PENETRATION THEORY ANALYSIS FOR NONISOTHERMAL GAS ABSORPTION ACCOMPANIED BY A SECOND-ORDER CHEMICAL REACTION

The penetration theory equations for nonisothermal gas absorption with second-order reaction were solved numerically using the Saul'yev method. Results for the enhancement factor and interfacial temperature rise were obtained for Hatta numbers between 1 and 10, It was found that the enhancement factor and interfacial temperature rise depend on four parameters; (i) the effective activation energy, ε_eff = (ε_R + ε_DA)/2 - ε_S, where ε_R, ε_DA, and ε_S are the activation energies for the reaction, diffusion, and solubility of the solute gas, respectively; (ii) the effective heat of generation, β_eff = (β_R + β_s)√Le, where β_R and β_s are the dimensionless heat of solution and reaction, respectively, and Le is the Lewis number; (iii) the product √rq where r is the ratio of the diffusivity of the liquid reactant to that of the solute gas and q is the ratio of the concentration of the liquid reactant in the bulk solution to that of the solute gas at the interface at the bulk temperature of the solution; and (iv) the activation energy for diffusion of the liquid reactant, ε_DB. This effectively reduces the number of parameters required to give a complete picture of the absorption from nine to four. The reduction is important since it reduces the number of van Krevelen-Hoftijzer plots and interfacial temperature-Hatta number plots required for the design of gas-liquid reactors.     

Modelling reactive absorption of CO2 in packed columns for post-combustion carbon capture applications

A rate-based process model for the reactive absorption of carbon dioxide (CO₂) from a gas mixture into an aqueous monoethanolamine (MEA) solution in a packed column is developed. The model is based on the fast second-order kinetics for the CO₂-MEA reactions and takes into account the mass transfer resistances. The heat effects associated with the absorption and chemical reaction are included through energy balances in the gas and liquid phases. Appropriate correlations for the key thermodynamic and transport properties and for the gas-liquid mass transfer are incorporated into the model to ensure reliable predictions. The model predictions are validated by simulating a series of experiments conducted in pilot and industrial scale absorption columns with random and structured packings reported in the literature. Comparisons between the simulation results and the experimental data reveal good quality predictions of the gas phase CO₂ and MEA concentrations and the liquid temperature along the column height. The sensitivity studies reveal that the correlations for the gas- and liquid-film mass transfer coefficients given by Onda et al. (1968) provide better predictions than the penetration theory of Higbie (1935) and the correlation of Bravo et al. (1985).     

PREDICTION OF PRESSURE DROP IN A VENTURI SCRUBBER: EFFECT OF LIQUID FILM AND RE-ENTRAINMENT

A mathematical model has been developed for prediction of pressure drop in a Venturi scrubber. This model includes the effect of the amount of liquid film and re-entrainment of liquid droplets from liquid film. The result of the present model is compared with experimental data of Viswanathan et al. (1985) as well as with the other models (Viswanathan et al., 1985; Boll, 1973). Results of this study indicate that at high liquid to gas ratios prediction of pressure drop can be improved by considering re-entrainment and liquid film effects. Also the effects of gas velocity and liquid to gas ratio were investigated on the rate of droplet re-entrainment and pressure drop.     

A solution strategy for the film model for non-isothermal gas–liquid reactions

A general solution strategy for the film model for gas–liquid reaction has been proposed using the boundary element method (BEM) of discretization over subintervals in gas–liquid films. Non-isothermal effects in the film are included and the associated temperature changes near the gas–liquid interface are computed. The accuracy of the solution procedure is first established using some simple isothermal and non-isothermal benchmark problems and with semi-analytical solutions. Then illustrative results are presented for a non-isothermal series reaction system to illustrate effects of various parameters such as Arrhenius number, solubility changes with temperature, effect of volatility of the liquid phase reactant, etc. The proposed solution method provides fast and accurate values for interfacial fluxes and fluxes into the bulk liquid in addition to concentration profiles. Hence the method is extremely useful for coupling local effects of the film model with global effects based on CFD coupled compartmental model for gas–liquid reactors.     

Kinetics of absorption of sulfur dioxide in dimethylaniline solution

Absorption of sulfur dioxide accompanied by reversible reaction in dimethylaniline has been studied using a short falling-film apparatus. Solutions of the amine in kerosene were used for this purpose. The effects of gas and liquid concentrations, contact time and temperature on the rate of absorption were investigated. Reaction equilibrium constant values were obtained at different temperatures from separate measurement of solubility of sulfur dioxide gas in kerosene as well as in dimethylaniline solutions. The heat of reaction was also calculated from these data. The absorption data could be satisfactorily interpreted by using the penetration theory of mass transfer with simultaneous pseudofirst order chemical reaction. The rate equations for the forward and reverse reactions were established.     

Mass transfer from a single moving spherical bubble in the presence of a complex chemical reaction

This paper analyses the problem of mass transfer from a spherical bubble (Re << 1) in the presence of an (m, n)th order liquid phase reaction. The approximate analytical results for enhancement factor obtained, using a linearization technique of the rate expression which is an extension of the one proposed by Hikita and Asai, are found to agree well with the one obtained from a numerical solution of the problem. The paper also presents numerical calculations of the rise in bubble interface temperature applying Danckwerts method to both the rigorous model as well as the extended penetration model of Ruckenstein et al. for the reaction process.     

THE DIFFUSIONAL LIMITATION ON THE TEMPERATURE RISE IN THE ABSORPTION OF CHEMICALLY REACTIVE GASES

The interfacial temperature is important in gas absorption because it sets the solubility. If the gas undergoes an exothermic reaction this temperature ordinarily exceeds the bulk liquid temperature. For a bimolecular reaction the pseudo-first-order approximation leads to a serviceable model; yet it must overestimate the temperature rise under fast reaction conditions. We correct this estimate by accounting for the depletion of the liquid-phase reactant near the surface. To do this we use an enhancement factor based on the van Krevelen-Hoftijzer approximation. This implies a simple formula for the temperature rise not unlike that based on the pseudo-first-order approximation. We investigate this formula and show that it exhibits either one or three solutions. We deduce criteria for predicting, a priori, both what the multiplicity is and whether or not the maximum temperature rise corresponding to instantaneous reaction obtains.     

氩流体汽液界面特性的平衡分子动力学模拟

采用L—J模型,对氩流体汽液界面特性进行了平衡分子动力学模拟,得到了密度、界面张力等参数的分布规律。模拟结果表明,随着氩流体体系温度的提高,液相主体密度和界面张力逐渐减小,汽相主体密度和界面厚度逐渐增大;随着截断半径的增大,界面张力逐渐增大,汽相主体密度及界面厚度稍有减小,液相主体密度稍有增大;随着模拟分子数的增加,界...     

大气环境中静态小液滴对周围气体吸收的研究

Absorption of gaseous species into stationary droplets is a fundamental interest of mass transfer between liquid droplets and ambient gas, which plays a key role in atmospheric environment control and many industrial applications. In this paper, two different considerations including equilibrium and non-equilibrium relations at the interface are used to analyze and predict the absorption time for a physical absorption at a relatively low solubility of gas. For the equilibrium pattern, in the beginning period of absorption, the mass transfer rate is considerably rapid and afterward becomes slower and slower and finally comes to almost zero as the droplet concentration closes to the saturated value. Differently, when the non-equilibrium model is adopted, the interfacial concentration increases gradually with the bulk concentration of liquid droplet, and the absorption rate mildly decelerates with the increase of bulk one throughout the process, which leads to a longer absorption time. Based on the diffusion equation of species, the concentration distribution within the droplet at different times is computed. A solution for CO2 absorption into a small water droplet is given.     

Investigations on hydrodynamics and mass transfer in gas–liquid stirred reactor using computational fluid dynamics

In this work, the hydrodynamics and mass transfer in a gas–liquid dual turbine stirred tank reactor are investigated using multiphase computational fluid dynamics coupled with population balance method (CFD–PBM). A steady state method of multiple frame of reference (MFR) approach is used to model the impeller and tank regions. The population balance for bubbles is considered using both homogeneous and inhomogeneous polydispersed flow (MUSIG) equations to account for bubble size distribution due to breakup and coalescence of bubbles. The gas–liquid mass transfer is implemented simultaneously along with the hydrodynamic simulation and the mass transfer coefficient is obtained theoretically using the equation based on the various approaches like penetration theory, slip velocity, eddy cell model and rigid based model. The CFD model predictions of local hydrodynamic parameters such as gas holdup, Sauter mean bubble diameter and interfacial area as well as averaged quantities of hydrodynamic and mass transfer parameters for different mass transfer theoretical models are compared with the reported experimental data of [Alves et al., 2002a] and [Alves et al., 2002b] . The predicted hydrodynamic and mass transfer parameters are in reasonable agreement with the experimental data.     

氨盐水碳酸化反应的机理与反应器模型Ⅰ碳酸化反应的动力学模型

对碳化过程的机理进行了深入的分析，将其考虑为一连串、可逆放热反应，其中ＣＯ２ 与ＮＨ３ 的反应为快速反应，发生在液膜之内，而ＮＨ２ＣＯＯ－ 的水解与ＮａＨＣＯ３ 的结晶则属慢反应，发生在液相本体。对膜与本体分别建立了数学模型。通过模型计算分析了碳化过程的动力学特征，指出在低碳化度和高碳化度时，气膜传质、液膜反应、本体水解和结晶将分别成为过程的速率控制步骤。     

MULTIPLE STEADY STATES IN NON-ISOTHERMAL FT SLURRY REACTOR

A model for a non-isothermal, semi-balch (stagnant slurry and flowing gas), laboratory scale Fischer-Tropsch (FT) slurry reactor is developed. The model assumes the existence of FT and water-gas shift (WGS) reactions. The reactor configuration is assumed to be the same as one used by Bhattacharjee et at. (1986). Gas-slurry mass transfer coefficients, solubility parameters and other physical transport and kinetic parameters used in the model are obtained from the reported studies of Lieb and Kuo (1984), Bhattacharjee et al. (1986), Deckwer et al. (1982, 1986) and Karandikar et al. (1987( for the FT slurry system

The model is used to evaluate the relevant kinetic constants and the heat generation parameters for the FT reaction from the experimental data of Bhattacharjee et al. (1986). The nature of the heat generation curves indicates that multiple steady states are likely to occur in a non-isothermal FT slurry reactor. The ignition temperatures are calculated as functions of gas hourly space velocity, activation energy for the FT reaction, reactor pressure, and coolant temperature and flow rate. In general, these temperatures are in good agreement with those reported by Bhattacharjee et al. (1986). The exact values of the ignition temperature are strongly affected by the magnitudes of the activation energy and the heat of FT reaction. Once the reactor is ignited, the catalyst changes its character leading to the multiple branches of heat generation and product distribution curves. The extinction temperature was, therefore, not observed in Bhattacharjee's experiments.     

吸收过程的界面非平衡传质机理

针对气体吸收过程,以分子热力学为基础,结合普遍化的化学势推动力通量方程,导出了传质存在时两相界面处的浓度关系,并针对不同情况进行了求解.提出了一个反映液相侧动力学状况的无因次数群Biot数Yo,Yo数越大界面处两相越偏离平衡.界面浓度是与Yo和液相主体浓度密切相关的.对于气相阻力可以忽略的吸收过程,两相传质速率的大小主要取决于液相的溶质界面浓度和液膜厚度.采用激光显微全息干涉技术对甲醇,乙醇,正丙醇静止吸收CO2时的界面浓度进行了测定,试验结果表明了本研究模型的正确性.     

INFLUENCE OF DIFFERENT CLOSURES ON THE HYDRODYNAMICS OF BUBBLE COLUMN FLOWS

Computational fluid dynamic (CFD) simulations are performed for two-dimensional bubble columns to examine the effect of different interfacial force closures on the computed liquid velocity and gas holdup profiles. In this regard, six different drag closure relationships and three different virtual mass formulations are incorporated in the framework of the Los Alamos National Laboratory's code CFDLIB. The Eulerian-Eulerian two-fluid model is used. The results are compared with the experimental results of Mudde et al. (1997), the gas holdup correlation of Anabtawi et al., (2003), and CFD simulations of Pan et al. (2000). With the exception of one, all the correlations studied give good agreement (within engineering accuracy) between the computed results and the experimental data.     

GAS ABSORPTION WITH CHEMICAL REACTION INVOLVING A VOLATILE LIQUID REACTANT: PENETRATION THEORY SOLUTION

A penetration theory analysis is presented for the problem of gas absorption, with chemical reaction involving a volatile liquid reactant. Model equations are derived and solution techniques are presented. It is shown that as long as the diffusivities of two reactants are equal, the enhancement factors predicted by film and penetration theories only mildly differ. Except for slow and instantaneous reaction regimes, the liquid reactant volatility can be markedly detrimental to enhancement of absorption rate by chemical reaction.     

INTERFACIAL TEMPERATURE RISE AND MULTIPLICITY IN NONISOTHERMAL GAS-LIQUID CSTRs

For exothermic gas-liquid reactions.the interfacial temperature affects the gas-solubility, interfacial reaction rate, mass transfer rate and the bulk temperature of the reactor. An overall heat balance on the reaction-diffusion 'film' relates the interfacial temperature to the bulk variables (temperature, concentration), and the interfacial variables (enhancement factor, etc.). While the interfacial balance shows (apparent) multiplicity of interfacial temperature for a given bulk temperature, uniqueness results when the interfacial balances are solved together with the mass and energy balances for the reactor bulk. It is shown that the state of interface and bulk are intimately related, and thus, consideration of interfacial temperature does not increase the multiplicty of a gas-liquid CSTR. Simple a priori estimates are derived for the interfacial temperature. All of the results are found to be rather independent of kinetic details. The interfacial temperature rise is encouraged by low interfacial heat and mass transfer coefficients, by small liquid residence time in the bulk and by increased heat losses from the reactor bulk.     

A refined model for ozone mass transfer in a semibatch stirred vessel

The mathematical model proposed by Anselmi et al. (1984) for a semibatch stirred gas‐liquid contactor is refined to describe the mass transfer of ozone absorption and decomposition in aqueous solution with the decomposition rate expression of general reaction orders (not necessarily integers). Three system equations are employed to describe the ozone concentrations in the bulk liquid (C_ALb), the hold‐up gas (C_AGi), and the outlet gas in the free volume above the liquid surface (C_AGe), respectively. The effect of ozone decomposition on the mass transfer, which is reflected by the enhancement factor (E_r) defined as the ratio of mass absorbed per unit area in time t with chemical reaction (r) to that without chemical reaction or of the purely physical absorption, is considered in the refined model. Furthermore, the refined model also takes into account the variation of E_r with C_ALb, which changes with time during the course of gas‐liquid contacting. Thus this analysis extends the applicability of the model of Anselmi et al. (1984) and is of special importance for ozone mass transfer in the cases of basic solutions and of low mass transfer coefficients, in which the effect of decomposition on absorption is significant, and in the system with variable liquid phase ozone concentration.     

Gas absorption with exothermic bimolecular reaction in a thin liquid film: Fast reactions

A problem of gas absorption with a fast nonisothermal bimolecular reaction in a thin liquid film has been analysed. Approximate analytical solutions for the interfacial temperature rise and enhancement factor have been derived incorporating the influence of depletion of liquid reactant concentration at the interface. The effects of heat generation, heat dissipation and reaction rate parameters on enhancement factor and interfacial temperature rise have been discussed. For a certain range of parameters, multiple steady state solutions of enhancement factor and interfacial temperature rise are observed. Another interesting observation is that as the value of a dimensionless parameter ? increases, the enhancement factor approaches its instantaneous asymptote which is the same as that for the isothermal case in an instantaneous regime. The analysis presented here is simple and avoids complex numerical computations and it is likely to be useful in design applications.     

(Gas‐)liquid‐solid circulating fluidized beds and their potential applications to bioreactor engineering

Compared with conventional fluidized beds, circulating fluidized beds have many advantages including better interfacial contacting and reduced backmixing (Lim et al., 1995). While there are many reports on the gas—solid circulating fluidized systems, liquid—solid and gas—liquid—solid circulating fluidized bed systems have been scantily studied. However, extending current knowledge obtained in gas—solid systems to liquid—solids and gas—liquid—solid three‐phase systems is shown to open new horizons for applications of circulating fluidized bed technology and expected to lead to the development of highly efficient liquid—solid and gas—liquid—solid reactors, especially for the ever growing field of biotechnology. In order to fully appreciate the potential of those two types of liquid phase circulating fluidized beds, recent progress is reviewed in this article. Their potential applications to biochemical processes are also discussed.     

Comparison of the single-bubble-class and modified two-bubble-class models of bubble column reactors

Gas phase conversions and product selectivities predicted by the single-bubble-class and modified two-bubble-class models of bubble column reactors are compared for a multistep gas-liquid reaction involving series/parallel steps. A situation is considered where the first reaction step is fast and occurs in the interfacial region while the other reaction steps are slow and occur only in the liquid bulk. Equivalent hydrodynamic and transport parameters provide a common basis for the comparison. The differences in the gas phase conversions predicted by these models are insignificant. However, the two models predict very different values of selectivities for the intermediate products. This analysis enables us to judge the range of applicability of the single-bubble-class model in design and scale-up of bubble column reactors.