Kinetic modeling series-parallel

An illustration of a series-parallel network is provided by the step-change polymerization kinetics model of Section 7.3.2. The following example continues the application of this model to steady-state operation of a CSTR. 

Kinetic mechanisms involving multiple reactions are by far more frequently encountered than single reactions. In the simplest cases, this leads to reaction schemes in series (at least one component acts as a reactant in one reaction and as a product in another, as in (2.7)-(2.8)), or in parallel (at least one component acts as a reactant or as a product in more than one reaction), or to a combination series-parallel. More complex systems can have up to hundreds or even thousands of intermediates and possible reactions, as in the case of biological processes [12], or of free-radical reactions (combustion [16], polymerization [4]), and simple reaction pathways cannot always be recognized. In these cases, the true reaction mechanism mostly remains an ideal matter of principle that can be only approximated by reduced kinetic models. Moreover, the values of the relevant kinetic parameters are mostly unknown or, at best, very uncertain. 

A parallel reaction is introduced in the kinetic model (3.58). When the results obtained with first-order kinetics, shown in Fig. 3.5, are compared with the corresponding first-order kinetic model with reactions in series (Fig. 3.3), a slight im-... 

In order to assess whether secondary reactions to form CO could be responsible for the experimental CO versus time curve shape, a series-parallel kinetic mechanism was added to the model. Tar and gas are produced in the initial weight loss reaction, but the tar also reacts to form gas. The rate coefficients used are similar to hydrocarbon cracking reactions. Fig. 5 presents the model predictions for a single pellet length. It is observed that the second volatiles maximum is enhanced. For other pellet lengths, the time of the second peak follows the same trends as in the experiments. While the physical model might be improved by the inclusion of finite rates of mass transfer, the porosity is quite large and Lee, et al have verified volatiles outflow is... 

Regarding fhe kinefic modeling, few contributions propose kinetic models for fhe PC oxidation of phenol and other aromatics (Chen and Ray, 1998, 1999 Li et al., 1999b Wei and Wan 1992 ), with kinetic models being based mainly on the initial rates of reacfion only. Such models fail to account for fhe formafion of fhe differenf reaction intermediates, which may play an important role in the overall mineralization rate. More recently, Salaices et al. (2004) developed a series-parallel kinetic model based on observable aromatic intermediates. This model was applied to a wide range of pH, phenol concenfrafion, and cafalysf t)q)e. In this model, however, some steps... 

Kinetic Model 2 (KM 2) lumped acids and CO2 production The kinetic model 1 considers only the oxidation of the major aromatic intermediates. As shown in the previous section, when most of the major intermediates have been depleted, there is still a substantial concentration of other remaining organic intermediates, as the TOC profile indicates. Therefore, it is of particular interest to calculate and predict the total mineralization times. Also, with TOC measurements, it is possible to approximate the amount of CO2 produced in the course of the reaction. In this new series-parallel model, the formation and disappearance of carboxylic acids as well as the production of CO2 has been incorporated. 

Figures 21a, b show the 4-CP, 4-CC, and HQ concentrations derived from inserting the estimated parameters in the kinetic model and a comparison with the experimental data under different operating conditions. Symbols correspond to experimental data and solid lines to model predictions calculated with Equations (64)-(66) and Equations (71)-(74). Eor these experimental runs, the RMSE was less than 14.4%. These experimental 4-CC and HQ concentrations are in agreement with the proposed kinetic mechanism of parallel formafion of fhe intermediate species (Figure 16), and also with the series-parallel kinetic model reported by Salaices et al. (2004) to describe the photocatalytic conversion of phenol in a slurry reactor under various operating conditions. ...

Figure 23a shows the predicted and experimental concentrations versus time of 4-CP, 4-CC, and HQ for a catalyst mass concentration of 0.5 x 10 g cm. As can be observed, the 4-CP concentration decreases throughout the experimental run following a first-order kinetics and the pollutant is completely degraded after 6h of irradiation. This figure also shows the formation and destruction of 4-CC and HQ, with a maximum at approximately Ih. Then, these two main intermediate species decrease gradually imtil they almost disappear at the end of the rim. The changes in the 4-CC and HQ concentrations are consistent with the proposed kinetic mechanism reported in Section 4.3, and with the series-parallel kinetic model... 

Schenk H.J., Horsfield B. (1998) Using natural maturation series to evaluate the utility of parallel reaction kinetic models an investigation ofToarcian shales and Carboniferous coals, Germany. Org. Geochem. 29, 137—54. 

The consideration of equations (1-12) and/or (1-13) leads to the advancement of photocatalytic conversion rate models, such as the series-parallel model proposed by Salaices et al. (2004) where the derived kinetic parameters are based on the iiradiated weight of catalyst. As such, these can be considered as intrinsic parameters with phenomenological meaning pertinent to the photocatalytic reaction. 

Kinetic Modeling of the Photocatalytic Reaction Network The Parallel-Series Approximation... 

Chapter V addresses the important task of accounting for the complex network of photochemical reactions, establishing viable kinetic modeling. This modeling is essentially based on a series-parallel model of the photocatalytic reaction network. 

Models for LLPTC become even more complicated for special cases such as PTC systems that involve reactions in both aqueous and organic phases, systems with a base reaction even in the absence of PT catalyst, or other complex series-parallel multiple reaction schemes. For example, Wang and Wu (1991) studied the kinetics and mass transfer implications of a sequential reaction using PTC... 

Regarding the chemical and electrochemical processes taking place in the inner layer, they are modelled as series-parallel elementary kinetic steps (see, for example, Franco " ). In this approach, for a given metallic element M (Pt or a transition metal, in the case of a bimetallic) at the catalyst level... 

In this chapter, we develop some guidelines regarding choice of reactor and operating conditions for reaction networks of the types introduced in Chapter 5. These involve features of reversible, parallel, and series reactions. We first consider these features separately in turn, and then in some combinations. The necessary aspects of reaction kinetics for these systems are developed in Chapter 5, together with stoichiometric analysis and variables, such as yield and fractional yield or selectivity, describing product distribution. We continue to consider only ideal reactor models and homogeneous or pseudohomogeneous systems. 

Apply the tanks-in-series model to the following kinetics scheme involving reactions in parallel ... 

---