Constant-Density PFTR

We now consider solutions to the preceding equation for simple kinetics. For reactant species A va = 1) the equation becomes 

This equation must be integrated between z = 0, where Ca = Cao to position z, where Ca = Ca(z), to position L, where Ca = Ca C), 

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. 

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. 

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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. 

Reactors have volume V. Continuous-flow reactors have volumetric flow rate V, and constant-density reactors have residence time X = V/v. Until Chapter 8 all continuous reactors are either completely mixed (the CSTR) or completely unmixed (the PFTR). 

In deriving these equations we have made many assumptions to keep them simple. We have assumed constant density so that we can use concentration as the composition variable. We have also assumed that the parameters in these systems are independent of temperature and composition. Thus parameters such as AAr, pCp, and JJ are considered to be constants, even though we know they all depend at least weakly on temperature. To be exact, we would have to find the heat of reaction, heat capacity, and heat transfer coefficient as functions of temperature and composition, and for the PFTR insert them within the integrals we must solve for temperature and composition. However, in most situations these variations are small, and the equations written will give good approximations to actual performance. 

When the density varies with conversion, the analogy between the batch reactor and the PFTR dt dx) is no longer appropriate. In the batch reactor with ideal gases, the density varies with conversion in a constant-pressure reactor but not in a constant-volume reactor. In a flow reactor, the reactor volume is fixed, no matter what the density. In a flow reactor the volumetric flow rate changes with conversion if there is a mole number change with ideal gases. 

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