# Gas absorption with instantaneous chemical reaction in a falling film for parallel and countercurrent flows

01 Feb 1990-Chemical Engineering Communications (Taylor & Francis Group)-Vol. 88, Iss: 1, pp 105-117

TL;DR: In this article, a theoretical analysis for the absorption of a gas accompanied by instantaneous chemical reaction with a dissolved reagent in a falling liquid film of liquid is presented, where the reaction occurs on a moving front inside the liquid film separating the zones containing either of the reactants.

Abstract: A theoretical analysis is presented for the absorption of a gas accompanied by instantaneous chemical reaction with a dissolved reagent in a falling liquid film of liquid. The reaction occurs on a moving front inside the liquid film separating the zones containing either of the reactants. The governing equations are solved by using a coordinate transformation to immobilize the reaction front. The effects of the different system parameters on the reaction front profile, absorption rate and enhancement factor are presented for both cocurrent and countercurrent flow of the gas. In the former case the reaction front profile shows a maximum, but in the later case it is monotonic in the axial distance along the film. The enhancement factor plots exhibit maxima in both the cases.

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TL;DR: In this paper, an approximate analysis of gas absorption with instantaneous reaction in a liquid layer of finite thickness in plug flow is presented, where an approximate solution to the enhancement factor for the case of unequal diffusivities between the dissolved gas and the liquid reactant has been derived and validated by numerical simulation.

Abstract: An approximate analysis of gas absorption with instantaneous reaction in a liquid layer of finite thickness in plug flow is presented. An approximate solution to the enhancement factor for the case of unequal diffusivities between the dissolved gas and the liquid reactant has been derived and validated by numerical simulation. Depending on the diffusivity ratio of the liquid reactant to the dissolved gas (?), the enhancement factor tends to be either lower or higher than the prediction of the classical enhancement factor equation based on the penetration theory (Ei,pen) at Fourier numbers typically larger than 0.1. An empirical correlation valid for all Fourier numbers is proposed to allow a quick estimation of the enhancement factor, which describes the prediction of the approximate solution and the simulation data with a relative error below 5?% under the investigated conditions (? = 0.3–4, Ei,pen = 2–1000).

12 citations

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TL;DR: In this paper, an analytical solution to the enhancement factor has been derived for the case of a first-order reaction, and the exact solution has been obtained via numerical simulation for second-order reactions.

Abstract: Gas absorption accompanied by an irreversible chemical reaction of first-order or second-order in a liquid layer of finite thickness in plug flow has been investigated. The analytical solution to the enhancement factor has been derived for the case of a first-order reaction, and the exact solution to the enhancement factor has been obtained via numerical simulation for the case of a second-order reaction. The enhancement factor in both cases is presented as a function of the Fourier number and tends to deviate from the prediction of the existing enhancement factor expressions based on the penetration theory at Fourier numbers above 0.1 due to the absence of a well-mixed bulk region in the liquid layer. Approximate enhancement factor expressions that describe the analytical and exact solutions with an accuracy of 5 % and 9 %, respectively, have been proposed.

6 citations

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TL;DR: In this article, a numerical analysis on gas absorption accompanied by an instantaneous reaction or a second-order reaction into a liquid layer of finite thickness in laminar flow is presented, where a similar influence of the reactant diffusivity ratio, the Fourier number, and the Hatta number is reported compared to the ideal situation in which the liquid layer is in plug flow motion.

Abstract: Numerical analysis on gas absorption accompanied by an instantaneous reaction or a second-order reaction into a liquid layer of finite thickness in laminar flow is presented. A similar influence of the reactant diffusivity ratio, the Fourier number, and the Hatta number on the enhancement factor is reported compared to the ideal situation in which the liquid layer is in plug flow motion. Approximate enhancement factor expressions are developed for both reaction cases by analogy to the plug flow situation, where the predictions according to the original penetration theory tend to give erroneous results in the enhancement factor at Fourier numbers above 0.1. The developed expressions in the case of a second-order reaction can be extrapolated for estimating the enhancement factor in the more general case of a (1, n)-th-order reaction.

3 citations

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TL;DR: In this paper, a numerical analysis for gas absorption accompanied by a second-order reaction into a liquid layer of finite thickness in laminar flow is presented, with the gas-phase mass transfer resistance and the axial decrease of the solute concentration due to absorption being taken into account.

Abstract: Numerical analysis is presented for gas absorption accompanied by a second-order reaction into a liquid layer of finite thickness in laminar flow, with the gas-phase mass transfer resistance and the axial decrease of the gas-phase solute concentration due to absorption being taken into account. Both cocurrent and countercurrent flow modes are analyzed, where the presence of significant resistance or axial decrease of the solute concentration in the gas phase can lead to substantially lower rates of gas absorption than those found when the influence of gas-phase mass transfer is not considered. Approximate expressions describing the exact numerical solution to the enhancement factor in the cocurrent flow mode are developed and can be extrapolated for estimating the enhancement factor in a more general case of a (1, n)-th-order reaction in which the influence of gas-phase mass transfer cannot be neglected.

3 citations

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TL;DR: A multiphase and multicomponent mass transfer model of CO2 absorbed in aqueous N-methyldiethanolamine and piperazine (PZ) was built in this paper.

Abstract: A multiphase and multicomponent mass transfer model of CO2 absorbed in aqueous N-methyldiethanolamine and piperazine (PZ) was built in the study. In the model, a simple method of mass transfer between phases was proposed. Besides, the hydrodynamics, thermodynamics, and complex reversible chemical reaction were considered simultaneously. The model was validated by comparing with the previous experimental data which showed that simulated results can represent the experimental data with reasonable accuracy. Based on the model, the effects of gas velocity, liquid load and CO2 loading on the absorption rate, and enhancement factor were analyzed. Model results showed that the enhancement factor increased with a rising gas velocity while decreased with a rising liquid load or CO2 loading. The change of enhancement factor with CO2 loading was similar to that of equilibrium concentration of PZ which indicated that PZ was significant to the absorption process. Furthermore, the distributions of specie concentrations were discussed in detail. (c) 2016 American Institute of Chemical Engineers AIChE J, 63: 2386-2393, 2017

1 citations

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01 Jan 1984

TL;DR: In this paper, a front-tracking method is used to solve moving boundary problems and an analytical solution of seepage problems is proposed. But this method is not suitable for solving free boundary problems.

Abstract: 1. Moving boundary problems: formulation 2. Free boundary problems: formulation 3. Analytical solutions 4. Front-tracking methods 5. Front-fixing methods 6. Fixed-domain methods 7. Analytical solution of seepage problems 8. Numerical solution of free boundary problems References Author index Subject index

1,880 citations

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139 citations

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TL;DR: In this article, the authors investigated the effect of the film thickness and velocity profile on the absorption rate and enhancement factor of a very deep stagnant liquid with the same surface exposure time but no chemical reaction.

Abstract: The differential equation describing the absorption of a gas by a liquid film failing down a vertical wall can be solved, in the simple cases of (a) physical absorption and (b) absorption with first-order chemical reaction, by the method of separation of variables and subsequent solution of the space equation with Kummer's function [7]. The resultant concentration profiles are used to evaluate absorption rates and enhancement factors (here defined as the ratio of the actual absorption rate to that in a very deep stagnant liquid with the same surface exposure time but no chemical reaction). It is found that the film thickness and velocity profile only have an influence when the dimensionless group ϕ = f 2 k / D is less than 5 ( D being the diffusivity of the dissolved gas in the liquid, f the film thickness and k the reaction rate constant). When the Hatta number, √ M ′, is greater than 0.7, the enhancement factor is given, for all values of ϕ, by a simplified form of the solution with an error of less than 2%.

23 citations

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TL;DR: In this paper, an analytical solution of the governing differential equation for gas absorption in laminar falling films with the first order homogeneous reaction and external gas phase mass transfer resistance is shown.

Abstract: An analytical solution of the governing differential equation for gas absorption in laminar falling films with the first order homogeneous reaction and external gas phase mass transfer resistance is shown. The analysis is simplified by introducing a phenomenological mass transfer coefficient, Bi , that is a Biot number. An enhancement factor is defined as the ratio of the calculated absorption rates and the absorption rates found from a simple penetration model. It is shown also that external gas phase mass transfer resistances can significantly lower the absorption rates compared with those found when gas phase resistances are not present.

17 citations