Non-isothermal interphase diffusion with consecutive reactions

Multi-step heterogeneous consecutive reactions on non-porous catalyst were studied when external mass transfer occuring under non-isothermal condition mainly affects the reaction rates, and useful equations were derived in terms of the dimensionless groups and the measurables by the combination of mass balances with heat balance around the surface of the catalysts. From the analyses of the equations derived, the enhancements for the surface concentrations of the intermediates were regarded to be identical to those under isothermal condition,and those for the effectiveness factors for the intermediate steps were conculded to be the very multiplications of those through isothermal process by the ratios of the rate constants of the reactions for the corresponding steps at the surface conditions to those at the bulk condition.     

Transesterification kinetics of triglycerides for a modified lipase inn-hexane

A simple kinetic model for the transesterification of triglycerides catalyzed by a modified lipase inn-hexane has been proposed. The model assumes that the enzyme has 1,3-positional specificity and does not distinguish among the different fatty acid residues considered in this study. The model is based on material balances of consecutive second-order reversible reactions and requires only one parameter that can easily be determined experimentally. The differential rate equations have been solved analytically to give explicit equations that link the concentrations of all possible triglycerides to the initial conditions and the reaction time. The model was in good agreement with experimental data for different biocatalyst concentrations with the same value of the specific rate constant. The same value of specific rate constant also gave a good fit with experimental data for an acidolysis reaction between a triglyceride and a fatty acid, implying that the modified lipase did not distinguish between free fatty acids and fatty acid residues attached to the 1 and 3 positions of glycerol backbone.     

Mass transfer with chemical reaction—I. A second-order irreversible reaction

The process of simultaneous absorption of two gases which react between themselves in an inert liquid is examined in the realistic limit of fast reaction. In this limit the nonlinear mass balance equations based on film theory are solved analytically using the method of matched asymptotic expansions. Explicit analytical expressions for the enhancement factors and concentration profiles of the gaseous solutes are derived. Results are given for the case where the two gases undergo an irreversible chemical reaction and the reaction rate is first order with respect to each of the solute concentrations. The nonlinear mass-transfer equations are also solved numerically using a shooting technique. When the dimensionless reaction rate constant is large, the analytical solution for the enhancement factor is found to be in excellent agreement with the numerical solution, with an error of less than 0.2% (better than any previously achieved).     

Control of transport phenomena in the interior of the reforming catalyst grain: A new approach to the optimisation of the reforming process

The aim of the study was to provide favourable conditions for the transport of the reagents by modifying the porous structure and shape of the reforming catalyst grain. The study entailed the analysis of the transport phenomena and reactions that occur in spherical, cylindrical and slab-shaped catalyst grains. To upgrade the efficiency of the catalyst, use was made of analytical equations that describe the changes in the concentrations of the reagents in the catalyst grain. The equations were derived from the mass balances and the kinetic scheme assumed for the reforming process. By virtue of the coefficients of reagent diffusion, the equations are a function of the porous structure parameters and can therefore define a more or less advantageous profile of concentrations. The modification of the profile by minimising the objective function proposed in the paper leads to the reduction in the influence of diffusion resistance on the course of the reforming process. The study demonstrates that after the porous structure of the experimental catalyst had been changed, it was possible to increase its specific surface area and mechanical strength and, at the same time, noticeably improve the conditions for the transport of reagents.     

Process control of a gaseous diffusion cascade for isotopic separation of uranium

Various aspects of dynamics and process control of a gaseous diffusion cascade are described. The cascade enriches uranium hexafluoride gas (HEX) in the light isotope of uranium in a countercurrent flow. The linearized equations describing the equipment models are derived. One can then write the mass balances on the high and low pressure sides of a stage and the overall heat balance of a stage. These heat and mass balances are linear difference equations on the stage number with time derivatives which are then replaced by jω factors to examine the effects of cyclic perturbations. The mass balances are first treated for a cascade section of 12 stages with temperatures assumed constant. The effect of a perturbation of pressure on one of the stages is described first for ω = 0 (that is for steady state). Then Nyquist diagrams are obtained. The effect of transport change is also studied.Then temperature is introduced, assuming pressures to be constant. The cases of a section of 12 stages and a cascade of 120 stages are examined. Again Nyquist diagrams of temperature frequency response to a perturbation on one stage are calculated. Process control of the heat exchangers is introduced. The method used to solve the difference equations may be applied to other types of perturbations and to the complete scheme of process control.     

Modified correction-factor analysis of solvent extraction in rectangular membrane modules

The expressions of mass-transfer rate for membrane extraction through a rectangular module have been derived under cocurrent-flow, countercurrent-flow and cross-flow operation based on the modified correction-factor analysis. These expressions are explicit and the results can be readily calculated without using try-and-error method, which should be employed in the conventional correction-factor analysis for designing heat and mass exchangers. The correction factors for both cocurrent-flow and countercurrent-flow operations may be taken as unity when the logarithmic-mean concentration differences are properly selected. For cross-flow operation, the correction factors are function of flow rate, mass-transfer area, distribution coefficient and overall mass-transfer coefficient, and some values of them are given graphically.     

On material balances for chemically reacting systems

This paper is concerned with the relationship between element and species material balances for steady-state chemically reacting systems. Conditions are given under which element and species balances are equivalent and can be used interchangeably. The number of independent equations furnished by both the species and element balances as well as conditions for a proper specification of information are deduced. A method for constructing a maximal set of independent reactions is presented.     

MASS TRANSFER EFFECTS ON THE ETCH RATE OF GAAS IN FLOW SYSTEMS

In industrial wet etching reactors, the fluid contacts the substrate surface as a spray of flowing stream, thus introducing mass-transfer resistances to the reaction rate. The etching of gallium arsenide in H₂O₂-NH₄OH-H₂O solutions was studied using an open-channel flow reactor to simulate the industrial conditions. The etch rate was always lower than that obtained under kinetic control, and the dependence of etch rate on H₂O₂ concentration shifted closer to first order. From the calculation of the ratio of rate constant to mass-transfer coefficient, the reaction-rate and mass-transfer resistances were both significant in this system. When the mass-transfer coefficient was calculated from equations for flow past a flat plate, the prediction of etch rate was good, particularly when the starting length for velocity boundary layer development ahead of concentration boundary layer development was taken into account. Another approach for the calculation of mass-transfer coefficient, based on the assumptions for flow between parallel plates, best represented the relative insensitivity of etch rate to fluid velocity.     

Analysis of non-isothermal catalytic reactions. Limiting effect of non-key component

An improved method for predicting effectiveness factors for pseudo first order catalytic reactions with limiting non-key reactant has been derived. The method takes account of intraparticle temperature and concentration profiles in addition to interphase effects and solution of the system equations is obtained using the orthogonal collocation technique which is simple and involves only algebraic equations. The depth of penetration of reactant is also determined by this method. The results are discussed and compared with earliler work.     

MASS TRANSFER EFFECTS ON THE ETCH RATE OF GAAS IN FLOW SYSTEMS

In industrial wet etching reactors, the fluid contacts the substrate surface as a spray of flowing stream, thus introducing mass-transfer resistances to the reaction rate. The etching of gallium arsenide in H₂O₂-NH₄OH-H₂O solutions was studied using an open-channel flow reactor to simulate the industrial conditions. The etch rate was always lower than that obtained under kinetic control, and the dependence of etch rate on H₂O₂ concentration shifted closer to first order. From the calculation of the ratio of rate constant to mass-transfer coefficient, the reaction-rate and mass-transfer resistances were both significant in this system. When the mass-transfer coefficient was calculated from equations for flow past a flat plate, the prediction of etch rate was good, particularly when the starting length for velocity boundary layer development ahead of concentration boundary layer development was taken into account. Another approach for the calculation of mass-transfer coefficient, based on the assumptions for flow between parallel plates, best represented the relative insensitivity of etch rate to fluid velocity.     

Gas-phase mass-transfer measurements in a falling-film microreactor

The industrial-scale performance of gas–liquid reactors is difficult to control when very rapid or highly exothermic reactions are involved. Microstructured reactors offer new opportunities for these reactions by enabling precise heat management and accurate control of operating conditions.The present study examines experimentally the gas-phase mass-transfer characteristics of a reactor tool for the characterization of gas–liquid reactions: a falling-film microreactor. A well-known chemical test system, the absorption of sulfur dioxide SO₂ by sodium hydroxide NaOH is employed to determine the characteristics. The measurements of inlet and outlet concentrations in the gas phase enable the mass-transfer coefficient to be determined.The mass-transfer characteristics, in terms of dimensionless Sherwood number Sh_G, are then related to the hydrodynamic characteristics of the gas phase, through the Reynolds number Re_G, and the physico-chemical properties of the reactional system, through the Schmidt number Sc_G. A strong dependence of dimensionless Sherwood number on gas-phase Reynolds number is observed, probably resulting from the specific features of the geometry of the gas-phase inlet.     

Gasification of coal-derived chars in synthesis gas mixtures under intraparticle mass-transfer-controlled conditions

A model has been formulated to describe the quasi-steady-state gasification of coal-derived chars in gas mixtures where both the reactants carbon dioxide and steam, and the gasification products carbon monoxide and hydrogen are present. As such, these conditions reflect the situation found in most practical gasification systems.The model presented is applied under conditions where intraparticle mass transfer is rate-controlling. Intraparticle heat transfer is neglected. In view of the non-equimolar gasification reactions, the mass flux equations are derived from the continuum limit of the dusty gas model. These flux equations are combined with strongly non-linear Langmuir-Hinshelwood kinetics for the gasification reactions. The model accounts for local variations of the diffusive and convective permeability parameters, as well as variations in the reactive surface area, during burnoff of a char particle.The impact of the various relevant mass-transfer parameters, the gasification temperature and pressure, and the char particle size on the gasification behaviour is discussed. A comparison is made between the present model and existing models, and various modelling approaches are critically reviewed.     

Rigorous simulation and design of columns for gas absorption and chemical reaction—I: Packed columns

A rigorous computer model is developed for the simulation of absorption and single or complex reactions in packed or plate columns.Part I deals with the packed-column version. It allows the computation of the concentration and pressure profiles along the column and of the concentration profiles in both the gas and liquid film at any height in the column. The use of mass-transfer coefficients leads to the real—not the theoretical—height of the column. The rigorous solution is compared with approximate solutions.Part II deals with the plate-column version. Here too, mass-transfer coefficients are used. Non-isothermal conditions are taken care of through enthalpy balances.The computer program is presented in some detail and applications to industrial situations are illustrated.     

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.     

化学吸收法测定新型复合转子旋转床气液有效比表面积及液相传质系数

用不同浓度的NaOH溶液吸收CO2,分别测定新型复合转子旋转床的气液有效比表面积和液相传质系数,考察了液量、气量和转速的影响. 结果表明,新型复合转子旋转床的有效比表面积和液相传质系数均随液量、气量和转速增大而增大. 在相同操作条件下,与折流式旋转床相比,新型复合转子旋转床转子的有效比表面积增大7%~159%,液相传质系数降低7.7%~18.2%,最终液相体积传质系数增大4%~132%.     

General rate equations and their applications for cyclic reaction networks: multi-cycle systems

The network reduction technique and the Bodenstein approximation of quasi-stationary behavior of reaction intermediates were systematically applied to derive general yield ratio and rate equations for multi-cycle reaction networks in homogeneous catalysis. Dual-cycle reaction networks connected by a linear pathway, multi-cycle networks stemming from the same intermediate, and single-cycle with arbitrary number of pathways between two intermediates were considered. The general yield ratio and rate equations derived in this study are applicable for most enzymatic reactions and for homogeneous catalytic reactions. Examples of homogeneous catalysis were used to illustrate the application of the general yield ratio and rate equations for network elucidation.     

气-液两相降膜流动及传质过程的CFD研究

利用VOF法建立了考虑表面张力动量源项、气液相间摩擦力动量源项以及相问传质源项的CFD计算模型,定量描述了气．液两相逆流降膜传质过程。根据CFD模型,计算了不同液相进口浓度和不同气相流量条件下,异丙醇稀溶液的解吸过程,模拟得到的液相出口浓度与实验数据吻合很好。相界面处的浓度分布表明。随自由表面波动,界面浓度会发生剧烈脉动。液相总传质系数增强因子R的实验值与CFD模拟均表明,即使在很小的传质推动力下R也大于1。由于CFD模型不考虑Rayleigh-Benard-Maragoni效应,则这种现象,可解释为界面波动对传质增强的结果。这也证明增强界面波动是一种强化传质分离过程的有效途径。     

Analysis of diffusional effects in immobilised two-enzyme systems

The effect of diffusional resistances (both inter- and intramembrane) on the kinetic behaviour of an immobilised two-enzyme system carrying out a consecutive sequence of reactions S → P₁ → P₂ is analysed for the case in which the intrinsic kinetics can be considered to be first order. The method of solution consists in first representing the diffusion–reaction equations in matrix notation and applying the similarity transformation to reduce the equations to a set of uncoupled equations in pseudoconcentrations. The set of uncoupled equations are solved analytically for the appropriate boundary conditions. The solution to the original problem is then recovered by applying the reverse transformation. Two geometries have been treated, the spherical capsule and the flat plate membrane. The diffusional resistances may be described adequately by two dimensionless numbers, the Thiele modulus and modified Sherwood number. The influence of these parameters on the concentration profiles and “effectiveness factors” have been presented graphically. The analysis is also extended to the prediction of the performance of a packed bed enzyme reactor.     

Catalyst particle effectiveness with unsymmetrical boundary conditions

In trickle-bed reactors part of the surface of the catalyst particles may be covered by liquid and part by gas. Under such conditions conventional expressions for effectiveness factors are not applicable because the surface concentration is not uniform. In this paper more general equations for both particle and overall effectiveness factors are derived. The first development is for slab geometry where the two plane surfaces of equal areas have different reactant concentrations. This is followed by treatment of a cubic particle where one or more faces are covered by liquid. Approximate methods are then presented for evaluating the effectiveness factor for any fractional liquid coverage, f. Comparison of the results at permissible values of f indicates that a simple weighting-factor method gives good results. The method is illustrated by comparing predicted and experimental reaction rates for a case where experimental results are available—the hydrogenation of α-methyl styrene.