Penetration theory for gas absorption accompanied by a second order chemical reaction

Abstract

The penetration-theory solution for the effect of a second-order irreversible liquid-phase chemical reaction on the rate of gas absorption has been computed numerically on an IBM-704 computer. A linearized, time-centered, implicit finite-difference method was used to solve the nonlinear partial-differential equations. The method was very effective, permitting the solution of the equations for a wide range of the parameters of interest. The penetration-theory results are compared with the film-theory solution, and it is shown that the sdutions to the two theories agree within 16% i f they are compared for conditions which produce the same asymptotic solution for a n infinitely rapid chemical reaction. A simplified equation and some correction charts are presented which permit a rapid, accurate estimation of the penetration-theory s2lution over a wide range of variables.The problem of predicting the effect of a simultaneous liquid-phase chemical reaction on the rate of gas absorption has often been approached by adopting a simplified model of the liquid flow pattern which could then be treated mathematically. In the years since Hatta (11) first used the filmtheory model to analyze the effect of an infinitely rapid, irreversibIe bi-molecular reaction, a number of types of chemical reaction have been treated from the viewpoints of the film-theory and the penetration-theory models. The use of these two models to analyze the effect of a simultaneous chemical reaction on the rate of gas absorption is reviewed by Sherwood and Pigford ( 1 8 ) .One interesting aspect of this problem is that it is often found that the predicted answer is surprisingly insensitive to the liquid flow pattern model that is chosen. This was pointed out by Peaceman ( I s ) , who compared the film-and penetration-theory solutions for several kinds of chemical reactions and found that they were in close agreement. Furthermore several recent publications have considered the effect of an infinitely rapid bimolecular reaction on the rate of mass transfer from a solid surface to a fluid stream, and results for laminar and turbulent boundary-layer models show surprising agreement with film and penetration theory results (3, 8,15,19).It is the purpose of this paper to present a solution to the penetrationtheory equations for gas absorption accompanied by a second-order chemical reaction of finite rate and to com- J. F. Hurley is at Dewey and Almy ChemicalCompany, Cambridge, Massachusetts. Page 226pare this solution with the film-theory solution. T H E SECOND-ORDER R E A C T I O NThe problem to be considered is that in which a gaseous species A dissolves into the liquid phase [Equation ( 1 ) ] and then reacts irreversibly with species B according to Equation ( 2 ) :A,,, + B,,, + products irreversibly ( 2 )Species 3 is a nonvolatile solute which has been dissolved into the liquid phase prior to its introduction into the gas absorber. It is assumed that gasphase resistance to absorption is negligible, and thus the concentration of species A at the gas-liqui...

Gas absorption accompanied by a second‐order chemical reaction modeled according to the danckwerts surface renewal theory

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“…(3a) means that chemical equilibrium is reached at the beginning of the gas-liquid contact, which is a good assumption for cases of practical importance [6]. (3a) means that chemical equilibrium is reached at the beginning of the gas-liquid contact, which is a good assumption for cases of practical importance [6].…”