Numerical example, catalytic reactor design

The concentration and temperature Tg will, for example, be conditions of reactant concentration and temperature in the bulk gas at some point within a catalytic reactor. Because both c g and Tg will vary with position in a reactor in which there is significant conversion, eqns. (1) and (15) have to be coupled with equations describing the reactor environment (see Sect. 6) for the purpose of commerical reactor design. Because of the nonlinearity of the equations, the problem can only be solved in this form by numerical techniques [5, 6]. However, an approximation may be made which gives an asymptotically exact solution [7] or, alternatively, the exponential function of temperature may be expanded to give equations which can be solved analytically [8, 9]. A convenient solution to the problem may be presented in the form of families of curves for the effectiveness factor as a function of the Thiele modulus. Figure 3 shows these curves for the case of a first-order irreversible reaction occurring in spherical catalyst particles. Two additional independent dimensionless paramters are introduced into the problem and these are defined as... 

Our intention in this chapter is limited, however formulate approaches to the design of two main classes of catalytic reactors, fixed and fluidized bed briefly describe selected procedures along with a few numerical (or methodological) examples to illustrate their use and outline a procedure for incorporating the effects of catalyst deactivation in reactor design and operation. 

The basic problem in the design of a heterogeneous reactor is to determine the quantity of catalyst and/or reactor size required for a given conversion and flow rate. In order to obtain this, information on the rate equaiion(s) and their parameter(s) must be made available. A rigorous approach to the evaluation of reaction velocity constants has yet to be accomplished for catalytic reactions at this time, industry still relies on the procedures set forth in the previous chapter. For example, in catalytic combustion leac-tioas, the rate equation is extremely complex and cannot be obtained either analytically or numerically. A number of equations may result and some simplification is often warranted. As mentioned earlier, in many cases it is safe to assume that the expression may be satisfactorily expressed by the rate equation of a single step. 

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