Ideal reactor design equations

Equations (19) and (22) are theoretically pleasing but their practical utility is limited. In a troubleshooting problem eq. (22) would allow us to recover E(s) of the system but we rarely deal with a homogeneous system of linear reactions I In a design problem we often do not know the actual RTD and are trying to design an ideal reactor. If the RTD can be predicted based on a nonideal reactor model, then species concentrations can also be calculated based on that model. Then eq. (22) represents at best only a mathematical short-cut I... 

Design equation— ideal batch reactor— homogeneous reaction (moles)... 

Design equation— ideal hatch reactor— homogeneous reaction (fractional conversion)... 

For the ideal reactors considered, the design equations are based on the mass conservation equations. With this in mind, a suitable component is chosen (i.e., reactant or product). Consider an element of volume, 6V, and the changes occurring between time t and t + 6t (Figure 5-2) ... 

Introduction to Reactor Design Fundamentals for Ideal Systems 393 For the first order reaetion, the design equation is... 

The design equations for a chemical reactor contain several parameters that are functions of temperature. Equation (7.17) applies to a nonisothermal batch reactor and is exemplary of the physical property variations that can be important even for ideal reactors. Note that the word ideal has three uses in this chapter. In connection with reactors, ideal refers to the quality of mixing in the vessel. Ideal batch reactors and CSTRs have perfect internal mixing. Ideal PFRs are perfectly mixed in the radial direction and have no mixing in the axial direction. These ideal reactors may be nonisothermal and may have physical properties that vary with temperature, pressure, and composition. 

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... 

At steady-state conditions, the mass balance design equations for the ideal tubular reactor apply. These equations may be expressed as... 

A simulation model needs to be developed for each reactor compartment within each time interval. An ideal-batch reactor has neither inflow nor outflow of reactants or products while the reaction is carried out. Assuming the reaction mixture is perfectly mixed within each reactor compartment, there is no variation in the rate of reaction throughout the reactor volume. The design equation for a batch reactor in differential form is from Chapter 5 ... 

Table 8.1 summarizes the fundamental design relationships for the various types of ideal reactors in terms of equations for reactor space times and mean residence times. The equations are given in terms of both the general rate expression and nth-order kinetics. 

Summary of design equations for ideal reactors (continued)... 

In this chapter we deal with single reactions. These are reactions whose progress can be described and followed adequately by using one and only one rate expression coupled with the necessary stoichiometric and equilibrium expressions. For such reactions product distribution is fixed hence, the important factor in comparing designs is the reactor size. We consider in turn the size comparison of various single and multiple ideal reactor systems. Then we introduce the recycle reactor and develop its performance equations. Finally, we treat a rather unique type of reaction, the autocatalytic reaction, and show how to apply our findings to it. 

There are many ways that two phases can be contacted, and for each the design equation will be unique. Design equations for these ideal flow patterns may be developed without too much difficulty. However, when real flow deviates considerably from these, we can do one of two things we may develop models to mirror actual flow closely, or we may calculate performance with ideal patterns which bracket actual flow. Fortunately, most real reactors for heterogeneous systems can be satisfactorily approximated by one of the five ideal flow patterns of Fig. 17.1. Notable exceptions are the reactions which take place in fluidized beds. There special models must be developed. 

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... 

Then, by the general design equation, our ideal batch reactor equation becomes... 

To achieve desired conversions predicted by ideal design equations, plug flow is required. This implies turbulent flow and higher energy costs if packing is used. Mass transfer can also be a problem. Axial diffusion or dispersion tends to decrease residence time in the reactor. High values of the length-to-diameter ratios (L/D > 100) tend to minimize this problem and also help heat transfer. 

The various types of reactors employed in the processing of fluids in the chemical process industries (CPI) were reviewed in Chapter 4. Design equations were also derived (Chapters 5 and 6) for ideal reactors, namely the continuous flow stirred tank reactor (CFSTR), batch, and plug flow under isothermal and non-isothermal conditions, which established equilibrium conversions for reversible reactions and optimum temperature progressions of industrial reactions. 

The classification in Figure 5 serves the description of the reactors used. Here, two ideal contacting types are used, the plug flow mode and the ideally mixed mode, both for the fluid and the solid phase. By appi-cation of the design equations of these ideal reactor types the experimental results are interpreted in a straightforward manner. For two phases, two contacting types and two operation modes (batch and flow) eight combinations arise ... 

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