Modeling of the Dispersed-Phase Size Distribution in Bubble Columns

Abstract

A population balance model formulation for predicting the size distribution of the dispersed gas phase in bubble column reactors is presented. Extended source term parametrizations for the breakup and coalescence mechanisms are included in a computational fluid dynamics (CFD) model and tested on a fairly simple flow formulation corresponding to locally obtained experimental data. Most CFD codes are based on the assumption of a monodisperse bubble size distribution resulting in an inaccurate prediction of the hold-up. Comparing the results obtained by the breakup model versions against experimental data indicates that the extended model provides an improved description of the bubble size distribution, hold-up, and thus also the volume-averaged gas-phase velocity.

Bubble Column Reactors

“…Sha et al [146,147] developed a similar multi-fluid model for the simulation of gas-liquid bubbly flow. To guarantee the conservation of mass the population balance part of the model was solved by the discrete solution method presented by Hagesaether et al [56]. The 3D transient simulations of a rectangular column with dimensions 150 × 30 × 2000 mm and the gas evenly distributed at the bottom were run using the commercial software CFX4.4.…”

“…The author(s) also claimed that this model contains no adjustable parameters, a better phrase may be no additional adjustable parameters as both the isotropic turbulence-and the probability theories involved contain adjustable parameters and distribution functions. Hagesaether et al [53][54][55][56] continued the population balance model development of Luo within the framework of an idealized plug flow model, whereas Bertola et al [14] combined the extended population balance module with a 2D algebraic slip mixture model for the flow pattern. Bertola et al [14] studied the effect of the bubble size distribution on the flow fields in bubble columns.…”

Population balance modelling of polydispersed particles in reactive flows

“…Multi-fluid methods have also been employed in the context of bubble flows by Jakobsen, Svendsen, et al [91], [102] and Dorao et al [52] -see the recent review by Jakobsen et al [103] -as well as chemical reactors such as fluidised beds [100]. The multi-fluid approach is fully consistent with population balance formulations for inertial particles (such as the Williams equation), apart from the fact that the latter allows for particles of the same size, at the same position and time instance, to have a distribution of velocities.…”

Multi‐Phase‐Multi‐Size‐Group Model for the Inclusion of Population Balances into the CFD Simulation of Gas‐Liquid Bubbly Flows

“…A general problem concerning the solution of population balances is the simultaneous conservation of both number and mass balances (Ramkrishna [19]). To guarantee the conservation of both number and mass balances we have adopted the population balance solution method presented by Hagesaether et al [20] and Hagesaether [21] to calculate the birth and death terms of coalescence and breakage for each bubble size group.…”