The effect of diffusivity on gas-liquid mass transfer in stirred vessels. Experiments at atmospheric and elevated pressures

Mass transfer has been studied in gas-liquid stirred vessels with horizontal interfaces which appeared to the eye to be completely smooth. Special attention has been paid to the influence of the coefficient of molecular diffusion. The results are compared with those published before. The simplifying assumptions of identical hydrodynamical conditions at the same stirrer speed in one particular geometry, which have been made in some previous investigations, is shown to be wrong and may lead to incorrect conclusions on the influence of the diffusion coefficient. For the gas phase the mass transfer can be described by the penetration theory (Higbie, R., 1935, Trans. Am. Inst. Chem. Engrs35, 36–60) or surface renewal model (Danckwerts, P. V., 1951, Ind. Engng Chem.43, 1460–1467). With the use of a dimensionless equation, Sh, Re and Sc numbers, all data, even experiments carried out at elevated pressures, could be well correlated. For the liquid phase the results indicate that the mass transfer cannot be described by a simple model. The King model (King, C.J., 1976, Ind. Engng Chem. Fundam.5, 1–8), a combination of molecular and eddy diffusivity, is able to explain qualitatively the observed phenomena and the literature data.     

Remarks upon thermokinetic parameters of the one-and two-dimensional mathematical models of heat transfer in a tubular flow apparatus with a packed bed

Considerable discrepancies have been observed between the published correlations concerning the overall heat transfer coefficient α, as well as the effective thermal conductivity λ_e,r and the wall heat transfer coefficient α_w, which are the respective thermokinetic parameters of the one- and two-dimensional mathematical models of heat transfer in a tubular flow apparatus with a packed bed.A precise method has been elaborated for evaluation of these parameters using the data collected in the same experiment. This method has allowed us to point out the reasons for the scatter of the empirical correlations published by several authors, and to verify the coincidence of the experimentally determined and theoretically predicted values of the model parameters for various beds; the best fitting of the data was observed for beds packed with spherical pellets. The theoretically developed relation between the values of the parameters of both the mathematical models has been verified experimentally and it was proved that, if the experiment is performed correctly, no correlation factor is needed in that relation, as has been proposed by several investigators.     

Effect of chemical reaction on particle to gas heat transfer

Particle to gas heat transfer studies were carried out by employing the endothermic cyclohexane dehydrogenation reaction. The calculated heat transfer coefficients were on the lower side of those previously reported in the literature for unreactive systems. Previous studies of other investigators with reactive systems suggest that particle to gas heat transfer coefficients may increase with exothermic reaction due to the product molecules leaving the catalyst surface with excess vibrational energy. For an endothermic reaction this effect would result in the calculation of a lower heat transfer coefficient.     

基于重置温度方法的双参数介尺度气固传热模型构建

颗粒聚团等介尺度结构在气固两相流中普遍存在,这些介尺度非均匀结构直接影响气固流动特性及气固接触效率,进而影响气固相间传热、传质及化学反应过程。在更适合工业大尺度气固传热模拟的粗网格方法中缺乏准确度高、简单易用且可以考虑介尺度非均匀结构影响的传热模型。采用计算流体力学-离散单元法（CFD-DEM）研究了气固两相流相间传热,为了保证气固相间持续传热,采用了两种维持气固相间传热温差的方法,并讨论了两种方法的优缺点。方法一：给气相能量方程添加热源项;方法二：每间隔一段时间重置气相温度,重置温度后气固两相自由传热,两种方法中均保持固相温度不变。结果表明聚团界面位置的局部单位体积气固传热量最大,重置温度方法在稀相和界面位置的局部单位体积传热量与总单位体积传热量之比大于热源项方法,而在浓相位置的局部单位体积传热量与总单位体积传热量之比小于热源项方法。通过过滤CFD-DEM计算数据,为重置温度方法构建了双参数（过滤固含率、过滤尺度）传热系数修正因子模型,通过先验分析评价了模型的表现,研究表明所构建模型在过滤网格尺度为5~40倍颗粒直径范围内优于文献中已有的双参数模型。     

Software-guided Microfluidic Reaction Calorimeter Based on Thermoelectric Modules

A software-guided, continuous reaction calorimeter based on thermoelectric modules for direct heat flux measurements is presented. Sensors and actuators of the calorimeter's setup are implemented within a lab automation system, which enables the automated calibration of the heat flux sensors and investigations of chemical reactions through sequential function charts. Functionality of the calibration is shown by heat transfer experiments. Additionally, the calorimeter's performance is demonstrated by good agreement of conducted neutralization experiments with literature data.     

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.     

直接接触式环流换热器传热研究

首次开发了直接接触式环流换热器 ( DCRE)。分散相液滴不断吸热气化 ,导致气升管轴向上连续相和分散相的温度变化 ,从而产生不同的传热推动力 ,形成体积传热系数分布。在实验基础上 ,重点讨论工质的进料量、连续相和分散相间的传热温差对体积传热系数的影响 ,并从单个液滴气化传热的机理出发 ,推导出体积传热系数分布的表达式及平均体积传热系数的准数关联式。     

A graphical design method for reaction–extraction processes in quaternary systems

This paper proposes a graphical design method for quaternary systems in simultaneous chemical and physical liquid–liquid equilibrium (reaction–separation process). The reactive phase equilibrium data and the stage by stage calculation are represented into two projections diagrams with rectangular coordinates. The graphical method has been applied to reversible reactive systems where all of the components of the reaction have the same stoichiometric coefficient. This graphical method allows estimating the number of reactive theoretical stages, the limits of the solvent to feed ratio (D/F), the extent of reaction and the conversion. Results obtained for seven design problems (involving four different reactive systems) are in good agreement with state of the art simulation software and with literature.     

Temperature oscillation calorimetry for the determination of the heat capacity in a small-scale reactor

This contribution describes a method for heat capacity determination in a small-scale reaction calorimeter under quasi-isothermal conditions ( to ). The heat capacity of the reactor content is calculated from the amplitudes and the phase shifts of the reactor temperature, of the electrical heater and of the cooling rate when forced temperature oscillations are applied. The heat capacities of eight solvents (water, ethanol, methanol, acetone, 1-octanol, diethylenglycol, toluene, and 1-butanol) covering a wide range of viscosity were calculated for various experimental conditions, including reactor volume and stirrer speed. Systematic deviations were detected when compared to the corresponding literature values. Straight line calibration with the total heat transfer coefficient and two modern multivariate calibration techniques (partial least squares and neural network) were applied to correct for these deviations. The different calibrations show similar precision and allow for an online determination of the heat capacity with an accuracy comparable to other published methods. Successful applications include the determination of the heat capacities for n-heptane, for various homogenous ethanol/water mixtures, and during the course of the hydrolysis of concentrated sulfuric acid.     

Dynamics of a continuous stirred tank reactor for styrene polymerization initiated by a binary initiator mixture. II: Effect of viscosity dependent heat transfer coefficient

The dynamic behavior of the solution polymerization of styrene in a continuous stirred tank reactor is analyzed with a mixture of tert-butyl perbenzoate and benzoyl peroxide as an initiator system. In the modeling of the reactor, a viscosity dependent reactor wall heat transfer coefficient is used to account for the changing heat transfer efficiency as monomer conversion and polymer molecular weight increase. The steady state and bifurcation behaviors have been investigated with the reactor residence time, initiator feed composition, initiator concentration, feed solvent volume fraction, and coolant temperature as bifurcation parameters. Unlike the reactors with constant heat transfer coefficient, the present system exhibits relatively simple steady state and dynamic bifurcation behaviors. Oscillatory behavior is observed only when the solvent volume fraction in the feed exceeds 0.2. The dynamic simulation of the reactor also indicates that a feedback temperature controller may fail to maintain the reactor temperature when the heat transfer coefficient changes as a result of process disturbances.     

Hydrodynamics and volumetric gas-liquid mass transfer coefficient of a stirred vessel equipped with a gas-inducing impeller

Hydrodynamic and mass transfer characteristics of a gas-liquid stirred tank provided with a radial gas-inducing turbine were studied. The effect of the rotation speed and the liquid submergence on global hydrodynamic and mass transfer parameters such as the critical impeller speed, the induced gas flow rate, the gas holdup, the power consumption and the volumetric gas-liquid mass transfer coefficient were investigated. The experiments are mainly conducted with air-water system. In the case of critical impeller speed determination, two liquid viscosities have been used. The volumetric gas-liquid mass transfer coefficient k_La has been obtained by two different techniques. The gas holdup, the induced gas rate and the volumetric gas-liquid mass transfer coefficient are increasing functions with the rotation speed and decreasing ones with the liquid submergence. The effects of these operating parameters on the measured global parameters have been taken into account by introducing the dimensionless modified Froude number and correlations have been proposed for this type of impeller.     

NUMERICAL STUDY OF DEVELOPED LAMINAR MIXED CONVECTION OF Al2O3/WATER NANOFLUID IN AN ANNULUS

This work aims to study the combined free and forced convection of an Al₂O₃/water nanofluid flowing throughout an annulus. A set of three-dimensional elliptic governing equations were solved numerically using the finite volume technique. The effect of the volume fraction of the nanoparticles and the Richardson number on the thermal and hydrodynamic parameters was extensively investigated. The distribution of the axial velocity and temperature at different cross sections is shown. The axial variation of the frictional and heat transfer coefficients is presented. Results indicate that the Richardson number does not influence the frictional coefficient, while the heat transfer coefficient directly depends on the Ri number. The dimensional axial velocity continually increases with greater volume fraction of nanoparticles at the upper and lower sides of the annulus, while this behavior for dimensionless axial velocity is not continuous. The results indicate that any increase in the volume fraction results in secondary flow enhancement and, therefore, a delay in the occurrence of the maximum heat transfer coefficient.     

Mathematical model and analysis of PMMA solution processes

A mathematical model of reactors for the polymerization of methylmethacrylate (MMA) has been developed and analyzed in order to better understand the reactor dynamics and to determine conditions for improved operation. The exploration of the effect of heat transfer in an MMA polymerization reactor system has been conducted by the development of a detailed model. Two correlations for the overall heat transfer coefficient have been used to study the effect of heat transfer. The heat transfer coefficient estimated by an empirical correlation (Kravaris) is only a function of conversion. Due to its simplicity, it may not express very well the true heat transfer phenomena. But in Henderson’s correlation, it is related to the viscosity of the reaction mixture, which in turn depends on the reaction temperature and volume fraction of each species in the reactor. The steady state solutions of mass and energy balances in the reactor depend on the nature of the heat transfer correlation, as does the number of isola branches. Henderson’s correlation may be preferred to calculate the dynamics of the PMMA reactors. The addition of jacket dynamics to the system results in no isola solution branches and no Hopf bifurcations.     

Impact of agitation and aeration on hydraulics and oxygen transfer in an aeration ditch: Local and global measurements

In urban waste water treatment plants one of the most developed processes to treat pollutants is the activated sludge basin. The aim of this paper is to present results on the hydraulics and aeration performance of an aerated basin at pilot plant scale. Local gas retention, gas velocity and bubble size have been measured and linked to the classical global measurements of oxygen transfer coefficient and of horizontal liquid velocity. Different operating conditions have been tested to show the impact of each parameter on hydraulics and aeration performance.The increase of air flow rate induces an increase of the local gas retention, of the gas velocity as well as of the Sauter diameter. Changes in these local parameters do exhibit a strong impact on the oxygen transfer coefficient. Hence these local measurements are used to discuss and gain a deeper understanding of the oxygen transfer phenomena.An augmentation of the horizontal liquid velocity results in higher values for the global oxygen transfer coefficient. This is confirmed by observation and local measurements, which show a stronger inclination of the air plume with increasing velocity. This translates to a larger course for the bubbles to cover before reaching the surface.With respect to global oxygen transfer measurements, the optimal position of the agitator was found to be near the bottom of the reactor for the type of pilot plant studied. In addition it can be stated that the horizontal position of the impeller has a large impact on the liquid horizontal velocity. Improved understanding is gained through local investigations, which reveal the increased inclination of the air plume as one major cause.     

Kinetic Modelling in Automotive Catalysis

There are no general accepted models for CO and HC oxidation and NO _x reduction in automotive catalysis. Many factors affect the observed kinetics e.g. the catalyst preparation method and conditioning, the composition of the exhaust gases, mass and heat transfer, and all the reaction conditions that the catalyst has been exposed to prior to an experiment. However, most experiments are done under idealized conditions with a fresh catalyst and without water, SO₂, etc. Simple models will only describe the individual experiments and more complex models require determination of the parameters from independent measurements under realistic conditions. The kinetic models available in the literature are only reliable for the exact catalyst and reaction conditions for which they have been developed.     

Calibrating Picosecond Time Resolved Optical Calorimetry: Absolute Enthalpies from Investigations of Mixtures

A method for quantifying the absolute enthalpy release detected in picosecond optical calorimetry (transient grating spectroscopy) is described. Excitation and analysis of thermal phase grating waveforms from mixtures containing both a fully characterized calibration compound and a precursor to a reactive intermediate of interest provides a value of the total heat release attending formation and decay of the reactive intermediate, within the time window of the experiment. This information can be used to obtain the absolute reaction enthalpies accompanying formation and decay of the reactive intermediate. The calibration method is demonstrated using tetraphenylethylene as the ground-state precursor to its zwitterionic, twisted excited state and copper (II) bis(2,2,6,6-tetramethyl-3,5-heptanedionate) as the calibration compound. The results suggest that 96 ± 6% of the exciting photon's energy (284 nm, 101 kcal/mole) is released within 10 ns. This is in reasonable agreement with the literature lower limit of 97.5% energy release. Limitations of the mixture method for calibration and relevant control experiments are described.     

Kinetic simulation of methane hydrate formation and dissociation in porous media

The vast amount of hydrocarbon gas deposited in the earth's crust as gas hydrates has significant implications for future energy supply and global climate. A 3-D simulator for methane hydrate formation and dissociation in porous media is developed for designing and interpreting laboratory and field hydrate experiments. Four components (hydrate, methane, water and salt) and five phases (hydrate, gas, aqueous-phase, ice and salt precipitate) are considered in the simulator. The intrinsic kinetics of hydrate formation or dissociation is considered using the Kim-Bishnoi model. Water freezing and ice melting are tracked with primary variable switch method (PVSM) by assuming equilibrium phase transition. Mass transport, including two-phase flow and molecular diffusions, and heat transfer involved in formation or dissociation of hydrates are included in the governing equations, which are discretized with finite volume difference method and are solved in a fully implicit manner. The developed simulator is used here to study the formation and the dissociation of hydrates in laboratory-scale core samples. In hydrate formation from the system of gas and ice (G+I) and in hydrate dissociation systems where ice appears, the equilibrium between aqueous-phase and ice (A-I) is found to have a “blocking” effect on heat transfer when salt is absent from the system. Increase of initial temperature (at constant outlet pressure), introduction of salt component into the system, decrease of outlet pressure, and increase of boundary heat transfer coefficient can lead to faster hydrate dissociation.     

Solid effects on hydrodynamics and heat transfer in an external loop airlift reactor

The effect of a solid presence on global hydrodynamic parameters and heat transfer in an external loop airlift reactor has been experimentally investigated. Results obtained in both two- and three-phase flow are presented in this study. Two different external loop airlift reactor sizes have been used and local hydrodynamic characteristics including local gas hold-up and bubble velocity have been obtained in two-phase flow. Optical and ultrasound probes have been used to obtain this information, respectively. It was found that an increase of solid hold-up leads to a decrease of liquid velocity and heat transfer coefficient. Measured in a two- and three-phase reactor using a horizontal-heating probe, a correlation of the average gas hold-up and heat transfer coefficient is proposed. Correlation parameters are identified in homogeneous and heterogeneous flow regimes, which have been derived from the gas slip velocity concept. The experimental liquid velocity and gas hold-up in the riser have been represented in a satisfactory way by a hydrodynamic model, either in the absence or in the presence of solid particles.     

减压膜蒸馏过程纤维膜表面热质传递特征模拟分析

采用CFD数值模拟的方法,建立了错流式单根中空纤维减压膜蒸馏过程的三维计算模型,对纤维膜表面不同位置的局部热量和质量传递特征进行了研究。研究结果表明,纤维膜表面的速度分布、温度分布、对流传热系数分布以及蒸发速率均随着位置的改变而改变,且具有相似的规律,在相位角60°到90°之间有最大值,而在相位角0°和180°附近其值较小;料液流速显著影响纤维膜表面的热质传递参数的分布,蒸发速率和传热系数均随着流速的提高而增大;传热系数随着真空度的提高而迅速降低。本研究结果加深了对中空纤维减压膜蒸馏过程的认识,对膜过程强化具有指导意义。     

Optical methods to investigate the enhancement factor of an oxygen‐sensitive colorimetric reaction using microreactors

Visualization of mass transfer is a powerful tool to improve understanding of local phenomenon. The use of an oxygen‐sensitive dye (colorimetric technique) (Dietrich et al., Chem Eng Sci. 2013; 100:172–182) has showed its relevancy for locally visualizing and characterizing gas–liquid mass transfer at different scales (Kherbeche et al., Chem Eng Sci. 2013; 100: 515–528; Yang et al., Chem Eng Sci. 2016; 143:364–368). At present, the occurrence of a possible enhancement of the gas–liquid mass transfer by this reaction has not been yet demonstrated. This article aims at filling this gap by evaluating the Hatta number Ha and the enhancement factor E associated with the oxygen colorimetric reaction when implementing in milli/micro channels. For that, as data on the kinetic of the colorimetric reaction are seldom in the literature, the reaction characteristic time was first estimated by carrying out experiments in a microchannel equipped with a micromixer. The diffusion coefficients of dihydroresorufin and O₂ were then determined by implementing two original optical methods in a specific coflow microchannel device, coupled with theoretical modelling. The knowledge of these parameters enabled at last to demonstrate that no enhancement of the gas–liquid mass transfer by this colorimetric reaction existed. Complementary information about the reliability of the colorimetric technique to characterize the gas–liquid mass transfer in milli/micro systems was also given. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2272–2284, 2017