Analysis of numerical instability in single-stage gas permeation

A single-stage co-current gas permeation process with two permeable components and one non-permeable component is modeled with a sweep gas in the permeation side. The introduction of sweep gas in the permeate side give rise to a singular point in the resulting differential equations. To solve the model equations for a wide range of stage cuts, one need to avoid this singular point because the system becomes unstable, resulting in floating-point error. Present work analyzes this instability from different points of view and a method is proposed to overcome this instability with some examples.