Ideal, Isothermal Reactors

Reactors are mostly not isothermal, as heat is consumed or released, and perfect mixing or a perfect heat exchange with the surrounding is impossible. However, some reactors are almost isothermal, such as, for example, a well-mixed continuous stirred tank reactor (CSTR). In a batchwise operated stirred tank or in a plug-flow reactor (PFR), isothermal conditions with regard to reaction or residence time (axial position), respectively, are hard to realize. However, the assumption of an isothermal system is helpful for a first examination of reactor types as it simplifies the equations and we can focus on concentration and mixing effects only. Thus, here, we inspect isothermal reactors. Thermal effects are considered in Section 4.10.3. 

If not otherwise stated, the following simplifications and assumptions are used  

Solutions for deviating conditions are here only given for selected situations (e.g., reactions with changing volume are examined in Topic 4.10.1) and we refer to 

Other textbooks for further studies (Baems et al., 2006 Westerterp, van Swaaij, and Beenackers, 1998). 

Section 1.2 developed rate expressions for elementary reactions. These expressions are now combined with the material balances of Section 1.1 to develop reactor design equations, that is, equations to predict final concentrations in a batch reactor or outlet concentrations in a flow reactor. Since reaction rate expressions have units of concentration per time, it may seem that is identical to da/dt. This is true only for 

Consider a well-mixed batch reactor with a key reactant A, during time t to time t -i- 6t, where 6t is very small. For a well-mixed batch system, assume the following  

Introduction to Reactor Design Fundamentals for Ideal Systems 265 

Assume 6V[ to be (i.e., the volume of the fluid in the reaetor), the total reaetor volume. Suppose that at time t = 0, the number of moles of A in V] = N Q time t = t, the number of moles of A 

The rate of reaetion (-r ) also varies with time t, sinee the eon-eentration ehanges with time. Using Taylor s series y = f(t), gives 

266 Modeling of Chemioal Kinetios and Reaotor Design The average rate of reaetion during 6t is 

The perfectly mixed, continuous-how stirred tank reactor (CSTR) 

This chapter discusses the hrst three types, which are overwhelmingly the most important. The fourth type is interesting theoretically, but has limited practical importance. It is discussed in Chapter 15. 

The completely segregated, continuous-flow stirred tank reactor 

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Reactor design usually begins in the laboratory with a kinetic study. Data are taken in small-scale, specially designed equipment that hopefully (but not inevitably) approximates an ideal, isothermal reactor batch, perfectly mixed stirred tank, or piston flow. The laboratory data are fit to a kinetic model using the methods of Chapter 7. The kinetic model is then combined with a transport model to give the overall design. 

Rate of Homogeneous Reactions in Ideal Isothermal Reactors... 

For ideal isothermal reactors, the conversion of a reactant A can be calculated by one parameter, the Damkoehler number. (For a cascade of CSTRs we also need the number of CSTRs.) For a reaction order n and a rate constant k, Da equals for a batch reactor (t = reaction time) and r (r = resi-... 

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