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Unformatted text preview: 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 10: Non-ideal Reactor Mixing Patterns This lecture covers residence time distribution (RTD), the tanks in series model, and combinations of ideal reactors. Non-Ideal Mixing PFR CSTR Figure 1. Ideal PFR with pulse input. A pulse input will yield an output profile that is a pulse input. Figure 2. Ideal CSTR with pulse input. A pulse input will yield an output profile that is a sharp peak with a tail. Real mixed tank stagnant bypassing mixing recirculation eddies volumes Figure 3. A real mixed tank. In a real mixed tank there are portions that are not well mixed due to stagnant volumes, recirculation eddies, and mixing bypasses. In a real PFR there is back-mixing and axial dispersion. In a packed bed reactor (PBR) channeling can occur. This is where the fluid channels through the solid medium. Residence Time Distribution A useful diagnostic tool is the residence time distribution (RTD). The residence time is how long a particle stays in the reactor once entering. E ( t ) dt Probability that a fluid element entering the vessel at t=0 exits between time t and t+dt. Probability density function for exit time, t, as a random variable. Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. t E t dt Probability that fluid element exits before time t. ( ) E t dt Probability of exiting at time later than t. ( ) t mean t = tE ( ) t dt = = E ( ) dt = 1 normalized t variance = 2 = t 2 E t dt (measures the broadness of the distribution) ( ) ( ) E after t...
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