(666d) A Rigorous Model for Mass Transfer, Chemical Reactions and Mixing in Large Bubble and Droplet Swarms

The understanding of reactive multiphase flows is extremely important in many areas of chemical engineering including the pharmaceutical or the fine chemical industry. However, a direct simulation and hence a full mechanistic understanding of full-scale systems cannot be achieved due to their complexity. For example, our previous high-fidelity simulations were still limited to relatively small bubble swarms.1,2 Detailed computer models for larger bubble swarms are still not sophisticated enough to understand the effect of process parameters on, e.g., the selectivity of a reaction. Clearly, a rigorous model that incorporates mass transfer, complex chemical reaction networks and mixing in the involved phases is still missing.

In our work we establish such a rigorous model to predict the outcome of reaction networks in multiphase systems, i.e., bubble and droplet swarms. The starting point of our analysis are direct numerical simulations (DNS) of mass transfer in and around three-dimensional, deforming bubbles. The new aspect of our current work is that we are now able to perform mass transfer calculations for moderately high Schmidt numbers (Sc up to 100) also accounting for multicomponent diffusion. Such an analysis has not been performed yet. This is due to the difficulty to computationally resolve the extreme fine concentration boundary layers near the interface.

In a next step, we calibrate a relatively simple reactive mass transfer model for the region near the interface with our DNS results. This enables us in a final step to study large bubble swarms (up to approx. one Million individual bubbles) using a newly developed Euler-Lagrangian (EL) bubble tracking code3 in stirred and unstirred systems. Hence, we are able for the first time to analyze reactive mass transfer as well as mixing for typical lab-scale bubble columns in extremely high detail.

Our results show that the three-dimensional DNS is able to reproduce correlations for the Sherwood number up to a Peclet number in the order of 104. Also, we are the first that reveal and analyze the concentration field behind deformable bubbles for high Schmidt numbers. This is extremely important for the development of sophisticated reaction models in, e.g., Large Eddy Simulations of multiphase flow.

Our EL simulations show that scalar mixing in multiphase systems yields a log-normal distribution of the scale of segregation. Also, we show that a non-dimensional quantity calculated from the scale of segregation does not depend on the bubble size but is only a function of the gas feed rate, i.e., the power input. This knowledge will be extremely useful in the scale-up of mixing sensitive reaction networks in multiphase reactors.

References

(1) Radl S, Tryggvason G, Khinast JG. Flow and Mass Transfer of Fully Resolved Bubbles in Non-Newtonian Fluids. AIChE Journal. 2007;53:1861-1878.

(2) Radl S, Koynov A, Tryggvason G, Khinast JG. DNS-based Prediction of the Selectivity of Fast Multiphase Reactions: Hydrogenation of Nitroarenes. Chem Eng Sci. 2008;63:3279-3291.

(3) Radl S, Suzzi D, Khinast JG. Assessment of Micro- and Mesomixing in Bubble Swarms via Simulations. Chemical engineering transactions. 2009;17:507-512.