 mol m-*,and pH 9.9 A, nm
400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550
e,
m2.mo1-l 838.25 923.16 991.26 1058.81 1186.84 1397.11 1656.65 1927.88 2115.22 2105.14 1989.20 1793.69 1373.63 807.63 381.59 170.96
A, nm
c,
560 570 580 590 600 610 620 630 640 650 660 670 680 690 700
m2-mo1-l 93.11 53.04 36.59 9.89 14.14 12.6 9.78 0.0 0.0 0.0 0.0 3.04 0.0 0.25 0.0
agitation and waiting 30 min before analysis. The orange - ~ spectrosolution was diluted to some 0.04 m ~ l - m for photometric measurements. The absorption spectra of all three solutions were identical, and no evidence of bisazo dye was found. Using HPLC, no peaks indicating isomers or bisazo dye were observed. 3.9. Reaction Kinetics. Stopped-flow measurements with absorption detection at 490 nm were carried out as before (Bourne et al., 1990). The mean and standard deviation of k, in four runs were
k3 = 124.5 f 1.0 m3-rnol-'.s-'
(4)
The values for the primary couplings of 1-naphthol (Figure 1) were
kl, = 921 f 31 m3-mol-1.s-1 3.5. Preparation of 1-[(4'-Sulfophenyl)azo]-2naphthol (Q). A sample of 17.3 g (0.1 mol) of sulfanilic acid (Merck 686) was diazotized and added dropwise at room temperature to 14.42 g (0.1 mol) of 2-naphthol which was dissolved in 150 mL of ethanol and stirred. Precipitation of the dye was induced by adding sodium chloride. After washing with a little acetone, the dye was purified by triple recrystallization from water. 3.6. Identification of Q. Identification and determination of purity were carried out by HPLC analpis, thin film chromatography, spectrophotometry, elementary analysis, atomic absorption spectroscopy, and 'H NMR. Elementary analysis confirmed that the dye crystals were the monosodium salt having a molar mass of 350.28 gmol-l and a purity in excess of 99.5%. The dye Q (C.I. Acid Orange 7) is classified as nongenotoxic, and a carcinogenic effect has not been indicated. A specific toxicity of 2naphthol (mutagenesis, carcinogenesis) has not been reported (ETAD, 1990). 3.7. Extinction Coefficients of Q. Table IV gives the measured extinction coefficients for Q in the solvent (refer to sections 3.2 and 3.4). The maximum value was 2138.2 m2*mol-' at 484 nm. The maxima of the monoazo dyes formed from 1-naphthol occurred near 510 nm (Bourne et al., 1990). Sufficient differences in the spectra were available to resolve Q from o-R and p-R (see below). 3.8. Formation of 8: Isomers, etc. In the coupling of 2-naphthol with diazonium ions only one monoam dye, coupled in the 1-position, has been observed and would be expected based on the three possible mesomers of 2naphthol (Saunders, 1985). As a further confirmation, 1 equiv of 2-naphthol was coupled with (a) 0.5, (b) 1.2, and (c) 1.6 equiv of diazotized sulfanilic acid using intensive
and
k l p = 12238 f 446 m3.rnol-'d
(5)
while for the secondary couplings (Figure 1)
kzo = 1.835 f 0.018 m3.mol-1.s-1 and
k, = 22.25 f 0.25 m3*mol-'d
(6)
These five second-order rate constants refer to stoichiometric reagent concentrations (e.g., 1-naphthol),not to the reactive ionic species (e.g., 1-naphtholate anion). Conversion to this basis may be made using the pK values in section 3.3 if required. 3.10. Solubilities. Under the conditions pertaining here, the solubility of diazotized sulfanilic acid is at least -~ 70 m ~ l - m - ~For . 1-naphthol values of 0.3 m ~ l - r n (Lauer, 1937) and 9.09 m~lmm-~ (Bourne and Tovstiga, 1985) and for 2-naphthol values of 0.536 m ~ l - r n (Lauer, -~ 1937) and 5 m ~ l - m (Knox -~ and Richards, 1919) have been published for distilled water at 25 "C. It was observed that both naphthols are soluble up to at least 5 m ~ l - m - ~A. total naphthol concentration not exceeding 5 mol~m-~ is recommended when using the test reaction system. The dyes were also soluble under these conditions. 4. Application of Improved Reaction System To
Investigate Micromixing 4.1. Introduction. The reaction system (Figure 1)may also be written as A1 + B A1 + B
klo
kIP
0-R
(7)
p-R
(8)
-
+ kzP p-R + B -!% O-R B
Ind. Eng. Chem. Res., Vol. 31, No. 3,1992 953
S
.reactor geometry
.chemical test system
- initial concentrations - volume ratio - feed time
S
~
rate constants
A2+Bkl-Q The product distribution of the compet.,.Je, consecutive part is then defined (compare eq 1) as
nnalrrk
.modelling of reaction zone -initial values of E ( W k g ) - experimental conditions
.method
. measure the concentrations
while that of the competitive (or parallel reaction) part may be defined as
The initial stoichiometric ratio of l-naphthol (Al) to diazonium ion (B) is YA1 = NAIO/NBO (14) while that of 2-naphthol (A2) to l-naphthol is
E = NA20/NA1
(15)
0
(It follows that the initial molar ratio of 2-naphthol to dediazonium ion is fyA1.) The Damkohler number E, fined as before (Bourne and Maire, 1991a) by
D a = E k20CB0 ( l + a) is a ratio of characteristic times for micromixing by eddy engulfment (Baldyga and Bourne, 1989, 1990) and for chemical reaction. The engulfment rate coefficient E is related to the turbulent energy dissipation rate e through
E = 0.058(e/~)O.~
(17)
The engulfment model of micromixing may be applied when Sc > cA0 and relates product distribution (XS’ and XQ) to mixing intensity (E) for given reactions (Baldyga and Bourne, 1989). Thus XS’ (or XQ) = f(kinetics, 7~1,E, a) (18)
z,
The specific case here will be running reactions 7-11 a t 25 OC and with I = 444.4 mol.mg (pH 9.9) in a semibatch reactor with slow feeding. The product distributions XS’ and XQ will be measured and e will be deduced from the micromixing model as shown in Figure 2. Analogous to Table I, the maximum rate of energy dissipation which can be determined using the improved reaction system will be found by simulation. Then experimental results for a stirred tank reactor will be given where e has been determined from the former l-naphthol system as well as from the extended diazo coupling (1- and 2-naphthols). 4.2. Product Distribution in the Chemical (Slow Reaction) Regime. With increasing mixing intensity XS’ and XQ will tend to asymptotic values which no longer depend on E but which can be calculated directly from the reaction kinetics and the stoichiometric ratios. Such calculations serve as a check on the numerical integration of the micromixing model and offer a rapid orientation as to how small XS’ and XQ can possibly become. From eqs 5 and 6 the rate constant for any primary coupling of l-naphthol greatly exceeds that for the corresponding secondary coupling. With yA1> 0.5 or more conservatively >1, little S should be formed in the chemical regime. (This will also be evident in setion 4.4.) Equations 9 and 10 will therefore be neglected and eqs 7 and 8 may be summed
%=(LE) cAl 0 K
= kl/k3
(24)
After introducing the overall maw balances omitting S for the reactions in eqs 11 and 19, and defining the dimensionless unreacted concentration of 2-naphthol by = cA2/cA20
(25)
= 1+ 5 - 1/YA1
(26)
x is the solution of
z“+
Numerical solution for given kinetics (24) and given stoichiometricratios (14) and (15) yields x and hence, from the overall balance for eq 11, the concentration of product Q. The concentration of R then follows from the overall balance for eq 19. XQ is then calculated from eq 13. Minimum values of XQ when yAl = 1.2, K = 106 (from eqs 4 and 5) and E = 1, 3, and 5 were 0.019, 0.053, and
954 Ind. Eng. Chem. Res., Vol. 31, No. 3, 1992 Table V. Influence of Volume Ratio a on Values of Energy Dissipation Rates Attainable with Extended Test System for 4 = 1 t, W-kg-' -:
-+
XQ 0.04 0.04
'"I
CBO = 41.6 m01.m-3 106580
CBO
=
60 m01.m-3 26 195
~~
5 1 0 . ~ 10"
IO
Figure 3. Influence of the stoichiometric ratio 5 on XS' and XQ in a semibatch reactor without self-engulfment. Operating parameters are yA = 1.2 and (Y = 20. The arrows on the ordinates show the asymptotic product distributions of the new test system. t .C
-5
10
-4
10
-3
10
.2
10
0
-1
10
10
Da
Figure 4. Influence of the volumetric ratio (Y on XS' and XQ in a semibatch reactor without self-engulfment. Operating parameters are yA = 1.2,OL = 20,and OL = 100. The arrow on the ordinates show the asymptotic product distributions of the new test system.
0.082, respectively. They are plotted in Figures 3 and 4. 4.3. Product Distribution in the Fully Mixing Controlled (InstantaneousReaction) Regime. When the mixing rate is very low relative to the potential reaction rate, intense segregation of reactants occurs and the product distribution attains another asymptotic value, where again XS' and XQ become independent of t. The intermediates o-R and p-R are fully converted to secondary product S in this regime, so that eqs 7-10 become A1 + 2B = S (27) A2+B=Q (11) Reaction rates in the instantaneous regime depend only on collision frequencies, which in turn are proportional to concentrations (Baldyga and Bourne, 1990). Therefore -dCAl - - -C A l dCA2
cA2
and, when t ' 0 , cA2 = &A1 , from eq 15. The solution of eq 28 is cA2 = {cAl. Introducing the overall balances for eqs 11and 27, when the limiting reagent B has been consumed, and using the definition (13) when c,R = cpR = 0, XQ in the instantaneous regime is given by XQ = t / ( t + 2) (29) As expected, this is independent of yA1. When { = 1,3, and 5, XQ becomes 0.333,0.6, and 0.714, respectively. Also these asymptotes are plotted in Figures 3 and 4. From the
~ m ~ ) . m o l * m - ~ Ei 41.6 1.8246 X lo-' 20.83 9.4190 X 13.88 6.0190X
XQ0.04 0.08 0.105
1 3
5
Fa
-6
20 100
Da 1.8246 X 10"' 1.1037 X 10"'
Table VI. Values of Energy Dissipation Rates Detectable with Extended Test System for E = 1.3. and 5
1 0 . ~ 10.~ 1 0 . ~
10
-
a
a em,-
W-kg-' 106580 100274 109 031
t,
describes the maximum concentration of feed stream B, cA1 + cA2 < 5 m ~ l . m - ~ is, obeyed.
so the constraint,
definition (12) and (13) it follows that XS' = 1 - XQ in this regime. 4.4. Product Distribution in the Mixing-Controlled (Fast Reaction) Regime. Simple calculations, as for the asymptotic product distributions in the slow and instantaneous reaction cases, are not possible here. The engulfment micromixing model is used here again (Bourne and Maire, 1991a) to calculate XQ and XS' as functions of E, a,and 5 when yA1= 1.2 (refer to eq 18) in the fast regime, where both kinetics and micromixing control product distribution. Figures 3 and 4 show how XQ and XS' vary with % when a and 5 respectively are held constant. Both measures of product distribution vary from a slow reaction regime (%< lob), where XS' < 0.001 (refer to section 4.2), through the fast regime, where XS' and XQ depend to the instantaneous regime, where XQ strongly on becomes independent of E. Unlike the case of two parallel reactions (Baldyga and Bourne, 1990),XQ does not necessarily vary monotonically between its values in the chemical and instantaneous regimes. For example, when 5 = 1these limits are 0.019 and 0.333. When a = 20, XQ exhibits a maximum (0.383) at E = 0.2 and decreases to the asymptotic value (0.333) as E continues to increase. Such maxima are not evident in Figures 3 and 4, which employ doublelogarithmic coordinates. Because XQ varies slowly and not monotonically in this high& region, it should be avoided in micromixing determinations. Maximum sensitivity is attained in the steep part of Figures 3 and 4. Table V and Figure 4 refer to 5 = 1. In the table the total naphthol concentration does not exceed 5 m~l.m-~. Spectrophotometric determination of XQ gives adequate resolution down to XQ = 0.04. Table V gives the Damkohler numbers and energy dissipation rates corresponding to this product distribution when operating a semibatch reactor at the feed concentrations and volume ratios in the table. Figure 4 shows that XS' = 0.002, which is below ita analytical limit of resolution, so that the whole system (7)-(11) is behaving like two parallel reactions (11) and (19), which are influenced by mixing. Suppression of the formation of S at high mixing rates not only simplifies the reaction system but also limits possible, incompletely characterized side reactions involving S (Bourne et al., 1990). Table VI and Figure 3 refer to a = 20. In the chemical regime (extremely high mixing intensity) the limiting values of XQ weie 0,019, 0.053, and 0.082 when the naphthol ratios were 1,3, and 5, respectively. In Table VI
z,
Ind. Eng. Chem. Res., Vol. 31, No. 3, 1992 955
1
/
1
-6
10
-5
10
.3
.4
10
10
Da
H
t -2
10
0
.1
10
10
-
Figure 5. Comparison between former (XS; 5 = 0) and extended (XQ; 5 = 1,3, and 5) reaction systems. Operating parameters are YA = 1.2 and LY = 20.
minimal values of XQ, which can be resolved analytically with adequate accuracy (10.005) and which significantly exceed the limiting values in the chemical regime, are considered. The energy dissipation rates corresponding to the tabulated experimental conditions are then on the order of 106 W-kg'. Figure 3 shows that XS' is then below its analytical limit, the more so the higher 4 becomes (Le., as 2-naphthol increasingly competes for diazonium ions). Again the whole system behaves like two parallel reactions (11)and (19). Figure 5 refers to a = 20 and as before to yA1= 1.2. The coupling of 1-naphthol alone (E = 0) (Bourne et al., 1990) is represented by the curve XS, defined in eq 1. The simultaneous coupling of 1-and 2-naphthols is represented at three stoichiometric ratios 4 by the curves XQ. Assuming that XS can be accurately determined down to 0.05, then the smallest value of E and the highest energy dissipation rate which can reliably be determined are 5.8 X and 220 Wskg', respectively. The extended reaction system exhibits adequate sensitivity of XQ down to = lo4, which allows c = lo5 W0kg-l (Table VI) to be determined. By accelerating the reactions, it is possible to study higher intensity mixing than with the diazo coupling of 1-naphthol alone. 4.5. Experiments with Former and Extended Test Reactions in a Stirred Tank Reactor. 4.5.1. Description of Apparatus. The 2.5-L reactor shown in Figure 6 was employed, including four wall baffles and a six-bladed Rushton turbine. The direction in which fresh feed is transported after leaving the upper ( 0 ) and lower (u) feed points was traced as follows. Sodium hydroxide containing phenolphthalein was added in turn at each feed point to less concentrated hydrochloric acid in the tank. The acid and base concentrations corresponded to those of the naphthols and the diazonium ion during the subsequent couplings. For the lower feed point (u) reacting fluid was drawn into the impeller and radially discharged from it. Red fluid was observed to persist in the radial discharge for distances of 0.01-0.02 m from the impeller tip. The distance from the tip to the wall was 0.044 m. As in earlier observations using neutralizations (Rice et al., 19641, reaction took place near the impeller and did not extend to the wall. Strong gradients in the energy dissipation rate exist near the impeller, whereas c is much lower, but more uniform near the upper feed point (0). Reacting fluid rotated and moved axially toward the turbine in these upper regions: red fluid disappeared over an axial distance between 0.02 and 0.05 m and spread out transversely by about 0.015 m. Neutralization was always completed before fluid reached the impeller (distance from
D
dl
c
Figure 6. Stirred tank (2.5 L). The feed pipe consists of a PVC tube (inner diameter = 0.0008m), which ia fitted into a stainless steel tube. Two feed points were chosen (upper feed point (o), 0.133 m, and lower feed point (u), 0.053 m above tank bottom). The other dimensions are D = 0.14 m, H = 0.28 m, d l = 0.014 m, d2 = 0.01 m, d3 = 0.052 m, h l = 0.1154 m, h2 = 0.047 m, h3 = 0.1094 m, and h4 = 0.0294 m. The radial distance between stirrer shaft and each feed point w a ~0.0133 m. .L
0.25
*
+
+
+
+ +
0.20* , ?n
-
3 0.15-
%
0
+
0.10.
0.00
0
XS' XQ
1
1000
2000
feed time
3000
4000
[SI
Figure 7. Experimentaldetermination of the critical feed time using the upper feed point ( 0 ) and the extended reaction system. Operating parameters are a = 50, 5 = 1, YA = 1.2, cgg = 2 m~l.m-~, and stirrer speed = 240 rpm.
feed point o to impeller was 0.08 m). 4.5.2. Determination of Critical Feed Time. To ensure that only micromixing influences the product distributions XS and XQ, the critical feed time was determined for each feed point. For the lower feed point (u) XS was measured for various feed times when a = 50, yA1 = 1.1, N = 249 rpm, and cBO = 60 m ~ l m - ~XS . became independent of feed time when more than 900 s was employed. A simple correlation for the critical feed time for feed points located in the radial impeller discharge (Bourne and Thoma, 1991) predicted 480 s. Feed point u was located in the impeller suction, and a feed time of 900 s was choaen for all subsequent couplings. The feed rate was kept constant and checked gravimetrically (Lemer, 1991). For the upper feed point (0)Figure 7 shows how XS' and XQ varied with feed time when the extended test reactions were used (yA1 = 1.2,4 = 1, a = 50, N = 240 rpm, and cm = 2 m~l.m-~). Figure 7 indicates that XS' and XQ begin to depart from their asymptotic values when feed times shorter than 2300 s are used. This was subsequently used as the critical feed time. As progressively shorter feed times are implemented, XS' first increases, signaling the occurrence of macroscopic concentration gradients (Bourne and Thoma, 1991) while XQ decreases. Feed times below approximately 500 s caused a fall in XS', which had been
956 Ind. Eng. Chem. Res.,Vol. 31, No. 3, 1992 0.12 m 0.10-
Table VIII. Lower Feed Point (u): Results from Experiments with Different Stoichiometric Ratios e and Stirrer Speedsa
a a
€ 5
0.08(I)
x
Q
0.06-
m m
0.04-
0.02-c 200
Q Q '
I
400
,
1
600
N
'
1
800
'
I
I
1000
[rprnl
Figure 8. Influence of increasing stirrer speed on the product ratio XS (former test system) using the lower feed point (u). Operating parameters are a = 50,t= 0, YA = 1.1,cm = 60 mol-m", and feed time = 900 s. Table VU. Changing c Values When Increasing the Stirrer Speed N. rDm XS e. W-krr-l e. WSka-l @ 3.7 0.049 77 240 0.118 0.095 64 0.099 6.1 300 8.9 0.164 54 360 0.086 0.261 50 0.074 13.2 420 18.4 0.389 47 480 0.065 25.6 0.554 46 0.057 540 0.760 42 0.052 32.1 600 39.1 1.012 38 0.048 660 45.7 1.314 35 0.045 720 1.671 54 0.034 89.9 780 96.6 2.087 46 840 0.033 ~~~
interpreted earlier (Bourne and Hilber, 1990) as faster micromixing promoted by the rapidly rising contribution from the kinetic energy of the feed stream in a region (upper part of tank) of otherwise weak turbulence. XQ also responds in this situation, as its increase shows (Figure 7). The longer critical feed time at o than at u is consistent with other measurements (Bourne and Thoma, 1991). 4.5.3. Former and Extended Test Reactions at the Lower Feed Point (u). Figure 8 refers to the former test reacton (1-naphthol alone) when 7 A 1 = 1.1,[ = 0, a = 50, cBo= 60 m~i-m-~, and feed time = 900 s. The discontinuity above 720 rpm correlated with air being increasingly drawn into the tank by the stirrer. Table W contains the energy diesipations corresponding to the product distributions in Figure 8, as well as the averge dissipation rate, e, calculated from the power number, speed and size of turbine, and mass of fluid in the tank. Q is the ratio t/z. The micromixing model used here (Bourne and Maire, 1991a) treats t as uniform in the mixing-reaction zone and represents the simplest approach. It is well-known that a wide range of velocity fluctuations and energy dissipation rates exist in stirred tank reactors with e and Q typically varying by 3 orders of magnitude. The influence of e gradients has been modeled (Baldyga and Bourne, 1988), but a fullanalysis of the resdta in Table VII is not essential to understand why Q varies with N. Earlier experimental work and some guiding principles (Bourne and Dell'Ava, 1987) show that as the stirrer speed is increased, the reaction zone shrinks toward the feed point. (This arises through the competition between transport and mixing.) Here feed point u was located in the impeller suction and so with rising speed the reacting fluid moves back from the impeller toward u, causing 9 to decrease (Table VII). Two preliminary sets of results employing the extended reaction system were obtained using 7A1 = 1.2, a = 50, cm = 2 m~l.m-~, and feed time = 900 s. Table VI11 reports
N 240 300 360 420 480 540 600 660 240 300 360 420 480 540 600 660
XS'
4 0.00678 0.00758 0.00753 0.00808 0.00717 0.00796 0.00778 0.00787 0.00891 0.00874 0.00534 0.006 22 0.006.99 0.00663 0.00306 0.00538
XQ
4 0.3250 0.2956 0.2703 0.2509 0.2317 0.2188 0.2072 0.1971 0.0867 0.0758 0.0640 0.0580 0.0530 0.0480 0.0459 0.0397
XQ
3 0.3452 5 0.3137 5 0.2863 0.2646 5 5 0.2436 5 0.2291 0.2170 5 0.2051 5 1 0.0959 1 0.0827 1 0.0684 1 0.0628 1 0.0572 1 0.0517 1 0.0476 1 0.0469 The analysis was carried out with a four- and a three-parameter regression (4and 3,respectively). Table IX. Results from the Lower Feed Point (u) t: cm, m ~ l - m - ~N,rpm Y A XS XQ 5 5 660 1.2 0.2969 5 25 1.2 660 0.4961 5 2 660 1.2 0.2052 2 5 0.3137 300 1.2 1 2 660 1.2 0.0469 1 2 300 1.2 0.0827 0 60 660 1.1 0.0476 0 60 300 1.1 0.0993 Table X. Results from the Umer Feed Point ( 0 ) 5 ~m,mol.m-~N,rpm Y A XS XQ 1 2 300 1.2 0.2359 2 300 1.2 0.5944 5 0 2 300 1.2 0.0462 0 20 300 1.2 0.2060
t,
W-kg-' 80 138 67 10 73 6.8 40 6.1
c,
Wakg-' 0.082 0.21 0.052 0.076
four- and three-parameter regressions in the diode array spectrophotometer. It is recommended to begin with a simultaneous determination of four dyes (0-R,p-R, S, and Q), although when, as here, barely significant quantities of bisazo dyestuff are present, the three-component regression (0-R, p-R, and Q) is almost as good. In both evaluations the residual spectra were less than 1% in absorption units,indicating no systematic difference between three- and four-component regressions. Three replicate experiments ( Y =~ 1.2, ~ f = 5, a = 50, cm = 5 m~l-m-~, N = 660 rpm) were conducted to establish reproducibility. The mean and standard deviations of the product distributions were XS' = 0.0085 f 0.0012 XQ = 0.3017 f 0.0078 indicating a relative error on the order of 2-370 in XQ. More recent tests to establish the reproducibility of the mixing experiment and the spectrophotometric analysis gave a standard deviation of 0.003 (Zimmermann, 1991). Table IX reports experiments at two stirrer speeds in which the former ( f = 0) and extended diazo couplings were employed to estimate t. The average values, z, were 0.095 W0kg-l at 300 rpm and 1.01 W-kg-' at 660 rpm. The results will be discussed in section 4.5.5. 4.5.4. Former and Extended Test Reactions at the Upper Feed Point ( 0 ) . Table X reports experiments using the 1-naphthol coupling (5 = 0) and the extended test reactions to estimate e. Along with results from Table IX, these results will be discussed in the next section.
Ind. Eng. Chem. Res., Vol. 31, No. 3,1992 957 4.5.5. Comparison of Former and Extended Test Reactions. Three factors cause scatter and inaccuracy in energy dissipation rates determined through applying a micromixing model to product distributions measured in stirred tank reactors. (a) If, as here, the model is based on a uniform energy dissipation rate in the mixing-reaction zone, inaccuracy will arise from the spatial gradients present in the tank. A feed point near the impeller will be more strongly influenced than one near the liquid surface. For example, in Table IX (N = 660 rpm, [ = 5) the higher .the concentration level the larger e becomes (67,80, (cm = 2,5, and 25 rn~l-rn-~), and 138 W-kg-'). Reaction will have been faster as the concentration rose, moving the reaction zone nearer to the impeller. The inhomogenities in the turbulence make the stirred tank an unattractive device for relatively precise experiments. (b) The limits of analytical error for XS and XQ are 10.005 (Bourne et al., 1990) and 0.008 (section 4.5.3). These will have the smallest effect on E when the experiments are conducted in the steepest part of the X vs E plot (refer to Figures 3-5). Because of the complex, nonlinear character of the micromixing model, it is impossible to make any simple, general statement about the effect of analytical errors on e, but the following example is not untypical. Using the l-naphthol coupling (Table M), a value XS = 0.0476 was measured (N = 660 rpm) and e = 40 W-kg-' was deduced. If the correct value of XS had been 0.04, then e would have increased to 70 Wmkg-'. (c) It follows from eqs 16 and 17 that e Any error in E arising from the analytical method and the local slope of the X - E plot (see b) is therefore doubled e is evaluated. (On the other hand, if e is given and the product distribution is to be found, this factor has a damping effect on error.) Table X contains a high value of e = 0.21 Wskg', when [ = 5. Reference to Figure 5 shows that this point (XQ = 0.594) lies on a rather flat part of the XQ-E plot with consequent loss of accuracy. The remaining three values are close, and their average (0.07 W-kg-l), corresponding to ch = 0.74, is reasonable considering the spreading of the reaction zone toward the impeller, which is larger the smaller the tank (Bourne and Dell'Ava, 1987). Setting ch = 0.9, product distributions XS and XQ were calculated for the experimental conditions in Table X and it was also checked that reaction was complete before the feed reached the turbine. The calculated XQ values were 0.234 and 0.610, while the calculated XS were 0.036 and 0.199. These agreed reasonably well with the measurements in Table X, and ch = 0.9 (and e = 0.086 W0kg-l) is also plausible as an average over the path of the reacting fluid.
-
5. Conclusions
The diazo coupling between 1-naphthol and diazotized sulfanilic acid in aqueous solution at 298 K and optimal pH (9.9) is limited to determining energy dissipation rates in mixers up to 200-400 Wnkg-'. Many alternative test reactions were considered in the light of six desirable characteristics. It was decided to extend the existing reactions to the simultaneous diazo coupling of a mixture of 1-and %-naphtholswith diazotized sulfanilic acid in aqueous solution at 298 K and pH 9.9 (I = 444.4 m01.m-3). Extinction coefficients for the naphthols are provided to enable a check on their concentrations prior to reaction. Extinction coefficients are given for the four dyes which
can be formed when 1-and 2-naphthols are simultaneously coupled. Spectrophotometric analysis combined with four-component regression using a diode array instrument provides rapid analysis of dye samples. The analytical errors in the two measwea of product distribution XS' and XQ are in the range *(0.003-0.008) and can probably be reduced by further work. The kinetics of the coupling of 2-naphthol were accurately determined using a stoppedflow apparatus. The extended test reactions permit energy dissipation rates on the order of lo6 W0kg-l to be determined in aqueous solutions using a range of operating conditions (volume ratio a,naphthol ratio [,concentration level). The ratio of 2- to l-naphthol is a new degree of freedom in the extended system and offers the experimentalist more flexibility when running experiments to characterize a given flow field. Suitable conditions can be selected by considering the product distributions XQ and XS' attainable in the chemical (slow reaction) and totally mixing-controlled (instantaneousreaction) regimes, which can easily be calculated, and especially by simulating the fast reaction regime with the engulfment model of micromixing. At high energy dissipation rates the five chemical reactions reduce to two parallel or competitive steps and insignificant quantities of bisazo dye are formed. A limited application and a comparison of the extended and existing test reaction systems in a semibatch, stirred tank reactor have been carried out. The interpretation of the measurements was complicated by the spreading of the reaction zone through regimea of varying energy dissipation rate, and in this sense, the stirred tank is not well suited to such measurements. Nevertheless, all observed trends could be interpreted qualitatively and the existing and extended test reactions gave very similar estimates of energy diasipation rates under given conditions.
Acknowledgment We thank Prof. H. Zollinger, ETH, for his help in screening the possible reaction systems, Prof. P. L. Luisi, ETH, for the use of the stopped-flow apparatus, and also H. Maire for many valuable discussions about the extended reaction system. Nomenclature A1 = l-naphthol A2 = 2-naphthol B = diazotized sulfanilic acid c = concentration, molm3 D = tank diameter, m E = Damkbhler number E = engulfment rate coefficient, s-' H = tank height, m h = vertical position in tank, m I = ionic strength, m ~ l - m - ~ k = rate constant, m3.rnol-'.s-' N = number of moles, mol N = stirrer speed, rpm o-R, o = ortho monoazo dyestuff (2-[(4'-sulfophenyl)azo]-lnaphthol) P = product p-R,p = para monoazo dyestuff (4-[(rl'-sulfophenyl)azo]-lnaphthol) Q = 2-naphthol monoazo dyestuff (1-[ (4'-sulfophenyl)azo]2-naphthol) R = intermediate, s u m of o-R and p-R,mol~m-~ S = bisazo dyestuff (2,4bia[(4'-sulfophenyl)azo)]-l-naphthol) T = temperature, K x = variable XS' = product yield (extended test reaction)
958 Ind. Eng. Chem. Res., Vol. 31, No. 3, 1992
XS = product yield (former test reaction) XQ = product yield (extended test reaction) Greek Letters = volume ratio VA/VB yAl = stoichiometric ratio NA1 O/NBO t = turbulent energy dissipation rate, W-kg-' t = molar extinction coefficient, m2.mol-' Q = relative energy dissipation rate K = ratio of rate constants k l / k s X = wavelength, nm Y = kinematic viscosity, m 2 d 5 = stoichiometric ratio NA20/NAlo a!
---
Subscripts l o = reaction A1 o-R lp = reaction A1 p-R 20 = reaction p-R S 2p = reaction o-R S 3 = reaction A2 Q A1 = 1-naphthol A2 = 2-naphthol av = average B = diazotized sulfanilic acid F = feed i = component i i = inner loc = local max = maximal min = minimal o = 0-R p=p-R R sum of 0-R and p-R
s,s=s
tot = total Registry No.
Q, 138152-14-4; o-R, 138152-15-5; p-R, 138152-16-6; S, 138152-17-7; 1-naphthol, 90-15-3; 2-naphthol, 135-19-3; sulfanilic acid, 121-57-3.
Literature Cited Baldyga, J.; Bourne, J. R. Calculation of micromixing in inhomogeneous stirred tank reactors. Chem. Eng. Res. Des. 1988, 66, 33. Baldyga, J.; Bourne, J. R. Simplificationof micromixing calculations, Part 1. Chem. Eng. J. 1989,42,83. Baldyga, J.; Bourne, J. R. The effect of micromixing on parallel reactions. Chem. Eng. Sei. 1990, 45, 907.
Bourne, J. R.; Tovstiga, G. Measurement of the diffusivity of 1naphthol in water with a rotating disk. Chem. Eng. Commun. 1985, 36, 67. Bourne, J. R.; Dell'Ava, P. M. Micro- and macromixing in stirred tank reactors of different sizes. Chem. Eng. Res. Des. 1987,65, 180. Bourne, J. R.; Hilber, C. P. The productivity of micromixing controlled reactions. Chem. Eng. Res. Des. 1990,68, 51. Bourne, J. R.; Maire, H. Influence of the kinetic model on simulating the micromixing of 1-naphthol and diazotized sulfanilic acid. Znd. Eng. Chem. Res. 1991a, 30,1385. Bourne, J. R.; Maire, H. Micromixing and fast chemical reactions in static mixers. Chem. Eng. Process. 1991b, 30, 23. Bourne, J. R.; Thoma, S. Some factors determining the critical feed time of a semi-batch reactor. Chem. Eng. Res. Des. 1991,69,321. Bourne, J. R.; Kut, Oe. M.; Lenzner, J.; Maire, H. Kinetics of the diazo coupling between 1-naphthol and diazotized sulfanilic acid. Znd. Eng. Chem. Res. 1990,29, 1761. Daviea, J. T. A physical interpretation of drop sizes in homogenizers and agitated tanks,including the dispersion of viscous oils. Chem. Eng. Sci. 1987, 42, 1671. ETAD, Ecological and Toxicological Association of the Dyestuff Manufacturing Industry, CH-4005 Basle, Switzerland, 1990. Garcia-Rosas,J.; Petrozzi, S. Influence of mixing on the azo-coupling of 1-naphthol and diazotized aniline. Chimia 1990,44, 366. Knox, J.; Richards, M. B. The basic properties of oxygen in organic acids and phenols; and the quadrivalency of oxygen. J. Chem. SOC.(London) 1919,115, 508. Lauer, K. Der Einfluss des Lijsungsmittels auf den Ablauf chemischer Reaktionen, XIV Mitteil.: Zur Kenntnis der aromatischen Kohlenwasserstoffe. Ber. Dtsch. Chem. Ges. 1937, 70, 1127. Lenzner, J. Der Einsatz rascher, kompetitiver Reaktionen zur Untersuchung von Mischeinrichtungen. Ph.D. Thesis No. 9469, El" Ziuich, 1991. Rice, A. W.; Toor, H. L.; Manning, F. S. Scale of mixing in a stirred vessel. AZChE J. 1964, 10, 125. Saunders, K. H. Aromatic Diazo Compounds, 3rd ed.; Arnold: London, 1985. Schofield, K. Aromatic Nitration; Cambridge University Press: Cambridge, 1980. Tolgyesi, W. S. Relative reactivity of toluene-benzene in nitronium tetrafluoroborate nitration. Can. J. Chem. 1965,43, 343. Wood, P. B.; Higginson, W. C. E. Kinetic studies of oxidationlreduction of cobalbethylenediamminetetraaceticacid complexes. J. Chem. SOC.(A) 1966, 1645. Zimmermann, B. Technisch-ChemischesLaboratorium, ETH Ziirich. Private communication, 1991. Received for reuiew August 7, 1991 Accepted November 25, 1991
