Mass transfer and selectivity of ozone reactions

The present research concerns the behavior of mass transport in absorption of ozone accompanied by decomposition and ozonation reactions in aqueous solutions. On the basis of the film theory, a mathematical model has been formulated for the transport process taking into account molecular diffusion and the simultaneous decomposition and ozonation reactions of different orders. Analytical approximate and finite difference methods have been employed to predict concentration profiles, enhancement factor and selectivity of the chemical mass transfer in gas-liquid systems. The rate of mass transfer is enhanced by the chemical reactions as well as the availability of liquid reactant in the aqueous phase. When the ozonation reaction is much faster than the decomposition reaction, a large fraction of the absorbed ozone is utilized effectively in reacting with the liquid constituent and a high selectivity of the gas-liquid reactions can be obtained. Calculated results indicate that removal of certain organic pollutants by the oxidation process may be effective only in acidic or neutral solutions where a high mass transfer rate and selectivity is achieved.     

ENHANCEMENT FACTOR OF GAS ABSORPTION ACCOMPANIED BY REVERSIBLE CYCLIC CHEMICAL REACTIONS

Theoretical effect of mass transfer by reversible cyclic chemical reactions is studied in this paper. On the basis of the film theory, an analytical equation has been derived to express the enhancement factor of gas absorption with first-order reversible cyclic chemical reactions. The finite difference method has been used to study the enhancement of gas absorption with second-order reversible cyclic reactions. The results indicate that the gas absorption rate is enhanced by the forward reaction rate, while is suppressed by the backward reaction. Although the diffusivity has some effects on enhancement factor, the influence is not as much as that of reaction rate. The theoretical equations are used to predict the enhancement factors for absorptions of carbon dioxide in acidic solution and l-butene in liquid phosphoric acid.     

ENHANCEMENT FACTOR OF GAS ABSORPTION ACCOMPANIED BY REVERSIBLE CYCLIC CHEMICAL REACTIONS

Theoretical effect of mass transfer by reversible cyclic chemical reactions is studied in this paper. On the basis of the film theory, an analytical equation has been derived to express the enhancement factor of gas absorption with first-order reversible cyclic chemical reactions. The finite difference method has been used to study the enhancement of gas absorption with second-order reversible cyclic reactions. The results indicate that the gas absorption rate is enhanced by the forward reaction rate, while is suppressed by the backward reaction. Although the diffusivity has some effects on enhancement factor, the influence is not as much as that of reaction rate. The theoretical equations are used to predict the enhancement factors for absorptions of carbon dioxide in acidic solution and l-butene in liquid phosphoric acid.     

伴有二级不可逆反应的非牛顿幂律流体薄膜流中化学吸收的研究

本文对伴有二级不可逆反应的非牛顿幂律流体降膜流中的吸收过程进行了研究,提出扩散反应方程和它的解,并得到实验验证.     

甲基二乙醇胺水溶液在改进的湿壁塔上吸收二氧化碳的动力学模型

To get more accurate kinetic data of the absorption of CO2 into aqueous solution of N-methyldiethanolamine, a wetted wall column was modified to more uniformly distribute the liquid on the column surface and gas in the absorbing chamber and change the length of the column. The average liquid film thickness and the liquid-phase mass transfer coefficient were measured, and a correlation for the Sherwood number, Reynolds number and Schmidt number was obtained for the modified wetted wall column. The equilibrium concentrations in chemical reactions were calculated with a minor absolute error for calculating the rate constant more accurately. A mathematical model for the CO2 absorption was established based on the diffusional mass transfer accompanied with parallel reversible reactions, and the partial differential equation was solved by Laplace transform. An analytical expression for the concentration of carbon dioxide as a function of time and penetration depth in liquid film and the average interphase mass transfer rate was obtained. This model was also used to calculate the rate constant for a second-order reaction, which was in good agreement with reported data.     

HEAT EFFECTS FOR PHYSICAL AND CHEMICAL ABSORPTION IN TURBULENT LIQUID FILMS

An eddy diffusivity model was used to describe simultaneous heat and mass transfer for chemical absorption in turbulent liquid films. For absorption accompanied by a first-order reaction an approximate expression for the mass transfer coefficient is derived and shown to be in excellent agreement with exact numerical calculations. An equation is developed for the temperature rise at the free surface due to both the heat of reaction and the heat of solution. Relationships are also developed for the concentration of the liquid phase product at the free surface and the depletion of the liquid phase reactant at the free surface.

The temperature rise at the free surface for gas absorption accompanied by an instantaneous reaction due to both the heat of solution and the heat of reaction was determined. An equation is also derived for the concentration of liquid phase product at the free surface for the case of an instantaneous reaction.     

HEAT EFFECTS FOR PHYSICAL AND CHEMICAL ABSORPTION IN TURBULENT LIQUID FILMS

An eddy diffusivity model was used to describe simultaneous heat and mass transfer for chemical absorption in turbulent liquid films. For absorption accompanied by a first-order reaction an approximate expression for the mass transfer coefficient is derived and shown to be in excellent agreement with exact numerical calculations. An equation is developed for the temperature rise at the free surface due to both the heat of reaction and the heat of solution. Relationships are also developed for the concentration of the liquid phase product at the free surface and the depletion of the liquid phase reactant at the free surface.

The temperature rise at the free surface for gas absorption accompanied by an instantaneous reaction due to both the heat of solution and the heat of reaction was determined. An equation is also derived for the concentration of liquid phase product at the free surface for the case of an instantaneous reaction.     

Design calculations for countercurrent gas-liquid reactors

A mathematical model has been developed for a countercurrent differential contactor in which a gas-liquid reaction occurs. The local mass transfer rates near the gas-liquid interface are computed from a stagnant film model that includes a second-order reaction term. The contactor model accounts for enhancement of the gas absorption rate as well as the contributions to liquid reactant conversion from both the boundary layer region and the bulk liquid.Orthogonal collocation based on Lobatto polynomials has been used to solve the nonlinear equations for both the local mass transfer rates and the macroscopic differential mass balances. Parametric studies indicate that the number of transfer units, the chemical reaction kinetics and the absorption factor all play important roles in determining reactor performance. Collocation techniques are also employed to solve the design equations that include liquid-phase axial dispersion in the countercurrent gas-liquid reactor. These techniques have been found to be sufficiently efficient and robust that they should be useful for reactor design and parameter estimation applications.     

Effects of catalyst fragmentation during propylene polymerization. IV: Comparison between gas phase and bulk polymerization processes

A comparative study of the effects of catalyst fragmentation in the gas phase and bulk polymerization processes in performed. Typical operating conditions for each process are used for the comparison. The monomer concentration in the bulk process is nearly one order of magnitude larger than that in the gas phase process. The energy transfer conditions between the particle and the fluid phase are better in the liquid phase. The rate of mass transfer within the macroparticle at the initial steps of the polymerization is found to be slower in the bulk process than in the gas phase process. In the liquid phase process, fragmentation takes place more slowly. Temperature excursion values are smaller even though the dimensionless monomer concentrations are, in fact, greater because of the higher monomer concentration available in the liquid phase. The final steady rate of reaction and the ultimate catalyst yield reflect this phenomenon. Although the microparticle nucleus size affects both processes, the diffusion control that occurs when the fragments are large affects the gas phase process more intensely. In the bulk process, even at the lowest value reached by the rate of reaction, this is still sufficiently high so as to produce high yields.     

DESORPTION WITH CHEMICAL REACTION IN CONTACTING DEVICES

Chemical processes where a gas is absorbed into a liquid and reacts to give a product that desorbs back into the gas are quite common in the industry. In this study, the reaction between the absorbed gaseous reactant and a nonvolatile reactant is considered to be slow, fast or instantaneous, while the volatile product may react further in a slow reaction. Effects of various operating parameters such as the liquid and gas flow rates, the gas-liquid interfacial area and the coefficients for mass transfer are examined. Situations can arise where the absorbing gas reacts but the product diffuses completely to the bulk of the liquid, and the rate of desorption is null. The expressions presented here define conditions to avoid this situation and allow the calculation of the optimal design and operation of the gas-liquid contacting device     

Investigations of mass transfer with chemical reactions in two-phase liquid–liquid systems

A new method based on experimental determination of the product distribution of a set of complex test reactions has been introduced and applied to study mass transfer in liquid–liquid systems. The test reactions consist of two parallel reactions, one of them being instantaneous and the second fast relative to mass transfer. Two reactants are transferred from the dispersed, organic phase (phase volume 1% vol) to the continuous aqueous phase, where the third reactant is present. Experiments were carried out in a batch system agitated with either a six-blade paddle impeller or a high-shear rotor–stator LR4 Silverson mixer to disperse drops and increase the mass transfer rate. The product distribution and the drop size distribution were measured using gas chromatography–mass spectroscopy and Malvern MasterSizer, respectively with pH variation recorded during the process. The results show that the focused supply of energy in the Silverson mixer is effective for the short term irreversible drop break-up process producing smaller droplets than the six-blade paddle impeller. However for the long term mass transfer process the paddle impeller is more effective due to more uniform supply of energy and better mixing throughout the tank compared to the more localized mixing of the Silverson.     

Fundamental analysis of the dynamics,mass transfer,and coagulation in wet spinning of fibers

New models are developed to analyze the wet spinning process. These involve a formulation of simultaneous overall mass, force, and solvent mass transfer balances. In the first-order model, internal concentration gradients and mass transfer resistance within the fiber are neglected. It is equivalent to the Kase–Matsuo melt spinning model. In the second-order model, concentration gradients and diffusion within the fiber are included. Comparison is made with an experimental study of wet spinning nylon-66 fibers. The first-order model seriously underpredicts final fiber diameter under conditions of specified spinline tension and spinning efflux. The second-order model gives better agreement between theory and experiment.     

中空纤维膜接触器脱碳和传质性能的数值研究

中空纤维膜吸收烟气中CO₂是一种清洁、高效、最具潜力的脱碳技术方法之一。本文建立了一个二维的中空纤维膜接触器平行逆流吸收混合气中CO₂的非润湿模型。考虑轴向和径向扩散,模拟了EEA、EDA和PZ 3种吸收剂在不同操作条件下对CO₂的脱除效果和传质性能。结果表明：脱碳性能从大到小为PZ>EDA>EEA;气相参数对脱碳和传质的影响比液相参数更显著;提高气体流速、CO₂浓度和气温,脱碳率均会下降;提高液速、吸收剂浓度和液温,脱碳率均增大,而传质速率只有在提高气温时会下降,其他参数的升高均会使其增大;应采用适当的液相参数,防止操作参数过高带来的不利影响。     

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.     

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.     

Enhancement of oxygen mass transfer rate in the presence of nanosized particles

Absorption of gases into a liquid is essentially important for two- or three-phase reactions, because the diffusion of a sparingly soluble gas, like oxygen, across a gas-liquid interface generally limits the reaction rates. Using a third, dispersed phase, the mass transfer rate could be significantly increased. The question arises how the absorption rate can be described in the presence of very fine, nanometer size particles or droplets. Its mathematical model should take into account the specific properties of the nanoparticles, e.g. the Brownian motion of particles, its effect on the diffusion of the bulk phase molecules, the mass transfer rate into the nanoparticles, its dependency on the particle size, etc. The mass transfer rate of oxygen, in the presence of nanometer size, organic droplets, has been investigated both experimentally, using organic submicron n-hexadecane droplets, and theoretically. The effect of the Brownian motion of the nanoparticles as well as its effect on the diffusivity in the nanofluid has been discussed. Accordingly, the enhanced diffusion coefficient, due to the convective motion of the continuous liquid phase induced by the moving particles, has been predicted and its effect on the mass transfer enhancement has been calculated using both homogeneous and heterogeneous mathematical models. The predicted data were compared to the measured ones.     

CONVECTWE DRYING MODEL OF SOUTHERN PINE

A transient one dimensional first principles model is developed for the drying of a porous material (wood is used as an example) that includes both heat and mass transfer. Heat transfer by conduction and convection, mass transfer by binary gas diffusion, pressure-driven bulk flow in the gas and liquid, and diffusion of bound water are included in the analysis. The diffusive mass transfer terms are modeled using a Fickian approach, while the bulk flow is modeled assuming Darcian flow. Depending on the state (pendular or funicular) of the moisture in the wood, appropriate terms are considered in the development of the governing mass equations. The results provide distributions within the material of each moisture phase (vapor, liquid, and bound), temperature, and total pressure. Information regarding the drying rate and evaporation rate is also presented. Average distributions are obtained as a function of time, and compared with experimental data from the literature. It is observed that the total pressure within the material can be considerably above one atmosphere during the drying process.     

Kinetics of fast alkaline hydrolysis of esters

The kinetics of alkaline hydrolysis of a variety of esters (liquid and solid), which are sparingly soluble in water, was studied by using the theory of mass transfer accompanied by fast pseudo first-order reaction. This method, under certain conditions, can cover a wide range of second-order rate constants (～ 1 to 10⁴ 1/g mole sec). Whenever possible the values of the rate constants obtained by the above method were compared with those obtained by a study of the kinetics in the homogeneous phase.     

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.     

CONVECTWE DRYING MODEL OF SOUTHERN PINE

ABSTRACT

A transient one dimensional first principles model is developed for the drying of a porous material (wood is used as an example) that includes both heat and mass transfer. Heat transfer by conduction and convection, mass transfer by binary gas diffusion, pressure-driven bulk flow in the gas and liquid, and diffusion of bound water are included in the analysis. The diffusive mass transfer terms are modeled using a Fickian approach, while the bulk flow is modeled assuming Darcian flow. Depending on the state (pendular or funicular) of the moisture in the wood, appropriate terms are considered in the development of the governing mass equations. The results provide distributions within the material of each moisture phase (vapor, liquid, and bound), temperature, and total pressure. Information regarding the drying rate and evaporation rate is also presented. Average distributions are obtained as a function of time, and compared with experimental data from the literature. It is observed that the total pressure within the material can be considerably above one atmosphere during the drying process.