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).     

Theory of chemical desorption

The general problem of desorption of a volatile component accompanied by chemical reaction is considered. Basic points of difference between chemical absorption and desorption are emphasized. The conditions required for chemical absorption theory to apply to chemical desorption are established. A general procedure for solving chemical desorption problems when the rates of reaction are very high is developed; the procedure applies up to and including the limit where the reactions are instantaneous.     

纳微界面增强CO2吸收及机理分析

CO₂捕集与分离是解决当前全球温室效应和发展可再生能源的关键步骤,传统CO₂分离及过程强化方法存在速率与效率的博弈。纳微界面强化广泛用于多相传递的化工过程,其对CO₂传递过程的影响也比较显著。本综述从纳微界面处CO₂传递模型的建立及阻力调控、纳微界面处CO₂平衡态化学位的获取(推动力调控)以及界面强化机制的分子模拟分析等三个方面进行阐述。基于上述结果进一步分析真实吸收塔分离CO₂过程的阻力调控并提出“三段式强化方案”,以优化CO₂分离过程的投资与运行成本。     

Simultaneous absorption of two gases reacting between themselves in a liquid—I exact solutions

Simultaneous absorption and irreversible second order chemical reaction of two gases in an inert liquid have been considered. The nonlinear differential equations describing the absorption process have been solved analytically for particular cases by the use of the Weierstrass elliptic function and Airy functions. It is impossible to obtain a general analytical solution and therefore the accurate numerical solution for the diffusion-reaction process based on the film theory has been developed. The approximate formula for the enhancement factor E_A, in the range of large values of the dimensionless parameter M is given.     

Diffusion,swelling, and consolidation in glassy polystyrene microspheres

The effects of prior thermal and swelling history on the kinetics and apparent equilibria of subsequent n-hexane sorption in monodisperse, submicrometer diameter, glassy polystyrene microspheres were studied. Repetitive sorption and desorption cycling was compared with continuous sorption and desorption experiments. The apparent equilibrium uptake of n-hexane in preswollen samples decreased monotonically with the cumulative time under vacuum independent of the cycle frequency or the number of sorption-desorption cycles. This consolidation was modeled as a first order relaxation process with a single characteristic relaxation time. “As-received” samples swelled in the presence of the penetrant and the apparent equilibrium n-hexane content increased monotonically with the time under n-hexane. The Berens-Hopfenberg diffusion-relaxation model accurately describes the cyclic and continuous swelling behavior of the “as-received” sample. At each temperature studied, a true equilibrium n-hexane content was approached asymptotically for the preswollen and “as-received” samples after sufficient time under vacuum or n-hexane, respectively. Whereas the apparent sorption equilibria were controlled by the cumulative time under vacuum or n-hexane for the preswollen and “as-received” samples, respectively, the absorption kinetics are subject to a systematic variation which depends only on the immediate prior vacuum history of the sample. The temperature dependence of the kinetic and equilibrium parameters describing diffusion, consolidation, and swelling suggests a unified molecular interpretation of these diverse glassy-state transport and relaxation processes.     

Calculation of multicomponent multiphase equilibria

An algorithm which gives very good first trial values for the computation of chemical equilibrium composition is proposed. It is based on writing the chemical reactions in “canonical form” and changing the independent component set until it is formed by the species present in greatest quantity at equilibrium. The advancement degrees ξ_r of the reactions are calculated considering the reactions to occur independently of any other. By applying a similar procedure to the series reactor method, a new powerful solution algorithm of the Rosenbrook's type is obtained. In the first method we linearize the equilibrium equations written making null the gradient of the free energy of the system with respect to the corresponding ξ_r whilst in the second one we make successive unidimensional searches solving the equations for ξ_r     

Modeling the Absorption of Acidic Gases by Alkanolamine Solutions Incorporating Several Reactions

A general model, based on double film theory, is developed to study absorption with chemical reactions. In the liquid film region, the model is a set of differential equations that describe the mass transfer accompanying several chemical reactions; the resolution of the system is achieved by the finite difference method using an implicit scheme combined with Newton's method. Continuity equations and equilibrium coefficients are exploited in the treatment of the bulk region, which is based on the Newton‐Raphson method; the results are used directly as boundary conditions in the liquid film equations. Maxwell‐Stefan equations have been used as a rigorous approach in this model.     

Simultaneous absorption with reversible instantaneous chemical reaction

The approach presented recently [1] for analyzing absorption and desorption mass transfer problems with instantaneous chemical reaction is extended to the case of simultaneous absorption of two gases, A and A′. The analysis is developed for arbitrary stoichiometry. The following simple case is discussed in detail:A + B₁?B₂A′ + B₁?B₃ where B₁ is the liquid phase reactant and B₂, B₃ the reaction products. The analysis takes into account the “shift” reaction, which for the simple case above is:A + B₃?A′ + B₂This reaction takes place in the region near the interface. The analysis differs from previous work which, with one exception, ignored the “shift” reaction and restricted attention to zero values of the concentrations of B₂ and B₃ in the bulk liquid.The analysis shows that the conditions where the physical driving forces (a_i-a_o) for absorption of both gases are large and positive does not imply that the chemical driving forces (α_i-α_o) are both positive. In fact, it is shown that cases arise where one component may desorb even though its physical driving force is positive.A simplified thermodynamic model useful for extrapolation of mixed CO₂ and H₂S equilibrium data in amine solutions to very low values of acid gas loading in solution is developed. Tower profiles for simultaneous absorption of CO₂ and H₂S in monoethanolmine solution are considered in light of the new analysis. The good kinetic selectivity measured for H₂S at the absorber lean end is due to the fact that carbon dioxide is not absorbed in the instantaneous reaction regime. At the absorber rich end, where a temperature bulge develops, CO₂ is absorbed in the instantaneous regime, causing H₂S to be desorbed even though its physical driving force favors absorption.     

Promotion of CO2 mass transfer in carbonate solutions

A general, physico-chemical analysis of mass transfer rate promotion in the system CO₂-potassium carbonate-water-promoter is presented. Different possible mechanisms of promoter action including homogeneous catalysis, “shuttle” mechanism and surface reactions are discussed and classified. A unified picture of promoter chemistry is presented, showing that differences between inorganic and organic promoters are predominently quantitative, not qualitative.The “shuttle” mechanism is analyzed for absorption. The analysis leads to the prediction that the CO₂ mass transfer rate may be influenced by the liquid hold up. This is related to the fact that, although the reaction in the interface region may be fast enough to enhance the mass transfer rate, the different reaction in the bulk may not be fast enough to maintain chemical equlibrium. This complex type of chemical absorption process has not been considered previously in the literature.     

A study on desorption resistance in pervaporation of single component through dense membranes

Desorption resistance taking place between a membrane surface and a permeate vapor phase, which had not accounted for an overall mass transfer resistance in pervaporation, was studied. The resistance-in-series concept and Flory-Huggins thermodynamics were used to establish model equations for evaluating the desorption resistance in the permeation of a single component. In order to exclude any possible concentration polarization of permeants occurring in feed adjacent to a membrane surface, the permeations of pure water through polyether imide membranes with various thicknesses were observed at different permeate pressures. From the permeation data of pure water through the membranes with help of the model equations, both the permeability coefficient based on a general flux equation expressed in terms of the chemical potential driving force and the desorption resistance were determined quantitatively. According to the model equations, the desorption resistance could be affected by two factors: membrane thickness and permeate pressure. The magnitude of the desorption resistance was dependent mainly on permeate pressure, and the importance of the resistance relative to diffusion resistance in the membrane for the overall process became more significant with decreasing membrane thickness at a given permeate pressure. As the membrane thickness decreased and/or the permeate pressure increased, the desorption resistance was observed to be more significant, causing higher chemical activity and a higher concentration of the permeant at the downstream interface of the membrane. In some cases, the desorption resistance was predominant over the diffusion resistance in very thin membrane thicknesses. This study seeks to emphasize the importance of the desorption resistance on the transport of components at small membrane thicknesses or high permeate pressure. © 1997 John Wiley & Sons, Inc.     

冷冻干燥过程强化中冷冻阶段优化的研究进展

冷冻干燥产品质量高,但时间长、能耗高。本文综述了冷冻干燥过程强化中冷冻阶段的优化方法,控制冷冻速率、调节冰晶成核和退火处理可以获得大而均匀的冰晶从而提高升华干燥阶段速率,但物料内部比表面积的减小会降低解吸干燥阶段速率,这类常规的冷冻阶段优化方法对弱吸湿性的物料有一定的强化效果。有机溶剂具有较高的蒸气压,作为共溶剂时可以增加传质推动力,但较低的有机溶剂残留量要求阻碍了其进一步应用。“初始非饱和多孔介质冷冻干燥”的技术思想是将液体物料首先制备成具有一定初始孔隙的冷冻物料,然后再进行冷冻干燥。物料具有的初始孔隙为水蒸气的迁移提供了便捷的通道,而且纤薄的固体基质也有利于结合水的解吸,可以同时强化升华干燥阶段和解吸干燥阶段。该技术思想是过程低消耗和产品高质量的完美结合,为解决冷冻干燥过程速率低的问题提供了新的方案。     

Numerical calculation of simultaneous mass transfer of two gases accompanied by complex reversible reactions

A discretization technique is described, which makes it possible to calculate numerically mass transfer behaviour between two media in which complex chemical reactions occur. To show the stability of the technique it has been applied to the industrially well-known system of simultaneous absorption or desorption of H₂S and CO₂ to or from an amine solution, accompanied by simultaneously occurring strongly interfering overall chemical reaction(s) of complex, non elementary kinetics. For previously published limit cases of the transfer system considered, i.e. for the single transfer of H₂S or CO₂ accompanied by reversible chemical reaction, a comparison has been made with analytical and approximate solutions of previous authors. The agreement is very good. In studying simultaneous transfer of H₂S and CO₂, on which hardly any previous work was available, special attention has been paid to the effects of the reversibility of the reactions involved. It has been shown how, under certain conditions due to reversibility occurring in the transferzone, desorption takes place though absorption would be expected on basis of the driving forces. This revealed that not only enhancement factors larger than unity but also smaller, even negative values are possible.     

Gas absorption with or without chemical reaction in laminar non-newtonian falling liquid films

An analytical solution is presented for gas absorption with or without a first-order or zero-order chemical reaction in a laminar non-Newtonian power-l model falling liquid film. For physical absorption, the first ten eigenvalues, series coefficients and related quantities are computed accurately by a quasinumerical method which shows considerable improvement over previous investigations. The range of applicability of the penetration theory solution is also established to indicate in what regions will the finite film thickness and complete velocity profile be important in determining the absorption rate. It is found that the range of dimensionless axial contact length X* in which the penetration theory is valid diminishes rapidly with increasi values of the power-law index n. For chemical absorption, the solution can be obtained by a linear superposition principle in terms of a “transie part” in which the effect of hydrodynamics within the liquid film is of importance and a “steady part” in which the reaction rate is controlling. In the “transient part” solution, the first ten eigenvalues and related quantities are reported for a variety of values of n and the dimensionl reaction rate parameter k_l* or k₀*. Certain asymptotic solutions from the penetration theory are also given and their range of applicab estimated. For any given n, it is estimated that only when k₁* or k₀* is less than approximately 10 will the finite film thickness and velocity profile have any effect on the absorption rate as compared to that calculated from the penetration theory with chemical reaction. The non-Newt character of the liquid film also has a significant influence on the absorption rate. At a fixed X*, the absorption enhancement due to reaction is when n = ∞ and is smallest when n = 0. The solutions obtained in this work are useful either for predicting absorption rates or for deter molecular diffusivity (and reaction rate constant) of gases in non-Newtonian falling liquid films.     

The asymptotic status of the Sherwood-Pigford model in the theory of absorption with chemical reaction

The Sherwood-Pigford model for absorption accompanied by instantaneous irreversible chemical reaction is an essentially discontinuous one, where a moving front across which concentration gradients suffer a discontinuity is assumed to exist. The case where the reaction is both instantaneous and irreversible is a doubly singular one. In this paper, a boundary-layer analysis is developed which shows that, for irreversible reactions, the Sherwood-Pigford model equations are approached asymptotically for arbitrary kinetics when an appropriate time scale of the reaction becomes sufficiently small. It is also shown that the same limit is approached for arbitrary stoichiometry in the case of instantaneous reactions when the ratio of the interface to the bulk concentration of volatile component becomes sufficiently large. Finally, a general estimate is obtained of the thickness of the reaction zone (which is assumed to be zero in the Sherwood-Pigford model) for the general case where the reaction is neither instantaneous nor irreversible.     

Kinetic and mass transfer studies in the catalytic oxidation of thiophenol in a gas—liquid reactor

A study has been made of the absorption of gaseous oxygen in a thiophenol solution. The chemical reaction which occurred in solution was promoted by a copper chloride—pyridine catalyst. There were two reaction products, diphenyldisulphide and diphenylthiolsulphinate. In some experiments the liquid was unstirred, in other experiments the liquid was either stirred with a rotating bar or vigorously agitated with a vibrating disc.The reaction process was apparently zero order with respect to the thiophenol. The concentration of the catalyst affected both the reaction rate and the product ratio. The relationship between the absorption rate and catalyst concentration depended markedly on the mixing conditions within the reactor. The course of the absorption cannot be described simply in terms of the “classical” regimes of mass transfer with chemical reaction. However, it is probable that the absorption is in the transition region between the “diffusion” and “fast” regimes at low catalyst concentration and approaches the “instantaneous” regime at high catalyst concentrations. The relative yield of disulphide increases as the catalyst concentration increases and as the temperature increases. Improvements in the agitation of the liquid can lower the proportion of disulphide in the reaction product.These results have important implications for the processes which use this catalyst in the “selective” manufacture of disulphides and polydisulphides.     

ABSORPTION AND DESORPTION TO AND FROM LIQUID FILMS ON INCLINED PLANES

Two published theoretical models are examined and applied to experimental results for absorption and desorption. The system used was CO₂/H₂O and studies were made for liquid film flow down inclined planes. Experimental results give “Reduced” values of mass ransfer rates.

Interferometric studies give interfacial concentration, penetration and film depths, and take-up of carbon dioxide. In the case of desorption the interferograms are distorted by “deflections.”

All the experimental values for absorption and desorption differ from those calculated from theoretical models.

Desorption is not a mirror image of absorption, and it is approximately 75% of the transfer rate of absorption over a wide operating range.

A comparison is made of the behaviour of static pools and flowing liquid films.     

Hygrothermal aging of rubber modified and mineral filled dicyandiamide cured digylcidyl ether of bisphenol A epoxy resin. I. Diffusion behavior

The effect of hydration–dehydration cycling on the properties of a rubber modified, mineral filled epoxy resin is reported. This resin was based on diglycidyl ether of bisphenol A and cured with dicyandiamide. The material was aged in deionized water and a 5% (w/w) NaCl solution at 65°C. Gravimetric measurements, transmission electron microscopy, and diffusive reflectance IR Fourier transform spectroscopy were used to monitor the water sorption and physical and chemical changes occurring in the material. Two‐stage absorption was observed with deionized water, and the quasiequilibrium‐state water content was independent of the hygrothermal history. The equilibrium weight after dehydration depended on the hygrothermal history due to the presence of irreversibly absorbed water and leaching of material. The first stage of the absorption was found to be Fickian and was interpreted as being related to the process of saturation of the epoxy matrix. The driving force for the second stage was the osmotic pressure, and it was not observed when the material was aged in NaCl solution. The water caused irreversible damage to the resin through microcavity formation, and part of the water was molecularly dispersed in the epoxy matrix and part resided in microcavities. Absorption–desorption cycling resulted in an increased rate of absorption during subsequent rehydration. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 3468–3476, 2001     

A quin-diagonal algorithm to describe mass transfer and backmixing in extraction

Specific algorithms are especially effective and economical when used to solve sets of linear-algebraic equations when the coefficients of the equations are adjacent to the diagonal elements. The Thomas algorithm is well known and has been used in many areas of chemical engineering when “tridiagonal” sets of equations are encountered. A similar algorithm is developed for use when the coefficients take a quin(5)-diagonal configuration. Its application to multistage mass transfer operations is demonstrated and the effects of deviation from equilibrium and backmixing are illustrated for multistage extraction operations.     

Absorption of acetone in a two-impinging-streams absorber

The effectiveness of various spray absorption configurations (as shown in Fig. 1 of the paper), which are based on the new technique of “absorption in two-impinging-streams” as well as on conventional absorption techniques in a single spray, were tested by absorbing acetone from air into a water spray. The major conclusions are: (1) absorption rates of acetone into two-impinging-streams (configurations “a” and “c” in Fig. 1) are significantly higher (up to a factor of four) than absorption rates into two streams separately operated (configurations “b” and “d”) under identical conditions and (2) absorption rates of acetone in two-impinging-streams are higher than in a single stream (configurations “e”-“h” in Fig. 1), but the enhancement is less pronounced than above.     

Enhancement factors for gas-absorption with second-order irreversible chemical reaction

A relatively simple and explicit mathematical expression has been developed for estimating the enhancement factors for mass transfer accompanied by a second-order irreversible chemical reaction. The development is based on asymptotic characteristics, i.e., limiting solutions, for second-order enhancement factors. The resulting mathematical relation and other approximate analytical formulations previously presented in the literature have been critically compared with a numerical solution for the diffusion-reaction process based on film theory.