Pipelines, axial mixing

Mixing of elements initially at different axial positions in a pipeline is axial mixing. Radial mixing occurs between fluid elements passing a given point at the same time, as, for example, between fluids mixing in a pipeline tee. 

The opposite of the large diameter pipeline with little axial or radial mixing is the perfect backmixed reactor with instantaneous mixing and uniformity. For polystyrene reactors with several hours of residence time, complete mixing in 1-2 min is usually adequate to satisfy a practical definition of perfectly mixed. The probability of exit of any fluid element from this type of reactor is independent of when it entered. The residence time distribution is exponential and the molecular weight distribution in the case of no termination is Mw/Mn = 2.0, which will spread out to 2.3 when chain transfer controls. If product requirements necessitate a narrower residence time distribution, one can utilize several of these reactors in series. This becomes necessary to control the grafting distribution in rubber modified polystyrene. 

There is also axial dispersion. Again this is not mixing but a mechanism that introduces a residence time distribution. If a pulse is added to a turbulent pipeline, it will gradually lengthen with time. The best discussion of this is in Levenspiel s book (1967), where the work of Levenspiel and Bischoff is discussed. Mixing time, an important concept for reactive mixing, is given by... 

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