Enhancement factors for gas absorption with reversible reaction

An approximate analytical expression is derived for the enhancement factor for absorption with a reversible chemical reaction which is second-order in each direction, with corresponding stoichiometry and equal diffusivities of reactants, using the Danckwerts model of mass transfer. The result agrees with simpler limiting expressions for the enhancement factors for irreversible reactions, reactions slow enough to give negligible depletion of reactants, and instantaneous reactions. The result agrees satisfactorily with the available corresponding data for numerical solutions of the differential equations for the Higbie model, with the exception of one case, where the deviation is probably due to an error in the numerical solution, or its graphical representation. No numerical solutions are available for comparison when concentrations of solute and reaction products in the bulk of the liquid are appreciable. The method seems applicable also to more complex kinetics.     

Enhancement of liquid extraction by an instantaneous,irreversible reaction

A quasi-steady state analysis was applied to the enhancement of liquid extraction by a chemical reaction. Ethylene glycol drops were allowed to fall through a stationary heptane phase containing iodine (component A) in a 2.42 cm I.D. column operated at varying heights. The overall mass transfer coefficient, after elimination of end effects, for iodine from heptane into the glycol drops was determined to be K° = 0.213 mol/(s.m.²). By the addition of sodium thiosulfate (component B, Na₂S₂O₃) to the inlet glycol, an instantaneous and irreversible reaction I₂ + 2Na₂S₂O₃ → Na₂S₄O₆ + 2NaI took place in the glycol phase, increasing the value of K to a maximum value of 0.5 mol/(s.m₂).     

Optimum length/diameter ratio of plastic rings for gas absorption with irreversible chemical reaction

The effect of length/diameter ratio of cylindrical packing materials on the liquid-side mass transfer coefficient (k_L) and the effective gas-li interfacial area (a) has been investigated experimentally using polyethylene rings of 1.6cm o.d. with length/diameter ratios of 0.34, 0.69 1.00. Accord to the results of Danckwerts' plots, while length/diameter ratio decreases k_L also decreases but a increases.The optimum length/diameter ratio at which the liquid-film controlled gas absorption is maximum, has been determined at various liquid flowrates for bo     

On a numerical relaxation method for a chemical reaction-diffusion problem with an instantaneous and irreversible reaction

In this paper we deal with a numerical method for a free boundary value problem in 1D, describing a chemical diffusion problem accompanied by an irreversible and instantaneous reaction which gives rise to a moving internal boundary. Basically, the method consists of four steps: (1) a Landau transformation mapping each of the 2 time varying intervals on a fixed domain, which results in a strongly nonlinear boundary value problem; (2) a central difference method with respect to the space variable, that takes properly into account the various transition conditions; (3) the construction of an ODE containing a relaxation parameter ε to represent the movement of the internal boundary; (4) a time integration of the resulting stiff system of ODEs by suitable computer packages. The numerical method is evaluated by comparison with an analytical solution for a special but nontrivial case, and by a mass-balance argument. The presented method can be extended to the case of several irreversible and instantaneous reactions.     

Transient diffusion with n-order irreversible chemical reaction: A finite element approach

Using the GALERKIN procedure, a finite element approximation of the non linear equation describing transient diffusion with irreversible chemical reactThe outlined method, accounting for a variety of complex geometrical domains and boundary conditions, is applicable to a wide variety of problems in wh     

Formal potential estimation for a quasi-reversible charge transfer followed by a first-order irreversible chemical reaction

A method is presented for estimating the formal potential of a quasi-reversible charge-transfer with a coupled following chemical reaction. The method is based on the dc polarographic half-wave potential variation with drop-time. Results of data analysis of digitally simulated polarograms using following first-order rate constants of 10⁵ and 10⁷ s^?1 indicate that formal potential estimates are generally accurate to within 3–4 mV. Effects of error in the required estimates of the first-order chemical rate constant and the charge-transfer coefficient are described. The charge-transfer standard rate constant can also be estimated.     

Enhancement of the interfacial transfer of iodine by chemical reaction

Enhancement of the air‐water interfacial transfer of I₂ by reaction with I^? was investigated in order to evaluate a mechanistic model. Separate systems for evaporation and absorption of I₂ were studied. The overall mass transfer coefficient increased from 2 × 10^?4 to 2.5 × 10^?3 cm/s as I^? concentration increased from 10^?4 to 10^?1 M. At I^? concentrations greater than 10^?1 M, the interfacial transfer of I₂ was gas‐side limited. The model gave a good representation of these results.     

Mass transfer accompanied by equilibrium and second-order irreversible reactions

A general derivation based on film theory for simultaneous irreversible and equilibrium reactions is presented and expressions for the enhancement factor are obtained. In limiting cases the enhancement factor reduces to a simple ratio of diffusivities or to a simpler reaction system. In addition the geometrical contributions to the mass transfer coefficient for spherical and cylindrical coordinates are discussed.     

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.     

多级串联等体积全混流反应器与平推流反应器的等效性研究——以二级不可逆反应为例

在多级串联全混流反应器中针对二级不可逆反应,推导出第N级串级反应器的出口浓度表达式.为与平推流反应器进行比较,引人反应器的相对效率,在平推流反应器中一定的转化率条件下,考察反应速率常数和反应物初始摩尔比大于1的情况下对串联级数的影响.通过实例计算,得出随着相对效率的增大,串联反应器级数随之增大.而当串联级数达到5时,相...     

Ion exchange with irreversible reaction in deep fluidized beds

The exchange of CI^? ion between dilute aqueous solutions of hydrochloric acid and the ion exchange resin IRA-425 in fluidized beds was studied in a laboratory size column. Analysis of the experimental data showed that axial mixing of particles in deep beds was incomplete and also that packed and fluidized bed break-through curves were similar. A model is proposed describing the bed as a series of mixing stages for solids with axially dispersed flow of liquid. Data are presented in support of such a concept. An empirical method is proposed for prediction of the break-through curves at various operating conditions, requiring only a very limited amount of experimentation.     

Bubble dissolution with chemical reaction

The dissolution of an isolated stationary gas bubble, enhanced by a chemical reaction, in a large body of liquid is investigated. A theoretical model which properly accounts for the movement of the interface due to dissolution is formulated and solved using the method of finite differences. The finite difference results are used as a standard of comparison for the testing of various approximate solutions. These include a perturbation expansion, a quasi-stationary approximation and a quasi-steady approximation. The results of this work indicate that the quasi-steady approximation, which provides very simple analytical solutions, is an excellent one in the presence of a sufficiently rapid chemical reaction.     

Maximal and minimal solutions,effectiveness factors for chemical reaction in porous catalysts

A chemical reaction in a porous catalyst particle is considered. It is shown that in both the isothermal and non-isothermal cases, with either Dirichlet or third kind boundary conditions, two sequences of functions can be obtained, one of which converges to the maximal solution and the other to the minimal solution. Corresponding to these two sequences of functions, two sequences of numbers, which converge to the maximal and the minimal effectiveness factors, can be obtained. It is shown that in the isothermal case, the maximal (minimal) solution has the minimal (maximal) effectiveness factor while in the non-isothermal case, the maximal (minimal) temperature solution has the maximal (minimal) effectiveness factor. Two numerical examples are given to illustrate the results.     

A three-zone model for mass transfer accompanied by equilibrium and very fast second-order irreversible reactions

A three-zone model for mass transfer accompanied by equilibrium and very rapid second-order irreversible chemical reaction is developed and the concept of an equilibrium plane is introduced. The model is applicable to both strong and weak electrolytes and is successfully used to model the dissolution of benzoic acid in sodium hydroxide.     

Numerical study of heat and mass transfer in the microwave-assisted and conventional packed bed reactors with an irreversible first-order endothermic chemical reaction

This paper presents a numerical study on heat and mass transfer in the microwave-assisted and conventional packed bed reactors with an irreversible first-order endothermic chemical reaction. The numerical simulations have been carried out using one-dimensional heterogeneous reactor models for the both reactors. The obtained results have been compared applying the criterion of the same electrical powers utilized in the reactors. The effects of the inlet gas temperature and microwave power, gas velocity, bed porosity and the heat of reaction on performance of the packed bed reactors have been presented.     

Enhancement of absorption caused by density driven convection at gas—liquid interface induced by absorption with chemical reaction

The superimposition of mechanical agitation and density-driven cellular convection has been studied. The experiments were carried out using a sodium sulfite solution into which oxygen was being absorbed across the liquid surface. Experimental results suggest that, with respect to the convective pattern, two regions exist in the neighbourhood of the liquid surface: (i) at low agitation rates the cellular convection is stable and no bulk liquid penetrates into the interface, (ii) at high agitation rates both the cellular convection and the surface renewal proceed simultaneously. For the second case, a mathematical model based on the integral balance method was derived and good agreement between the enhancement factors estimated from the model and those found experimentally was attained.     

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.