Scale-up and design of bubble column and other gas-liquid reactors can be difficult if the interfacial area and mass transfer parameters need to be known. Determining the values of these parameters for a lab or pilot plant system is not easy because it often requires separate chemicals and sensors from that needed for the regular reaction. Fortunately, there are many cases where this information is not needed. This post discusses those cases and how to determine if your system is also in that category.
Gas absorption with reaction is commonly divided into five regions: diffusion controlled, slow reaction, transition, fast reaction, and instantaneous reaction. The plot below (there is no Fig 1 in the blog) shows how the dimensionless gas absorption rate per unit volume of reactor liquid (Y axis) varies with the reaction rate (X axis). The parameter for the various curves is the interfacial area times the film thickness, i.e. the film volume/reactor liquid volume.
The above plot illustrates the following:
Although the gas-liquid mass transfer is important for all but one region, that region is often where a reactor operates. Note that the Reaction Parameter (Thiele modulus) can change four orders of magnitude within the slow reaction regime. That is eight orders of magnitude for the reaction rate constant. [This range is based on an assumption where the diffusion regime begins as the rate is lowered.]
Others have examined commercial reactions and determined the following processes most often operated in the slow reaction region:
Checking the regime
The plot also gives a means of checking where your system operates. If you have a suspended catalyst, you can change the Thiele modulus by changing the catalyst concentration. The Thiele modulus will be proportional to the square root of the catalyst concentration. If you change the Thiele modulus and the gas absorption rate changes, your reaction is in either the slow or fast reaction region. The plot also shows that the slope of the curves in the fast region is one half of the slope in the slow region. Comparing the slope of your data to the plot will distinguish your system's region even if you haven't calculated the full Thiele modulus.
If the absorption rate remains constant, your system is most likely in the transition region for a suspended catalyst system.
Other design implications
E. Alper et al, Adv in Biotechnology, vol 1: Scientific and Engineering Principles, ed M., p 511 Moo-Young, Pergamon Press (1981)
E. Alper and W.-D. Deckwer, Chem Eng Sci, 36, p 1927 (1981)