Plug flow reactor ideal design

Catal5dic gas-phase reactions are generally carried out in continuous fixed-bed reactors, which in the ideal case operate without backmixing. The model reactor is the ideal plug flow reactor, the design equation of which is derived from the mass-balance equation. As we have already learnt, in heterogeneous catalysis the effective reaction rate is usually expressed relative to the catalyst mass / cat, which gives Equation (14-1). The left side of this equation is known as the time factor the quotient is proportional to the residence time on the catalyst. 

Equations (59) and (60) are in a form often used for tubular, idealized, plug-flow reactors when the reaction rate is based on the volume of the reactor. When the reaction is heterogeneous, such as one occurring on the surface of a catalyst, it is common practice to base the reaction rate on the mass of the catalyst rather than on the volume of the reactor and substitute ric for r,. The resulting design equation equivalent to Eq. (60) is... 

The fluidized-bed reactor involves a rapid movement of the solid catalytic particles throughout the bed so that the operation can come close to one of uniform temperature throughout the reactor. The actual flow pattern for the operation of a fluidized bed is very complex and is between that for the ideal back-mix reactor and the ideal plug-flow reactor so that special methods for design may be required to approximate the real situation. 

These were calculated by numerical integration of Equation (8). SD must be less than SD if an ideal plug-flow reactor is to be designed and operated. 

The evaluation of catalyst effectiveness requires a knowledge of the intrinsic chemical reaction rates at various reaction conditions and compositions. These data have to be used for catalyst improvement and for the design and operation of many reactors. The determination of the real reaction rates presents many problems because of the speed, complexity and high exo- or endothermicity of the reactions involved. The measured conversion rate may not represent the true reaction kinetics due to interface and intraparticle heat and mass transfer resistances and nonuniformities in the temperature and concentration profiles in the fluid and catalyst phases in the experimental reactor. Therefore, for the interpretation of experimental data the experiments should preferably be done under reaction conditions, where transport effects can be either eliminated or easily taken into account. In particular, the concentration and temperature distributions in the experimental reactor should preferably be described by plug flow or ideal mixing models. 

This chapter discusses four methods of gas phase ceramic powder synthesis by flames, fiunaces, lasers, and plasmas. In each case, the reaction thermodynamics and kinetics are similar, but the reactor design is different. To account for the particle size distribution produced in a gas phase synthesis reactor, the population balance must account for nudeation, atomistic growth (also called vapor condensation) and particle—particle segregation. These gas phase reactors are real life examples of idealized plug flow reactors that are modeled by the dispersion model for plve flow. To obtain narrow size distribution ceramic powders by gas phase synthesis, dispersion must be minimized because it leads to a broadening of the particle size distribution. Finally the gas must be quickly quenched or cooled to freeze the ceramic particles, which are often liquid at the reaction temperature, and thus prevent further aggregation. 

For each of the ideal reactor types, viz. ideal batch reactor, plug-flow reactor (PFR), and continuous-flow stirred-tank reactor (CSTR), continuity equations or design equations can be derived using mass (or rather molar) balance equations for each species involved. 

Adams et al. (/. Catalysis 3, 379, 1964) investigated these reactions and expressed the rate of each as second order (first order with respect to each reactant). Formulate the dimensionless, reaction-based design equations for an ideal batch reactor, plug-flow reactor, and a CSTR. 

Formulate the dimensionless, reaction-based design equations for ideal batch reactor, plug-flow reactor, and CSTR using the heuristic rule. ... 

Consequently, we see that Equation (1-11) applies equally well to our model of tubular reactors of variable and constant cross-sectional area, although it is doubtful that one would find a reactor of the shape shown in Figure 1-11 unless it were designed by Pablo Picasso. The conclusion drawn from the application of the design equation to Picasso s reactor is an imponant one the degree of completion of a reaction achieved in an ideal plug-flow reactor tPFR) does not depend on its shape, only on its total volume. 

Most large reactors do not fit the foregoing criteria, but in many cases the deviations from ideal reactors are small, and the equations for ideal reactors can be used for approximate design calculations and sometimes for determining optimum reaction conditions. In this chapter, ideal stirred-tank reactors are considered first and then plug-flow reactors are discussed. The effects of heat transfer, mass transfer, and partial mixing in real reactors are treated in later chapters. 

The coimterpart of the ideal plug flow reactor is the ideal continuous stirred-tank reactor with complete backmixing of the rection mass. Because of the ideal mixing, the reaction rate is constant, and a simple design equation is obtained for the catalysis reactor (Eq. 14-3). 

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