Dr. Roland Rzehak
Phone: +49 351 260 3475

Euler-Euler-modeling of reactive flow in bubble columns

In the frame of a project within the DFG priority program 1740 “Influence of Local Transport Processes on Chemical Reactions in Bubble Flows” closure models for chemical reaction as well as the associated mass transport are included in the Euler-Euler description of bubbly flows.

In contrast to mere fluid dynamics, mass transport has been considered in this context only in relatively few works, in particular with simultaneous occurrence of a chemical reaction. An overview of the processes that need to be modeled and their relation is shown in the following figure.

An important parameter in this context is the time scale of the reaction: fast reactions are essentially completed within the boundary layer around the bubbles, slow reactions in contrast take place predominantly in the bulk of the liquid phase. Slow reactions can be described as a succession of non-reactive mass transfer and reaction in the liquid. To this end, models are needed for the (physical) mass transfer coefficient [1-3] as well as the turbulent mass transport and the micromixing taking into account the bubble-induced turbulence [4].

In the case of fast reactions a model is required for the enhancement-factor [5-7], which multiplies the mass transfer coefficient. The turbulent mass transport then is relevant only for the removal of reaction products (reverse direction of reactant B in the figure). For reactions of intermediate rate all of these processes play a non-negligible role. In addition the enhancement-factor becomes a function of the concentration of the transferred species (reactant A) in the bulk liquid.

comparison of the calculated gas fractions
Fig. 3: Comparison of the calculated gas fractions with (left) and without (right) reaction (gassing with CO₂ and N₂, respectively).

So far the work focused on the modeling of the enhancement-factor, which depends on the type of the reaction. To begin with, the frequently arising case of a bimolecular second order reaction was investigated. This can be observed under suitable conditions in the absorption of CO₂ in caustic solutions. The full reaction network for the chemisorption of CO₂ in NaOH is pictured in figure 2.

There are two reaction pathways, hydroxylation (I) and hydration (III), the relative importance of which depends on the pH-value. Subsequent is the equilibrium between hydrogencarbonate und carbonate (II). A complete model for the reaction rates and physico-chemical properties was assembled from the literature.

Several models for the enhancement-factor were compared. A comparison with experimental measurements taken in a bubble column was performed. A comparison of the calculated gas fractions with (left) and without (right) reaction (gassing with CO₂ and N₂, respectively) is presented in figure 3.

Further model validation studies are in progress.

Building on the results, in the future also reversible reactions as well as parallel and consecutive reactions will be investigated. Central to this topic is the question of the selectivity between different reaction products. On the scale of the bubble column this quantity is determined by the ratio of the times scales of reaction and mixing.


  1. R. Rzehak,
    Modeling of Mass-transfer in bubbly flows encompassing different mechanisms,
    Chemical Engineering Science 151 (2016), 139–143.
  2. R. Rzehak, E. Krepper,
    Euler-Euler simulation of mass-transfer in bubbly flows,
    Chemical Engineering Science 155 (2016), 459–46.
  3. R. Rzehak, S. Kriebitzsch, E. Krepper,
    Euler-Euler modeling of hydrodynamics and mass-transfer in bubbly flows,
    Proc. 9th International Conference on Multiphase Flow (ICMF2016), Firenze, Italy, 2016.
  4. J. Parekh, R. Rzehak,
    Euler-Euler multiphase CFD-simulation with full Reynolds-stress model and anisotropic bubble-induced turbulence,
    International Journal of Multiphase Flow (2017), in preparation.
  5. M. Krauß, R. Rzehak,
    Reactive absorption of CO₂ in NaOH: Detailed study of enhancement-factor models,
    Chemical Engineering Science 166 (2017), 193-209.
  6. M. Krauß, R. Rzehak,
    Reactive absorption of CO₂ in NaOH: An Euler-Euler simulation study,
    Chemical Engineering Technology (2017), under review.
  7. R. Rzehak, M. Krauß,
    Modeling of fluid dynamics, mass transfer, and chemical reaction in bubbly flows,
    Proc. 12th International Conference on CFD in Oil & Gas, Metallurgical and Process Industries (CFD2017), Trondheim, Norway, 2017.


Dr. Roland Rzehak
Phone: +49 351 260 3475