Chemical reactors classical models

Many elements of a mathematical model of the catalytic converter are available in the classical chemical reactor engineering literature. There are also many novel features in the automotive catalytic converter that need further analysis or even new formulations the transient analysis of catalytic beds, the shallow pellet bed, the monolith and the stacked and rolled screens, the negative order kinetics of CO oxidation over platinum,... 

Part 1 Control of Chemical Processes. Some common problems in chemical processes are presented and either classical solutions or physical interpretation of controllers are discussed. Thus, the first chapter includes modeling and local control whereas the second chapter is focussed on nonlinear control design from heat balance on chemical reactors. The three first chapters deal with regulation problems while the last one is devoted to a tracking one. 

In this section the classical heat and mass transfer theories are examined. The singular surface jump conditions for the primitive quantities, as derived in the framework of the standard averaging procedures, are approximated by the classical chemical engineering stagnant film theory normally used in chemical reactor models. The relevant transport phenomena solutions and the classical theories on heat and mass transfer considering both low- and high mass transfer rates are summarized in the subsequent subsections. 

Residence time distribution (RTD) is a classical tool in the prediction of the comportment of a chemical reactor provided that the reaction kinetics and mass transfer characteristics of the system are known, the reactor performance can be calculated by combining kinetic and mass transfer models to an appropriate residence time distribution model. RTDs can be determined experimentally, as described in classical textbooks of chemical reaction engineering (e.g. Levenspiel 1999). RTD experiments are typically carried out as pulse or step-response experiments. The technique is principally elegant, but it requires the access to the real reactor system. In large-scale production, experimental RTD studies are not always possible or allowed. Furthermore, a predictive tool is needed, as the design of a new reactor is considered. 

Vertical CVD Reactors. Models of vertical reactors fall into two broad groups. In the first group, the flow field is assumed to be described by the one-dimensional similarity solution to one of the classical axisymmetric flows rotating-disk flow, impinging-jet flow, or stagnation point flow (222). A detailed chemical mechanism is included in the model. In the second category, the finite dimension of the susceptor and the presence of the reactor walls are included in a detailed treatment of axisymmetric flow phenomena, including inertia- and buoyancy-driven recirculations, whereas the chemical mechanism is simplified to a few surface and gas-phase reactions. 

In both models the only model parameter used is the mean residence time tpp and tpsR F gtire 6 shows the reactor dynamics of the PFR and the PSR in the normalised time and frequency domain (dimensionless time 0 = t/T, dimensionless frequency fg = l/2jt9). In the time domain the step response F(9) as well as the impulse response E(0) (which is the RTD) can be discussed. This type of data presentation is normally used in chemical engineering application. But the same data can also be presented in the frequency domain, the so called Bode plot. This type of presentation allows to identify effects which are not visible in the classical used plot in the time domain. The Bode plot consists of the magnitude Gj 030)1 and the phase arg G(jO)0). ... 

Another class of equations subsumes kinetic and phase transformations of all involved reactants. Such equations describe how the reactants molecules are transformed and distributed in the reactor depending on time and other environmental parameters. Depending on the kind of chemical processes under consideration, both classes of equations are of varying importance for modelling. E.g. for catalytic packed-bed reactors the chemicals reaction rates heavily depend on local physical conditions at the (solid) catalyst material. The precise modelling of the local physical conditions and the mixture of chemicals flowing is important and complex in this case. In contrast, for classic stirred-tank reactors kinetic and phase transformations are comparatively easy to model. 

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