1147
Ind. Eng. Chem. Res. 1990,29, 1147-1152
Hydrodesulfurization of Thiophene over CoMo, NiMo, and NiW/A1203 Catalysts: Kinetics and Adsorption Son-Ki Ihm,* Sang-Jin Moon, and Hyung-Joon Choi Department of Chemical Engineering, Korea Advanced Znstitute of Science and Technology, P.O. Box 131, Cheongryang, Seoul, Korea
Three commercial catalytic systems, CoMo/A1203,NiMo/A1203, and NiW/A1203, were used for the of thiophene. Some Langmuir-Hinshelwood type kinetic study of the hydrodesulfurization (HDS) rate equations were discriminated for each catalyst by using a nonlinear regression method. Adsorption equilibrium constants were measured a t the reaction temperatures independently by the chromatographic pulse technique. The effects of different kinds of active metals on the type of rate equation and kinetic parameters obtained were compared. The same type of rate equations gave good correlations under the reaction condition of atmospheric pressure and 275-325 OC, irrespective of the kinds of active metals. However, the NiW system showed the possibility of higher hydrogenation functionality through the relatively weaker adsorption of thiophene and H2S than for the CoMo or NiMo system. It was also found that hydrogen adsorption was very weak compared to other reactants and was not a dissociative type under the present reaction conditions. The results of the kinetic study were very consistent with those of the separate adsorption study. Many investigations have been made on the kinetics and the reaction mechanism of the hydrodesulfurization (HDS) of thiophene (Lee and Butt, 1977; Morooka and Hamrin, 1977; Vrinat, 1983). It appears, however, that most of the results have been obtained from the CoMo/A1203system and that some disagreements still exist concerning the adsorption mode or the adsorption site for thiophene and hydrogen, the possible occurrence of desulfurization and hydrogenation on the different sites, and the effect of promoters (i.e., Co or Ni) on the kinetic parameters. Moreover, with the severe feedstocks supplied, other catalytic systems such as NiMo/A1,03 and NiW/A1203are increasingly used (Satterfield et al., 1980; Cerny and Trka, 1984). The development of new catalytic systems such as CoMo/carbon and Pt/A1203is also being pursued (Duchet et al., 1983; Dhainut et al., 1982). In many cases the catalytic behavior of the NiW/AlZO3 system has been assumed to be similar to that of the CoMo/AlZO3system since tungsten sulfide is equivalent to molybdenum sulfide in its crystalline structure. Consequently few kinetic studies have been reported for the NiW/Al2O3 system. However, their sulfides reveal different physicochemical properties in many aspects, and they might show different kinetic and adsorption behavior (Furimsky, 1980). In the present study, three commercial catalysts, CoMo/Ala03, NiMo/A1203, and NiW/A1,03, were compared to see the effects of different kinds of active metals on the thiophene HDS kinetics and adsorption properties.
Experimental Section Catalysts and Materials. The three catalysts used were commercial products of Harshaw Co.: CoMo/AlZO3 (HT400E), NiMo/A1203 (HT500E), and NiW/A1,03 (Ni4301E). They were supplied as 1/16-in.extrudates and were crushed and sieved to 100-150 mesh before use. The details of their properties are shown in Table I. Thiophene (Aldrich, 99+ % ) and hydrogen sulfide (Matheson, 99.5 % ) were used as received without further purification. Hydrogen (Matheson, UHP grade), helium (Matheson, UHP grade), nitrogen (Dongin, UHP grade), and 1-butene (Matheson, cp grade) were purified through a 5A molecular sieve trap and a copper-platinum trap.
* To whom correspondence should be addressed. 0888-5885/90/2629-1147$02.50/0
Table I. Properties of Harshaw Catalyst
property COO content, wt % NiO content, wt % Moos content, wt % W03 content, wt % pore vol, cm3/g surface area, m2/g app density, g/cm3 solid density, g/cm3
CoMo (HT400E), 3.15
catalyst NiMo (HTBOOE) .
15.40
3.00 14.95
0.45 227 1.33 3.29
0.41 210 1.38 3.62
NiW (NI4301E) 6.10 19.30 0.35 240 1.47 3.02
Reaction Apparatus and Procedure. The schematic drawing of the reaction apparatus is depicted in Figure 1. Thiophene was introduced into the vaporizer by a syringe pump (Sage Instruments, Model 341A) through a length of 1/16-in.stainless steel tubing. Gas mixtures of hydrogen, hydrogen sulfide and helium were prepared in a mixing tank equipped with a magnetic impeller and a high-resolution pressure gauge and flowed into the vaporizer through a gas mass flow controller (Datametrics Model 831). The reactant mixture of vaporized thiophene and the gas mixture then entered the flow microreactor consisting of a 3/8-in.-o.d.X 20-cm-long stainless steel tubing and a heating block. The catalytic bed of 1.0-cm height was filled with a mixture of catalyst sample (typically 20 mg) and quartz powder (about 200 mg), and the rest of the reactor was filled with the proper amount of carborundum. The temperature of the bed was controlled at a constant level (h0.5 "C) by a Chromel-Alumel type temperature controller. The products sampled through a six-port valve were analyzed by a gas chromatograph (GC, Gow-Mac 750, FID) with a numerical integrator. Both a OV-101 column (1/8 in., 6 ft) and a n-octane on Poracil C column ( l / 8 in., 6 ft) operating in a switching mode were used for analysis. Before the reactions were started, the catalyst was presulfided for 2 h at 400 "C in situ undr a flow of 10% H,S/H, at 60 cm3/min and then flushed for 1h at 400 OC by Nz. The details of the reaction conditions are shown in Table 11, and it was confirmed through preliminary experiments and calculations that mass- and heat-transfer limitations could be neglected (Choi, 1987). Helium was used to control the partial pressure of each reactant, and the total conversion of thiophene was kept below 6%, 0 1990 American Chemical Society
1148 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990
Table IV. Kinetic Data VP
partial pressure, atm 325 "C
T P TI UF F
41
Trap pressure gauge
W vp IT
MIXing tank
Mass flow c o n t r o l l e r
sv
Rotameter Syringe p u m p
GC IT
Thiophene r e s e i v o ~ r i'aporlzer Reactor Sampling v a l v e Gas chromatograph integrator
Figure 1. Schematic diagram of the reaction apparatus. 300 "C
Table 11. Reaction Variables variables reaction temp, "C partial pressure, atm hydrogen thiophene hydrogen sulfide thiophene flow rate, mol/h catalyst loading, mg particle size, mesh
operation range 275-325 0.44-1.16 0.03-0.43 0-0.09 4.85 X 10-3-3.86 20-40 100-150
ref condition 325 0.94 0.06 0
X
6.48 X 20 100-150
Table 111. Characteristics of the Catalvtic Packed Columns column mass of catalyst, g particle size, mesh length, cm bed void fraction
CoMo 5.59 60-80 30.2 0.344
NiMo 5.69 60-80 30.1 0.391
NiW 5.78 60-80 29.9 0.382
which had been necessary for the approximation under the differential reactor condition. Each catalyst reached a steady state after about 6 h under the reference condition, and the variations of reaction temperature and partial pressure of each reactant were followed. Adsorption Apparatus and Procedure. The apparatus consisted of a gas chromatograph (Varian 920, TCD) equipped with the catalytic packed column, a six-port valve for injection of a gas pulse (pulse size, 0.5 cm3), and a five-way valve for switching of each gas stream. The thiophene pulse (pulse size, 0.1 p L ) was injected by a Hamilton microsyringe. The retention times of each pulse was recorded on a numerical integrator. The details of each packed column are shown in Table I11 (refer to Table I for the properties of each catalyst). The catalytic bed was presulfided and flushed in situ in the GC oven according to the same procedure as explained in the reaction experiments, and the adsorption experiment was started. The flow rates of helium ranged from 10 to 40 cm3/min (at 25 "C), and the oven temperature was kept at 275,300, or 325 "C. The differences in retention times between nitrogen and other adsorbents were measured with the variation of carrier flow rate and oven temperature. The details of theoretical background for calculation of the adsorption equilibrium constant are shown in Schneider and Smith (1968),and the procedures are shown in Gonzalez and Siri (1985). The adsorption equilibrium constants were calculated from the following equation, which was proposed by Gonzalez and Siri: &I
= FI
(Fl)i
= (1- ~ ) / ~ ( P ~ K A ) L (A) /u
where A p , is the net retention time of each adsorbent pulse
275 "C
Pr
Pw
0.075 0.109 0.184 0.296 0.433 0.109 0.109 0.109 0.109 0.109 0.109 0.029 0.053 0.166 0.228 0.304 0.075 0.109 0.184 0.296 0.433 0.109 0.109 0.109 0.109 0.109 0.109 0.029 0.053 0.166 0.228 0.304 0.075 0.109 0.184 0.296 0.433 0.109 0.109 0.109 0.109 0.109 0.109 0.029 0.053 0.166 0.228 0.304
0.657 0.657 0.657 0.657 0.640 0.437 0.821 1.040 0.603 0.603 0.603 1.162 1.128 0.997 0.944 0.806 0.657 0.657 0.657 0.657 0.640 0.437 0.821 1.040 0.603 0.603 0.603 1.162 1.128 0.997 0.944 0.806 0.657 0.657 0.657 0.657 0.640 0.437 0.821 1.040 0.603 0.603 0.603 1.162 1.128 0.997 0.944 0.806
Ps 0 0 0 0 0
0 0 0 0.011 0.055 0.109 0.009 0.019 0.017 0.011 0.040 0 0 0 0 0 0 0 0 0.011 0.055 0.109 0.009 0.019 0.017 0.011 0.040 0 0 0 0 0 0 0 0 0.011 0.055 0.109 0.009 0.019 0.017 0.011 0.040
reaction rate x lo', mol/(g cat.-s) CoMo NiMo NiW 3.765 4.170 1.176 5.205 5.842 1.737 6.561 9.187 2.322 9.584 12.051 3.605 11.306 16.111 5.477 4.083 6.373 1.960 6.834 8.126 2.300 7.231 2.677 5.482 2.399 4.570 3.693 1.747 2.815 3.168 1.357 2.046 3.989 1.161 3.123 4.748 1.393 3.974 9.532 14.906 13.258 17.819 17.342 2.105 3.345 1.053 2.868 4.327 1.198 3.148 6.669 1.283 4.642 7.935 2.209 6.478 10.791 3.411 2.448 4.702 0.988 4.235 6.209 1.259 4.484 1.407 3.902 1.356 2.221 2.532 1.091 1.535 2.259 0.687 1.139 2.853 0.987 1.500 3.023 1.284 1.950 5.616 10.015 7.227 12.614 12.068 0.842 2.049 0.485 1.084 2.637 0.576 1.761 3.926 0.780 5.067 1.053 2.565 3.236 5.866 2.005 1.257 2.817 0.507 4.087 0.614 1.947 1.172 2.089 2.649 1.186 1.339 1.703 0.665 0.899 1.254 0.350 0.673 1.787 0.532 0.700 1.771 0.512 1.025 5.871 3.722 7.636 3.408 6.923
and KA is the adsorption equilibrium constant of the adsorbent.
Results and Discussion Determination of the Kinetics. The major products from the thiophene HDS reaction were 1-butene, cis-2butene, trans-2-butene, and a rather small portion of nbutane. Tetrahydrothiophene was detected in trace amounts under some reaction conditions (below 1%of the products). Generally it was found that the relative portion of the hydrogenated compounds such as n-butane and tetrahydrothiophene increased in the order CoMo < NiMo < NiW and that H2S added in the feed retarded the rate, whereas C4compounds has little effect on the rate. Thus, the strong inhibition effect of H,S and a weak effect of C4 products, which was consistent with other works (Vrinat, 1983),had been assumed a priori for experimental design and also for the selection of kinetic correlations. The kinetic data obtained at 275, 300, and 325 " C on CoMo, NiMo, and NiW systems are shown in Table IV. Fourteen models of Langmuir-Hinshelwood type kinetic equations were considered to fit the data, and they are
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1149 Table V. Langmuir-Hinshelwood Type Rate Equations Considered for the Correlation of the Kinetic Data
r = (kPTPHnl)/[(l
+ KTPT+ K$s + (KHPH)")'(l + (KHPH)nS)m]
model 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 2 3 3 2 3 1 2 1 2 1 1 2 1 2
m 0 0 0 0 0 0 0 1 1 2 1 1 2 2
nl 1 1 2 1 1 1 1 1 1 2 0.5 0.5 1 1
n2
nl
1 1 1 0.5 0.5
* * * * * * *
* *
1 1 1 0.5 0.5 0.5 0.5
"The * indicates that the (KHPH)"?term does not appear in the kinetic equation.
listed in Table V. These models can be discriminated in terms of the different reaction mechanisms involved as follows: (1)the mode of thiophene adsorption (r-bonding or a-bonding); (2) the dissociative or molecular type adsorption of hydrogen; (3) the competitive or noncompetitive adsorption of thiophene and hydrogen. These equations were examined via a nonlinear least-squares regression method (Kuster and Mize, 1973). The criteria for selection of the best fitting equations were as follows: (1)a positive value for the rate constants and adsorption equilibrium constants; (2) a positive value for the reaction activation energy and for the heat of adsorption; (3) the smallest value of the sum of squares. Table VI shows the sum of squares of the difference between the experimental and calculated values in the regression. CoMo/A1203. Three equations (models 1, 6, and 7) showed a good fitting to the data. However, model 1
showed negative value for Ks and KH,and model 6 gave negative heats of adsorption in thiophene and H2S. Thus, model 7 was selected. NiMo/A120s. Three equations (models 1,6, and 7) were superior for fitting the data. Model 1was discarded due to the negative value for KH. All the parameters of models 6 and 7 satisfied selection criteria 1 and 2 above. However, model 6 showed a slightly higher value of the sum of squares than did model 7 and values that were too large for KT and Ks. Thus, model 7 was selected. NiW/A1203. Four equations (models 1,7-9) revealed a good correlation with the data. Model 9 showed little variation in KT and Ks with temperature, whereas models of 1, 7, and 8 satisfied the above criteria well and gave nearly the same degree of error. Model 7 was preferred in the NiW system to model 1 as a single-site model since model 7 was selected also in the CoMo and NiMo systems. Model 8 was also chosen as a dual-site model since it showed the smallest error value among the three models and it was possible to assess the relative size of KH, KT, and Ks. The model equations and their parameters selected for each catalyst are summarized in Table VII. It is interesting that the three catalytic systems with different kinds of active metals are well correlated by model 7 and that the NiW system was fitted by model 7 as well as model 8. Model 7 implies a single type of adsorption site with one-point adsorption of thiophene and a relatively weak adsorption of hydrogen, or a Rideal mechanism of hydrogen with two-point adsorption of thiophene. On the other hand, model 8 indicates a noncompetitiveadsorption of thiophene and hydrogen with one-point adsorption of thiophene on one site and the molecular adsorption of hydrogen on the other site. Accordingly, it is presumed that the NiW system has a relatively higher hydrogen adsorption capability than the CoMo or NiMo system, possibly due to the relatively weak adsorption of thiophene and hydrogen sulfide. It is shown in Table VI that the adsorption constants KT and Ks decrease in the following order: CoMo > NiMo > NiW.
Table VI. Sum of Squares of the Difference between Experimtmtal and Calculated Values in the Best Fitting Rate Equations ( X lo-')" model 1 2 3 6 7 8 9
275 "C
CoMo 300 "C
325 "C
275 "C
NiMo 300 "C
325 "C
41.1 41.3
78.8 75.4
49.7 48.1
143.4 139.3
263.8 236.7
* 15.8 27.8
275 "C 7.2 7.5 7.1 7.1 7.1 7.2
NiW 300 "C 8.7 8.8 9.4 9.0 9.0 8.4 8.8
325 OC 13.6 13.7 15.4 14.6 14.1 13.1 13.5
"The * showed the negative value of the parameters or that it failed to converge. Models 4, 5, and 10-14 were not included in the table due to the negative parameters for all cases.
Table VII. Rate Equations That Best Fit the Kinetic Data catalyst CoMo" NiMo" NiWa NiWb
temp, OC 275 300 325 275 300 325 275 300 325 275 300 325
i03k, mol/(pwatm*) 4.38 5.10 8.97 5.35 8.06 10.91 1.00 1.63 2.62 1.12
2.54 4.18
K r , atm-' 2.29 1.15 1.07 1.20
0.94 0.78 0.56 0.44 0.41 1.51 1.45 1.37
Ks, atm-' 4.18 3.89 3.69 2.17 1.53 1.28 0.84 0.46 0.24 2.14 2.01 1.60
Kw, atm-'
E, kcal/mol 10.07 9.27 13.91
0.08 0.57 0.64
17.35
1150 Ind. Eng. Chem. Res., Vol. 29, No. 7 , 1990
0
275
4
3 0 0 OC
0
OC
3 2 5 OC
P
0
E*S
A
Thiophene
0
?-Butene
0.2
0.1
L/U
(
min
)
Figure 2. Effect of the adsorption temperature on thiophene retention time over the CoMo/A1203catalyst.
Figure 3. Difference of the retention time among the adsorbents over the CoMo/A1203catalyst a t 300 O C .
Hydrogen sulfide acted as a poison and showed a slightly stronger adsorption than did thiophene in all systems. Also it was believed that hydrogen adsorption was not of the dissociative type under the experimental conditions since all the equations assuming the dissociative adsorption failed in the correlation. The apparent activation energy of the CoMo system was about 10 kcal/mol and was fairly well consistent with other studies performed under similar reaction conditions (Lee and Butt, 1977; Morooka and Hamrin, 1977). The NiW system, in contrast, showed a higher temperature dependence with a larger value, about 14 kcal/mol. Although the NiMo system followed a similar trend to the CoMo system in many aspects, it showed higher rate constants together with lower activation energies. Measurements of the Adsorption Equilibrium Constants. The net retention times of each reactant referenced to the inert gas (nitrogen) are shown in Figures 2-5. Figure 2 shows the influence of adsorption temperature on thiophene retention time over the CoMo system. It indicated clearly that the slope proportional to the adsorption constants decreased with temperature. The difference in retention times among the adsorbents over the CoMo system at 300 OC is shown in Figure 3. The slopes decreased in the order hydrogen sulfide > thiophene > 1-butene > hydrogen. It was noted that the slope for hydrogen was neglibible compared to the slope of the others, implying its weak adsorption over the CoMo system. Figure 4 shows the difference in retention times of each adsorbate (thiophene, 1-butene, and Ha)among the three catalytic sytems at 300 OC. The ordinate axes of the figures were normalized by adopting Aplcu/pp(l - tu) instead of Apl so that the slopes indicate the adsorption equilibrium constants directly. The slope of each adsorbent in parts A-C in Figure 4 decreased in the order CoMo > NiMo > NiW. However, the retention times of hydrogen showed somewhat different results compared to the other adsorbents in all catalytic systems (Figure 5). They increased slightly the reversed order CoMo < NiMo < NiW. It is
Table VIII. Adsorption Equilibrium Constants Obtained from the ChromatoaraDhic Pulse Techniaue constant, cm3/g temp, "C CoMo NiMo Ni W KT
K, KB
KH
275 300 325 275 300 325 275 300 325 275-325
8.42 5.16 3.21 11.16 6.68 4.15 1.38 1.00 0.74 0.13 f 0.01
6.01 4.06 2.75 6.83 5.46 4.40 1.21 0.91 0.66 0.14 f 0.02
3.04 1.98 1.26 6.65 4.70 3.24 0.72 0.52 0.38 0.17 i 0.02
also noted that the slope does not show any temperature dependence. The adsorption equilibrium constants obtained from these slopes were summarized in Table VIII. The adsorption constants of H2S were slightly higher than those of thiophene in all systems. Meanwhile, those of 1-butene were in the range to 1/5 of thiophene. In general, the NiW system showed much smaller values of the adsorption constants than did the other systems, except for hydrogen. Although the absolute values of hydrogen were very small compared to the other adsorbents, the value was the largest in the NiW system. These results represent that hydrogen adsorption was more important in the NiW system because of the relatively weak adsorption of the other reactants. The different kinetic correlation by model 8 for the NiW system was ascribed to the higher hydrogen adsorption, and the difference among the catalytic systems would become more significant at such a high hydrogen pressure as applied to the real commercial process. It was noted that the adsorption parameters of Table VI1 obtained from the simple kinetic correlation showed a very similar trend to those of Table VI11 obtained from the direct adsorption measurements. Conclusion The kinetic and adsorption studies on thiophene hydrodesulfurization were made on three catalytic systems,
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1151
0
P
COMO
0.2
0.1
L/U
(
min )
Figure 5. Difference of the hydrogen retention time among the catalytic systems at (closed symbols) 275 O C , (open symbols) 300 O C , and (slashed symbols) 325 O C .
CoMo/A1203,NiMo/A1203, and NiW/A1203. The effects of different kinds of active metals on the kinetics were discussed. The adsorption equilibrium constants were measured from a separate adsorption study and compared with the results of the kinetic study. The major conclusions are (i) the three catalytic systems show the same type of rate equation under atmospheric hydrogen pressure irrespective of the kinds of active metals, (ii) the NiW system shows the possibility of higher hydrogenation functionality through the relatively weaker adsorption of thiophene and H2S than does the CoMo or NiMo system, (iii) hydrogen adsorption is very weak compared to other reactants and not of dissociative type under the present reaction condition, and (iv) the adsorption constants of thiophene, H2S,and 1-butene decrease in the order CoMo > NiMo > NiW, whereas hydrogen shows the reversed order.
Nomenclature E = apparent activation energy, kcal/mol K , = adsorption equilibrium constant of each adsorbent in eq A, cm3/g KB, K H ,Ks, KT = adsorption equilibrium constants of 1butene, hydrogen, H2S, and thiophene, respectively, atm-' k = apparent rate constant, mol/(g catalyst-s.atm2) L = packed bed length, cm PH,Ps,PT= partial pressure of hydrogen, H#, and thiophene, respectively, atm r = reaction rate, mol/(g catalyst4 u = interstitial carrier velocity, cm/min Superscripts 1, m , nl, n2,n3 = reaction order in Table V IJ/U
(min
)
(CI
Figure 4. Difference of the retention time among the catalytic systems at 300 O C in (A) thiophene, (B)H2S, and (C)1-butene.
Greek Letters = void fraction in the bed pl = retention time of each adsorbent pulse, min (Y
(pl) = retention time of the reference pulse, pp = apparent density of catalyst, cm3/g
min
Ind. Eng. Chem. Res. 1990,29, 1152-1160
1152
Registry No. HT400E, 113255-47-3; HTSOOE, 113255-48-4; NI4301E, 126925-24-4;Co, 7440-484; Mo, 7439-987; Ni, 7440-02-0; W, 7440-33-7.
Rev. Sci. Eng. 1980,22 (3), 371-400. Gonzalez, M. G.; Siri, G . J. Adsorption studies on cobalt-molybdenum catalysts by gas chromatography. Appl. Catal. 1985, 14, 23-32. ~~
Literature Cited Cerny, M.; Trka, A. Formation of sulfur compounds during the hydrodenitrogenation of aniline, cyclohexylamine, benzylamine, and 2-phenylethylamine on a nickel-tungsten catalyst in the presence of hydrogen sulfide. Collect. Czech. Chem. Commun. 1984, 49, 2387-2392. Choi, H. J. A study on the kinetics of hydrodesulfurization of thiophene. Master Thesis, Korea Advanced Institute of Science and Technology, Seoul, 1987. Dhainaut, E.; Charcosset, H.; Gachet, C.; Mourgues, L. Dibenzothiophene hydrodesulfurization by noble metal supported catalysts. AppE. Catal. 1982, 2, 75-86. Duchet, J. C.; Van Oers, E. M.; de Beer, V. H. J.; Prins, R. Carbonsumorted sulfide catalvsts. J. Catal. 1983. 80.386-402. Furimsky, E. Role of MoSiand WS, in hydrodesulfurization. Catal.
~~
Kuster, J. L.; Mize, J. H. Optimization Technique with FORTRAN; McGraw-Hill: New York, 1973. Lee, H. C.; Butt, J. B. Kinetics of the desulfurization of thiophene: Reaction of thiophene and butene. J . Catal. 1977,49, 320-331. Morooka, S.; Hamrin, C. E. Desulfurization of model coal sulfur compounds by coal mineral matter and a cobalt molybdate catalyst-I. Chem. Eng. Sci. 1977, 32, 125-133. Satterfield, C. N.; Modell, M.; Wilkens, J. A. Simultaneous catalytic hydrodesulfurization of pyridine and hydrodesulfurization of thiophene. Ind. Eng. Chem. Process Des. Deu. 1980,19,154-160. Schneider, P.; Smith, J. M. Chromatographic study of surface diffusion. AIChE J . 1968, 14, 886-895. Vrinat, M. i.The Kinetics of the hydrodesulfurization process-A review. Appl. Catal. 1983,6, 137-158. Received for review Julv 13. 1989 Aciepted February 9; 1990
Kinetic Modeling of Free-Radical Polymerization: A Conservational Polymerization and Molecular Weight Distribution Model M a r k Chaimberg a n d Yoram Cohen* Department of Chemical Engineering, University of California, Los Angeles, California 90024
A new computational model for free-radical polymerization reactions was developed. The model algorithm is based on the use of an implicit numerical technique to solve for the coupled monomer and total growing polymer concentration differential equations. Determination of the monomer and total growing polymer concentrations ensures that conservation of mass is maintained without the need to solve the large number of differential equations associated with the growing polymer concentrations for each individual chain length. Acceleration of the numerical calculations was achieved by lumping the growing polymer chains into distinct groups. The proposed numerical scheme generates the monomer conversion and a complete molecular weight distribution (MWD) of the growing and dead polymer chains. The current formulation allows for the incorporation of nonidealities, such as the onset of gelation and chain-length-dependent reaction rate coefficients. The application of the proposed model was demonstrated for the batch free-radical solution polymerization of styrene and the high conversion bulk polymerization of methyl methacrylate. Introduction The four major steps in the mechanism of free-radical polymerization, initiation, propagation, chain transfer, and termination, were described in the early work of Flory (1937). This reaction system can be represented by an infinite set of nonlinear differential equations, which describe the time rate of change in the concentration of every species. A variety of methods have been implemented both to generate solutions to the system of equations and to obtain information on the rate of polymerization and the resulting molecular weight distribution (MWD) (Ray, 1972). Early efforts to obtain an analytic solution to the rate of polymerization included the use of a quasi-steady-state assumption (QSSA) for the free-radical species and the long chain hypothesis (LCH) for growing polymer chains (Bamford and Tompa, 1954). In general terms, the QSSA states that the rate of radical initiation is approximately equal to the rate of radical termination. The LCH is based on the requirement that propagation is the dominant reaction for the consumption of monomer. The QSSA and LCH are commonly employed to simplify the calculation scheme of numerical algorithms. In conjunction with the
* Author
to whom correspondence should be addressed. 0888-5885/90/2629-1152$02.50/0
QSSA and LCH, a number of mathematical techniques, such as generating functions (Bamford and Jenkins, 1960), z transformations (Tirrell et al., 1975), and Laplace transformations (Bamford and Tompa, 1954), have been used to generate the polymer MWD. The use of the QSSA converts the time-dependent differential equations for the concentrations of the growing polymer species into time-invariant algebraic equations. Consequently,the remaining differential equations for the time rate of change in the concentrations of the monomer and dead polymer species no longer form a consistent overall mass balance. Relaxation of the mass balance constraint for the system of equations can result in small errors in the calculation of the individual species concentrations at each time step of integration. Furthermore, as the numerical simulation time increases, the error propagation in the individual species concentrations may become significant, thereby resulting in large errors in the overall mass balance (Gelinas, 1972; Edelson, 1973). Accurate determination of the overall mass balance is essential for polymerization reaction systems in which there is a significant degree of chain transfer to dead polymer chains or for graft polymerization reactions, which result in the formation of both homopolymer and grafted polymer species (Chaimberg et al., 1989; Domb and Avny, 1984; Vasantha et al., 1987; Raval et al., 1988). 0 1990 American Chemical Society
