Concentration, kinetic modeling

A feed concentration of 15 g glucose and 15 g xylose per litre was used over a feed rate of 20-200 ml/hr. Samples were taken at successive points along the reactor length, and the usual analysis for glucose and xylose consumption, organic acid production and cell density were done. A kinetic model for the growth and fermentation of P. acidipropionici was obtained from these data. 

Table 8.1 presents the results of the ICR retention time studies, sugar concentration (dual substrate) studies and cell density. The kinetic model for ICR was derived on the basis of a first order reaction, plug flow and steady-state behaviour. 

Our initial experimental results indicated that the kinetic model— first order in liquid phase CO concentration—was the leading candidate. We designed an experimental program specifically for this reaction model. The integrated rate expression (see Appendix for nomenclature) can be written as ... 

The preferred kinetic model for the metathesis of acyclic alkenes is a Langmuir type model, with a rate-determining reaction between two adsorbed (complexed) molecules. For the metathesis of cycloalkenes, the kinetic model of Calderon as depicted in Fig. 4 agrees well with the experimental results. A scheme involving carbene complexes (Fig. 5) is less likely, which is consistent with the conclusion drawn from mechanistic considerations (Section III). However, Calderon s model might also fit the experimental data in the case of acyclic alkenes. If, for instance, the concentration of the dialkene complex is independent of the concentration of free alkene, the reaction will be first order with respect to the alkene. This has in fact been observed (Section IV.C.2) but, within certain limits, a first-order relationship can also be obtained from many hyperbolic models. Moreover, it seems unreasonable to assume that one single kinetic model could represent the experimental results of all systems under consideration. Clearly, further experimental work is needed to arrive at more definite conclusions. Especially, it is necessary to investigate whether conclusions derived for a particular system are valid for all catalyst systems. 

The change of shape of the kinetic curves with monomer and inhibitor concentration at ethylene polymerization by chromium oxide catalysts may be satisfactory described 115) by the kinetic model based on reactions (8)-(14). 

The radical chain mechanism of the sulfochlorination is very similar to that of the chlorination. Accordingly, in normal cases the regioselectivities of the sulfochlorination and the chlorination are equal. For example, (-1) substituents decrease the reactivities of the adjacent C-H bond. This influence can even be observed at the y position. Thus, the consecutive second sulfochlorination affords no geminal or vicinal disulfochlorides in the product. Where there are differences between the regioselectivities of sulfochlorination and chlorination (as in the case of isoalkanes), it is because under the conditions of sulfochlorination, chlorination also takes place to a considerable extent. Figure 6 shows the main components of a sulfochlorination mixture. Today the kinetics and the regioselectivity of the sulfochlorination of /z-alkanes are so well known that the kinetic modeling of the concentration-conversion curves is possible for all partners of the reaction [12]. 

In conclusion, we have reviewed how our kinetic model did simulate the experiments for the thermally-initiated styrene polymerization. The results of our kinetic model compared closely with some published isothermal experiments on thermally-initiated styrene and on styrene and MMA using initiators. These experiments and other modeling efforts have provided us with useful guidelines in analyzing more complex systems. With such modeling efforts, we can assess the hazards of a polymer reaction system at various tempera-atures and initiator concentrations by knowing certain physical, chemical and kinetic parameters. 

Example 4.6 Use the kinetic model of Example 4.5 to determine the outlet concentration for the loop reactor if the operating conditions are the same as in Run 1. 

An analogous situation occurs in the catalytic cracking of mixed feed gas oils, where certain components of the feed are more difficult to crack (less reactive or more refractory) than the others. The heterogeneity in reactivities (in the form of Equations 3 and 5) makes kinetic modelling difficult. However, Kemp and Wojclechowskl (11) describe a technique which lumps the rate constants and concentrations into overall quantities and then, because of the effects of heterogeneity, account for the changes of these quantities with time, or extent of reaction. First a fractional activity is defined as... 

Elucidation of degradation kinetics for the reactive extrusion of polypropylene is constrained by the lack of kinetic data at times less than the minimum residence time in the extruder. The objectives of this work were to develop an experimental technique which could provide samples for short reaction times and to further develop a previously published kinetic model. Two experimental methods were examined the classical "ampoule technique" used for polymerization kinetics and a new method based upon reaction in a static mixer attached to a single screw extruder. The "ampoule technique was found to have too many practical limitations. The "static mixer method" also has some difficult aspects but did provide samples at a reaction time of 18.6 s and is potentially capable of supplying samples at lower times with high reproducibility. Kinetic model improvements were implemented to remove an artificial high molecular weight tail which appeared at high initiator concentrations and to reduce step size sensitivity. 

In this work, the MeOH kinetic model of Lee et al. [9] is adopted for the micro-channel fluid dynamics analysis. Pressure and concentration distributions are investigated and represented to provide the physico-chemical insight on the transport phenomena in the microscale flow chamber. The mass, momentum, and species equations were employed with kinetic equations that describe the chemical reaction characteristics to solve flow-field, methanol conversion rate, and species concentration variations along the micro-reformer channel. 

The kinetics of the ammonia synthesis have been discussed as an example of micro-kinetic modeling in Chapter 7. Here we present a brief description of the process, concentrating on how process variables are related to the microscopic details and the optimization of the synthesis. 

Two kinetic experiments with different CD concentrations were used for kinetic modeling. In this simulation all of the rate constants not involved in the hydrogenation step were not altered. The calculated and simulated kinetic curves and optical yield-conversion dependencies are shown in Figure 9a and 9b. The results of kinetic modeling indicates that the whole kinetic curve and the optical yield - conversion dependencies can be well described by a kinetic model derived from the shielding effect model. 

There are several examples in the literature of GFC now being utilized for small molecule analysis (17). However, in this case, attempts to obtain monomer concentrations for kinetic modelling were frustrated by irreproducible impurity peak interference with monomer peaks, time varying refractometer responses and insufficient resolution for utilization of a reference peak. This last point meant that injected concentration would have to be extremely reproducible. 

An alternate approach is to utilize the chromatogram heights as representative of individual concentrations of molecular size. From the kinetic modeling viewpoint, this leads to treating the polymerization as a well-characterized, multi-component reaction system. 

Phrasing kinetic models in terms of instantaneous property distributions which are summed to provide distributions at any conversion is then highly rewarding. The variation of individual concentrations with time from the GPC readily provides significant insight into the model requirements. 

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