The simultaneous graphical solution of heat and material balance for adiabatic reactors

It is an advantage that the linear relationship between conversion and adiabatic temperature rise is valid for all reactor types, therefore we get a general linear plot of our reactor temperature versus the conversion (with T0 as Y-axis intersection). When we put into that plot additionally the 1/r - function for r(U,T), - that is we take a U-value, search it's T value calculate the k-value for this temperature and then the r value using the related k and U (e.g.: r = k(T)*CA,0*(1-U) for a 1 st order reaction), - then we can find our space time graphically in this 1/r-plot in the same manner as shown for isothermal reactions. The difference is that our r is now not only f(U) but also f(T). Let us look at a plot for an irreversible exothermal 1st order reaction:

the data: k = 0.2283 exp(-3450/T) 1/sec, CA,0 = 1500 mol/m3, delta Tad= 95 K, T0= 293 K

We see something really interesting here: We have an 'initially falling' function curve, and as the space-time for the not-back-mixed reactor types corresponds to the area under the function curve, we have to realize that these reactor types are not so 'good' in this sector, - up to about 75 % conversion the totally back-mixed CSTR would even be better !! But best would be to take a reactor combination. Here we have another example for the necessity of reactor combinations instead of 'merely' not-back-mixed reactor types.

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