PFTR

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 will define these descriptions of reactors later, with the steady-state PFTR and CSTR being the most considered reactors in this course. 

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.

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... 

Example 3-3 The reaction A B, r = kCA occurs in PFTR with 90% conversion. If k = 0.5 min , C o = 2 moles/liter, and v = 4 liters/min, what residence time and reactor volume will be required ... 

I CSTR and that the residence time and reactor volume required are considerably i smaller in a PFTR than in a CSTR. 

Thus, while the PFTR reactor volume is much smaller than the CSTR for this conversion, the PFTR tube length may become impractical, particularly when pumping costs are considered. 

In a PFTR the time t that a molecule has spent in the reactor is z/u, and the time for the molecule to leave the reactor is Lju, which is the total time that a molecule has spent in the reactor,... 

Therefore, to find the behavior of a PFTR for kinetics that we have solved in a batch reactor, all we have to do is make the transformation tbatch —> tpFTR- The solution for the th-order irreversible reaction fi om Chapter 2 is... 

The PFTR was in fact assumed to be in a steady state in which no parameters vary with time (but they obviously vary with position), whereas the batch reactor is assumed to be spatially uniform and vary only with time. In the argument we switched to a moving coordinate system in which we traveled down the reactor with the fluid velocity , and in that case we follow the change in reactant molecules undergoing reaction as they move down the tube. This is identical to the situation in a batch reactor ... 

The PFTR is the clear winner in this comparison if reactor volume is the only criterion. The choice is not that simple because of the costs of the reactors and pumping costs. 

Obviously, batch and PFTR will give the same conversion, but the CSTR gives a lower conversion for the same reaction time (batch) or residence time (continuous). 

We can immediately see major reactor design considerations between batch, CSTR, and PFTR. Table 3-1 shows the first of many situations where we are interested in the design of a reactor. We may be interested in choosing rninimum volume or many other process variables in designing the best reactor for a given process. 

Comparisons of Possible Advantages (- -) and Disadvantages (—) of Batch, CSTR, and PFTR Reactors... 

Ratio of Residence Times and Reactor Volumes in CSTR and PFTR versus Conversion for a First-Order Irreversible Reaction... 

It is clear that the CSTR quickly becomes extremely large (large volume or large residence time) compared to the PFTR for high conversions for these kinetics. It is instructive to plot Ca/Cao versus z to see how Ca decreases in the two ideal reactors (Figure 3-3). 

The example in Figure 3-3 is for a first order irreversible reaction. We can generalize this to say that the PFTR requires a smaller reactor volume for given conversion for any... 

Figure 3-3 Plots of Ca (r) and Ca (t) in PFTR and CSTR for a first-order irreversible reaction A -> B, r = Ca. By plotting versus let, the graphs appear identical for any value of k.

Figure 3-5 Residence times in CSTR (shaded rectangle) and PFTR (area under curve) from the 1/r plot.

From these graphs of 1 /r versus Cao Ca w can construct the residence times in PFTR and CSTR, as shown in Figure 3-5. 

Thus it is evident that a PFTR is always the reactor of choice (smaller for greater than zero-order kinetics in an isothermal reactor. The CSTR may stUl be favored for n > 0 for cost reasons as long as the conversion is not too high, but the isothermal PFTR is much superior at high conversions whenever n > 0. 

The question of choosing a PFTR or a CSTR will occur throughout this book. From the preceding arguments it is clear that the PFTR usuaUy requires a smaller reactor volume for a given conversion, but even here the CSTR may be preferred because it may have lower material cost (pipe is more expensive than a pot). We will later see other situations where a CSTR is clearly preferred, for example, in some situations to maximize reaction selectivity, in most nonisothermal reactors, and in polymerization processes where plugging a tube with overpolymerized solid polymer could be disastrous. 

For the PFTR we return to the original mass-balance equation... 

These expressions are appropriate whether or not the density of the fluid varies with conversion. The latter is also valid if the cross section of the tube varies with z. Note the similarity (and difference) between the CSTR and PFTR expressions, the first being Fao times X/r(X) and the second Fao times the integral of dX/r X). 

This expression can be inserted into the CSTR and PFTR mass-balance equations to yield... 

These equations are significantly more complicated to solve than those for constant density. If we specify the reactor volume and must calculate the conversion, for second-order kinetics we have to solve a cubic polynomial for the CSTR and a transcendental equation for the PFTR In principle, the problems are similar to the same problems with constant density, but the algebra is more comphcated. Because we want to illustrate the principles of chemical reactors in this book without becoming lost in the calculations, we win usually assume constant density in most of our development and in problems. 

---