Modeling and simulation of mixing in water-in-oil emulsion flow through a valve-like element using a population balance model

Emulsion flows are very common in natural processes as well as in several engineering areas, such as in the process of desalting crude oil that occurs in refineries. This kind of flow is described as a polydispersed multiphase flow. In this work, we evaluated the behavior of water-in-oil emulsion flowing through a duct with an element used to mimic the effect of a globe valve. An Eulerian multi-fluid approach was employed by solving the population balance equation coupled with computational fluid dynamics. Coalescence and breakage models recently developed were extended to this inhomogeneous model. A bivariate population balance problem was also solved to demonstrate the mixing caused by the valve-like element. The simulated results showed good agreement with the available experimental data for the Sauter and DeBroukere mean diameters.     

Simulation of oscillatory baffled column: CFD and population balance

In the present work, an attempt has been made to combine population balance and a CFD approach for simulating the flow in oscillatory baffled column (OBC). Three-dimensional Euler-Euler two-fluid simulations are carried out for the experimental data of Oliveira and Ni [2001. Gas hold-up and bubble diameter in a gassed oscillatory baffled column. Chemical Engineering Science 56, 6143-6148]. The experimental data include the average hold-up profile and bubble size distribution in the OBC. All the non-drag forces (turbulent dispersion force, lift force) and the drag force are incorporated in the model. The coalescence and breakage effects of the gas bubbles are modeled according to the coalescence by the random collision driven by turbulence and wake entrainment while for bubble breakage by the impact of turbulent eddies. Predicted liquid velocity and averaged gas hold-up are compared with the experimental data. The profile of the mean bubble diameter in the column and its variation with the superficial gas velocity is studied. Bubble size distribution obtained by the model is compared with the experimental data.     

A coupled CFD-population balance approach for nanoparticle synthesis in turbulent reacting flows

This paper investigates the first part of a two-stage methodology for the detailed fully coupled modelling of nanoparticle formation in turbulent reacting flows. We use a projected fields (PF) method to approximate the joint composition probability density function (PDF) transport equation that describes the evolution of the nanoparticles. The method combines detailed chemistry and the method of moments with interpolative closure (MoMIC) population balance model in a commercial computational fluid dynamics (CFD) code. We show details of the implementation and present an extensive set of numerical experiments and validation. We consider the example of the chloride process for the industrial synthesis of titania. We show good agreement with experimental data and present fully coupled detailed chemistry CFD simulations of nanoparticle formation in a representative ‘slot’ reactor geometry. The simulations show that inception occurs in a mixing zone near the reactor inlets. Most of the nanoparticle mass is due to surface growth downstream of the mixing zone with a narrower size distribution occurring in the regions of higher surface growth. The predicted temperature and particle properties are compared to a perfect mixing case. The implications for the second part of the methodology, where it is proposed to post-process the data using a more detailed particle model, are discussed critically.     

Simulating the early stage of high-shear granulation using a two-dimensional Monte-Carlo approach

A two-dimensional (2-D) model of a granulation process is presented in this paper. It aims to simulate an entire granulation batch without the use of an initial experimental or fictitious 2-D density function, by taking the experimental operating conditions into account. The mass of liquid and solid in the granules are the two predicted internal variables. The 2-D population balance equation is solved by a Constant Number Monte-Carlo method. This is a stochastic technique tracking the evolution of a population, whilst performing the calculations with a fixed number of particles. This is achieved by reducing or increasing the sample volume when an event results in a net production or a net decrease in the number of particles, respectively. An original multi-population approach is developed to describe the early stage of the process, where small numbers of granules are formed amongst a large number of primary particles. It consists of separating the primary particles from the granule population. A specific intensive variable is introduced to keep track of the repartition of masses. The overall density function is reconstructed a posteriori from the combination of the two populations. This approach allows the simulation to commence from the initial addition of liquid at the start of the process, rather than to start from an early granule size distribution. The early stage of the granulation process, frequently referred as nucleation, can therefore be studied numerically. Four different mechanisms are implemented. Nucleation and re-wetting describe the addition of liquid to the system. The interactions between liquid and solid phases are modelled by a layering process. An aggregation model is also included to simulate the growth of particles undergoing frequent collisions. Finally, the relevance of this new model is demonstrated by confronting the simulations to real experimental data.     

Numerical simulation of two-phase flow with bubble break-up and coalescence coupled with population balance modeling

A computational fluid dynamic (CFD) model was developed with an improved source term based on previous work by Hagesaether et al. [1] for bubble break up and bubble coalescence to carry out numerical prediction of number density of different bubble class in turbulent dispersed flow. The numerical prediction was based on two fluid models, using the Eulerian–Eulerian approach where the liquid phase was treated as a continuum and the gas phase (bubbles) was considered as a dispersed phase. Bubble–bubble interactions, such as breakage due to turbulence and coalescence due to the combined effect of turbulence and laminar shear were considered. The result shows that the radial distributions of number densities of lower bubble classes are more than its higher counterpart. The result also shows that the Sauter mean diameter increases with the increase of height up to 1 m and then become steady. Simulated results are found to be in good agreement with the experimental data.     

Droplet coalescence model optimization using a detailed population balance model for RDC extraction column

Single droplet experiments in a small lab scale Rotating Disk Contactor (RDC) for two different liquid–liquid systems were used to evaluate the coalescence parameters necessary for column simulations. Five different coalescence models are studied; the models parameters were obtained by an inverse solution of the population balance model using the extended fixed-pivot technique for the discretization of the droplet internal coordinate. The estimated coalescence parameters by solving the inverse problem were found dependent on the chemical test system. The Coulaloglou and Tavlarides model was found to be the best model to predict the experimental data for both test systems. These parameters were used to study the hydrodynamics and mass transfer behavior of pilot plant RDC extraction column using the simulation tool LLECMOD. This is performed for two different liquid–liquid systems as recommended by the European Federation of Chemical Engineering (EFCE) (butylacetate–acetone–water (b–a–w) and toluene–acetone–water (t–a–w)). The simulated Sauter mean droplet diameter, hold-up values and concentration profiles for organic and aqueous phase were found to be well predicted compared to the experimental data.     

Three-dimensional mathematical modeling of dispersed two-phase flow using class method of population balance in bubble columns

Computational fluid dynamics (CFD) simulations of bubble columns have received recently much attention and several multiphase models have been developed, tested, and validated through comparison with experimental data. In this work, we propose a model for two-phase flows at high phase fractions. The inter-phase forces (drag, lift and virtual mass) with different closure terms are used and coupled with a classes method (CM) for population balance. This in order to predict bubble’s size distribution in the column which results of break-up and coalescence of bubbles. Since these mechanisms result greatly of turbulence, a dispersed k– turbulent model is used.The results are compared to experimental data available from the literature using a mean bubble diameter approach and CM approach and the appropriate formulations for inter-phase forces in order to predict the flow are highlighted.The above models are implemented using the open source package OpenFoam.     

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

A CFD model for the simulation of gas‐liquid bubbly flow is developed. In the model, the multi‐phase flow is simulated by an Eulerian‐Eulerian approach using several phase definitions (from 3 to 10). The bubble size distribution is simulated by a solution of the discretized population balance equation with coalescence and break‐up of bubbles. The number of the discretized population balance equations in the model is larger than the number of the phases used in the flow field simulation. A desired accuracy in the simulation can be achieved by choosing a suitable number of phases as a compromise between accuracy and computational cost. With this model, more detailed flow hydrodynamics and bubble size distribution can be obtained. The model was tested with different operating conditions and for different numbers of dispersed phases in a bubble column, and was verified with a bubble size distribution obtained experimentally.     

Numerical Investigation of the Effect of Impeller Design Parameters on the Performance of a Multiphase Baffle‐Stirred Reactor

The turbulent gas‐liquid flow field in an industrial 100‐m³ stirred tank was calculated by using computational fluid dynamics based on the finite‐volume method. Turbulent effects were modeled with the shear stress transport model, and gas‐liquid bubbly flow was modeled with the Eulerian‐Eulerian approach using the Grace correlation for the drag force interphase momentum transfer. The relative motion between the rotating impeller and the stationary baffled tank was considered by using a multiple frames of reference algorithm. The effects of Rushton and pitched‐blade impeller design parameters such as blade geometry, location, and pumping direction on the mixing performance were investigated. It was found that a combination of Rushton turbines with up‐pumping pitched‐blade turbines provides the best mixing performance in terms of gas holdup and interfacial area density. The approach outlined in this work is useful for performance optimization of biotechnology reactors, as typically found in fermentation processes.     

Modelling and simulation of suspension polymerization of vinyl chloride via population balance model

A detailed population balance model is presented for suspension polymerization of vinyl chloride in an isothermal batch reactor perfectly mixed on macrolevel. Coalescence and breakage of monomer droplets, as well as mass exchange of species between the droplets induced by collisions, termed micromixing, are also included into the model forming a complex three-scale system. The resulted population balance equation is solved by coupling the deterministic continuous time computation of polymerization reactions inside the droplets with the random coalescence and breakage events of droplets using Monte Carlo simulation. The results obtained by simulation revealed that aggregation, breakage and micro-mixing of species induced by droplet collisions affect the process significantly.     

CFD simulation of bubble columns incorporating population balance modeling

A computational fluid dynamics (CFD)-code has been developed using finite volume method in Eulerian framework for the simulation of axisymmetric steady state flows in bubble columns. The population balance equation for bubble number density has been included in the CFD code. The fixed pivot method of Kumar and Ramkrishna [1996. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chemical Engineering Science 51, 1311-1332] has been used to discretize the population balance equation. The turbulence in the liquid phase has been modeled by a k-ε model. The novel feature of the framework is that it includes the size-specific bubble velocities obtained by assuming mechanical equilibrium for each bubble and hence it is a generalized multi-fluid model. With appropriate closures for the drag and lift forces, it allows for different velocities for bubbles of different sizes and hence the proper spatial distributions of bubbles are predicted. Accordingly the proper distributions of gas hold-up, liquid circulation velocities and turbulence intensities in the column are predicted. A survey of the literature shows that the algebraic manipulations of either bubble coalescence or break-up rate were mainly guided by the need to obtain the equilibrium bubble size distributions in the column. The model of Prince and Blanch [1990. Bubble coalescence and break-up in air-sparged bubble columns. A.I.Ch.E. Journal 36, 1485-1499] is known to overpredict the bubble collision frequencies in bubble columns. It has been modified to incorporate the effect of gas phase dispersion number. The predictions of the model are in good agreement with the experimental data of Bhole et al. [2006. Laser Doppler anemometer measurements in bubble column: effect of sparger. Industrial & Engineering Chemistry Research 45, 9201-9207] obtained using Laser Doppler anemometry. Comparison of simulation results with the experimental measurements of Sanyal et al. [1999. Numerical simulation of gas-liquid dynamics in cylindrical bubble column reactors. Chemical Engineering Science 54, 5071-5083] and Olmos et al. [2001. Numerical simulation of multiphase flow in bubble column reactors: influence of bubble coalescence and breakup. Chemical Engineering Science 56, 6359-6365] also show a good agreement for liquid velocity and gas hold-up profiles.     

Modelling of dense and complex granular flow in high shear mixer granulator—A CFD approach

In the aspect of granulation process control, the numerical simulations appear to be a cost-effective and flexible tool to investigate the flow structure of granular materials in mixer granulators of various configurations and operating conditions. Computational fluid dynamics (CFD) is used in this study to model the granular flow in a vertical high shear mixer granulator. The simulation is based on the continuum model of dense-gas kinetic theory [Gidaspow, D., Bezburuah, R., Ding, J., 1992. Hydrodynamics of circulating fluidized beds, kinetic theory approach. In: Fluidization, vol. VII, Proceedings of the 7th Engineering Foundation Conference on Fluidization, Brisbane, Australia, pp. 75-82] with consideration of inter-particle friction force at dense condition [Schaeffer, D.G., 1987. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations 66 (1), 19-50]. This study aims to verify this numerical method in modelling dense and complex granular flows, where the solids motion obtained from the simulation is validated against the experimental results of positron emission particle tracking (PEPT) technique [Ng, B.H., Kwan, C.C., Ding, Y.L., Ghadiri, M., Fan, X.F., 2007. Solids motion of calcium carbonate particles in a high shear mixer granulator: a comparison between dry and wet conditions. Powder Technology 177 (1), 1-11]. In general, the Eulerian based continuum model captures the main features of solids motion in high shear mixer granulator including the bed height and dominating flow direction (the tangential velocity). However, the continuum based kinetic-frictional model is not capable of capturing the complex vertical swirl pattern. Quantitative comparison shows over-predictions in the tangential velocity and stiff drops of the tangential velocity at the wall region. These results demonstrate the deficiency in transmitting forces in the bed of granular materials which indicate the necessity to improve the constitutive relations of dense granular materials as a continuum.     

Modelling of flocculation using a population balance equation

In this paper, a model based on a population balance equation (PBE) is developed. It aims at reproducing experimental floc size distributions obtained at steady state in a jar-test. The objective is to develop a simple model, based on physical phenomena, and that does not contain any adjustable parameters. Floc size distributions obtained using a part of a particle image velocimetry (PIV) device and image analysis are used to develop mathematical expressions for the aggregation and breakage kernels. A critical volume beyond which breakage is of significant importance is identified and related to the hydrodynamics. Hydrodynamic sequencing allows the distribution of the daughter particles resulting from a breakage event to be established. The model is finally successfully validated against experimental results.     

CFD modelling of a “stabilized cool flame” reactor with reduced mechanisms and a direct integration approach

Controlled liquid fuels droplet evaporation under “stabilized cool flame” (SCF) conditions can lead to a homogeneous, heated air-fuel vapor mixture that can be subsequently either burnt or utilized in fuel reforming of fuel cell applications. The work focuses on the numerical modelling of diesel spray evaporation in an “SCF” reactor, operating under atmospheric pressure conditions. An “in-house” developed CFD code is used to predict flow characteristics. The complex oxidative phenomena encountered under SCF conditions are accounted for by implementing two reduced chemical kinetic schemes consisting of five (S5) and seven (S7) active species. Species conservation differential equations as well as reaction and heat release rates provided by the S5 and S7 schemes are solved in each computational cell via a direct integration approach. Comparison with experiments indicates that the implemented computational approach can successfully capture the major characteristics of the reactor's thermal field, especially when increasing air inlet temperatures.     

Population balance modelling of granulation with a physically based coalescence kernel

It was previously published by the authors that granules can either coalesce through Type I (when granules coalesce by viscous dissipation in the surface liquid layer before their surfaces touch) or Type II (when granules are slowed to a halt during rebound, after their surfaces have made contact) (AIChE J. 46 (3) (2000) 529). Based on this coalescence mechanism, a new coalescence kernel for population balance modelling of granule growth is presented. The kernel is constant such that only collisions satisfying the conditions for one of the two coalescence types are successful. One constant rate is assigned to each type of coalescence and zero is for the case of rebound. As the conditions for Types I and II coalescence are dependent on granule and binder properties, the coalescence kernel is thus physically based. Simulation results of a variety of binder and granule materials show good agreement with experimental data.     

Effects of cross-flow velocity, capillary pressure and oil viscosity on oil-in-water drop formation from a capillary

The formation of oil drops from a single capillary with a diameter of 200 μm into a cross-flowing continuous water phase has been studied experimentally with the particle image velocimetry (PIV) technique and numerically with the computational fluid dynamics (CFD) software Fluent. The drop formation time and the volume of the detached drop were used as validation parameters and the results from the two methods corresponded well, with a difference of less than 5% for the drop formation time and 10% for the drop volume. The cross-flow velocity has a major impact on drop size, which decreases as the cross-flow increases. An increase in cross-flow, oil viscosity and capillary pressure displace the position of necking and drop detachment away from the capillary opening, which will have a decreasing effect on the final size of the drop.     

Surface protection of mild steel using benzimidazole derivatives: experimental and theoretical approach

Interaction of organic molecules with the surface of metals plays important role in many applications. In particular, surface protective applications need much explanation from both experimental and theoretical point of view. Herein, we have investigated the surface adsorption characteristics and corrosion inhibition behavior of two new benzimidazole derivatives namely 2-(2-Bromophenyl)-1H-benzimidazole (BPBA) and 2-(2-Bromophenyl)-1-methyl-1H-benzimidazole (BPMA) on mild steel in 0.5?M?HCl solution using experimental and theoretical approach. Electrochemical and weight loss experiments were used to elucidate the corrosion inhibition potentials of BPBA and BPMA. Attenuated total reflectance-Fourier transform infrared spectroscopy, contact angle, scanning electron microscopy, and X-ray photoelectron spectroscopy measurements were performed to confirm the adsorption of BPBA and BPMA on mild steel surface. Computer simulations were further employed to provide additional insights into the mechanism of interaction between the inhibitors and the steel surface. All the results confirmed that BPMA is a better corrosion inhibitor for mild steel than BPBA in 0.5?M HCl. This new inhibitors could find application industrially during processes such as oil well acidizing for steel protection against corrosion.     

Prediction of methane storage in covalent organic frameworks using big-data-mining approach

A combination of computational materials screening and machine learning (ML) technique is being adopted as a popular approach to study various materials toward application of interest. In this work, we began with high-throughput molecular simulations to calculate the methane storage (6.5 MPa) and deliverable (6.5-0.58 MPa) capacities of 404,460 covalent organic frameworks (COFs) at 298 K. Then, the full data sets with 23 features were randomly split into training and test sets in a ratio of 20:80, which were applied to evaluate the prediction abilities of several ML algorithms, including gradient boosting decision tree (GBDT), neural network (NN), support vector machine (SVM), random forest (RF) and decision tree (DT). The results indicate that the RF model has the highest prediction accuracy, which was further employed to reduce the dimension of features space and quantitatively analyze the relative importance of each feature value. The binary classification predictors built using the features with the highest influence weight can give a successful identification of top-performing candidates from the test set containing 323,168 COFs with an accuracy exceeding 96%. The deliverable capacities of the identified COFs were found to outperform those reported so far for various adsorbents. The findings may provide a useful guidance for the design and synthesis of new high-performance materials for methane storage application.