GAS ABSORPTION WITH ZERO-ORDER CHEMICAL REACTION G l A N N l A S T A R I T A A N D GIUSEPPE MARRUCCI lstituto di Chimica Industriale, Universitci di A'ajoli, llrajles, Italy
The phenomenon of gas absorption accompanied b y a chemical reaction of zero order taking place in a liquid moving in plug flow i s discussed mathematically. Rigorous analytic solutions are given for some limiting cases: absorbing component already present at zero time and low total contact times and steady-state concentration profiles in a liquid layer of infinite and of finite depth. A finite difference solution i s presented for the general case. The application of the equations obtained to the case of a sequence of plug-flow steps such as take place in a packed tower i s discussed, and the equations governing the total rate of absorption are given for possible limiting cases.
ARBON DIOXIDE
absorption in aqueous monoethanolamine
C solutions may be regarded, under some conditions, as a n
absorption process with zero-order chemical reaction taking place in the liquid phase (7). A somewhat similar problem of mass transfer with zeroorder chemical reaction was considered by Van de Vusse ( 4 ) , in the case of the liquid-phase oxidation of hydrocarbons. Van de Vusse has given a mathematical treatment of his problem, which is, as far as the authors know, the first publication concerning this type of phenomena. The phenomenon considered in this paper is the absorption of a gas: A , in a liquid containing a reactant, B, which undergoes a fast reaction with component A: A + B - r D f E
where the step function, H(c), is defined as:
>0
H(c)
=
1 when c
H(c)
=
0 when c _L 0
(2)
If the liquid is infinitely deep, the boundary conditions associated with Equation 1 are: t = 0,y t t
> 0,y
> 0, y -t
m,
> 0,c =
c =
0,c
= =
max
(3)
cg
(4)
GO'
(cg
- rt, 0 )
(5)
Equation 5 is required to fulfill the physically obvious condition that c is never negative. The dimensionless variables and parameters are defined as:
followed by a slow reaction reproducing reactant B, such as:
y = c,/co'
D-tB+F
Suppose that, with both reactions a t equilibrium, the concentrations D*,E*, and F* are much larger than B*. Under these conditions, the reaction rate is: r = k
(D -
x = -rt CO
'
BF D* E k D * (1 - B / B * ) B*F*) ~
and, considering the first reaction, BIB*
=
A*DE/AD*E* E A * / A
=
1 ____ 1 c/A*
+
In general, Equation 1 reduces to:
Hence : r ? kD*
C/A*
~
1
-+ c / A *
If c >> A*, the reaction may be considered of zero order, r E kD* = constant. liquid Stagnant or Moving in Plug Flow
Absorption with zero-order chemical reaction in a liquid stagnant or moving in plug flow, and separated by a plane gasliquid interface, is mathematically represented by the following differential equation: D?! !?
1
ay2
4
ac
= -
at
I&EC FUNDAMENTALS
+ rH(c)
It might a t first sight be thought that the case of a process starting with a finite value of p is of little practical interest; actually chemical absorption in a liquid which already contains a t time 0 a finite excess of dissolved gas is important in the case of a packed toicer absorption process. limiting Solutions of Equation 1 1
Solution for Low Values of X . is fulfilled : t
