Reactors for a Single Reaction

In this chapter we develop the performance equations for a single fluid reacting in the three ideal reactors shown in Fig. 5.1. We call these homogeneous reactions. Applications and extensions of these equations to various isothermal and noniso-thermal operations are considered in the following four chapters. 

In the batch reactor, or BR, of Fig. 5.1 the reactants are initially charged into a container, are well mixed, and are left to react for a certain period. The resultant mixture is then discharged. This is an unsteady-state operation where composition changes with time however, at any instant the composition throughout the reactor is uniform. 

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Generally, the temperature changes with time or, equivalently, with distance from the reactor inlet (for flow reactors). This change is usually controlled well in reaction calorimeters but can become uncontrolled in other conventional laboratory flow or (semi)batch reactors. The balance equations of a batch reactor for a single reaction of a-th order kinetics are given by ... 

Chapter 5 Ideal Reactors for a Single Reaction SOLUTION... 

COMPARISON OF BATCH, TUBULAR AND STIRRED-TANK REACTORS FOR A SINGLE REACTION. REACTOR OUTPUT... 

Figu re 6.3 Batch reactor For a single reaction of the type A + B -> P, both reactants A and B are charged initially into the vessel. Therefore, temperature control is practically the only way to influence the reaction course. 

Equation (7-54) allows calculation of the residence time required to achieve a given conversion or effluent composition. In the case of a network of reactions, knowing the reaction rates as a function of volumetric concentrations allows solution of the set of often nonlinear algebraic material balance equations using an implicit solver such as the multi variable Newton-Raphson method to determine the CSTR effluent concentration as a function of the residence time. As for batch reactors, for a single reaction all compositions can be expressed in terms of a component conversion or volumetric concentration, and Eq. (7-54) then becomes a single nonlinear algebraic equation solved by the Newton-Raphson method (for more details on this method see the relevant section this handbook). 

One-dimensional models basically assume that species concentrations and fluid temperature vary only in the axial direction. The only transport mechanism operating in this direction is the overall convective flow. The conservation equations may be obtained from mass and energy balance on a reference component A, over an elementary cross section of the tubular reactor. For a single reaction, the steady state conservation equations can be written for the pseudo-homogeneous model as follows ... 

Here, r j is the generalized rate of reaction for reaction j [in mol/(time x volume)] (it is equal to rj for a unit volume of reactor). For a single reaction, the design equation simply becomes... 

First, let us inspect the basic equations of a fixed reactor for a single reaction of reactant A and steady state, if the so-called pseudo-homogeneous two-dimensional model in its most complex form is used (for simplification, all data on chemical media and also the fluid velocity are considered to be constant throughout the reactor, that is, only the values of Tand c change) ... 

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