Conversions, predicting

The first quantitative model, which appeared in 1971, also accounted for possible charge-transfer complex formation (45). Deviation from the terminal model for bulk polymerization was shown to be due to antepenultimate effects (46). Mote recent work with numerical computation and C-nmr spectroscopy data on SAN sequence distributions indicates that the penultimate model is the most appropriate for bulk SAN copolymerization (47,48). A kinetic model for azeotropic SAN copolymerization in toluene has been developed that successfully predicts conversion, rate, and average molecular weight for conversions up to 50% (49). 

Conversions predicted from Equation (9.20) depend only on the values of kt and Pe. The predicted conversions are smaller than those for piston flow but larger than those for perfect mixing. In fact. 

FIGURE 9.10 Relative error in the predicted conversion of a first-order reaction due to assuming piston flow rather than axial dispersion, kt versus Pe. 

Using copolymerization theory and well known phase equilibrium laws a mathematical model is reported for predicting conversions in an emulsion polymerization reactor. The model is demonstrated to accurately predict conversions from the head space vapor compositions during copolymerization reactions for two commercial products. However, it appears that for products with compositions lower than the azeotropic compositions the model becomes semi-empirical. 

For a single continuous reactor, the model predicted the expected oscillatory behaviour. The oscillations disappeared when a seeded feed stream was used. Figure 5c shows a single CSTR behaviour when different start-up conditions are applied. The solid line corresponds to the reactor starting up full of water. The expected overshoot, when the reactor starts full of the emulsion recipe, is correctly predicted by the model and furthermore the model numerical predictions (conversion — 25%, diameter - 1500 A) are in a reasonable range. 

The E-Z Solve software can be used to integrate equations 15.2-4 and 15.2-11 numerically, while simultaneously updating q, u, p, Re, and / at each step (file exl5-8.msp). The predicted conversion for isothermal, nonisobaric conditions is 0.247 the calculated pressure drop is 114 kPa. If the pressure drop is ignored (i.e., P = 400 kPa throughout the reactor), the resulting conversion is 0.274. Thus, for this case, it is important that the pressure drop be accounted for. 

Thus, for known kinetics and a specified residence time distribution, we can predict the fractional conversion of reactant which the system of Fig. 9 would achieve. Recall, however, that this performance is also expected from any other system with the same E(t) no matter what detailed mixing process gave rise to that RTD. Equation (34) therefore applies to all reactor systems when first-order reactions take place therein. In the following example, we apply this equation to the design of the ideal CSTR and PFR reactors discussed in Chap. 2. The predicted conversion is, of course, identical to that which would be derived from conventional mass balance equations. 

PREDICTING CONVERSION FROM A REACTOR SYSTEM IN WHICH A FIRST-ORDER REACTION IS TAKING PLACE. USE OF THE SYSTEM TRANSFER FUNCTION... 

Although it also is subject to the limitations of a single characterizing parameter which is not well correlated, the Peclet number, the dispersion model predicts conversions or residence times unambiguously. For a reaction with rate equation rc = fcC , this model is represented by the differential equation... 

If the intermolecular forces between solute particles and solvent molecules are weaker than the forces between solvent molecules alone, then the solvent molecules are less tightly held in the solution and the vapor pressure is higher than Raoult s law predicts. Conversely, if the intermolecular forces between solute and solvent molecules are stronger than the forces between solvent molecules alone, then the solvent molecules are more tightly held in the solution and the vapor pressure is lower than predicted. Solutions of ionic substances, in particular, often have a vapor pressure significantly lower than predicted, because the ion-dipole forces between dissolved ions and polar water molecules are so strong. 

This capability has many varied uses. It can direct research away from the blind alleys of infeasible reactions. It should be used more by those wanting to maximize production. Here is a yardstick by which to measure actual processes Do they approach the predicted conversion to products What are the effects of variables such as temperature, pressure and initial composition ... 

Figure 5.8 Comparison of experimental and predicted conversion vs In (t) curves, using an overall rate constant including chemical and diffusional resistances. (Wisanrakkit and Gillham, 1990 - Copyright 2001 - Reprinted by permission of John Wiley Sons, Inc.)... 

Predicted conversion profiles for a particular case are plotted in Fig. 9.19. For contact times such as those used in industrial practice (up to 30 s), they are extremely sharp. There is a moving conversion boundary, generated by the high value of the activation energy of the novolac-hexa reaction. 

Borroni B, Colciaghi F, Caltagirone C, et al. Platelet amyloid precursor protein abnormalities in mild cognitive impairment predict conversion to dementia of Alzheimer type A 2-year follow-up study. Arch Neurol 2003 60(12) 1740-1744. 

Most reactors used in industrial operations run isother-mally. For adiabatic operation, principles of thermodynamics are combined with reactor design equations to predict conversion with changing temperature. Rates of reaction normally increase with temperature, but chemical equilibrium must be checked to determine ultimate levels of conversion. The search for an optimum isothermal temperature is common for series or parallel reactions, since the rate constants change differently for each reaction. Special operating conditions must be considered for any highly endothermic or exothermic reaction. 

Fig. 12.10. Comparison between experimentally determined and predicted conversions of cyclohexane in the membrane reactor (Eq. (37)) as a function of the sweep (dilution) ratio (Eq. (36)) at 473 K for three different cyclohexane feed concentrations (right, 3.7 vol% center, 4.9 vol% left, 5.8 vol%). The corresponding equilibrium conversions, Xeq, are indicated by dashed lines.

Figure 1 shows the effect of gas flow rate predicted by the model on the solid conversion for a CO rich gas mixture. Three gas flow rates of 9,7 and 5 m/s are shown. Also illustrated is the predicted conversion for the model which does not include the... 

Application of the computational techniques to predict conversions on pads of industrial gauzes give results which are rather lower than practical experience suggests, due probably to interruptions of the boundary layer and the larger surface area associated with the roughness of the active commercial gauzes. 

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