Wednesday, February 29, 2012

Process Wednesday: 3 different kinds of mixing

In the middle of a terribly interesting article on using reverse addition to eliminate a symmetrical anhydride side product during a mixed anhydride formation, Chaudhary et al. [1] decide to talk about the different kinds of mixing (emphasis mine):
The aforementioned experiments are also useful for inferring the cause of the higher amounts of 1 observed at the end of the reaction at larger scales. Bourne [2] has identified three mixing stages for single-phase fluids: (a) distributive, or macromixing, in which large fluid eddies exchange positions and mass, but with compositional uniformity occurring only at a scale greater than the eddy size; (b) dispersive, or mesomixing, in which larger eddies are reduced in size due to turbulent shear and finer-grained mixture forms, but with the mixture remaining highly segregated at the molecular scale; (c) diffusive, or micromixing, in which molecular diffusion occurs over short distances between finely dispersed structures to give a mixture that is randomized on the molecular scale. Good micromixing is thus a prerequisite to avoiding compositional inhomogeneities on the molecular scale (i.e., high local concentrations) that can impact selectivity of chemical reactions. The macromixing time typically increases with increasing scale. 
For example, when scaling up at constant power per unit volume in geometrically similar vessels, the macromixing time varies as the 2/3 power of the vessel diameter. At constant power per unit volume, however, the micromixing time is not impacted significantly. Thus, given that the stages occur mostly in series, one should expect a longer time to achieve uniformity at the molecular scale with increasing scale (i.e. macromixing becomes the limiting mixing process).
I don't know what I thought about the time it took for material to achieve homogeneity in a 1 liter flask (in this case.) But now I'm aware of the eddies!

[1] Apurva Chaudhary, Michael J. Girgis, Mahavir Prashad, Bin Hu, Denis Har, Oljan Repicˇ, and Thomas J. Blacklock. "CO2 Offgas as a Mechanistic Probe and Scale-up Tool in N-Acylations Using Mixed Anhydrides from Amino Acids and Isobutyl Chloroformate." Organic Process Research & Development 2003, 7, 888−895. 

[2] Bourne, J. R. Mixing in Single-phase Chemical Reactors. In Mixing in the Process Industries, 2nd ed.; Harnby, N., Edwards, M. F., Nienow, A. W., Eds.; Butterworth Heinman: Woburn, MA, 1992.


  1. The mention of multiscale processes made me recall something...

  2. Obtaining homogeneity in a reactor larger than a lab vessel is generally not practical. In a large tank (one I can crawl into or larger) the power required to homogenize a reaction mixture on a time scale comparable with the reaction rate is often not available. For this reason it is very hard to scale up processes with competing side reactions. Also, in-process sampling on large scale is less informative than in the lab because of this heterogeneity.

    We can (and should) model scale up on geometry, power per volume, tip speed, etc., but in the end the first large run is always and experiment.

    1. That's kind of horrifying and fascinating all at the same time.

    2. Do you mean the crawling into the reactor or not thinking "one flask = one mixture"? :)
      The mantra is "define process objectives" before you do the process.

    3. I am horrified by the comment that in-process checks are less informative; how else can you determine these things?

      Also, the comment that "the first large run is always an experiment" is so true, and so paranoia-inducing.

      I don't think I've ever worked in an environment where the process objectives have been really truly known and set in stone. They seem to move constantly.

  3. Process objectives can/should move as process knowledge grows. Still, we need them at all stages of development. Process checks reflect exactly what is sampled: a local environment. I used to runs screens in banks of 2 mL vials. I would sample them using a pipette. If you scale up this system geometrically you can also get the average reaction mixture. Only the "pipette" would require a crane at 500 gal scale :).

    To homogenize a large reactor on a small vial time scale requires power that is not practical. In this case the power scales like diameter^5 (in turbulent flow regime). Fortunately, we mostly use batch reactors and have the luxory of waiting.