The Plug-Flow Tubular Reactor Reprise

Example 2. The Plug-Flow Tubular Reactor (Reprise) 

We have seen that the basic P model has the form of a first-order partial differential Eq. (22) describing each narrow slice as a little batch reactor being transported through the reactor at constant speed. This equation was so elementary that it could be solved at sight in Eq. (30). When we added a longitudinal dispersion term governed by Fick s law and took the steady state, Eq. (40), we had a second-order o.d.e. with controversial boundary conditions. This is the model with ( ) = c(z)lcm and Pe = vLID, Da = kL/v, 

We have justified the second set of boundary conditions by the fact that when Pe 0 (i.e., the dispersion is so large that the reactor is uniform, like C ), the C equation is recaptured. If we put y = 2/(2 + Pe) the solution of Eq. (43) can be written 

FIGURE 4 Exit concentrations as functions of Da for five reactors. 

There are other ways to devise homotopic families [270], the simplest being to divide the C into a series (S ) of N equal reactors and use them in series. Because u -i — u — (DaIN)u , we can write 

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