Droplet population balance modelling—hydrodynamics and mass transfer

The hydrodynamic and mass transfer behavior of a rotating disc contactor extraction (RDC) column based on a bivariate population balance model is investigated using the generalized fixed-pivot technique for the discretization of droplet internal coordinate. Single-droplet and swarm-droplet studies in small lab-scale devices were used to evaluate breakage and coalescence parameters necessary for column simulations. The breakage probability of single droplets was measured and a new correlation was developed, which also takes viscosity effects into account. Coalescence probability studies resulted in chemical system dependent parameters, which were obtained by an inverse solution of a simplified balance model. In a final study, the hydrodynamic and mass transfer behavior of pilot plant RDC columns have been simulated based on the parameter set derived from the lab-scale units. The simulated mean Sauter diameter, hold-up values and concentration profiles were found to be well predicted at different operating conditions. The relative error for the simulated mean Sauter diameters is about 15%, for the hold-up about 20% and for the concentration profiles about 20%.     

Effect of spent grains on flow regime transition in bubble column

It is well known that two main flow regimes are present in bubble columns, being the evaluation of transition between homogeneous and heterogeneous regimes of crucial importance for reactor design. For air–water systems, several models have been satisfactorily proposed to explain this phenomenon. However when gas–liquid–solids systems are considered, solid particles influence on regime transition is not yet clear, in spite of the amount of research developed over the past years.The objective of this work is to evaluate the effect of a specific solid phase – spent grains – on homogeneous regime stability and regime transition. Spent grains are cellulose-based particles that have been used to immobilize cells on biotechnology process. These particles are wettable and have a density close to water and its influence on bubble column reactors is particularly important in order to establish the limits were both regimes prevail.A cylindrical Plexiglax BC of 18 L volume was used with air, water and spent grains at different concentrations (0–20% (wt._{WET BASIS}/vol.)) as gas, liquid and solid phases. Regime transition was determined according to the drift-flux and slip speed concept.It was found that at studied concentrations of spent grains, critical gas hold-up decreases as solids concentration increases. At the highest solids concentration and lowest gas flow rates no fluidization of the solid phase was observed. It is believed that the critical hold-up decrease was mainly due to bubble coalescence, as larger bubbles were observed when heterogeneous regime was present. This coalescence may be caused by the non-uniform distribution of solid phase on the column and the interaction of spent grains with bubbles in the liquid–gas interface     

The Droplet Population Balance Model – Estimation of Breakage and Coalescence

A droplet population balance model is employed in order to describe the hydrodynamic behavior of solvent extraction columns. This model describes the axial change of local column holdup and local droplet size distributions due to the basic phenomena, like droplet rising, axial dispersion, droplet breakage and coalescence. In order to reduce experimental efforts, single and swarm droplet experiments in small lab‐scale devices were performed. For this, a rotating disc contactor (RDC) with one compartment and a Venturi tube were used to investigate droplet breakage and droplet coalescence. In case of breakage the experiments were made for different droplet sizes at different rotor speeds for the EFCE system toluene/water, whereas the investigations of the coalescence phenomena depending on droplet size and holdup were done with the EFCE system n‐butylacetate/water.     

A Genetic Algorithm Based Approach to Coalescence Parameters: Estimation in Liquid‐Liquid Extraction Columns

The population balance model is a useful tool for the design and prediction of a range of processes that involve dispersed phases and particulates. The inverse problem method for the droplet population balance model is applied to estimate coalescences parameters for two‐phase liquid‐liquid systems. This is undertaken for two systems, namely toluene/water and n‐butyl acetate/water in a rotating disc contactor (RDC), using a droplet population balance model. In the literature, the estimation procedure applied to this problem is often based on the deterministic optimization approach. These methods generate instabilities near a local minimum, inevitably requiring information about the derivatives at each iteration. To overcome these limitations, a method providing an estimate for the coalescences parameters is proposed. It is based on a simple and adapted structure of the genetic algorithm, for this particular problem. The agreement between the experimental observations and the simulations is encouraging and, in particular, the models used have proven to be suitable for the prediction of hold‐up and Sauter diameter profiles for these systems. Finally, these results demonstrate that the optimization procedure proposed is very convenient for estimating the coalescences parameters for extraction column systems.     

Quantifying sub-grid scale (SGS) turbulent dispersion force and its effect using one-equation SGS large eddy simulation (LES) model in a gas–liquid and a liquid–liquid system

The one-equation SGS LES model has shown promise in revealing flow details as compared to the Dynamic model, with the additional benefit of providing information on the modelled SGS-turbulent kinetic energy (Niceno et al., 2008). This information on SGS-turbulent kinetic energy (SGS-TKE) offers the possibility to more accurately model the physical phenomena at the sub-grid level, especially the modelling of the SGS-turbulent dispersion force (SGS-TDF). The use of SGS-TDF force has the potential to account for the dispersion of particles by sub-grid scale eddies in an LES framework, and through its use, one expects to overcome the conceptual drawback faced by Eulerian–Eulerian LES models. But, no work has ever been carried out to study this aspect. Niceno et al. (2008) could not study the impact of SGS-TDF effect as their grid size was comparable to the dispersed bubble diameter. A proper extension of research ahead would be to quantify the effect of sub-grid scale turbulent dispersion force for different particle systems, where the particle sizes would be smaller than filter-size. This work attempts to apply the concept developed by Lopez de Bertodano (1991) to approximate the turbulent diffusion of the particles by the sub-grid scale liquid eddies. This numerical experimentation has been done for a gas–liquid bubble column system (Tabib et al., 2008) and a liquid–liquid solvent extraction pump-mixer system ( [Tabib et al., 2010] and [28] ). In liquid–liquid extraction system, the organic droplet size is around 0.5 mm, and in bubble columns, the bubble size is around 3–5 mm. The simulations were run with mesh size coarser than droplet size in pump-mixer, and for bubble column, two simulations were run with mesh size finer and coarser than bubble diameter. The magnitude of SGS-TDF values in all the cases were compared with magnitude of other interfacial forces (like drag force, lift force, resolved turbulent dispersion force, force due to momentum advection and pressure). The results show that the relative magnitude of SGS-TDF as compared to other forces were higher for the pump-mixer than for the coarser and finer mesh bubble column simulations. This was because in the pump-mixer, the ratio of “dispersed phase particle diameter to the grid-size” was smaller than that for the bubble column runs. Also, the inclusion of SGS-TDF affected the radial hold-up, even though the magnitudes of these SGS-TDF forces appeared to be small. These results confirms that (a) the inclusion of SGS-TDF will have more pronounced effect for those Eulerian–Eulerian LES simulation where grid-size happens to be more than the particle size, and (b) that the SGS-TDF in combination with one-equation-SGS-TKE LES model serves as a tool to overcome a conceptual drawback of Eulerian–Eulerian LES model.     

Analysis of droplet expulsion in stagnant single water-in-oil-in-water double emulsion globules

Double emulsions created by phase inversion can be used for fast liquid–liquid separation; therefore, the coalescence behaviors of these types of multiple emulsions need to be predictable for different physical properties and drop size ratios. The aim of this study is to determine the influence of the effective overall drop diameter and the internal droplet size on the coalescence time and the coalescence behavior. Experimental investigations on the physical stability of single stagnant water-in-oil-in-water (W₁/O/W₂) double emulsion globules are performed. For this investigation, a formation device to inject one water droplet into an oil drop inside a water bulk phase is developed. The coalescence process of the sole internal water droplet floating on the O/W₂ interface with the water bulk phase, often termed droplet expulsion or external coalescence, is recorded with a high speed camera. Based on image analysis, the diameters of the effective overall drop D, containing the oil and entrapped water volume, and the internal water droplet d are determined. Additionally, the coalescence time τ, including the time from the first contact of the internal droplet and the drop-bulk interface to the film rupture is measured. A large increase in coalescence time with increasing water droplet diameters is found. For the investigated paraffin oil–water system and initial drop sizes, partial coalescence occurs. In this case, the diameter ratio of daughter-to-mother droplet ψ is determined.     

Gas–liquid and liquid–liquid mass transfer in microstructured reactors

This article is a comprehensive overview of gas–liquid and liquid–liquid mass transfer in microstructured reactors (MSR). MSR are known to offer high heat and mass transfer rates for two phase systems due to high surface to volume ratio as compared to conventional reactors. The reactions with fast kinetics controlled by mass transfer have been successfully intensified using MSR. The first part of the review deals with the methods of mass transfer characterization. Further, different dimensionless parameters used to analyze mass transfer in MSR are discussed. The literature data with different flow regimes and proposed empirical correlations for both gas–liquid and liquid–liquid systems is also presented. The conventional mass transfer models such as penetration and film theory are analyzed. Finally, the important issues of mass transfer in MSR are summed up.     

Phase equilibria of mixtures containing CO2 and organic acids using the UMR-PRU model

The UMR-PRU model, which has been successfully tested in the past to the predictions of different type of phase equilibrium and thermodynamic properties in binary and multicomponent systems, is applied in this work to phase equilibria in mixtures containing CO₂ and organic acids. New interaction parameters are determined by fitting only binary vapor–liquid equilibrium data and then they are used to predict the vapor–liquid, solid–gas and solid–liquid–gas equilibria in CO₂/organic acid systems. Furthermore, the UMR-PRU model with the newly derived interaction parameters is applied to the prediction of the phase equilibrium in ternary mixtures consisting of CO₂, organic acids and water. Satisfactory results are obtained in all cases.     

Liquid–liquid slug flow: Hydrodynamics and pressure drop

In this paper, the hydrodynamics and the pressure drop of liquid–liquid slug flow in round microcapillaries are presented. Two liquid–liquid flow systems are considered, viz. water-toluene and ethylene glycol/water-toluene. The slug lengths of the alternating continuous and dispersed phases were measured as a function of the slug velocity (0.03–0.5 m/s), the organic-to-aqueous flow ratio (0.1–4.0), and the microcapillary internal diameter (248 and 498 μm). The pressure drop is modeled as the sum of two contributions: the frictional and the interface pressure drop. Two models are presented, viz. the stagnant film model and the moving film model. Both models account for the presence of a thin liquid film between the dispersed phase slug and the capillary wall. It is found that the film velocity is of negligible influence on the pressure drop. Therefore, the stagnant film model is adequate to accurately predict the liquid–liquid slug flow pressure drop. The influence of inertia and the consequent change of the slug cap curvature are accounted for by modifying Bretherton’s curvature parameter in the interface pressure drop equation. The stagnant film model is in good agreement with experimental data with a mean relative error of less than 7%.     

Experimental model validation for n-propyl propionate synthesis in a reactive distillation column coupled with a liquid–liquid phase separator

In the synthesis of some organic esters, reactive distillation coupled with a liquid–liquid phase separator is often used to increase the product purity or to recover the reactants. In this article, we present a comprehensive experimental and theoretical study on the heterogeneously catalysed synthesis of n-propyl propionate by reactive distillation and a subsequent liquid–liquid phase separator. The experiments were performed in a pilot-scale reactive distillation column. Data-reconciliation tests proved that the experimental results obtained comprise a complete, reliable set of composition and temperature profiles along the pilot-scale reactive distillation column and can be used for further model validation. A nonequilibrium-stage model was applied to predict the experimental results. Simulation studies demonstrated that the composition and temperature profiles in the rectifying section of the column were highly sensitive to the composition of the reflux stream entering the column. Deviations between the experimental and predicted composition profiles in the rectifying section were identified. An explanation for the deviations is given in this article.     

Two-phase microfluidic flows

Two phase systems are ubiquitous in processes and products, and in both cases performance is maximized when precise control over the individual phases, and the ensemble, is possible. Microfluidic technologies afford higher levels of control over two-phase systems than is possible in macroscopic process equipment, opening avenues to controlled reactions as well as products having tightly controlled properties including emulsion size distribution. A review of recent progress in two-phase flows in microfluidic devices is presented. The fundamentals of two-phase flows including some important dimensionless numbers are firstly introduced, followed by a review of two-phase flow regimes in gas–liquid and liquid–liquid systems, focusing on microfluidic methods for controlling droplet formation and coalescence. Applications of two-phase microfluidic flows are briefly reviewed, including new approaches to the formation of well-defined complex emulsion which, like a Matryoshka doll, have structure within structure. The large number of recent publications reviewed in this paper highlights the tremendous interest in the fundamental study and use of controlled microfluidic two-phase flows, driven by the promise of highly controlled processes and new products having controlled complexity.     

Numerical solution of the bivariate population balance equation for the interacting hydrodynamics and mass transfer in liquid-liquid extraction columns

A comprehensive model for predicting the interacting hydrodynamics and mass transfer is formulated on the basis of a spatially distributed population balance equation in terms of the bivariate number density function with respect to droplet diameter and solute concentration. The two macro- (droplet breakage and coalescence) and micro- (interphase mass transfer) droplet phenomena are allowed to interact through the dispersion interfacial tension. The resulting model equations are composed of a system of partial and algebraic equations that are dominated by convection, and hence it calls for a specialized discretization approach. The model equations are applied to a laboratory segment of an RDC column using an experimentally validated droplet transport and interaction functions. Aside from the model spatial discretization, two methods for the discretization of the droplet diameter are extended to include the droplet solute concentration. These methods are the generalized fixed-pivot technique (GFP) and the quadrature method of moments (QMOM). The numerical results obtained from the two extended methods are almost identical, and the CPU time of both methods is found acceptable so that the two methods are being extended to simulate a full-scale liquid-liquid extraction column.     

Mass transfer from nanofluid drops in a pulsed liquid–liquid extraction column

Mass transfer in gas–liquid systems has been significantly enhanced by recent developments in nanotechnology. However, the influence of nanoparticles in liquid–liquid systems has received much less attention. In the present study, both experimental and theoretical works were performed to investigate the influence of nanoparticles on the mass transfer behaviour of drops inside a pulsed liquid–liquid extraction column (PLLEC). The chemical system of kerosene–acetic acid–water was used, and the drops were organic nanofluids containing hydrophobic SiO₂ nanoparticles at concentrations of 0.01, 0.05, and 0.1 vol%. The experimental results indicate that the addition of 0.1 vol% nanoparticles to the base fluid improves the mass transfer performance by up to 60%. The increase in mass transfer with increased nanoparticle content was more apparent for lower pulsation intensities (0.3–1.3 cm/s). At high pulsation intensities, the Sauter mean diameter (d₃₂) decreased to smaller sizes (1.1–2.2 mm), leading to decreased Brownian motion in the nanoparticles. Using an analogy for heat and mass transfer, an approach for determining the mass diffusion coefficient was suggested. A new predictive correlation was proposed to calculate the effective diffusivity and mass transfer coefficient in terms of the nanoparticle volume fraction, Reynolds number, and Schmidt number. Finally, model predictions were directly compared with the experimental results for different nanofluids. The absolute average relative error (%AARE) of the proposed correlation for the mass transfer coefficient and effective diffusivity were 5.3% and 5.4%, respectively.     

New Approach in the Prediction of RDC Liquid‐Liquid Extraction Column Parameters

The liquid‐liquid extraction process is well‐known for its complexity and often entails intensive modeling and computational efforts to simulate its dynamic behavior. This paper presents a new application of the Genetic Algorithm (GA) to predict the modeling parameters of a chemical pilot plant involving a rotating disc liquid‐liquid extraction contactor (RDC). In this process, the droplet behavior of the dispersed phase has a strong influence on the mass transfer performance of the column. The mass transfer mechanism inside the drops of the dispersed phase was modeled by the Handlos‐Baron circulating drop model with consideration of the effect of forward mixing. Using the Genetic Algorithm method and the Numerical Analysis Group (NAG) software, the mass transfer and axial dispersion coefficients in the continuous phase in these columns were optimized. In order to obtain the RDC column parameters, a least‐square function of differences between the simulated and experimental concentration profiles (SSD) and 95 % confidence limit in the plug flow number of the transfer unit prediction were considered. The minus 95 % confidence limit and sum of square deviations for the GA method justified it as a successful method for optimization of the mass transfer and axial dispersion coefficients of liquid‐liquid extraction columns.     

Study of droplet behaviour along a pulsed liquid–liquid extraction column in the presence of nanoparticles

In this article, droplet size and its distribution along a pulsed liquid–liquid extraction column, is studied where SiO₂ nanoparticles with concentrations of 0.01, 0.05 and 0.1 vol.% and different hydrophobicities are applied to the dispersed phase. Using ultrasonication, nanoparticles were dispersed in kerosene as the base fluid. Nanofluids' stability was ensured using a UV–vis spectrophotometer. Some 22,000 droplets were measured by photographic technique and results were compared with systems containing no‐nanoparticles (Water–Acetic acid–Kerosene). Addition of nanoparticles changed the droplet shape from ellipsoidal to spherical. Also, there was a marked influence on droplet breakage and droplet coalescence at 0.01 vol.%, and 0.05 vol.% or higher volume fractions, respectively. © 2012 Canadian Society for Chemical Engineering     

Turbulent liquid–liquid dispersion in SMV static mixer at high dispersed phase concentration

The aim of this paper is to investigate the influence of physico-chemical parameters on liquid–liquid dispersion at high dispersed phase concentration in Sulzer SMV™ mixer. Four different oil-in-water systems involving two different surfactants are used in order to evaluate the effect of interfacial tension, densities and viscosities ratio on mean droplets size diameters. Moreover the influence of the dispersed phase concentration on the pressure drop as well as on the droplet size distribution is investigated. Two different droplets size distribution analysis techniques are used in order to compare the resulting Sauter mean diameters. The comparison between residence time in the mixer and surfactants adsorption kinetics leads to take into account the evolution of the interfacial tension between both phases at short times. Finally experimental results are correlated as a function of dimensionless Reynolds and Weber numbers.     

Behavior of Liquid–Liquid Two-Phase Systems in Rotating Coiled Columns

The distribution and motion of liquid–liquid two-phase systems in thin tubes under conditions modeling rotation (including planetary rotation) of chromatographic columns are considered. Criteria are derived that determine the conditions for transition between various types of distribution of the liquid phases in a column using different physicochemical and rotation parameters.     

Experimental investigation on solid dispersion,power consumption and scale-up in moderate to dense solid–liquid suspensions

Detailed particle concentration distribution in dense solid–liquid suspension was measured by means of fiber optic probes. The effect of solid loading, impeller speed, and impeller type and clearance was investigated. Results were compared with modeling approaches to show the accuracy of sedimentation–dispersion model and its capability to describe complex phenomena taking place in dense liquid–solid mixing systems. Variation of power numbers by changing impeller clearance and solid loading were also investigated. It was shown that the impeller power number for a slurry system exhibited different trends in a moderate or dense liquid–solid system. In addition, scale-up rules to achieve the same level of homogeneity on a large scale as the laboratory scale were evaluated.     

Experimental Investigation and CFD Modeling of Hydrodynamic Parameters in a Pulsed Packed Column

In this work, a combination of computational fluid dynamics (CFD) and droplet population-balance model (DPBM) in the framework of Fluent was applied to simulate the drop-size distributions and flow fields in a pilot-plant liquid–liquid extraction pulsed packed column. The three-dimensional unsteady-state liquid–liquid flow was modeled using the Eulerian two-fluid equations in conjunction with the realizable k – ε turbulence model. The classes method (CM) was chosen for solving population-balance equations. Two models for breakage and coalescence, the models of Luo and Garthe, were used in the CFD code. The model was validated by comparing the simulated drop-size distributions and holdup with experimental measurements. After the validation of the model, the effects of the operating conditions (feed rates and pulsation) on the dispersed phase holdup and drop-size distributions were studied. The results of linked CFD-DPBM model and experiments revealed that the dispersed phase holdup was increased when the organic and aqueous flow rates increased and when the intensity of pulse was increased, the holdup increased. Increasing the dispersed and continuous feed rates caused the Sauter mean diameter of the drops decreased and when the intensity of pulse was increased, because of high droplets break up rate, the Sauter mean diameter decreased. Results of linked CFD-DPBM model show that the CFD-DPBM tool is able to predict hydrodynamic parameters in a pulsed packed column.