THE OVERALL REACTOR MODELS

Integration of the above steps into the formulation of the overall reactor model and the inclusion of heat transfer between the catalyst bed and external cooling or heating media. 

The integration of the catalyst bed module into the overall reactor model depends largely on the configuration of the reactor system and the mode of its operation. In principle, the adiabatic single bed reactor is the simplest since for this configuration and mode of operation the catalyst bed module represents the overall... 

Brief literature review for the mathematical modelling of industrial ammonia converters Modelling of ammonia converters The catalyst pellets Elfectiveness factor for the catalyst pellets of ammonia converters The overall reactor model for the catalyst bed module... 

Chapter 5 is dedicated to the single particle problem, the main building block of the overall reactor model. Both porous and non-porous catalyst pellets are considered. The modelling of diffusion and chemical reaction in porous catalyst pellets is treated using two degrees of model sophistication, namely the approximate Fickian type description of the diffusion process and the more rigorous formulation based on the Stefan-Maxwell equations for diffusion in multicomponent systems. 

In all cases, the overall reactor model should be as rigorous as possible in all aspects other than the kinetic model otherwise deviation from industrial data may be due to inaccuracies other than those in the kinetic model. 

The overall reactor model comprises, as the heart of it, the single catalyst pellet model which is formulated in an overall framework that includes the changes in the bulk fluid phase. The equations for the catalyst pellet coupled with the equations for the bulk fluid phase represent what we may call in certain cases, the overall reactor model or in a more restricted sense, the catalyst bed module. This catalyst bed module may represent the overall reactor model in certain cases such as the single adiabatic catalytic packed bed reactor. In other cases, this module may represent only the essential part of the overall reactor model such as in non-adiabatic and multi-bed reactors. 

The heterogeneous model is developed in terms of the bulk variables with the effectiveness factor introduced to account for the diffusional limitations. Certain assumptions have to be made for the overall reactor model, these are ... 

A control algorithm has been derived that has improved the dynamic decoupling of the two outputs MW and S while maintaining a minimum "cost of operation" at the steady state. This algorithm combines precompensation on the flow rate to the reactor with state variable feedback to improve the overall speed of response. Although based on the linearized model, the algorithm has been demonstrated to work well for the nonlinear reactor model. 

This approach was successfully used in modeling the CVD of silicon nitride (Si3N4) films [18, 19, 22, 23]. Alternatively, molecular dynamics (MD) simulations can be used instead of or in combination with the MC approach to simulate kinetic steps of film evolution during the growth process (see, for example, a study of Zr02 deposition on the Si(100) surface [24]). Finally, the results of these simulations (overall reaction constants and film characteristics) can be used in the subsequent reactor modeling and the detailed calculations of film structure and properties, including defects and impurities. 

The model of the overall reactor was used to examine various scenarios, such as a cup with enlarged bottom orifice or the total absence of a cup. This type of malfunctioning mixing element (enlarged orifice or absent mixing cup) offers a point of... 

Using the latter two relations we may also approximate the residual dissipation rate, e.g., in terms of the residual viscosity determined by other LES closures, in case this parameter is needed for reactor modeling purposes like in population balance kernels and in species mixing model parameterizations provided that the overall closure models remain consistent [21]. 

Chapter 6 is concerned with the integration of the single catalyst pellet model into an overall reactor model and presents a number of detailed examples of the modelling and verification of important industrial catalytic reactors. Optimization of these reactors is also described together with the development of user friendly software packages. 

Although the development of overall reactor models will be treated in Chapter 6, it is interesting at this stage to present some of the implications of the non-monotonic kinetics of the steam reforming reactions on the overall reactor behaviour using models of different degrees of sophistication. 

The overall description (model) of a reactor is obtained through process synthesis by combining models of reactor hydrodynamics, mass transfer and heat exchange with an appropriate cell (subcellular) or population model ( 1).Description of a population should take into consideration possible dispersed or aggregated (the distinct morphological appearances of a culture pellets, mycelium, flocks, growth on reactor wall in the form of microbial film) forms of population. Biomass support particles are gaining appreciable importance in aerobic (40) as well as in anaerobic processes. 

The developed dynamic reactor model for the simulation studies of the unsteady-state-operated trickle-flow reactor is based on an extended axial dispersion model to predict the overall reactor performance incorporating partial wetting. This heterogeneous model consists of unsteady-state mass and enthalpy balances of the reaction components within the gas, liquid and catalyst phase. The individual mass-transfer steps at a partially wetted catalyst particle are shown in Fig. 4.5. 

The aim of the current study is to model the FT hydrocarbon product distribution on a cobalt-based catalyst under fixed-bed reactor conditions for both conventional (gas-phase) and non-conventional (near-critical and supercritical) phase media, as a first step towards modeling the overall reactor bed behavior. 

When Eq. (4) is coupled with controlling equations of mass and momentum for gas phase and solid phase, the detailed flow-reaction—diffusion process in a MTO fluidized bed reactor can be simulated (Zhao et al., 2013). In practical applications, simplified models for two-phase hydrodynamics are also proposed (Abba et al., 2003 Bos et al., 1995 Zhang et al., 2012), in which the detailed flow patterns cannot be calculated but it is very efficient in the overall reactor performance evaluation. 

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