Gas Absorption Computed Using the Successive Over-Relaxation (SOR) Method

accurate McCabe & Thiele diagram

cumulative error with SOR method

ω

1.25

Consider a tray absorption column used to remove an impurity from a gas stream. A pure solvent is used for this absorption operation. The solvent molar flow rate is

L=200kmol/hr

and the gas molar flow rate is

G=100kmol/hr

. Both

L

and

G

are considered constant (i.e., the dilute system hypothesis remains valid). The number of equilibrium stages is

10

, the value of the slope

m

of the equilibrium line (

y

A

=m

x

A

) is set to

1.4

, the solvent-to-gas molar flow rate ratio

L/G=2

, and the mole fraction of the impurity in the gas fed to the absorption column is chosen to be

0.1

.

This Demonstration computes the exact McCabe–Thiele diagram using matrix inversion. The horizontal lines represent the theoretical equilibrium stages in the absorption column. The successive over-relaxation (SOR) method is compared to the exact solution by plotting the cumulative squared error versus the number of iterations. The parameter

ω

is chosen to be between

0

and

2.02

. For

ω=2.01

(see the last snapshot showing large growing error), you can see that the SOR method fails to give good results. A theorem of Kahan states that the SOR method will converge only if

ω

is chosen in the interval

[0,2]

. For

ω=1.0

, the SOR method is identical to the Gauss–Seidel technique.