Another design option: quench cooling
The previous post explored the interstage cooling option for managing the exothermic heat of reaction. This post will examine the quench cooling option.
Quench cooling involves mixing a cold quench stream with the hot outlet stream from a previous bed. Normally, the quench stream is a portion of the overall reactor feed stream. This quench stream may be used for more than one bed. The quench stream will have a constant fractional extent of reaction and temperature.
Finding the mixing point
In order to construct the operating curve for the staged beds, we need to determine the extent of reaction of the mixed stream at the desired bed inlet temperature. For this we need the adiabatic mixing equation.
We know that a mixing operation is linear. Therefore, the first equation below equates the overall slope of the mixing line on the right hand side to the slope between the quench point, q, and the mixing point at temperature, t. This equation is then solved for the mixed extent as a function of t.
Once the mixing point has been found, we can determine the equilibrium outlet condition as before.
Example: t = 550 K
The interstage cooling option discussed in the previous post used 400 K for the bed inlet temperatures. The plot below shows what would be achieved using the quench method but with 550 K as the desired inlet temperature. The quench is unreacted feed at 50 C.
We aren't making much progress with the reaction with this method. The problem is because the maximum conversion that this method can achieve is equal to the conversion that can be achieved with one bed with the quench as the feed. The "limit" curve depicts that maximum.
So we've determined that quench cooling isn't a good option for this reaction. What is needed for the quench method to be attractive for other reaction systems? First, an equilibrium curve that is shifted to higher temperatures farther from the quench temperature would help. Second, lower heat of reaction would also help by increasing the slope of the bed operating curves and the limit curve. Both of these conditions would allow greater conversion per bed and reduce the amount of quench fluid needed.