118
Ind. Eng. Chem. Res. 1999, 38, 118-125
Kinetics of 5,5′-Dihydroxy-2,2′-dinaphthylcarbamide-7,7′-disulfonic Acid Synthesis by Phosgenation of 2-Amino-5-naphthol-7-sulfonic Acid in Alkaline Solution G. Wielgosinski† and A. Kraslawski*,‡ Faculty of Process and Environmental Engineering, Technical University of Lodz, ul. Wolczanska 175, PL-90-924 Lodz, Poland, and Department of Chemical Technology, Lappeenranta University of Technology, FIN-53 851 Lappeenranta, Finland
The kinetics of phosgenation of 2-amino-5-naphthol-7-sulfonic acid in alkaline solution has been investigated at 323-353 K. The experiments in a flat contact surface reactor have been carried out, and the model of the reaction has been proposed. Apparent kinetic constants were calculated. The proposed model was verified in the packed absorption column. The predicted concentrations of 5,5′-dihydroxy-2,2′-dinaphthylcarbamide-7,7′-disulfonic acid and 2-amino-5-naphthol-7-sulfonic acid vs column height were compared with the experimental results. The statistical analysis showed a very good agreement between the experimental data and the concentrations obtained from the model. Introduction 5,5′-Dihydroxy-2,2′-dinaphthylcarbamide-7,7′-disulfonic acid is an important intermediate in the production of dyes and photosensitive materials. The objective of this work is to determine the kinetics of the heterogeneous reaction of synthesis of 5,5′-dihydroxy-2,2′-dinaphthylcarbamide-7,7′-disulfonic acid. The process is realized in the system phosgene-water-NaOH-2amino-5-naphthol-7-sulfonic acid (I-acid). It is an example of absorption with consecutive-parallel chemical reactions. There are no papers published on the kinetics of the above-mentioned reaction. The realization of this study has required the determination of density and viscosity of the aqueous solutions of I-acid and 5,5′dihydroxy-2,2′-dinaphthylcarbamide-7,7′-disulfonic acid as well as their diffusivity coefficients in water and aqueous solutions of NaOH. The additional problem has been the lack of precise analytical methods for the determination of the concentrations of I-acid and 5,5′dihydroxy-2,2′-dinaphthylcarbamide-7,7′-disulfonic acid in the reacting mixture. Experimental Section A series of experiments were conducted to (a) determine the density of the reaction mass as a function of temperature, (b) determine the viscosity of the reaction mass as a function of temperature, (c) determine the diffusion coefficient of I-acid in aqueous solutions of NaOH, (d) determine the mass-transfer coefficient in the gas phase in the reactor with the flat contact surface (system NH3-N2-H2SO4), (e) determine the masstransfer coefficient in the liquid phase in the reactor with the flat contact surface (system O2-H2O), (f) identify the rate constant of COCl2 decomposition in an aqueous solution of NaOH, (g) identify the rate constant of phosgenation of I-acid in an alkaline solution, and * To whom correspondence is addressed. E-mail: Andrzej.
[email protected]. † Technical University of Lodz. ‡ Lappeenranta University of Technology.
(h) verify the proposed model of the phosgenation of I-acid in a packed column. The density has been determined using a picnometer and viscosity by measurements conducted in a rotational viscosimeter. Moreover, experiments were carried out in a packed absorption column to verify the proposed model of the phosgenation of I-acid. Materials. Standard samples of 5,5′-dihydroxy-2,2′dinaphthylcarbamide-7,7′-disulfonic acid and 2-amino5-naphthol-7-sulfonic acid were obtained as sodium salts by repeated crystallization of the technical products from water and methanol. Analysis. Reversed-phase high-pressure liquid chromatography (HPLC) has been applied to the analysis of the composition of the reaction mixture. A highperformance liquid chromatograph with a UV detector (253.7 nm) was used. The separation of the components has been carried out on the column with the packing Li-Chrosorb Rp 10 µm (Merck). The column length was 250 mm and the diameter 4.4 mm. The eluent was the mixture of water-methanol, in the ratio 1:1 with the addition of tetra-n-butylammonium phosphate in a concentration of 0.01 mol/dm3. The flow rate was 2 × 10-3 cm3/s, and the amount of the solution chromatographed was 5 mL. Apparatus. The phosgenation of 2-amino-5-naphthol7-sulfonic acid is a gas-liquid reaction. The research of this process has been conducted in the unit presented in Figure 1. There are two main elements of this device: the reactor with the flat contact surface (1) and the packed absorption column (2). The reactor (1) was used for the studies of the reaction kinetics and the absorption column (2) for the verification of the proposed model of the process. The stream of phosgene was introduced into the reactor (1) or column (2) from the container (13), passing through heating sections (8 and 14) and the expander (15). The gas surplus was sent to the absorption column (7) where it was contacted with the concentrated NaOH. There were two liquid streams introduced into the unit: an alkaline solution of I-acid and a solution of NaOH. The liquids were sent from the heated tanks (3 and 4) to the heater (8) and next to the
10.1021/ie970714r CCC: $18.00 © 1999 American Chemical Society Published on Web 12/01/1998
Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 119
Figure 1. Experimental unit.
coefficients in gas and liquid phases as a function of the mixing speed. The studies were conducted in the reactor with the flat contact surface described above. The absorption of oxygen in water was examined. The masstransfer coefficient in the liquid phase has been studied by changing the liquid flow rate, speed of the impeller, and the geometry of the system. The last was realized by the use of three different lower parts of the reactor. From the work presented by Lipowska (1974), it is clear that mixing in the small reactors with the short residence times is strongly influenced by the in- and outcoming streams of reactants. To describe this phenomenon, two Reynolds numbers have been introduced: ReML for mechanical mixing in the reactor and ReFL for mixing by flowing streams. The following equation has been proposed as the result of our experiments: Figure 2. Flat contact surface reactor.
reactor (1) or column (2). The product of the reaction was stored in the tank (5). The flow reactor, Figure 2 was a modified apparatus proposed by Levenspiel and Godfrey (1974). It was composed of two cylindrical compartments separated by the removable, perforated wall. Both parts, upper for the gas phase and lower for the liquid phase, were equipped with agitators. The stirrers, turbine and propeller, ensured ideal mixing in both phases. To avoid the vortex formation, the lower part was additionally equipped with baffles fixed to the bottom of the tank. The reactor was equipped with a jacket to ensure isothermal conditions. The diameter of both compartments was 100 mm. The height of the upper, gas compartment was 50 mm. There were three different liquid compartments of heights 103, 123, and 143 mm and four different removable, perforated walls. They had 4, 37, 69, and 102 holes, respectively. The diameter of holes was 7 mm. It ensured areas of 2%, 18%, 34%, and 50% of the maximum contact area, respectively. An absorption column was composed of six removable, sections of packing, each 200 mm high. Raschig rings used were 10 × 10 × 1 mm. The column had a jacket to ensure the isothermal carrying out of the absorption and reaction. There were no axial or radial measurements of the temperature distribution to check isothermal conditions as the column diameter was only 100 mm.
ShL ) 0.065ReML0.96ReFL0.45ScL0.5
(1)
ShL ) kLD/DA
(2)
ReML ) nLd2FL/ηL
(3)
ReFL ) 4LFL/πDηL
(4)
ScL ) ηL/FLDA
(5)
where
The equation is valid in the following ranges of nondimensional numbers: 4000 < ReML < 13 000 and 20 < ReFL < 60. In the gas phase the following equation has been proposed based on our experiments:
ShG ) 0.96ReG0.87ScG0.33
(6)
ShG ) kGdG/DAc0
(7)
ReG ) nGdG2FG/ηG
(8)
ScG ) ηG/FGDA
(9)
c0 ) P/RT
(10)
where
The equation is valid for 800 < ReG < 7000.
Identification of the Mass-Transfer Coefficients
Identification of the Rate Constants
The studied reaction is an example of absorption with the chemical reaction. To determine the chemical kinetics of this reaction, the values of the mass-transfer coefficients have to be established first. It is necessary to determine the dependence of the mass-transfer
The system of reactions that is possible in the system phosgene-water-NaOH-I-acid during the phosgenation process of I-acid is given in Figure 3. Possible simplification of this complex reacting system is possible by taking into account information published by Stie-
120 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999
Figure 3. System of reactions.
Figure 4. Simplified system of reactions.
panow et al. (1975), Kazmierowicz et al. (1983), and Yen (1968) as well as the observation that some of the compounds mentioned in Figure 3 have not been found in the reaction products. As a consequence, the following simplified reaction is proposed: k1
A + 2B 98 P + 2H
(11)
The reaction of phosgene with water and NaOH could be described by the system of reactions presented in Figure 4. However, the results presented in the paper by Manogue and Pigford (1960) suggested the simplified reaction k2
A + 4N 98 2S + Z + 2W
(12)
Moreover, the reaction of HCl with NaOH also takes place: k3
H + N 98 S + W
(13)
The above reaction is instantaneous. Finally the system of equations (11) and (12) has been proposed to describe the reactions taking place in an alkaline solution between COCl2 and I-acid. Reaction of Phosgene-NaOH. The reaction between phosgene and NaOH has been studied by Manogue and Pigford (1960), Butler and Snelson (1979), Wielgosinski and Pelle (1990), and Griolet et al. (1996). In the presented paper the phosgene and NaOH reaction has been studied under the following conditions: NaOH
Figure 5. Mass balance in the flat contact surface reactor. Decomposition of phosgene in an alkaline solution.
concentration, 0.5-3.0 mol/dm3; temperature range, 323-353 K. The value of the rate constant k2 has been determined in the reactor with the flat contact surface based on the balance equations formulated under the following assumptions: (a) There is a steady state in the flow reactor. (b) The process is carried out in isothermal conditions. (c) Both phases are ideally mixed. (d) There is no influence of the mixing velocity in the gas phase on the mass transfer in the system. (e) Henry’s law is applicable. According to Figure 5, the following equations are formulated to describe the heterogeneous gas-liquid reaction of the decomposition of phosgene in an alkaline medium:
Mass balance in the gas phase FG FG ) RAF + G2 G1 MA MA
(14)
Mass balance in the liquid phase LcN1 ) rNV + LcN2
(15)
Chemical reaction rA ) k2cA2cN2
(16)
RAF ) rAV + LcA2
(17)
rN ) 4rA
(18)
Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 121 Table 1. Identification of Phosgene Decomposition in an Aqueous Solution of NaOH Lp
L (m3/s)
G (m3/s)
nL (1/s)
P (hPa)
T (K)
F (m2)
cN1 (kmol/m3)
cN2 (kmol/m3)
I (kmol/m3)
xM
E∞
E
k2 (m3/kmol‚s)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
2.8 × 10-6 2.8 × 10-6 2.8 × 10-6 2.8 × 10-6 2.8 × 10-6 2.8 × 10-6 2.8 × 10-6 2.6 × 10-6 2.8 × 10-6 2.9 × 10-6 2.8 × 10-6 2.6 × 10-6 2.7 × 10-6 2.8 × 10-6 2.8 × 10-6 2.8 × 10-6 2.8 × 10-6 2.8 × 10-6 2.7 × 10-6 2.7 × 10-6 2.9 × 10-6
6.9 × 10-6 6.4 × 10-6 6.4 × 10-6 6.4 × 10-6 7.2 × 10-6 1.0 × 10-5 6.7 × 10-6 6.7 × 10-6 6.4 × 10-6 6.7 × 10-6 6.9 × 10-6 7.2 × 10-6 6.4 × 10-6 6.7 × 10-6 6.4 × 10-6 6.7 × 10-6 6.7 × 10-6 6.7 × 10-6 7.2 × 10-6 6.7 × 10-6 6.1 × 10-6
10.0 10.0 10.3 10.0 5.8 5.3 10.2 10.2 10.3 11.7 9.7 10.0 10.3 10.2 9.8 10.0 12.5 7.5 10.0 10.2 9.8
1000 1000 1000 1000 996 996 996 996 1005 1005 1008 1008 998 998 998 998 998 995 995 995 995
353 353 335 336 353 353 343 344 353 360 353 352 357 358 329 328 351 352 354 353 353
1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.5 × 10-4 2.7 × 10-3 2.7 × 10-3 2.7 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3
2.000 1.000 2.000 1.000 2.000 1.000 2.000 1.000 2.000 3.000 2.000 1.000 2.000 1.000 2.000 1.000 2.000 1.000 2.500 1.500 3.500
1.900 0.950 1.920 0.960 1.940 0.970 1.910 0.960 1.990 2.680 1.810 0.910 1.900 0.940 1.930 0.960 1.880 0.960 2.360 1.420 3.320
1.975 0.988 1.980 0.990 1.985 0.993 1.978 0.990 1.998 2.920 1.953 0.978 1.975 0.985 1.983 0.990 1.970 0.990 2.465 1.480 3.455
1893 1293 1612 1148 3276 2447 1753 1247 1871 1934 1915 1295 1878 1270 1586 1048 1492 1680 2178 1609 2518
76.0 56.6 50.2 38.5 77.4 57.8 61.5 47.1 78.4 83.1 72.3 52.9 82.0 61.6 42.7 30.9 72.3 56.2 79.4 69.5 73.8
76.0 56.6 50.2 38.5 77.4 57.8 61.5 47.1 78.4 83.1 72.3 52.9 82.0 61.6 42.7 30.9 72.3 56.2 79.4 69.5 73.8
2.958 × 105 2.779 × 105 1.046 × 105 9.646 × 104 2.605 × 105 2.926 × 105 1.556 × 105 1.557 × 105 2.385 × 105 4.263 × 105 3.149 × 105 2.236 × 105 3.684 × 105 3.379 × 105 7.054 × 104 7.368 × 104 2.971 × 105 2.430 × 105 3.168 × 105 2.847 × 105 3.093 × 105
According to the assumption by Manogue and Pigford (1960), there is a second-order reaction
RA ) EkL(cA* - cA2)
layer:
(19)
DA
d2cA dx2
and based on Wellek et al. (1978)
1 1 ) + [E - 1]1.35 [E∞ - 1]1.35
(
1
)
xM -1 tghxM
1.35
DB
(20) DH
where
E∞ ) 1 + M)
DA cN2 DN 4cA*
DAk2cN2/kL2
DN (21)
cA* ) PA/HA
(23)
PA ) P - PW
(24)
To determine the dependence of rate constant k2 on temperature, a series of the experiments have been carried out. The results are given in Table 1.The values of the rate constant k2 have been calculated for every experiment carried out at the specific temperature. The optimization method of Rosenbrock with the GrammSchmidt modification was applied. The obtained values were used to get the following correlation:
ln k2 ) 27.5 + 0.15 ln(I) - 5300/T
(25)
Phosgenation Reaction of I-Acid. Identification of the reaction constant k1 of the reaction presented in eq 11 has been carried out in the flow reactor with the flat contact surface (Figure 2). The identification is realized by the solution of mass balances in the reactor and in the boundary layer. The adopted assumptions are the same as those for phosgene decomposition. Moreover, it was assumed that the reactions of phosgene decomposition and HCl neutralization are instantaneous. The second-order reaction rate has also been assumed. The following system of equations has been proposed for the description of the mass transfer in the boundary
d2cB
dx2 d2cN dx2 DP
(26)
) 2k1cAcB
(27)
) 2k1cAcB - k3cHcN
(28)
) 4k2cAcN + k3cHcN
(29)
dx2
d2cH
(22)
) k1cAcB + k2cAcN
d2cP dx2
) k1cAcB
(30)
The last of the above-mentioned assumptions allowed us to simplify the system of the eqs 26-30 to eqs 26, 27, and
DH
d2cH dx2
) 2k1cAcB
(31)
The boundary conditions for eqs 26, 27, and 31 are
x)0 x ) δx
cA ) cA* cA ) 0 x)δ
dcB/dx ) 0 cB ) cBx cB ) cB2
dcH/dx ) 0 (32) cH ) 0
cN ) 0 (33)
cN ) cN2
(34)
To determine two unknown variables δx and cBx, two additional equations have been formulated. They result from the mass balance in the boundary layer.
( )
cB2 - cBx dcH ) DH DB δ - δx dx
( )
dcA cN2 - 0 ) 4DA DN δ - δx dx
x)δx
x)δx
(
+ DH -
(35)
)
dcH dx
x)δx
(36)
ln k1 ) 13.5 835.7 - 49.85 ln [H+] T
and eqs 23 and 24. The system of differential and algebraic equations has been solved using Adam’s integration method (Collatz, 1966) and the Rosenbrock optimization with GrammSchmidt modification (Beveridge and Schechter, 1970). The value of rate constant k1 has been identified for every experimental temperature (Table 2). The obtained results have been correlated with the reaction temperature and the concentration of the hydrogen ions. Several forms of equations have been applied for the representation of k1 in the function of [H+] and T. Finally, on the basis of the statistical analysis, the following equation has been proposed:
(43)
The comparison of the experimental results k1E and those calculated from the model k1C is given in Table 3.
Verification of the Reaction Model
The proposed model of the phosgenation of 2-amino5-naphthol-7-sulfonic acid in an alkaline solution has been formulated by the system of equations (11)-(13). The rate constant values of the first two reactions have been identified on the basis of the experiments carried out in the reactor with the flat contact surface. The last reaction of the model, eq 13, is an instantaneous reaction. The verification of the proposed kinetics of the phosgenation reaction is done by carrying out the experiments and building the respective mathematical model 2.7 × 10-3 2.7 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 1.4 × 10-3 2.7 × 10-3 2.7 × 10-3 2.7 × 103 2.7 × 10-3 2.7 × 10-3 2.7 × 10-3 2.7 × 10-3
(42)
347 8.90 1.1 × 10-3 336 8.45 1.1 × 10-3 341 8.60 1.1 × 10-3 341 8.60 1.1 × 10-3 341 8.60 1.1 × 10-3 341 8.60 1.1 × 10-3 337 8.70 1.1 × 10-3 338 8.70 1.1 × 10-3 338 8.70 1.1 × 10-3 341 6.60 7.8 × 10-4 341 6.80 7.8 × 10-4 341 6.40 7.8 × 10-4 341 6.90 7.8 × 10-4 341 6.60 7.8 × 10-4 329 7.70 1.1 × 10-3 329 7.80 1.1 × 10-3 330 7.80 1.1 × 10-3 330 7.80 1.1 × 10-3 330 8.00 1.1 × 10-3 328 10.50 1.1 × 10-3 354 8.20 1.1 × 10-3
L2 ) L11 + L12
988 982 992 992 992 992 992 992 992 993 993 993 993 993 998 998 998 998 998 998 998
(41)
10.3 5.0 10.2 10.3 10.2 10.2 5.5 5.2 5.3 5.3 5.8 5.7 5.5 5.7 10.0 10.2 9.8 10.3 10.0 10.2 10.0
L11cN11 + L12cN12 ) RNF + L2cN2
6.3 × 10-6 6.3 × 10-6 6.3 × 10-6 6.3 × 10-6 6.3 × 10-6 6.3 × 10-6 6.3 × 10-6 6.3 × 10-6 6.3 × 10-6 7.2 × 10-6 7.2 × 10-6 7.2 × 10-6 7.2 × 10-6 7.2 × 10-6 7.2 × 10-6 7.2 × 10-6 7.2 × 10-6 7.2 × 10-6 7.2 × 10-6 7.2 × 10-6 6.3 × 10-6
(40)
8.2 × 10-7 8.2 × 10-7 8.2 × 10-7 8.2 × 10-7 8.2 × 10-7 8.2 × 10-7 8.2 × 10-7 8.2 × 10-7 8.2 × 10-7 8.5 × 10-7 8.5 × 10-7 8.5 × 10-7 8.5 × 10-7 8.5 × 10-7 1.4 × 10-6 1.4 × 10-6 1.4 × 10-6 1.4 × 10-6 1.4 × 10-6 2.2 × 10-6 1.4 × 10-6
L11c1 ) RBF + L2cB2
2.8 × 10-6 2.7 × 10-6 2.8 × 10-6 2.8 × 10-6 2.8 × 10-6 2.8 × 10-6 2.8 × 10-6 2.8 × 10-6 2.8 × 10-6 2.6 × 10-6 2.6 × 10-6 2.6 × 10-6 2.6 × 10-6 2.6 × 10-6 2.7 × 10-6 2.7 × 10-6 2.7 × 10-6 2.7 × 10-6 2.7 × 10-6 2.9 × 10-6 2.8 × 10-6
Mass balance in the liquid phase
0.2380 0.1840 0.1800 0.1800 0.1750 0.1780 0.2290 0.2280 0.2290 0.1750 0.1750 0.1750 0.1750 0.1750 0.2900 0.2900 0.2900 0.2900 0.290 0.2700 0.2300
0.4564 0.3724 0.3724 0.3725 0.3725 0.3724 0.4563 0.4563 0.4563 0.3809 0.3809 0.3910 0.3810 0.3810 0.5049 0.5049 0.5049 0.5049 0.5049 0.5548 0.5050
0.1350 0.1010 0.0950 0.0940 0.0910 0.0940 0.1210 0.1190 0.2100 0.0800 0.07800 0.0770 0.0810 0.8000 0.1290 0.1320 0.1340 0.1320 0.1350 0.1340 0.0800
0.0884 0.1353 0.0689 0.0659 0.0696 0.0694 0.1590 0.1617 0.127 0.1311 0.1236 0.1321 0.1321 0.1321 0.1148 0.1146 0.1195 0.1136 0.1195 0.1336 0.1052
0.0195 0.0270 0.0291 0.0281 0.0291 0.0285 0.0332 0.0275 0.0282 0.0230 0.0250 0.0260 0.0244 0.0240 0.0381 0.0339 0.0304 0.0301 0.0304 0.0071 0.0341
0.2082 0.1390 0.1731 0.1756 0.1733 0.1731 0.1764 0.1756 0.1750 0.1510 0.1158 0.1521 0.1500 0.1506 0.2273 0.2259 0.2225 0.2264 0.2220 0.2195 0.2366
0.0799 0.0491 0.0647 0.0655 0.0648 0.0650 0.0605 0.0595 0.0593 0.0494 0.0508 0.0484 0.0494 0.0492 0.0814 0.0822 0.0814 0.0824 0.0817 0.1009 0.0816
60 27 62 61 30 31 34 35 35 26 26 25 26 26 26 27 28 28 28 25 52
cB1 cN1 cB2 cN2 cP2 cS2 cZ2 (kmol/m3) (kmol/m3) (kmol/m3) (kmol/m3) (kmol/m3) (kmol/m3) (kmol/m3) E∞
(39)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
G1FG/MG ) RAF + G2FG/MG
F (m2)
Mass balance in the gas phase
VL (m3)
The mass balance for the reactor presented in Figure 6 is given by the following set of equations:
pH
(38)
nL P T (1/s) (hPa) (K)
cN2 - 0 RN ) DN δ - δx
G (m3/s)
(37)
L2 (m3/s)
Moreover, taking into account the reaction rate of I-acid and NaOH in the boundary layer
L1 (m3/s)
Figure 6. Mass balance in the flat contact surface reactor, I-acid synthesis.
Lp
cB2 - cBx RB ) DB δ - δx
Table 2. Identification of Kinetic Constant for the Synthesis of I-Acid
3914 13830 4198 4182 4211 4146 15774 17454 16512 26958 24206 25830 25148 24427 8149 7566 7573 7223 7246 2179 5143
M
3676.4 2877.5 3281.6 3390.1 3435.1 3274.3 3273.3 3402.1 3360.1 6371.1 6781.0 6992.8 6164.7 6365.0 4121.7 3841.0 3659.4 3838.7 3570.6 1355.4 4672.4
k1 (m3/kmol‚s)
122 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999
Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 123 Table 3. Comparison of the Experimental and Calculated Values of Constant k1 Lp
T (K)
pH
k1E (m3/kmol‚s)
k1C (m3/kmol‚s)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
347 336 341 341 341 341 337 338 338 341 341 341 341 341 329 329 330 330 330 328 354
8.90 8.45 8.60 8.60 8.60 8.60 8.70 8.70 8.70 6.60 6.80 6.40 6.90 6.60 7.70 7.80 7.80 7.80 8.00 10.50 8.20
3676 2877 3281 3390 3435 3274 3273 3402 3360 6371 6781 6992 6164 6365 4121 3841 3659 3838 3570 1355 4672
3398 3326 3421 3421 3421 3421 3104 3154 3154 6706 6269 7172 6026 6706 3854 3722 3782 3782 3528 1414 4739
Figure 7. Mass balance in the differential section of the packed column.
for the process realized in a packed column. The adopted model assumptions have been identical to those formulated at the identification of the reaction kinetics. The proposed model has the form presented below. For the differential element of the column, (Figure 7), the following system of equations is proposed:
Mass balance in the gas phase FG FG πD2 πD2 + NW (G + dG) a dh ) RA a dh + G MG 4 4 MG (44) and after the rearrangement
πD2 MG dG ) (RA - NW) a dh 4 FG
Figure 8. Concentration profile in the gas boundary layer.
(45) The mass-transfer coefficients in the gas phase are given as
Mass balance of phosgene in the gas phase dGyA πD2 MG ) RA a dh 4 FG
(46)
kGA ) DAGc0/δG
(52)
kGW ) DWGc0/δG
(53)
DAG ) DWG
(54)
kGA ) kGW ) kG
(55)
Mass balance in the liquid phase dL πD2 ML ) (RA - NW) a dh 4 FL
Assuming that
(47)
Mass balance of I-acid in the liquid phase dLcB πD2 ) -RB a dh 4
then
(48)
Mass balance of NaOH in the liquid phase dLcN πD2 ) -RN a dh 4
Introducing eqs 52 and 53 into eqs 50 and 51 and taking into account eq 55
(49)
Mass transfer in gas phase is described by Stefan-Maxwell equations
dyA yA(RA - NW) + RA dyW
RA ) -c0DAG
dyA + yA(RA - NW) dx
(50)
NW ) -c0DWG
dyW + yW(NW - RA) dx
(51)
yW(NW - RA) + NW
)
1 dx kGδG
(56)
)
1 dx kGδG
(57)
and after integration with the boundary conditions as in Figure 8
124 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999
Figure 9. Concentration profile in the liquid boundary layer.
(RA - NW)yA* - RA 1 1 ln ) 0 RA - NW k (R - N )y - R G
(58)
(NW - RA)yW* - NW 1 1 ln ) 0 NW - RA k (N - R )y - N G
(59)
A
W
W
A
A
A
W
W
Mass transfer in the liquid phase is described by eqs 18-20 and 24-25 at the boundary condition equations (21)-(23) (Figure 9). Moreover, the reaction rate of 5,5′dihydroxy-2,2′-dinaphthylcarbamide-7,7′-disulfonic acid synthesis is a function of the reaction rate of I-acid as follows:
1 RP ) RB 2
(60)
For the above-presented model, the boundary conditions are formulated as in Figure 10
h)0
cA ) cAK
cB ) cBK
L ) LK
cN ) cNK
cP ) cPK
G ) GK
yA ) yAP ) 1
Figure 10. Mass balance of the packed column, I-acid synthesis.
The differential equations (45)-(49) and algebraic equations (58), (59), and (63)-(65) with the boundary conditions (61) and (62); differential equations (26), (27), and (31) and algebraic equations (35) and (36) with the boundary conditions (32)-(34); and algebraic equations (37), (38), and (60) constitute the mathematical model of the countercurrent, packed column, where absorption with the chemical reaction of phosgene with the alkaline solution of I-acid takes place. To solve the above system, equations (45)-(49) have been integrated using the Merson method and eqs (26), (27), (31), (35), and (36) have been integrated by applying Adam’s method. The additional difficulty in solving this problem has been the nonlinearity of the algebraic equations (37), (38), (58), and (59). Moreover, not all data at the starting point (the top of the column) have been given. To solve the problem, the gas flow rate at the top of the column has been assumed. The integration has been carried out for the assumed height of the packing. As a result, the gas flow rate at the bottom of the column, G°, has been calculated. This value has next been compared to the experimental value of the gas flow, GE. The following objective function has been used:
yW ) yWP ) 0 (61) h)H
cA ) 0
L ) LP
cB )
G ) GP
cBP
cP )
yA ) yAK
0 cN ) cNP yW ) yWK (62)
Taking into account the incoming streams:
LP ) L1 + L2
(63)
L1cB1 L1 + L2
(64)
L1cN1 + L2cN2 L1 + L2
(65)
cBP ) cNP )
F(xi) )
(
)
GC - GE GE
2
(66)
The problem consisted of finding the minimum value of eq 66. The optimization has been carried out using the Powell method (Beveridge and Schechter, 1970). Finally the concentrations of I-acid and 5,5′-dihydroxy2,2′-dinaphthylcarbamide-7,7′-disulfonic acid have been calculated. The obtained results have been compared to the experimental values. The comparison of the experimental results k2exp and those calculated from the model k2calc are given in Table 4. The maximum error of the calculated values was 12% and the average 6% in comparison to the experimental values.
Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 125 Table 4. Comparison of the Experimental and Calculated Values of Constant k2 Lp
T (K)
I (kmol/m3)
k2E (m3/kmol‚s)
k2C (m3/kmol‚s)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
353 353 335 336 353 353 343 344 353 360 353 352 357 358 329 328 351 352 354 353 353
1.975 0.988 1.980 0.990 1.985 0.993 1.978 0.990 1.998 2.920 1.953 0.978 1.975 0.985 1.983 0.990 1.970 0.990 2.465 1.480 3.455
2.958 × 105 2.779 × 105 1.046 × 105 9.646 × 104 2.605 × 105 2.926 × 105 1.556 × 105 1.557 × 105 2.385 × 105 4.263 × 105 3.149 × 105 2.236 × 105 3.684 × 105 3.379 × 105 7.054 × 104 7.368 × 104 2.971 × 105 2.430 × 105 3.168 × 105 2.847 × 105 3.093 × 105
2.929 × 105 2.529 × 105 1.320 × 105 1.194 × 105 2.932 × 105 2.532 × 105 1.901 × 105 1.716 × 105 2.936 × 105 4.246 × 105 2.922 × 105 2.420 × 105 3.459 × 105 3.110 × 105 9.927 × 104 8.164 × 104 2.690 × 105 2.426 × 105 3.201 × 105 2.755 × 105 3.297 × 105
Ri ) rate of absorption with the chemical reaction of component i, kmol/m2‚s T ) temperature, K V ) gas flow rate, m3/s x ) distance coordinate, m Greek Symbols δ ) boundary layer thickness, m η ) dynamic viscosity, kg/ms F ) density, kg/m3 Subscripts A ) phosgene B ) I-acid G ) gas phase H ) hydrogen chloride L ) liquid phase N ) NaOH P ) I-acid urea S ) NaCl W ) H 2O Z ) sodium bicarbonate 1 ) inlet or the first rate reaction 2 ) outlet or the second rate reaction
Summary
Superscripts
The simplified reaction path has been proposed in this study for the synthesis of 5,5′-dihydroxy-2,2′-dinaphthylcarbamide-7,7′-disulfonic acid by phosgenation of I-acid in an alkaline solution. The synthesis of 5,5′-dihydroxy2,2′-dinaphthylcarbamide-7,7′-disulfonic acid is a fast reaction. Its rate constant is of magnitude 103 m3/kmol‚ s. The value of Hatta’s number is 103-104 in the studied conditions of the reaction. Equation 47 has been applied to describe the influence of temperature and acidity on the reaction constant k1. The second reaction, decomposition of phosgene, is a very fast reaction. Its rate constant, k2 described by eq 12, is of magnitude 104-105 m3/kmol‚s, and Hatta’s number is 103-104. The proposed kinetics describes in a satisfactory way the results obtained by the authors as well as the data published by Manogue and Pigford (1960). The proposed model has been verified in the packed column where absorption with the chemical reaction took place. The obtained confirmation of the model’s validity allows for its industrial applications.
* ) equilibrium C ) calculated value E ) experimental value K ) final condition P ) initial condition
Notation a ) packing characteristics, m2/m3 ci ) concentration of component i, kmol/m3 d ) impeller diameter, m D ) apparatus diameters, m Di ) kinematic diffusion coefficient of component i, m2/ s F ) interfacial area, m2 G ) gas flow rate, m3/s h ) height, m Hi ) Henry’s constant of component i, Pa‚m3/kmol [H+] ) concentration of H+ ions, kmol/m3 k ) rate constant, m3/kmol‚s or 1/s kL ) liquid-phase mass-transfer coefficient, m/s kG ) gas-phase mass-transfer coefficient, kmol/m2‚s L ) liquid flow rate, m3/s M ) molecular weight, kg/kmol Ni ) rate of absorption for component i, kmol/m2‚s P ) total pressure, N/m2 ri ) rate of the chemical reaction, kmol/m3‚s R ) gas constant, kJ/kmol‚K
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Received for review October 15, 1997 Revised manuscript received June 15, 1998 Accepted October 19, 1998 IE970714R
