Predicting Reactor Behavior with the Macrofluid Model

2 Predicting Reactor Behavior with the Macrofluid Model 

Consider a continuous reactor at steady state. A single reaction A —products is taking place. The exit-age distribution E t) of the reactor is known, and this distribution function describes the behavior of the packets of fluid, as weU as the behavior of the fluid as a whole. 

The concentration of reactant A in a packet that was in the reactor for a time r is Cpft). This concentration can be calculated by solving the design equation for an ideal batch reactor, if a single reaction is taking place, or by solving the appropriate set of material balances (design equations), if multiple reactions are taking place. 

The average concentration of A (or any other species) in the reactor effluent is obtained by taking a weighted average of Ca (t) over the range of times that fluid elements spent in the reactor. The weighting function is E(t). 

The concentration of A in a packet that was in the vessel for time t is just C t). The fraction of packets that were in the reactor for a time between t and t + dr is just E(t) dr. Therefore, 

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