Start-Up of a Plate Gas Absorption Unit

selection

numerical method

identical analytical approach

τ

1.561

α

0.85

0

10

20

30

40

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

time

output gas composition

The start-up behavior of a six-plate gas absorption unit is described by the following equations:

τ

dx

n

dt

=αx

n+1

-(α+1)x

n

+x

n-1

, where

n=1,…,6

,

τ=

H

mV

, and

α=

L

mV

.

L

and

V

are the liquid and gas flow rates;

m=0.72

is the equilibrium constant (i.e.,

y

n

=mx

n

for

n=1,…,6

, where

x

and

y

are the liquid and gas mole fractions), and

H

is the liquid hold-up in the plates. It is assumed that the liquid solvent entering the absorption column is solute free (i.e.,

x

7

=0)

. The gas to be treated entering the absorption column is such that

y

0

=0.3.

One can solve the system of ODEs using the built-in Mathematica function NDSolve. An elegant analytical solution was made available by Lapidus and Amundson in 1950 (and later by Acrivos and Amundson, 1955) and is described in detail by J. M. Douglas (see reference below). This Demonstration shows that both methods give the same result for the output gas composition versus time.