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

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 and the gas molar flow rate is . Both and are considered constant (i.e., the dilute system hypothesis remains valid). The number of equilibrium stages is , the value of the slope of the equilibrium line () is set to , the solvent-to-gas molar flow rate ratio , and the mole fraction of the impurity in the gas fed to the absorption column is chosen to be .

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 is chosen to be between and . For (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 is chosen in the interval . For , the SOR method is identical to the Gauss–Seidel technique.