Multidimensional population balance model for the simulation of turbulent gas–liquid systems in stirred tank reactors

Population Balance Models for Particulate Flows in Porous Media: Breakage and Shear-Induced Events

Transport and particulate processes are ubiquitous in environmental, industrial and biological applications, often involving complex geometries and porous media. In this work we present a general population balance model for particle transport at the pore-scale, including aggregation, breakage and surface deposition. The various terms in the equations are analysed with a dimensional analysis, including a novel collision-induced breakage mechanism, and split into one- and two-particles processes. While the first are linear processes, they might both depend on local flow properties (e.g. shear). This means that the upscaling (via volume averaging and homogenisation) to a macroscopic (Darcy-scale) description requires closures assumptions. We discuss this problem and derive an effective macroscopic term for the shear-induced events, such as breakage caused by shear forces on the transported particles. We focus on breakage events as prototype for linear shear-induced events and derive upscaled breakage frequencies in periodic geometries, starting from nonlinear power-law dependence on the local fluid shear rate. Results are presented for a two-dimensional channel flow and a three dimensional regular arrangement of spheres, for arbitrarily fast (mixing-limited) events. Implications for linearised shear-induced collisions are also discussed. This work lays the foundations of a new general framework for multiscale modelling of particulate flows.

CFD-PBM Simulation on Bubble Size Distribution in a Gas-Liquid-Solid Flow Three-Phase Flow Stirred Tank

The bubble size distribution, location distribution, and gas holdup in a gas-liquid-solid flow three-phase stirred tank were numerically simulated by the Eulerian-Eulerian method and the population balance model (PBM). The Euler-Euler method combined with the PBM model included the influence of bubble aggregation and fragmentation on the interfacial force, which can better predict the bubble size distribution and phase holdups. The simulation results show that there are some differences in the fluid morphology and gas dispersion characteristics in the stirred tank under different rotating speeds. With the increase of rotating speed, the content of small-diameter bubbles increases obviously, and they are mainly concentrated in areas with higher speeds. The higher the rotational speed, the more the bubbles with small diameters, but the content of bubbles with large diameters is less affected by the rotational speed. Small-size bubbles mainly exist in the region of high fluid velocity, while large-size bubbles mainly exist in the region of low hydrostatic pressure. Compared with the change of the bubble content at different speeds, the content of bubbles with diameters of 0.50-1.90 mm is largest at 2000 rpm, while the content of bubbles with diameters of 2.65-10.09 mm is largest at 1500 rpm. The simulation work has certain guiding significance for the research and development of the forced mineralization device and the understanding of the dispersion characteristics of bubbles in the stirred tank.

CFD-PBM simulation of hydrodynamics of microbubble column with shear-thinning fluid

A numerical simulation was performed to study the hydrodynamics of micro-bubble swarm in bubble column with polyacrylamide (PAM) aqueous solution by using computational fluid dynamics coupled with population balance models (CFD-PBM). By considering rheological characteristics of fluid, this approach was able to accurately predict the features of bubble swarm, and validated by comparing with the experimental results. The gas holdup, turbulent kinetic energy and liquid velocity of bubble column have been elucidated by considering the influences of superficial gas velocity and gas distributor size respectively. The results show that with the rise of the superficial gas velocity, the gas holdup and its peak width increase significantly. Especially, the curve peak corresponding to high gas velocity tends to drift obviously toward the right side. Except for the occurrence of a smooth holdup peak at the column center under the condition of the moderate distributor size, the gas holdups for the small and large distributor sizes become flat in the radial direction respectively. The distribution of turbulent kinetic energy presents an increasingly asymmetrical feature in the radial direction and also its variation amplitude enhances obviously with the rise of gas velocity. The increase in gas distributor size can enhance markedly turbulent kinetic energy as well as its overall influenced width. At the low and moderate superficial gas velocity, the curves of the liquid velocity in radial direction present the Gaussian distributions, whereas the perfect distribution always is broken in the symmetry for high gas velocity. Both liquid velocities around the bubble column center and the ones near both column walls go up consistently with the gas distributor size, especially near the walls at the large distributor size condition.

A model-driven approach towards rational microbial bioprocess optimization

Due to sustainability concerns, bio-based production capitalizing on microbes as cell factories is in demand to synthesize valuable products. Nevertheless, the nonhomogenous variations of the extracellular environment in bioprocesses often challenge the biomass growth and the bioproduction yield. To enable a more rational bioprocess optimization, we have established a model-driven approach that systematically integrates experiments with modeling, executed from flask to bioreactor scale, and using ferulic acid to vanillin bioconversion as a case study. The impacts of mass transfer and aeration on the biomass growth and bioproduction performances were examined using minimal small-scale experiments. An integrated model coupling the cell factory kinetics with the three-dimensional computational hydrodynamics of bioreactor was developed to better capture the spatiotemporal distributions of bioproduction. Full-factorial predictions were then performed to identify the desired operating conditions. A bioconversion yield of 94% was achieved, which is one of the highest for recombinant Escherichia coli using ferulic acid as the precursor.

A General Review of the Current Development of Mechanically Agitated Vessels

The mixing process in a mechanically agitated vessel is a widespread phenomenon which plays an important role among industrial processes. In that process, one of the crucial parameters, the mixing efficiency, depends on a large number of geometrical factors, as well as process parameters and complex interactions between the phases which are still not well understood. In the last decade, large progress has been made in optimisation, construction and numerical and experimental analysis of mechanically agitated vessels. In this review, the current state in this field has been presented. It shows that advanced computational fluid dynamic techniques for multiphase flow analysis with reactions and modern experimental techniques can be used with success to analyse in detail mixing features in liquid-liquid, gas-liquid, solid-liquid and in more than two-phase flows. The objective is to show the most important research recently carried out.

Numerical Methods for the Solution of Population Balance Equations Coupled with Computational Fluid Dynamics

This review article discusses the solution of population balance equations, for the simulation of disperse multiphase systems, tightly coupled with computational fluid dynamics. Although several methods are discussed, the focus is on quadrature-based moment methods (QBMMs) with particular attention to the quadrature method of moments, the conditional quadrature method of moments, and the direct quadrature method of moments. The relationship between the population balance equation, in its generalized form, and the Euler-Euler multiphase flow models, notably the two-fluid model, is thoroughly discussed. Then the closure problem and the use of Gaussian quadratures to overcome it are analyzed. The review concludes with the presentation of numerical issues and guidelines for users of these modeling approaches.

Numerical Simulation of Gas-Liquid Dispersion in A Stirred Tank Agitated by Punched Rigid-Flexible Impeller

The hydrodynamics of gas-liquid dispersion process in a stirred tank with rigid impellers, rigid-flexible impellers, and punched rigid-flexible impellers were investigated using a combined computational fluid dynamics (CFD) and population balance model (PBM) approach. A classical Eulerian-Eulerian approach coupled with standard k-e turbulence model was employed to simulate gas-liquid turbulent flow in the stirred tank. The multiple reference frame (MRF) approach was used to simulate impeller rotation. The effects of impeller type, flexible connection piece length, aperture size/ratio, impeller speed and superficial gas velocity on the local gas holdup and bubble size distribution for the gas-liquid dispersion process were investigated. Results showed that a long flexible connection piece length was conductive to the gas-liquid dispersion process. The optimum aperture ratio and aperture diameter were 12 % and 8 mm, respectively, for the gas-liquid dispersion process. Punched rigid-flexible impeller could reduce the differential pressure ahead and behind the impeller blade, decrease the size of low-pressure zone, and improve the water shear strain rate compared with rigid impeller and rigid-flexible impeller at the same Pg,v. It was found that punched rigid-flexible impeller was more efficient in terms of gas dispersibility than rigid impeller and rigid-flexible impeller.

Three-Way Coupling Simulation of a Gas-Liquid Stirred Tank using a Multi-Compartment Population Balance Model

Modelling of gas-liquid stirred tanks is very challenging due to the presence of strong bubble-liquid interactions. Depending upon the needs and desired accuracy, the simulation may be performed by considering one-way, two-way, three-way or four-way coupling between the primary and secondary phase. Accuracy of the prediction on the two-phase flow generally increases as the details of phase interactions increase but at the expense of higher computational cost. This study deals with two-way and three-way coupling of gas-liquid flow in stirred tanks which were then compared with results via four-way coupling. Population balance model (PBM) based on quadrature method of moments (QMOM) was implemented in a multi-compartment model of an aerated stirred tank to predict local bubble size. The multi-compartment model is regarded as three-way coupling because the local turbulent dissipation rates and flow rates were obtained from a two-way computational fluid dynamics (CFD) simulation. The predicted two-phase flows and local bubble size showed good agreement with experimental data.