Phenol-formaldehyde reaction reduced models

The chapter ends with a case study. Four different reduced kinetic models are derived from the detailed kinetic model of the phenol-formaldehyde reaction presented in the previous chapter, by lumping the components and the reactions. The best estimates of the relevant kinetic parameters (preexponential factors, activation energies, and heats of reaction) are computed by comparing those models with a wide set of simulated isothermal experimental data, obtained via the detailed model. Finally, the reduced models are validated and compared by using a different set of simulated nonisothermal data. 

According to the approach described in [11], two alternative reduced kinetic models are proposed here to describe the phenol-formaldehyde reaction network introduced in Sect. 2.4. This approach includes, first, the selection of a general class... 

The model-based controller-observer scheme requires to solve online the system of differential equations of the observer. The phenol-formaldehyde reaction model is characterized by 15 differential equations, and it is, thus, unsuitable for online computations. To overcome this problem, one of the reduced models developed in Sect. 3.8.1 can be adopted. In order to be consistent with the general form of nonchain reactions (2.27) adopted to develop the controller-observer scheme, the reduced model (3.57) with first-order kinetics has been used to design the observer. The mass balances of the reduced model are given by... 

In the case study, the adaptive model-based approach is designed on the basis of a reduced model of the phenol-formaldehyde reaction introduced in the Chap. 2. Noticeably, the results show that the model-based control scheme achieves very good performance even when a strongly simplified mathematical model of the reactive system is adopted for the design. 

In this section, the phenol-formaldehyde reactive system is considered as an example of identification of reduced kinetic models. The kinetic model containing 13 components and 89 reactions, developed in Sect. 2.4 to study the production of 1,3,5-methylolphenol, is too detailed and complex for control and monitoring purposes. Thus, in this section this model is referred to as detailed model, while four reduced kinetic models, based on lumped components and reactions, are developed. 

Peng and Riedl (1994) investigated the chemorheology of phenol formaldehyde resins filled with unmodified and methylolated lignin fillers. They found that both fillers reduced the reaction rate and that the chemorheology profile of filled systems is better represented by the WLF model than by the Arrenhius model. 

Phenol, here denoted as reactant A. Since the second reactant, formaldehyde, is fed to the reactor in large excess, its concentration can be assumed as a constant during the reaction thus, it does not explicitly appear in the rate expressions and has not been considered in the reduced kinetic models. 

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