A quick review of the benzene hydrogenation example
We have examined two reactor options for this reaction, both involving staged adiabatic beds. The first option used coolers to cool the inter-stage gas and the second option used cold feed to quench the gas. The first option looks feasible but the second option isn't practical for this reaction.
Another option: cooled tube reactor
In this option, the reactor also becomes a heat exchanger. The catalyst is loaded into many tubes and the tubes are cooled either by a non-boiling or boiling fluid. The tube diameter is determined by a model, but a typical size is about 1 inch.
Selecting the reaction temperature
The first task for designing this reactor is to determine the reaction temperature. Unless there are no other constraints, the optimum temperature would maximize the reaction rate. The easy way to find this optimum is to develop a contour plot of the reaction rate as a function of temperature and fractional extent of reaction. The reaction rate can be expressed in terms of these variables in the same manner that I expressed the equilibrium constant (post 8/9/2015).
In the plot below, I have placed the red arrow along the ridge of maximum rates. The rate contour with a zero value is the equilibrium curve. It may be difficult to see, but the rates are positive on one side and negative on the other side of that curve.
It looks like we should aim for a nominal temperature of 500 K. The reactor won't be isothermal so don't even think about designing with that assumption! By determining this approximate temperature, the cooling fluid can be selected. Once the cooling means has been determined, build a 2D model of the reactor to check for the peak catalyst temperature which will relate to catalyst life.
The method shown for this single reaction may also be used when the main reaction is equilibrium limited and the other reactions are minor. Often byproduct reactions have high activation energies and thus high temperatures will decrease the selectivity to the desired product. Thus, the hot spot in the reactor, determined by the 2D model, will be of interest for this reason in addition to the its effect on catalyst life.
Postpone the 2D model
I am going to suspend the benzene hydrogenation example at this point because I want to examine another topic. If you can't wait to see the 2D model, it is included in my reactor book. For readers of the book, you will note that the staged bed examples in the blog are improved from the book version.