Reactor performance based on residence-time distribution

4-2 REACTOR PERFORMANCE BASED ON RESIDENCE-TIME DISTRIBUTION 

Another approach to evaluate the performance of a trickle-bed reactor (particularly a pilot-scale reactor) is to incorporate the RTD with intrinsic kinetics. Since the liquid holdup, catalyst wetting, or the degree of axial dispersion can all be obtained from the RTD, this approach is not exclusive of the ones described above. For a first-order reaction, if the residence-time distribution E(t) and the degree of conversion are known, they can both be related by an expression 

E(t)dt is the fraction of the exit stream that was present in the reactor for a residence time between t and t + dt. For a plug flow, the above equation reduces to 

K = k /hiL, where hiL is the dynamic liquid holdup in the reactor. hdL is assumed to be constant along the length of the reactor. The reactor efficiency can be defined as 

The dynamic liquid holdup haL can be obtained from the mean residence time, liquid flow QL, and the reactor volume V as haL = tmQ JV. This approach for correlating the performances of pilot-scale hydrodesulfurization reactors was evaluated by Murphree et al.,31 Cecil et al.,s and Ross.40 It should be noted that the efficiency 0 is very sensitive to the percentage conversion at high conversion levels, where a small change in 0 can significantly change the level of conversion. 

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