The Plug-Flow Tubular Reactor

Consider a small element of volume, AV, of an ideal plug-flow tubular reactor, as shown in Fig. 4.6. 

A component balance equation can be derived for the element AV, based on the generalised component balance expression, where for any reactant, A 

The rate of accumulation of component A in element AV, is (AV dCA/dt), where, dCA/dt is the rate of change of concentration. 

The mass rate of flow of A into element AV is F Ca, and the rate of flow of A from element AV is F Ca + A(F Ca), where F is the volumetric flow rate. The rate of formation of A by reaction is rAAV, where rA is the rate per unit volume. 

Substituting these quantities, gives the resulting component balance equation 

We first assume that the tube has constant diameter D and also that the density does not vary with position (either liquids or gases with no mole number change, pressure drop, or temperature change with gases). In this case the linear velocity u with which the fluid flows through the tube is equal to the volumetric flow rate t divided by the cross-sectional tube area At (At = 7t j A for a cylindrical tube), 

A steady-state shell balance on species j in the element of length dz between z and 

The molar flow rate of species j is related to these quantities by the relation 

We next make a Taylor series expansion of the difference in Cj between z andz+dz and let dz 0, keeping only the lead term. 

This equation is not appropriate if all five of these conditions are not met. We can relax the third and fourth restrictions for the PFTR by considering the differential element of volume dV = At dz rather than the differential element of length dz. The mass-balance equation at a position where the fluid has moved from volume V to volume V + d V then becomes 

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Dynamic Simulation of the Plug-Flow Tubular Reactor... 

We will consider only the batch reactor in this chapter. This is a type of reactor that does not scale up well at all, and continuous reactors dominate the chemical industry. However, students are usually introduced to reactions and kinetics in physical chemistry courses through the batch reactor (one might conclude fi om chemistry courses that the batch reactor is the only one possible) so we wiU quickly summarize it here. As we vrill see in the next chapter, the equations and their solutions for the batch reactor are in fact identical to the plug flow tubular reactor, which is one of our favorite continuous reactors so we will not need to repeat all these definitions and derivations in the section on the plug flow tubular reactor. 

The chemical reactor is the unif in which chemical reactions occur. Reactors can be operated in batch (no mass flow into or out of the reactor) or flow modes. Flow reactors operate between hmits of completely unmixed contents (the plug-flow tubular reactor or PFTR) and completely mixed contents (the continuous stirred tank reactor or CSTR). A flow reactor may be operated in steady state (no variables vary with time) or transient modes. The properties of continuous flow reactors wiU be the main subject of this course, and an alternate title of this book could be Continuous Chemical Reactors. The next two chapters will deal with the characteristics of these reactors operated isothermaUy. We can categorize chemical reactors as shown in Figure 2-8. 

We can therefore replace dt by dz/u in all of the preceding differential equations for the mass balance in the batch reactor and use these equations to describe reactions during flow through a pipe. This reactor is called the plug-flow tubular reactor, which is the most important continuous reactor encountered in the chemical industry. 

Figure 3-2 The plug-flow tubular reactor (PFTR). The length of the reactor is L, the inlet molar flow rate of species j is and the outlet flow rate of species j is Fj.

The above equations are the same as those of the plug-flow tubular reactor for homogeneous reactions (Smith, 1981 Levenspiel, 1972). The differential form of equation (3.122) can be written in several equivalent forms (Levenspiel, 1972) ... 

C is a convenient abbreviation for the sesquipedalian continuous flow stirred tank reactor, and P might be coined for the plug flow tubular reactor. We might call the family that includes both T for tubular (SDM for standard dispersion model is sometimes used). 

The plug flow tubular reactor is a heat exchanger where the reaction occurs in the tubes. Construction is often varied. For example, the reactor may consist of a tube placed in a bath, a tube in a jacket, or a number of tubes immensed in a heat transfer medium for the reactor... 

There are four ideal reactors the batch reactor (real counterpart stirred tank reactor), semibatch reactor,1 continuous stirred tank reactor (CSTR), and the plug flow tubular reactor (PFTR) (real counterpart tube reactor). For production applications, there are also numerous other reactors [7-9], An overview of typical and advanced laboratory reactors was given by Kapteijn and Moulijn [6],... 

For each of the chemical species participating in the mechanism, a mass balance equation must be written. The appropriate form of the mass balance for the specific type of reactor at hand must be used. Two of the most common types of reactors used in industry are the CSTR (continuous stirred tank reactor) and the tubular reactor. The corresponding mathematical models for their idealized forms, based on transport phenomena equations and available in any standard chemical reactor text [17, 18], are the ideal CSTR and the ideal model for the plug flow tubular reactor (PFR). The ideal CSTR model is given by Equation 12.1 ... 

Chemical engineers have used various models to represent reactions in open systems. The simplest two, representing extreme viewpoints, are the continuous-flow, stirred-tank reactor (CSTR) and the plug-flow, tubular reactor (PFTR). The... 

The plug-flow tubular reactor (PFTR) rqnesents an extreme case. In it tho e is no back-mixing, and this model reactor is oftm consid ed as the spatial resolution of the temporal chemical process, inasmuch as the steady-state equations for the PFTR correspond to the time-depoident equations fm the wdl stirred batch reactor. Contonporary studies of PFTR date frmn 1956 ffilous and... 

More complex is the plug-flow tubular reactor (PFR or PFTR), in which the composition of the fluid, flowing as a plug, gradually changes down the length of the reactor, with no composition or temperature gradients in the radial direction. Furthermore, mass- and heat-transfer... 

Temperature and free-radical concentration are important features that vary along the length of the plug-flow tubular reactor model of the polymerization of ethylene/ Stirred-tank reactor models of the anionic polymerization of styrene and of butadiene have been described and tested against experiments. Mathematical modelling of polymerization reactions receives some attention in the book by Froment and Bischoff. ... 

In the three idealized types of reactors just discussed (the perfectly mixed batch reactor, the plug-flow tubular reactor [PFRj), and the perfectly mixed con-tinuous-stirred tank reactor [CSTR]), the design equations (i.e., mole balances) were developed based on reactor volume. The derivation of the design equation for a packed-bed catalytic reactor (PBR) will be carried out in a manner analogous to the development of the tubular de.sign equation. To accomplish this derivation, we simply replace the volume coordinate in Equation (1-10) with the catalyst mass (i.e., weight) coordinate W (Figure 1-14). 

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