The penetration theory for gas absorption accompanied by a first-order chemical reaction with a diffusing catalyst

The penetration theory solution is presented for gas absorption accompanied by a first-order chemical reaction catalysed by a species diffusing in the liquid phase. A full numerical solution was obtained for the enhancement factor, the factor by which the chemical reaction increases the rate of absorption. Asymptotic expansions were obtained by analytical methods, for both small and large values of the contact time.The results show that the enhancement factor increases indefinitely with the contact time and that it is substantially higher than the enhancement factor predicted by the film model. For large values of the contact time the predicted enhancement factors differ by a factor of two.     

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.     

Gas absorption with zero-order chemical reaction in a foam-bed reactor

A mathematical model for oxidation of aqueous alkaline solution of sodium dithionite using air as an oxidizing medium in a foam-bed reactor has been developed under pseudo-zero-order conditions of reaction and was found to be in good agreement with the experiments. Reactor conditions were 30°C at atmospheric pressure and surfactant used in the foam contactor was octyl phenoxy polyethoxyethanol (Triton X-100). The results of simulation for concentration profiles of the dissolved gas-phase reactant inside foam film based on above model are presented for different gas flow rates, reaction rates, and times of contact. The effects of variables such as superficial gas velocity and initial liquid-phase reactant concentration on conversion are also studied and compared with experiments on oxidation of sodium dithionite. The results indicate that the conversion increases with the increase in the superficial air velocity and initial dithionite concentration. The model predicts the experimentally obtained conversions reasonably well.     

Gas absorption and desorption with reversible instantaneous chemical reaction

The general problem of gas absorption and desorption accompanied by an instantaneous, reversible chemical reaction is approached from the viewpoint that chemical equilibrium prevails everywhere in the liquid phase. The approach allows absorption and desorption to be analysed along the same lines. A complete analytical solution is given for the film theory model and the penetration theory equations are set up in general form.The equations for the enhancement factor reduce to the classical “irreversible” result for absoption when the driving force, φ, becomes very large, rather than in the limit of very large equilibrium constant as the word irreversible seems to suggest. The corresponding asymptote for desorption is obtained by setting φ = 0. A third asymptotic region, in which φ is in the neighborhood of unity, is established for both absorption and desorption. Physically this is the region where driving forces are very small, which from an industrial viewpoint is what happens in absorption and desorption units near pinches.The asymptotic analysis for the pinch region is applied to hydrogen sulfide absorption and desorption from aqueous diisopropanolamine solution. For this system use of the “irreversible” equations grossly overestimates the enhancement factor. Gas-phase controls mass transfer at the lean end of the absorber but at the other terminal locations of the towers the liquid-phase resistance cannot be neglected.     

Variation of the enhancement factor in gas absorption with order of chemical reaction

The enhancement factor for the gas absorption with the two-step reversible and irreversible consecutive reaction, 2A?A*+A and A*+B→P in the film theory was derived by using the Van Krevelen approximation, and was compared with the exact numerical solution. The difference between the approximate and the exact enhancement factors is within a few per cent. The relation of the enhancement factor to the order of reaction in the whole regime from a simple irreversible reaction to an instantaneous rapid reaction was discussed.     

The effect of the gas side resistance on absorption with chemical reaction from binary mixtures

A predictive model based solely on the conservation equations of both phases is presented for the study of the effect of the gas-side resistance in multicomponent absorption with chemical reaction in a laminar liquid film. The model is applicable for short exposure times to a variety of flow patterns, e.g. a cylindrical jet, a wetted-wall column, or an inclined plane. The model may be applied to the wetted-wall column and the inclined plane for any contact time. The numerical scheme for the downstream solution has the advantage of utilising a similarity solution as its starting point. The model is applied to the system CS₂---N₂ where CS₂ is absorbed in an aqueous solution of amine and undergoes pseudo first order reaction. It was found that the a priori neglect of the gas-side resistance is not justified. The error introduced in evaluating the absorption flux by neglecting the gas-side resistance is dependent on the reaction rate constant, bulk concentration of the species, length of the absorber and the total pressure. Errors generally increased with increasing values of the above parameters. The gas-side resistance is reduced when the gaseous atmosphere is under forced convection.     

Effective interfacial area in packed beds for absorption with chemical reaction

The extended crossflow model is proposed and developed for describing gas absorption with chemical reaction in a packed bed operated in the trickle flow regime. The model involves the division of the total interfacial area into the interfacial area of the static hold-up and that of the dynamic hold-up. The concept of the effectiveness of the interfacial area of the static hold-up is presented. A procedure is developed for calculating the effectiveness, and consequently, the effective interfacial area for various different absorption processes with chemical reaction, both liquid phase controlled and gas phase controlled. The predictions based on the present model agree well with reported experimental data. The present model is shown to be simpler and more accurate than previous models.     

Gas absorption with an unusual chemical reaction: the chlorination of toluene

The rate of absorption of chlorine in a laminar jet of toluene, and the corresponding bulk liquid temperature increases, have been measured as a function of contact time. Since the reaction rate is very highly dependent on the concentration of dissolved chlorine, bulk mixing of the jet on entering the receiver effectively ‘freezes’ the reaction and enables experimental determination of the ratio

This ratio is independent of the mass diffusion coefficient for 1st order kinetics, and numerical studies show this is also true for nth order reactions. The ratio therefore should be particularly valuable for abstracting kinetic information from absorption rate data in systems where interfacial turbulence may occur. A numerical analysis, which takes into account the increasing interface temperature, indicates that the overall concentration dependency of the chlorine reaction rate can be fitted by an empirical fifth order equation.     

Penetration theory solution for gas absorption and chemical reaction in cocurrent and countercurrent flow wetted-wall columns

Penetration theory solutions are provided for gas absorption with or without a (pseudo) first-order irreversible chemical reaction in cocurrent and countercurrent flow wetted-wall columns, taking into account a constant gas-film resistance as well as the axial decrease in gas composition due to absorption, while assuming non-rippling laminar flow for the liquid phase and plug flow for the gas phase. Limiting solutions are also obtained for situations when either the gas phase resistance or the axial variation of gas composition is negligible. The results are suitable for ϕ ≥ 3 and can be used for both Newtonian and non-Newtonian liquids.     

Penetration model of gas absorption into slurry accompanied by an instantaneous irreversible chemical reaction

Recently, the problem of absorption of gases into nonhomogeneous solvents has drawn more attention than ever as it found in various fields such as flue gas scrubbing, hydroprocessing, coal conversion and medicine. Since the first treatment of this problem by Ramachandran and Sharma⁽¹⁾, several models based on the film concept have been proposed^(2-7). There is, however, no penetration theory for the evaluation of the rate of the absorption of a gas into a slurry containing suspended solid particles. In this paper, a penetration model is presented for the absorption of gas A into a slurry containing solid B with an instantaneous irreversible chemical reaction.     

Penetration model for absorption with chemical reaction in the presence of heat generation,bulk flow and effects of the gaseous environment

A penetration model for gas absorption into a laminar liquid stream in the presence of chemical reaction and large heat generation was investigated theoretically, accounting for the presence of the gaseous environment, not considered in previous analyses, as well as the transverse bulk flow contribution to the total mass transfer. A complete formulation was performed which is based solely upon the conservation equations in both phases with the appropriate matching conditions at the gas-liquid interface. A boundary layer model was assumed for the fluid mechanical behaviour of the gaseous surroundings. The liquid stream initially had a uniform velocity in the axial direction. After being exposed to the absorbed gas, the flow field in the liquid stream was found to conform with a uniform axial velocity along with a transverse component, solely dependent on the axial distance. The numerical solution was demonstrated for the absorption of chlorine into toluene which has been investigated experimentally by others. It was found that the effect of heat conduction from the liquid stream surface to the gaseous surroundings is negligible as compared to other heat contributions. The contribution due to the bulk flow of the absorbed gas, previously neglected, to the total absorption flux was found significant. In all cases it was appreciable at the entrance region and of the order of 17%. Evaluation of the above-mentioned experimental results revealed a deviation of 25% in the total absorption flux of chlorine between calculations based on a simplified model and the more general one presented here. It is thus concluded that the a priori neglect of the effect of the gaseous environment as well as bulk flow contribution is not justified for absorption of gases with high solubilities and large heat effects.     

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.     

Gas absorption with a first order chemical reaction and large heat effect

This paper considers the absorption of a gas with a first order chemical reaction and large heat effect. The partial differential equations describing the process are converted into differential difference equations which are solved recursively.     

旋流吸收器气液吸收传质过程研究

根据旋流吸收器中分散液相不同的运动形态建立了伴有化学反应的气液吸收传质模型,且该模型的表达形式与Danckwerts的表面更新理论一致。从模型上看,液侧传质系数kL正比于扩散系数DA和表面更新率S的平方根,这一正比关系还得到了实验结果的部分验证。根据实验结果可以看出,与其他吸收器相比,作为一种结构简单的静态设备,旋流吸收器同样可以提供一个强化传热、传质的流体力学环境。