Conversion-time data

It was found [1] that the values of and a, obtained in minimizing the error of fitting experimental conversion-time data, satisfactorily described the temporal evolutions of the molecular weight averages. Also, the model performed better in the description of the experimental data when a value of 3 = 1/2 was used. 

Experimental conversion-time data, obtained from the literature, on the bulk free radical polymerization of MMA initiated by AIBN at several temperatures and initiator concentrations, were described by the model. However, the expressions for the rate of conversion and gel effect index were first simplified and rearranged. ... 

By minimizing the error of fitting experimental x vs. t data with equation (16) after the onset of gel effect, the parameters CjL and C2 can be obtained. Figures 1-4 compare the predictions by the model with experimental conversion-time data. 

The shrinking core and the volume-reaction models have been examined to interpret the conversion-time data of combustion and steam gasification of the gingko nut shell char [4]. The shrinking core model provides the better agreement with the experimental data. With the shrinking core model, the relationship between [1-(1-X) ] and the reaction time t at 350°C -... 

More recently Penczek and his collaborators (134) have used l,3-dioxolan-2-ylium salts to initiate the polymerisation of THF in a variety of solvents. In these systems initiation is clean and efficient, and in the case of carbon tetrachloride as solvent, the only significant ionic species present are ion pairs. Rate constants /c for propagation in this solvent were obtained directly from conversion/time data and are a measure of the reactivity of ion pairs. At 25° C (tTHF]0 = 8.0 M) the value of /c (4.0 x 10 2 M-1 sec-1) was independent of the counter-ion employed, in the series AsFg, PFg, and SbFg. 

Using the E values evaluated from pore size distribution curves (Equation 1) corresponding to different degrees of conversion and the conversion-time data, the values of effective diffusivities of CO2 in the core and shell sections (D and D a respectively) are determined from Equations 8 and 9by a multiple regression analysis as 0.08 cmz/s and 0.12 cmz/s respectively at 860 °C. 

Figures 3 through 6 show conversion-time data for a number of vinyl acetate runs. The start-up procedure for these experiments consisted of filling the reaction vessel with degassed water prior to introducing any feed streams. Periodic samples were taken and the monomer conversion measured gravimetrically. As can be seen, some of the conversion transients did not reach a steady state. Tendency toward unsteady behavior and the magnitude of the oscillations seemed to increase with increasing initiator concentration and mean residence time. The influence of changing the emulsifier concentration is not clear.

Rewrite the design equation in terms of the measured variabte. When there is a net increase or decrease in the totai number of moles in a gas phase reaction, the reaction order may be determined from experiments performed with a constant-volume batch reactor by monitoring the total pressure as a function of time. The total pressure data should not be converted to conversion and then analyzed as conversion-time data just because the design equations are written in terms of the variable conversions. Rather, transform the design equation to the measured variable, which in this case is pressure. Consequently, we need to express the concentration in terms of total pressure and then substitute for the concemtation of A in Equation (E5-I.1),... 

P10-24c The reaction of cyclopentane to form n-pentane and coke was carried out over a palladium-alumina catalyst at 290°C [/. Catal., 54, 397 (1978)]. The following conversion-time data were obtained in a constant-volume batch reactor for a catalyst concentration of 0.01 kg/m and an initial reactant concentration of 0.03 kmol/m ... 

P10-25c The decomposition of spartanol to wulfrene and CO2 is often carried out at high temperatures [/ Theor. Exp., 15, 15 (2014)]. Consequently, the denominator of the catalytic rate law is easily approximated as unity, and the reaction is first-order with an activation energy of 150kJ/mol. Fortunately, the reaction is irreversible. Unfortunately, the catalyst over which the reaction occurs decays with time on stream. The following conversion-time data were obtained in a differential reactor ... 

In the case of alkyl vinyl ethers [27, 30] reaction rates were again high and the same experimental technique was used. However, the initiation reaction did not appear to be as fast as that in the polymerization of Al-vinylcarbazole, and the conversion/time data showed evidence of an initial acceleration to a maximum rate of polymerization, particularly in runs carried out at —25°C. The mechanism of initiation was assumed to involve direct addition of the initiating carbonium ion to the double bond of the monomer, in the light of related evidence from similar reaction in the presence of strong nucleophiles [80, 81]. At 0°C there was also an indication of a contribution from a termination reaction. Polymer yields were always in excess of 75%, however, and the termination process was neglected in the kinetic analysis. The simple scheme envisaged is ki... 

The left side of Eq. (6.99) is plotted against time t in Fig. 63 using the conversion-time data of the isoprene-AIBN system. The slope of the linear plot yields kd/2, and hence kd, of AIBN in isoprene. (kj, / ky ) jg tjjgn calculated from Eq. (6.98). This yields... 

This study has examined the effect of both steam-to-carbon (S C) ratio and temperature on deactivation. Conversion-time data during steam reforming were fitted to a transient reactor-model... 

The instantaneous conversion of EG or any other organic to CO2 would be characterized by the absence of chemical intermediates in the anolyte and a linear conversion-time (CO2 evolution) curve. In such a case, conversion would increase linearly with time to a maximum of 100%. Contrary to expectations, nonlinearity (curvature) was found to be one of the most obvious features of actual conversion-time data. A simple model has been formulated to explain thisnonlinear behavior by taking into account the sequential oxidation of known and suspected chemical intermediates [13]. 

The bulk iron oxide catalysts used in this work behaved selectively in methane combustion, giving only CO2 as a product below 700 C [8]. The evolution of methane conversion with time on stream after different periods of ageing at 600°C, is presented in figure 4 for the catalyst calcined at 500°C, while figure 5 shows the corresponding data for the catalysts calcined at 600 and 800°C. The examination of the conversion-time data show some interesting features. 

Some of the results obtained by fitting conversion-time data with equation 3. 

For reversible reactions the problem of interpretation becomes more difficult since we have basically the same number of data, conversion versus time, but two rate constants to determine. If eonversion data are available up to the point of equilibrium, we may use the equilibrium eomposition together with conversion-time data to solve for the two constants directly. Generally, however, we must assume that the experimenter does not have the time or patience to obtain true equilibrium information (bearing in mind that rates of reaetion are very slow at this point) so that a simple trial procedure is probably most eonvenient. For the first-order forward and reverse case of equation (1-61) one would choose a value of a, which is a function of both kf and k, and test for linearity by plotting In [a/ a — x)] versus time. The correct choice of a will result in a straight line of slope kf + k ), and then the values for a and the slope may be used to solve for the individual constants. If equilibrium data are available, the rate of reaction is zero and the rate equation used directly to obtain the equilibrium constant ... 

Most often for more complicated reactions than those discussed above, such as illustrated in Table 1.1b, direct methods of fitting conversion-time data become both tedious and difficult because of the convoluted form of the conversion equations and the number of rate constants incorporated in them. In such cases (and in the simpler ones also) the experimentalist can devise a number of special experiments which will simplify the subsequent task of interpretation. The most important of these are ... 

The values of k and q can be obtained from conversion-time data by methods already discussed. Additionally, a second series of experiments is now run in which Cbo > Cao> where ... 

By various combinations of these three methods, the kinetic constants of even very complex reactions can be obtained. At the least, one can expect to get preliminary values which can then be improved in obtaining a final fit to the conversion-time data. 

The information required here is not concentration versus time, but rate of reaction versus concentration. As will be seen later, some types of chemical reactors give this information directly, but the constant-volume, batch systems discussed here do not [ What does it profit you, anyway —F. Villon], In this case it is necessary to determine rates from conversion-time data by graphical or numerical methods, as indicated for the case of initial rates in Figure 1.25. In Figure 1.27 a curve is shown representing the concentration of a reactant A as a function of time, and we identify the two points Cai and Ca2 for the concentration at times q and t2- The mean value for the rate of reaction we can approximate algebraically by... 

What is the harm in differentiating polynomial fits of conversion-time data in order to obtain corresponding rate-conversion information ... 

From the conversion-time data of Problem 38, determine the corresponding rate-conversion information. Use this directly in the rate equation you postulated on the basis of the integral conversion data and compare the resulting rate constant with your previous values. 

Figure 4.23 Conversion-time data for the glyceride glycerine reaction.

In addition it must be observed that the thermal conversion obtained is specific for the manufacturing recipe in question. This means that a formal kinetics determined with the help of thermal conversion-time data sets must not be used for the assessment of a process modified either with respect to the mode of operation or the stoichiometric input ratio. 

Figure 2.3.5 shows the conversion-time data for the batch reactor polymerization of styrene in ether and acetone under FRRPP conditions (80°C). The half-life of the V501 initiator used in the ether system is about 130 min (Wako Chemicals, 1987). It is evident that there is a sharp rise in conversion at the beginning, followed by a period of reduced conversion rate. The onset of reduced conversion rate occurs at around 25%. 

Fig. 2.3.8 Conversion-time data for polymerization of 16.7 g styrene in 100 g ether using 0.17 g V-65 as initiator at 80°C, and 30 g styrene in 100 g ether using 0.15 g V-65 at 60° C (Replotted with permission from Caneba etal.,2003)...

As seen from phase equilibria and polymerization results, the entry of the FRRPP system in the phase envelope can be linked with the reduction in conversion rate. From conversion-time data alone, it was evident that the FRRPP system had better reaction control after the onset of phase separation, even though it might have a greater tendency to go into autoacceleration at the beginning of the reaction. 

In the previous section, conversion-time data indicate that for the FRRPP of styrene in ether, practical asymptotic values of 15 or 40% conversion were achieved for starting monomer compositions of 10 or 14.3 wt% (Figs. 2.3.5 and 2.3.8). From the phase envelopes shown in Fig. 2.3.1, these data correspond to overall polymer compositions in the reactor to be up to 2 or 4 wt% only. It should also be noted that number-average PS molecular weights were only up to 6,000 Da (Fig. 2.3.6) or 3,000 Da (Fig. 2.3.9), while thermodynamic data in Fig. 2.3.1 went down to PS molecular weight of only 25,000 Da. This means that the polymer may not have entered the polymer-rich regions in the phase diagram if it is required to cross the IPPC or spinodal, from a nonreactive standpoint. Indeed, reactor fluids have been shown to exhibit viscosities close to that of the solvent than a polymer solution at these conditions of FRRPP of styrene in ether. If the polymer macromolecules... 

In Fig. 3.1.2, conversion-time data are shown for mns similar to SAAl and SAA2, only that addition of initiator-containing fluid occurred within 5 min. The FRRPP run was ether based. The other runs involved the use of cyclohexane as solvent instead of pyridine. Cyclohexane precipitates PAA below the UCST, while it is a solvent to PS at the operating temperature. 

VA/AA copolymerizations have been found to produce materials with unimodal MWDs. Also, number-average moleeular weights were in the order of 30 kD. Some of the runs produced materials with relatively high AA contents (up to 32 wt%). Conversion-time data (Fig. 3.1.4) also indicate some adherence to a linear log-log plot. 

Fig. 3.2.1 The second-stage polymerization conversion-time data with addition of MAA in the intermediate solution of styrene polymerization in ether at 4 h into reaction...

Since the mechanism of the anionic dispersion pol3nnerization of styrene appears to follow a typical anionic homogeneous polymerization (i.e., "living" and narrow MWD s), it was felt that the kinetics should also be similar. For this study, the dispersion pol)niierization was carried out as previously described. At the end of any desired period of time, a few drops of methanol were added to terminate the pol3nnerization and the dispersion particles filtered, dried and weighed to give the required conversion/time data. 

The similarity of the Tg-time data in Figure 7 with the conversion-time data of Figure 5 is a consequence of the Tg-conversion relationship and illustrates... 

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