Variance of residence times

Levenspiel [9] gives the variance of residence time distribution, o- as... 

The second moment about the mean is a measme of the spread of the distribution about the mean. The variance of residence times in a perfectly mixed tank reactor is (let x = tlx)... 

Under the same boundary conditions as given by van Deemter (VI) the variance of residence times is given by... 

Then the mean residence time and variance of residence times (the same as would be given by the ideal tracer experiment) are... 

Exercise 7.9.6, Investigate the model in which the feed is split into fractions X and (I — X) and sent to parallel reactors whose volumes are in the ratio / (1 — p). Find the residence time distribution, and the mean and variance of residence times. For a first order reaction A —> B, show that the ratio of the concentration of A in the product stream for this system to its concentration from a single tank of the same mean residence time 0 is... 

An estimate of the Pe number can be obtained from an RTD measurement, that is, variance of residence times in the experiment. Empirical correlation giving the Pe number as a function of liquid Re (and possibly other dimensionless numbers) is also... 

Clearly the variance of residence times in the outflow is an important measure of the flow pattern in the system. A small dimensionless variance indicates little deviation from plug flow. Large variance, but less than unity, indicates imperfect mixing or distributed flow pathways with intermixing, while a variance larger than one points to stagnant zones. 

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