Expert ForumsMixing

Topic: Re: We would like to have a general idea of pumping number for our reactors. Can you help us with blend-time calculations?

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You seem to be making blend time calculations more complicated than they are or at least trying to describe your process results entirely on the basis of a blend time. The literature has blend time estimates with an expression much as you describe.  Just remember that actual blend time, even with the same mixer, will vary from addition to addition by +/- 10% or more just because of turbulence and addition rate or location.  The value of K in your expression is obviously just a function of uniformity and is typically assumed to follow an exponential decay.  Thus the blend time for 90% uniformity is about 0.65 times the blend time for 99% uniformity.  The blend time for 99.9% uniformity is about 1.5 time the blend time for 99% uniformity, etc. The values for "a" and "b" depend on the impeller type.  For typical radial-flow, straight-blade impellers, a = 4.8 and b = 2.3.  For typical axial-flow, pitched-blade impellers, a = 6.34 and b = 2.3.  For typical three-blade hydrofoil impellers, a = 16.4 and b = 1.7. The idea of moving away from correlations for blend time and using pumping number to estimate blending performance introduces new problems.  A typical use of pumping capacity to "estimate" blend time requires from 6 to 10 tank turnovers for blending uniformity.  The range of tank turnovers and differences in pumping effects on blend time with different impellers makes those estimates even less certain. In most cases, blend time estimates are much shorter than the expected residence time in a stirred vessel.  The only place that blending becomes critical is in chemical reactions.  With parallel or sequential chemical reactions, the location and rate of reactant addition is more important than bulk blend times predicted by formulas or pumping calculations.  If you are observing significant differences between reactors, your problems are more complicated than just blend times.  Even large tanks will blend to uniformity in only a few minutes with moderate to intense agitation.  You probably need to look beyond just blend time calculations to find differences in your process results.
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