Modeling of Bubble Column Reactors:  Progress and Limitations

Abstract

Bubble columns are widely used for carrying out gas−liquid and gas−liquid−solid reactions in a variety of industrial applications. The dispersion and interfacial heat- and mass-transfer fluxes, which often limit the overall chemical reaction rates, are closely related to the fluid dynamics of the system through the liquid−gas contact area and the turbulence properties of the flow. There is thus considerable interest, within both academia and industry, to improve the limited understanding of the complex multiphase flow phenomena involved, which is preventing optimal scale-up and design of these reactors. In this paper, the progress reported in the literature during the past decade regarding the use of averaged Eulerian multifluid models and computational fluid dynamics (CFD) to model vertical bubble-driven flows is reviewed. The limiting steps in the model derivation are the formulation of proper boundary conditions, closure laws determining turbulent effects, interfacial transfer fluxes, and the bubble coalescence and breakage processes. Examples of both classical and more recent modeling approaches are described, evaluated, and discussed. Physical mechanisms and numerical modes creating bubble movement in the radial direction are outlined. Special emphasis is placed on the population balance modeling of the bubble coalescence and breakage processes in two-phase bubble column reactors. The constitutive relations used to describe the bubble−bubble and bubble−turbulence interactions, the bubble coalescence and breakage criteria, and the daughter size distribution models are discussed with a focus on model limitations. The demand for amplified modeling, more accurate and stable numerical algorithms, and experimental analysis providing data for proper model validation is stressed.

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.…”

“…The multifluid model seems to be the way forward for a population balance formalism of turbulent flows with inertial particles, but its formulation and basic assumptions are still under development even for laminar flows. Progress in that direction has been made in the field of bubble flows, and the reader is referred to the review of Jakobsen et al [103] for that purpose. Finally, a number of works such as Archambault et al [8], [9] and Beck and Watkins [18], [20], [19] have attempted to describe sprays using a small number of low-order moments, an approach that can be considered to lie between the two-fluid and multi-fluid approaches.…”

“…For other aspects of sprays and spray combustion such as droplet behaviour, experimental approaches and technological aspects, or for a comprehensive review, the reader may consult the excellent reviews of Chigier [31], [32], Faeth [64], [63], Sirignano [223], [222], Bellan [23], Chiu [33], Aggarwal [2], Crowe et al [35], A. Williams [258]. Bubble flows share many of the same issues, with bubble coalescence and break-up being of primary importance in the modelling of bubble column reactors, hence similar methods have been applied; again, our review will not be comprehensive, for which the reader is referred to Jakobsen et al [102], [103]; here we will view the subject from the population balance perspective only.…”

“…Much of the research has been conducted with the objective of predicting the multiphase flow in vertical bubble flows [180] such as bubble column reactors, where the bubble size distribution can have a profound effect on the physicochemical phenomena. Since this research has been comprehensively reviewed by Jakobsen et al [103], the interested reader is referred to that work.…”

Numerical aspects and implementation of population balance equations coupled with turbulent fluid dynamics

“…Chen and his co-workers [6] studied the effect of different breakage and coalescence closures and they showed that incompatible kernels produce poor results. Certain experimental and theoretical models for breakage and coalescence kernels are regarded as milestones for the evolution of population balances in the framework of liquid/gas-liquid dispersed phase systems and the evolution of these models is presented in detail by [15].…”