Separation in vertical temperature gradient packed thermodiffusion cells: an unexpected physical explanation to a controversial experimental problem

New experimental material is presented and discussed to assess the physical phenomena yielding to almost complete solute separation in the so-called vertical gradient packed thermal diffusion column (PTC). The separation efficiency of this experimental device has been observed by some experimenters, but no convincing theory has been established so far. It has been assumed that thermal diffusion (or Soret effect) or even thermogravitational separation (coupling between thermal convection and thermal diffusion) could provide potential explanations for the observed phenomena. The experiments that are discussed here, suggest that thermal diffusion is likely to play but a marginal role in separation, whereas a distillation process promoted by a bubble, called gas membrane distillation, seems to provide a better explanation. This statement may have important consequences for the in situ separation of natural oils and for industrial applications.     

Experimental study of mass transfer limited reaction—Part I: Use of fibre optic spectrometry to infer asymmetric mass transfer coefficients

Mass transfer coefficients, often quantified using empirical correlations in chemical engineering, are useful in predicting the final concentration of the reactants [(Fogler 1992). In: Amundson (Ed.)., Element of Chemical Reaction Engineering, International Series in the Physical and Chemical Engineering, Princeton-Hall]. In the present work, we propose an inverse methodology to estimate mass transfer coefficients from the experimentally measured concentrations of the reactants. The potential of the inverse methodology is that asymmetric mass transfer coefficients of all the premixed reactants can be inferred, which has not been reported so far in literature. In general, only the slowest transfer coefficient estimate has been feasible before. We first review the potential reactions satisfying the required criteria and then discuss multi-component spectrum analysis to decipher the concentrations of the reactants from the absorbance spectrum of the reaction mixture using the principle of additivity. We show that linear additivity does not hold if there is any interaction between the reacting species. In that case, we use a non-linear calibration for the concentrations of the reactants. The mass transfer coefficients inferred using the inverse methodology are validated by solving the forward problem and could be potentially used to study transport limited characteristics of heterogeneous reactions.     

Methane hydrate formation and an inward growing shell model in water-in-oil dispersions

Significant factors controlling gas hydrate growth in water and water-in-oil dispersions have been tested. In particular, the influence of shear rate, presence of oil, and thermodynamic driving force (represented by pressure supersaturation) on hydrate growth rates is included. Formation rates in water show some discrepancy compared to previous work, which is likely caused by differences in the apparatus geometries. A model is proposed for growth of hydrate in oil, in which a hydrate shell forms on a water droplet, followed by additional conversion of the water core to hydrate.     

Experimental and numerical studies on the effects of pressure release rate on number density of bubbles and bubble growth in a polymeric foaming process

A simulation of simultaneous bubble nucleation and growth was performed for a batch physical foaming process of polypropylene (PP)/CO₂ system under finite pressure release rate. In the batch physical foaming process, CO₂ gas is dissolved in a polymer matrix under pressure. Then, the dissolved CO₂ in the polymer matrix becomes supersaturated when the pressure is released. A certain degree of supersaturation produces CO₂ bubbles in the polymer matrix. Bubbles are expanded by diffusion of the dissolved CO₂ into the bubbles. The pressure release rate is one of the control factors determining number density of bubbles and bubble growth rate.To study the effect of pressure release rate on foaming, this paper developed a simple kinetic model for the creation and expansion of bubbles based on the model of Flumerfelt's group, established in 1996 [Shafi, M.A., Lee, J.G., Flumerfelt, R.W., 1996. Prediction of cellular structure in free expansion polymer foam processing. Polymer Engineering and Science 36, 1950-1959]. It was revised according to the kinetic experimental data on the creation and expansion of bubbles under a finite pressure release rate. The model involved a bubble nucleation rate equation for bubble creation and a set of bubble growth rate equations for bubble expansion. The calculated results of the number density of bubbles and bubble growth rate agreed well with experimental results. The number density of bubbles increased with an increase in the pressure release rate. Simulation results indicated that the maximum bubble nucleation rate is determined by the balance between the pressure release rate and the consumption rate of the physical foaming agent by the growing bubbles. The bubble growth rate also increased with an increase in the pressure release rate. Viscosity-controlled and diffusion-controlled periods exist between the bubble nucleation and coalescence periods.     

Mass transfer of a rising bubble in molten glass with instantaneous oxidation-reduction reaction

The mass transfer around a rising bubble has been studied within the field of glass melting processes. Due to the large value of liquid viscosity, creeping flow was used. The rising bubble is assumed to have a clean interface with a total mobility and the exact solution of Hadamard or Rybczynski was used to define the velocity field around the bubble. The mass transfer of oxygen in the soda-lime-silica glass melt where oxidation-reduction reactions of iron oxides occur is also described.The dimensionless mass transfer coefficient, Sherwood number, was determined as a function of the Péclet number based on the terminal rise velocity of the bubble. Two different techniques have been used: the first based on the boundary layer theory and the second using a finite element method.In order to take into account the oxidation-reduction reaction in a unified framework, a modified Péclet number has been defined as a function of two dimensionless numbers. The first is strongly linked to the equilibrium constant of the chemical reaction and the second is the glass saturation, defined as the ratio of oxygen concentration in the bulk to that at the bubble surface. The Sherwood number, taking into account the chemical reactions, increases with iron content as well as with glass reduction (i.e. small saturation level).From an application point of view, the determination of a modified Péclet number is important because it is possible to use a similar expression (determined without the reaction) by replacing the classical Péclet number by the modified one proposed herewithin.     

Analysis of transient thickness of pneumatic foams

This paper presents a simple, experimentally validated approach to analyze the transient formation of a foam layer produced by injecting gas bubbles into a foaming solution. Based on experimental observations, three different regimes in the transient growth of the foam have been identified as a function of the superficial gas velocity. A model based on the mass conservation equation for the gas phase in the foam combined with three different models for the average porosity is proposed. It is shown that for practical calculations a constant average porosity equal to 0.82 can be used. The model predictions show very good agreement with experimental data for low superficial gas velocity and provide an upper limit of the foam thickness for intermediate and large superficial gas velocities. The paper discusses the physical mechanisms that may occur during the foam formation and the effects of the superficial gas velocity on the foam dynamics. The present analysis speculates several mechanisms for the bursting of the bubbles at the top of the foams and proposes the framework for more fundamental and detailed studies.     

Effects of water on steam rectification in a packed column

The effects of water on steam rectification, i.e., multi-stage saturated steam distillation, were investigated in a packed column. N-octane-p-xylene and 1,3,5-trimethylbenzene-1,2,4-trimethylbenzene were used as test systems. Both binary systems are nearly ideal systems and insoluble in water, thus the effects of water in steam rectification can be clearly and definitely revealed. Such unpolar organic liquid is named as “oil”. The water/oil at column top can be separated and refluxed at different ratio. Compared with conventional rectification, there are some peculiar phenomena in steam rectification. Water greatly enhances the flooding vapor velocity of the rectification, in addition, water plays a predominant role in pressure drop of the packed bed near flooding point. It is clear that liquid water in the packed bed can promote mass transfer of steam rectification, especially for materials with higher viscosity. In a word, steam rectification can be operated at low temperature with good mass transfer.     

Errors associated with swelling in the analysis of polymer-solvent diffusion measurements

Sorption curves are generated from a mathematical model which includes the influence of the polymer swelling for unsteady-state sorption of a vapor or liquid by a polymer. To investigate the simultaneous effects of the specific volumes of the polymer-penetrant pair and the difference between the final and initial equilibrium concentrations on the sorption curves, statistical experimental design approach is used. Simulation results obtained from the numerical solution of model equations are utilized to estimate the error that would occur if one simply evaluates the diffusion coefficient using the traditional formulas derived from the analytical solution of the sorption equation. An empirical expression is developed that describes the effects of the difference between the final and initial equilibrium concentrations and the specific volumes of the polymer and the penetrant on the magnitude of error in diffusivity associated with the use of one of these traditional formulas so called the initial slope method. The predictive ability of the regression model is tested by performing additional simulations not used in the regression analysis.     

Direct numerical simulations of mass transfer in square microchannels for liquid-liquid slug flow

Microreactors for the development of liquid-liquid processes are promising technologies since they are supposed to offer an enhancement of mass transfer compared to conventional devices due to the increase in the surface/volume ratio. But impact of the laminar flow should be negative and the effect is still to be evaluated. The present work focuses on the study of mass transfer in microchannels by means of 2D direct numerical simulations. We investigated liquid-liquid slug flow systems in square channel of depth. The droplet velocity ranges from 0.0015-0.25 m/s and the ratio between the channel depth and the droplet length varies between 0.4 and 11.2. Droplet side volumetric mass transfer coefficients were identified from concentration field computations and the evolution of these coefficients as a function of the flow parameters and the channel size is discussed. This study reveals that mass transfer is strongly influenced by the flow structure inside the droplet. Moreover, it shows that the confinement of the droplets due to the channel size leads to an enhancement of mass transfer compared to cases where the droplets are not constrained by the walls.     

Gas-liquid-liquid slug flow and mass transfer in hydrophilic and hydrophobic microreactors

Gas-liquid-liquid three-phase slug flow was generated in both hydrophilic and hydrophobic microreactors with double T-junctions. The bubble-droplet relative movement and the local mass transfer within the continuous slug and the dispersed droplet were investigated. It was found that bubbles moved faster than droplets under low capillary number (Ca), while droplets moved faster upon the increase of Ca due to the increased inertia. For the first time, we observed that the increased viscosity of droplets fastened the droplet movement. The mass transfer in the continuous slug was dominated by convection, leading to nearly constant global mass transfer coefficient (k_La); while that in the dispersed droplet was dominated by diffusion, resulting in k_L decreasing along the channel. Such features are analogical to the corresponding gas-liquid or liquid-liquid two-phase slug flow, but the formation of bubble-droplet clusters caused by relative movement lowered the absolute mass transfer coefficient. These results provide insights for the precise manipulation of gas-liquid-liquid slug flow in microreactors towards process optimization.     

Determination of the interfacial area and mass transfer coefficients in the Taylor gas–liquid flow in a microchannel

The interfacial area in the Taylor (slug) gas–liquid flow in a microchannel was measured by the Danckwerts' (chemical) method, using CO₂ absorption from the CO₂/N₂ mixture into KHCO₃/K₂CO₃ buffer solutions, containing NaOCl as a catalyst. The rate of absorption was determined and the Danckwerts' plots were constructed. Reasonable agreement with the geometrical area measured photographically was obtained. This fact allowed to determine for the first time the mass transfer coefficients separately for liquid film and liquid caps. A correlation for the calculation of mass transfer coefficients has been proposed.     

A qualitative computational study of mass transfer in upward bubble train flow through square and rectangular mini-channels

In this paper we present a new method for numerical simulation of conjugate mass transfer of a dilute species with resistance in both phases and an arbitrary equilibrium distribution coefficient. The method is based on the volume-of-fluid technique and accounts for the concentration jump at the interface by transforming the discontinuous physical concentration field into a continuous numerical one. The method is validated by several test problems and is used to investigate the mass transfer in upward bubble train flow within square and rectangular channels. Computations are performed for a single flow unit cell and a channel hydraulic diameter of 2 mm. The simulations consider the transfer of a dilute species from the dispersed gas into the continuous liquid phase. Optionally, the mass transfer is accompanied by a first-order homogeneous chemical reaction in the liquid phase or a first-order heterogeneous reaction at the channel walls. The results of this numerical study are qualitative in nature. First, because periodic boundary conditions in axial direction are not only used for the velocity field but also for the concentration field and second, because the species diffusivity in the liquid phase is arbitrarily increased so that the liquid phase Schmidt number is 0.8 and the thickness of the concentration and momentum boundary layer is similar. Two different equilibrium distribution coefficients are considered, one where the mass transfer is from high to low concentration, and one where it is vice versa. The numerical study focuses on the influence of the unit cell length, liquid slug length and channel aspect ratio on mass transfer. It is found that for the exposure times investigated the liquid film between the bubble and the wall is saturated and the mass transfer occurs by the major part through the bubble front and rear so that short unit cells are more efficient for mass transfer. Similar observations are made for the homogeneous reaction and for the heterogeneous reaction when the reaction is slow. In case of a fast heterogeneous reaction and when the main resistance to mass transfer is in the gas phase, it appears that for square channels long unit cells are more efficient, while large aspect ratio rectangular channels are more efficient than square channels, suggesting that for these conditions they might be more appropriate for use in monolithic catalysts.     

CFD investigation of the agitation in the desupersaturation during the wet-process phosphoric acid(WPPA) process

Desupersaturation is a complex cooling operation that involves hydrodynamic, thermal and mechanical phenomena. This process requires continuous agitation to avoid fouling problems and sludge deposition. The current work aims to investigate the well mixedness in the desupersaturation tank for optimal performance. For this purpose, a multi-fluid CFD study was conducted based on the Euler–Euler modeling approach, considering a multiphase flow involving a liquid phase(phosphoric acid) and a poly-dispersed solid phase, i.e. a sludge with three different sizes where each size is considered as a separate phase. First, the hydrodynamic behavior of the flow within the agitated desupersaturator is analyzed through the investigation of the velocity fields as well as the power and pumping numbers, to determine both the agitator capacity to pump the flow and its power consumption during the operation. Then, in order to assess the mixture homogeneity, we evaluated the solid suspension in the desupersaturation reactor following conventional methods and two new proposed methodologies: the first approach is to evaluate the suspension quality in the mixing system by compartment and the second consists on the assessment of the uniform convergence of the solid concentration. Furthermore, we calculated the time required to achieve a full suspension at different solid concentrations. On other hand, we conducted a detailed analysis of the solid distribution dependency on the impeller rotational speed at different solid volume fraction,which allows a good understanding of the parameters controlling the homogenization in the desupersaturator.     

Mass transfer in the core-annular and fast fluidization flow regimes of a CFB

In gas-solid reactors, particularly circulating fluidized beds (CFB) it is becoming increasingly more important to be able to predict the conversion and yield of reactant species given the ever rising cost of the reactants and the ever decreasing acceptable level of effluent contaminants. As such, the development and use of predictive models for the reactors is necessary for most processes today. These models all take into account, in some manner, the interphase mass transfer. The model developer, unless equipped with specific experimentally based empirical correlations for the reactor system under consideration, is required to go to the open literature to obtain correlations for the mass transfer coefficient between the solid and gas phases. This is a difficult task at present, since these literature values differ by up to 7 orders of magnitude. The wide variation in the prediction of mass transfer coefficients in the existing literature is credited to flow regime differences that can be identified in the cited literature upon careful inspection.A new theory is developed herein that takes into account the local hydrodynamics. The resulting model is compared with data generated in the NETL cold flow test facility and with values from the literature. The new theory and the experimental data agree quite well, providing a fundamentally based mass transfer model for predictive reactor simulation codes.     

泡沫精馏塔内泡沫液的传质模型

本文对泡沫精馏塔内泡沫的传质问题进行了分析，提出传质微分方程，得到了解析解，并用实验验证了解的正确性。     

Measurement and enhancement of gas-liquid mass transfer in milliliter-scale slurry reactors

Due to the limited availability of chemical reactants in the early process development of pharmaceuticals and fine chemicals, and sometimes the high-cost of catalyst, it is increasingly popular to use milliliter-scale slurry reactors with reaction volumes of 20 ml or less to screen catalyst candidates for three-phase reactions. To ensure the success of catalyst screening, it is advantageous to run reactions under kinetically controlled conditions so that the activities of different catalysts can be compared. Because catalysts with small particle sizes are used in slurry reactors, the reactions are susceptible to gas-liquid mass transfer limitations. This work presents an efficient way of enhancing gas-liquid mass transfer in milliliter-scale reactors through the use of magnetically driven agitation with complex motion. In the reactor described here, gas-liquid mass transfer coefficients can be doubled over those obtained with the agitation technique used in commercial milliliter-scale units. In addition, the reactor can achieve the top range of mass transfer coefficients obtained in a full-scale reactor. This work also presents the first measurements of gas-liquid mass transfer coefficients in milliliter-scale reactors, which are two orders-of-magnitude smaller than systems for which mass transfer coefficients have been reported earlier. Both physical and chemical absorption techniques are used.     

Gas–liquid mass transfer in periodically operated trickle-bed reactors: Influence of the liquid-phase physical properties and flow modulation

The influence of periodic operation on trickle-bed reactor (TBR) hydrodynamics and gas–liquid mass transfer was investigated. Two-phase pressure drop, dynamic liquid hold-up and gas–liquid mass transfer coefficient (k_La) were determined at various liquid flow rates and for different modes of liquid flow variation (increasing and decreasing liquid flow rate). The results reveal the considerable influence of type of liquid flow rate modulation on k_La values (deviations of up to 80% in k_La). Simulation studies on gas-limited reaction in a periodically operated TBR indicate that an enhancement in conversion of about 14% can be expected from an appropriate selection of the operating mode, thus clearly demonstrating the quantitative process intensification feasible through increased gas–liquid mass transfer.     

Development of a tool, using CFD, for the assessment of the disinfection process by ozonation in industrial scale drinking water treatment plants

Foreseen standards regarding microorganism content for drinking water require assessment of the capability of existing plants to reach the upcoming requirements. This paper presents the development of a tool to assess this capability in a commonly encountered key step of water disinfection: ozonation. In this paper, this tool is applied to the test case of an ozonation channel of the Belgian drinking water producer Vivaqua. This tool is based on a mathematical model of the momentum and mass transport phenomena in an ozonation channel. The gas–liquid flow is coupled to ozone mass transfer and kinetics describing the ozone and microorganisms concentrations decay. The degradation of Bacillus subtilis spores, as a representative of resistant microorganisms, is implemented in the model. The model takes explicitly into account the bubble size variation and its impact on mass transfer. Bubbles sizes and kinetics parameters are estimated based on dedicated experiments. The model is partially validated by comparing simulations results, obtained using computational fluid dynamics, to experimental residence time distributions, residual ozone concentration and Bacillus subtilis spores degradation efficiency measurements obtained on the studied ozonation channel. It is shown that, at the industrial scale, bubble diameter variation has a significant impact on ozone concentration in the liquid at the reactor exit. Using the tool, it is also shown that, the ozonation channel of Vivaqua can be used to achieve degradation of resistant microorganisms but only with its maximal flow rate and concentration of ozone injection. Moreover, at low operating temperature, some microorganisms that present latency towards reaction with dissolved ozone might hardly be destroyed.     

Rheological study of mixing in molten polymers: 2-mixing of reactive systems

Three reactive polymer systems have been examined with a new mixing device adapted on a classical rheometer in order to investigate reactive mixing situations encountered in polymer blends. After having characterized the bulk polymerization of ε-caprolactone (ε-CL), the polymerization of 40 wt% of ε-caprolactone into a copolymer of ethylene and vinyl acetate (EVA) was run into the rheo-mixer. The kinetics of the reaction in dispersed media was observed slightly different from that in bulk since the characteristic time of ε-caprolactone diffusion into EVA is much lower than its time of mixing. On the other hand, it was observed that the molecular weight distribution of the poly(ε-caprolactone) is broader in dispersed media (I_p=2.6) than in bulk (I_p=1.6). A broadening of the molecular weight distribution in dispersed media was pointed out due to the fact that ε-CL monomer is partitioned between the EVA and PCL phases leading to a non-homogeneous concentration of monomer in the reactive phase.The polycondensation of 40 wt% of a epoxy-amine system into a polystyrene matrix was also investigated and the morphology of the resulting material examined. A gradient of structure and conversion was detected in a blend obtained from the assembly of two initially non-reactive layers. The gradient reveals that the amine diffuses faster than the epoxy leading to non-stoichiometry of the reactive functions across the sample. When the blend was polymerized under shear, the kinetic of the reaction remained unchanged regardless the level of shear. However, the morphologies were significantly different, pointing out the importance of the coalescence and droplet deformation phenomena. Spherical droplets were observed at 0.15 s⁻¹, elongated droplets and fibers at 1.5 and 15 s⁻¹.     

Experimental study of mass transfer in a dense bubble swarm

We consider the liquid-side mass transfer coefficient k_L in a dense bubble swarm for a wide range of gas volume fraction (0.45%≤α_G≤16.5%). The study is performed for an air–water system in a square column. Bubble size, shape and velocity have been measured for different gas flow rates by means of a high speed camera. Gas volume fraction and bubble velocity have also been measured by a dual-tip optical probe. Both of these measurements show that the bubble vertical velocity decreases when increasing α_G in agreement with previous investigations. The mass transfer is measured from the time evolution of the dissolved oxygen concentration, which is obtained by the gassing-out method. The mass transfer coefficient is found to be very close to that of a single bubble provided the bubble Reynolds number is based on the average equivalent diameter 〈d_eq〉 and the vertical slip velocity 〈V_z〉.