Time scale mesomixing

The concepts of micromixing and mesomixing can be reduced to a set of simple guidelines. For fast reactions having time scales of seconds and tens of seconds ... 

The failure of conventional criteria may be due to the fact that it is not only one mixing process which can be limiting, rather for example an interplay of micromixing and mesomixing can influence the kinetic rates. Thus, by scaling up with constant micromixing times on different scales, the mesomixing times cannot be kept constant but will differ, and consequently the precipitation rates (e.g. nucleation rates) will tend to deviate with scale-up. 

The conventional scale-up criteria scale-up with constant stirrer speed , scale-up with constant tip speed and scale-up with constant specific energy input are all based on the assumption that only one mixing process is limiting. If, for example, the specific energy input is kept constant with scale-up, the same micromixing behaviour could be expected on different scales. The mesomixing time, however, will change with scale-up as a result, the kinetic rates and particle properties will be different and scale-up will fail. 

The importance of feed rate on yield for a mixing-sensitive reaction was demonstrated in Ref. ". The addition time in a semibatch reaction is often increased on scale-up because of heat transfer limitations. In the case of a mixing-sensitive reaction, the time of addition is increased on scale-up to compensate for the increase in blend time and to maintain the expected molar ratio at the feed point. The minimum feed time to achieve the expected yield is, therefore, scale dependent. Feed times that are too short will result in mesomixing conditions and reduced yield. 

Note This protocol is focused on mixing effects for the classic competitive-consecutive reaction system. Reaction systems may also include parallel reactions in which A, B, or R are reacting to form unwanted products that are not represented by the consecutive-competitive system as used to derive eq. (13-5). To keep these reactions from making more unwanted products on scale-up, the overall reaction (addition) time may have to be held constant. In this case, the mesomixing issue for the primary reactions, A - - B R and R - - B S, would predict that more S would be formed. These issues may require selection of an alternative reactor, such as an in-line mixer, for successful scale-up. 

Yield and/or selectivity of homogeneous consecutive-competitive reactions that are subject to mixing effects can be lower on scale-up if proper precautions are not taken for mixing the reagents—mesomixing problems get worse on scale-up and blend times increase. 

In order to determine the mesomixing time, a least square fit of the 300 ml continuous calcium oxalate (CaOx) precipitation results for the number mean size and nucleation rate was performed. From these calculations, the factor A in equation 8.15 was obtained as 17.7. Using the kinetic parameters determined from the laboratory-scale continuous experiments (Zauner, 1999), the large-scale experiments were simulated with the SFM and compared with the experimental findings. 

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