Modeling of Bubble Column Reactors: Progress and Limitations

Diffuse-Interface Blended Method for Imposing Physical Boundaries in Two-Fluid Flows

Multiphase flows are commonly found in chemical engineering processes such as distillation columns, bubble columns, fluidized beds and heat exchangers. The physical boundaries of domains in numerical simulations of multiphase flows are generally defined by a conformal unstructured mesh which, depending on the complexity of the physical system, results in time-consuming mesh generation which frequently requires user-intervention. Furthermore, the resulting conformal unstructured mesh could potentially contain a large number of skewed elements, which is undesirable for numerical stability and accuracy. The diffuse-interface approach allows for the use of a simple structured meshes to be used while still capturing the desired physical (e.g., solid-fluid) boundaries. In this work, a novel diffuse-interface method for the imposition of physical boundaries is developed for the incompressible two-fluid multiphase flow model. This model is appropriate for dispersed multiphase flows which are pervasive in chemical engineering processes, in that this flow regime results in high levels of mass and energy transfer between phases. A diffuse interface is used to define the physical boundaries and boundary conditions are imposed by blending the conservation equations from the two-fluid model with that of the nondeformable solid. The results from the diffuse-interface method are compared with results from a conformal unstructured mesh for different interface functions and widths. For small interface widths, the accuracy of the flow profile is unaffected by the choice of interface function and the phase fraction distribution and flow behavior are within 3% compared to those from a conformal mesh. As the interface width increases, the diffuse-interface solution deviates from the conformal mesh solution in both the localized gas fraction and the overall gas hold-up, resulting in a difference up to 30%. In the case of flow past a cylinder, where the solid interacts with the flow, the presence of the diffuse interface extends the thickness of the solid boundary and results in a deviation from the conformal mesh solution as time increases.

Structured population balances to support microalgae-based processes: Review of the state-of-art and perspectives analysis

Design and optimization of microalgae processes have traditionally relied on the application of unsegregated mathematical models, thus neglecting the impact of cell-to-cell heterogeneity. However, there is experimental evidence that the latter one, including but not limited to variation in mass/size, internal composition and cell cycle phase, can play a crucial role in both cultivation and downstream processes. Population balance equations (PBEs) represent a powerful approach to develop mathematical models describing the effect of cell-to-cell heterogeneity. In this work, the potential of PBEs for the analysis and design of microalgae processes are discussed. A detailed review of PBE applications to microalgae cultivation, harvesting and disruption is reported. The review is largely focused on the application of the univariate size/mass structured PBE, where the size/mass is the only internal variable used to identify the cell state. Nonetheless, the need, addressed by few studies, for additional or alternative internal variables to identify the cell cycle phase and/or provide information about the internal composition is discussed. Through the review, the limitations of previous studies are described, and areas are identified where the development of more reliable PBE models, driven by the increasing availability of single-cell experimental data, could support the understanding and purposeful exploitation of the mechanisms determining cell-to-cell heterogeneity.

Effective Analysis of Different Gas Diffusers on Bubble Hydrodynamics in Bubble Column and Airlift Reactors towards Mass Transfer Enhancement

Even bubble column reactors (BCR) and airlift reactors (ALR) have been developed in terms of various related aspects towards mass transfer enhancement, the effective analysis of gas diffuser types on mass transfer and gas–liquid hydrodynamic characteristics is still limited. Therefore, the present study aims to analyze the relative effect of different types of air diffusers on bubble hydrodynamics and mass transfer performance to understand their behaviors and define the best type. The experiments were conducted by varying different diffuser types, reactor types (BCR and ALR), and superficial gas velocity (Vg) (0.12 to 1.00 cm/s). Five air diffusers including commercial fine sand (F-sand) and coarse sand (C-sand) diffusers, and acrylic perforated diffusers with orifice sizes of 0.3 mm (H-0.3), 0.6 mm (H-0.6), and 1.2 mm (H-1.2), were used in this study. For every condition, it was analyzed in terms of bubble hydrodynamics and oxygen mass transfer coefficient (KLa). Lastly, the selected diffusers that provided the highest KLa coefficient were evaluated with a solid media addition case. The results of both reactor classes showed that F-sand, the smallest orifice diffuser, showed the smallest air bubbles (3.14–4.90 mm) compared to other diffusers, followed by C-sand, which larger about 22–28% on average than F-sand. ALR exhibited a better ability to maintain smaller bubbles than BCR. Moreover, F-sand and C-sand diffusers showed a slower rising velocity through their smaller bubbles and the tiny bubble recirculation in ALR. Using F-sand in ALR, the rising velocity is about 1.60–2.58 dm/s, which is slower than that in BCR about 39–54%. F-sand and C-sand were also found as the significant diffusers in terms of interfacial area and gas hold-up. Then, the KLa coefficient was estimated in every diffuser and reactor under the varying of Vg. Up to 270% higher KLa value was achieved from the use of F-sand and C-sand compared to other types due to their smaller bubbles generated/maintained and longer bubble retention time through slower rising velocity. After adding 10% ring shape plastic media into the reactors with F-sand and C-sand diffusers, a better performance was achieved in terms of KLa coefficient (up to 39%) as well as gas hold-up and liquid mixing. Lastly, ALR also had a larger portion of mixed flow pattern than BCR. This eventually promoted mass transfer by enhancing the mixed flow regime.

Effects of flow velocity and bubble size distribution on oxygen mass transfer in bubble column reactors-A critical evaluation of the computational fluid dynamics-population balance model

Computational fluid dynamics (CFD) is used to simulate a bubble column reactor operating in the bubbly (homogenous) regime. The Euler-Euler two-fluid model, integrated with the population balance model (PBM), is adopted to compute the flow and bubble size distribution (BSD). The CFD-PBM model is validated against published experimental data for BSD, global gas holdup, and oxygen mass transfer coefficient. The sensitivity of the model with respect to the specification of boundary conditions and the bubble coalescence/breakup models is assessed. The coalescence model of Prince and Blanch (1990) provides the best results, whereas the output is shown to be insensitive to the breakup model. The CFD-PBM study demonstrates the importance of considering the BSD in order to correctly model mass transfer. Results show that the constant bubble size assumption results in a large error in the oxygen mass transfer coefficient, while giving acceptable results for gas holdup. PRACTITIONER POINTS: Constant bubble size (CBS) and population balance model (PBM) are compared for a bubble column reactor. Both PBM and CBS can predict gas holdup; however, PBM can correctly predict gas-liquid mass transfer whereas CBS cannot. Best practices for selecting coalescence, breakup, and drag models are determined.

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.

Prediction of gas velocity in two-phase flow using developed fuzzy logic system with differential evolution algorithm

In this investigation, differential evolution (DE) algorithm with the fuzzy inference system (FIS) are combined and the DE algorithm is employed in FIS training process. Considered data in this study were extracted from simulation of a 2D two-phase reactor in which gas was sparged from bottom of reactor, and the injected gas velocities were between 0.05 to 0.11 m/s. After doing a couple of training by making some changes in DE parameters and FIS parameters, the greatest percentage of FIS capacity was achieved. By applying the optimized model, the gas phase velocity in x direction inside the reactor was predicted when the injected gas velocity was 0.08 m/s.

Predicting Air Superficial Velocity of Two-Phase Reactors Using ANFIS and CFD

In predicting the turbulence property of gas (bubble) flow in the domain of continuous fluid and liquid, the integration of machine learning and computational fluid dynamics (CFD) methods reduces the overall computational time. This combination enables us to see the effective input parameters in the engineering process and the impact of operating conditions on final outputs, such as gas hold-up, heat and mass transfer, and the flow regime (uniform bubble distribution or nonuniform bubble properties). This paper uses the combination of machine learning and single-size calculation of the Eulerian method to estimate the gas flow distribution in the continuous liquid fluid. To present the machine-learning method besides the Eulerian method, an adaptive neuro-fuzzy inference system (ANFIS) is used to train the CFD finding and then estimate the flow based on the machine-learning method. The gas velocity and turbulent eddy dissipation rate are trained throughout the bubble column reactor (BCR) for each CFD node, and the artificial BCR is predicted by the ANFIS method. This smart reactor can represent the artificial CFD of the BCR, resulting in the reduction of expensive numerical simulations. The results showed that the number of inputs could significantly change this method's accuracy, representing the intelligence of method in the learning data set. Additionally, the membership function specifications can impact the accuracy, particularly, when the process is trained with different inputs. The turbulent eddy dissipation rate can also be predicted by the ANFIS method with a similar model pattern for air superficial gas velocity.

Liquid temperature prediction in bubbly flow using ant colony optimization algorithm in the fuzzy inference system as a trainer

In the current research paper a novel hybrid model combining first-principle and artificial intelligence (AI) was developed for simulation of a chemical reactor. We study a 2-dimensional reactor with heating sources inside it by using computational fluid dynamics (CFD). The type of considered reactor is bubble column reactor (BCR) in which a two-phase system is created. Results from CFD were analyzed in two different stages. The first stage, which is the learning stage, takes advantage of the swarm intelligence of the ant colony. The second stage results from the first stage, and in this stage, the predictions are according to the previous stage. This stage is related to the fuzzy logic system, and the ant colony optimization learning framework is build-up this part of the model. Ants movements or swarm intelligence of ants lead to the optimization of physical, chemical, or any kind of processes in nature. From point to point optimization, we can access a kind of group optimization, meaning that a group of data is studied and optimized. In the current study, the swarm intelligence of ants was used to learn the data from CFD in different parts of the BCR. The learning was also used to map the input and output data and find out the complex connection between the parameters. The results from mapping the input and output data show the full learning framework. By using the AI framework, the learning process was transferred into the fuzzy logic process through membership function specifications; therefore, the fuzzy logic system could predict a group of data. The results from the swarm intelligence of ants and fuzzy logic suitably adapt to CFD results. Also, the ant colony optimization fuzzy inference system (ACOFIS) model is employed to predict the temperature distribution in the reactor based on the CFD results. The results indicated that instead of solving Navier–Stokes equations and complex solving procedures, the swarm intelligence could be used to predict a process. For better comparisons and assessment of the ACOFIS model, this model is compared with the genetic algorithm fuzzy inference system (GAFIS) and Particle swarm optimization fuzzy inference system (PSOFIS) method with regards to model accuracy, pattern recognition, and prediction capability. All models are at a similar level of accuracy and prediction ability, and the prediction time for all models is less than one second. The results show that the model’s accuracy with low computational learning time can be achieved with the high number of CIR (0.5) when the number of inputs ≥ 4. However, this finding is vice versa, when the number of inputs < 4. In this case, the CIR number should be 0.2 to achieve the best accuracy of the model. This finding could also highlight the importance of sensitivity analysis of tuning parameters to achieve an accurate model with a cost-effective computational run.

Mass transfer in aerated culture media combining mixed electrolytes and glucose

The combined effects of mixed electrolyte species and glucose on oxygen transfer were studied in a bubble column with aqueous solutions. Of particular interest was the presence of electrolytes containing ions which are prone to present solute-solute interactions or to crystallize. Without and at low concentration of glucose (≤ 5 g/L), the increasing concentration of electrolytes (nominal ionic strength: 0-0.43 M), up to a critical value, enhanced the volumetric mass transfer coefficient (k_La) and the availability of specific interfacial area (a), due to the inhibition of bubble coalescence. As the glucose concentration increased (10-40 g/L), the enhancing effects of electrolytes were gradually lost. The glucose interacted with electrolytes, reducing their ability to inhibit coalescence and to enhance the k_La. Salt crystallization occurred independently of the addition of glucose; however, it did not have significant effect on mass transfer. Finally, the changes in physicochemical properties were highly collinear with composition variables.

CFD Simulations of an Air-Water Bubble Column: Effect of Luo Coalescence Parameter and Breakup Kernels

In this work, CFD simulations of an air-water bubbling column were performed and validated with experimental data. The superficial gas velocities used for the experiments were 0.019 and 0.038 m/s and were considered as an homogeneous regime. The former involves simpler physics when compared to a heterogeneous regime where the superficial velocities are higher. In order to simulate the system, a population balance model (PBM) was solved numerically using a discrete method and a closure kernels involving the Luo coalescence model as well as two different breakup models: Luo's and Lehr's. For the multi-phase calculations, an eulerian framework was selected and the interphase momentum transfer included drag, lift, wall lubrication, and turbulent dispersion terms. A sensitivity analysis was performed on a Luo coalescence kernel by changing the coalescence parameter (c₀) from 1.1 to 0.1 and results showed that the radial profiles of gas holdup and axial liquid velocity were significantly affected by such parameter. From the simulation results, the main conclusions were: (a) A combination of the Luo coalescence and Luo breakup kernels (Luo-Luo) combined with a decreasing value of c₀ improves the gas holdup profiles as compared to empirical values. However, at the lowest value of c₀ investigated in this work, the axial liquid velocity deteriorates with regards to experimental data when using a superficial gas velocity of 0.019 m/s. (b) A combination of the Luo coalescence and Lehr breakup models (Luo-Lehr) was shown to improve the gas holdup values with experimental data when compared to the Luo-Luo kernels. However, as c₀ decreases, the Luo-Lehr models underestimate the axial liquid velocity profiles with regards to empirical values. (c) A first and second order numerical schemes allowed predicting similar radial profiles of gas holdup and axial liquid velocity. (d) The mesh sensitivity results show that a 3 mm mesh size can be considered as reasonable for simulating experimental data. (e) The inclusion of wall lubrication parameter was found to be significant, although only when using finer meshing. In addition, it allows an improvement of the axial liquid velocity at the core of the bubble column.