Reactor Design Equations

Integrating the mole balance equations gives us the design equations for the different reactor types  

In the next paragraph we are going to rewrite the above equations using conversion and introduce the term residence time . 

1 Design Equations Using Conversion. Recall from Section 

By substituting for N and F, in the design equations, these are transformed into the following  

The above equations are valid for the case of individual reactors. For the case of a series of continuous reactors, where the conversion at any point is defined with reference to the feed of the first reactor (FA0), the equations change to 

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Example 1.4 Determine the reactor design equations for the various elementary reactions in a piston flow reactor. Assume constant temperature, constant density, and constant reactor cross section. (Whether or not all these assumptions are needed will be explored in subsequent chapters.)... 

Example 1.5 Determine the reactor design equations for elementary reactions in a CSTR. 

Example 2.2 Derive the batch reactor design equations for the reaction set in Example 2.1. Assume a liquid-phase system with constant density. 

Example 2.12 illustrates a general result. If local stoichiometry is preserved, no more than M reactor design equations need to be solved to determine all... 

Chapter 1 treated the simplest type of piston flow reactor, one with constant density and constant reactor cross section. The reactor design equations for this type of piston flow reactor are directly analogous to the design equations for a constant-density batch reactor. What happens in time in the batch reactor happens in space in the piston flow reactor, and the transformation t = z/u converts one design equation to the other. For component A,... 

Computational Scheme for Gas-Phase PFRs. A general procedure for solving the reactor design equations for a piston flow reactor using the marching-ahead technique (Euler s method) has seven steps ... 

The reader will appreciate that the rules for what maximizes what can be quite complicated to deduce and even to express. The safe way is to write the reactor design equations for the given set of reactions and then to numerically determine the best values for reaction time and temperature. An interior optimum may not exist. When one does exist, it provides a good starting point for the more comprehensive optimization studies discussed in Chapter 6. 

Example 6.2 Cost-out a process that uses a single CSTR for the reaction. Solution The reactor design equations are very simple ... 

Pick a rate expression and assume values for its parameters. Solve the reactor design equations to predict the response. Call this prediction. ... 

Chapter 8 combined transport with kinetics in the purest and most fundamental way. The flow fields were deterministic, time-invariant, and calculable. The reactor design equations were applied to simple geometries, such as circular tubes, and were based on intrinsic properties of the fluid, such as molecular dif-fusivity and viscosity. Such reactors do exist, particularly in polymerizations as discussed in Chapter 13, but they are less typical of industrial practice than the more complex reactors considered in this chapter. 

Kinetic Rate Lam y/Vfateriat Balance reaction/deactivation/ reactor design equation, heat/mass transpat/ fluid-flow model,... 

Equating the time of passage through the tubular reactor to that of the time required for the batch reaction, gives the equivalent ideal-flow tubular reactor design equation as... 

The reactor (design) equation for stage 2, corresponding to equation (A), is... 

The viability of one particular use of a membrane reactor for partial oxidation reactions has been studied through mathematical modeling. The partial oxidation of methane has been used as a model selective oxidation reaction, where the intermediate product is much more reactive than the reactant. Kinetic data for V205/Si02 catalysts for methane partial oxidation are available in the literature and have been used in the modeling. Values have been selected for the other key parameters which appear in the dimensionless form of the reactor design equations based upon the physical properties of commercially available membrane materials. This parametric study has identified which parameters are most important, and what the values of these parameters must be to realize a performance enhancement over a plug-flow reactor. 

All chemical reactors have at least one thing in common Chemical species are created or destroyed. In developing a general reactor design equation, we focus on what happens to the number of moles of a particular species i. Consider a region of space where chemical species flow into the... 

A batch reactor has no inlet or outlet flows, so n, o = = 0. Perfect mixing is assumed for this ideal reactor, and the rate r is independent of position. This changes our generation term in the general reactor design equation to... 

For batch reactors, time is the key design variable. The batch reactor design equations answer the question How long does it take to obtain a specified conversion or concentration ... 

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