My column initially converges, but with a different feed it fails to converge

There might of course be a numerical problem, but the first thing to investigate should be if there is not a process reason why the column doesn’t converge anymore. The reasons can be fairly simple like having a flow spec in top or bottom that is higher than the feed. But the reason can be a bit more hidden. Here is an example case of a demethaniser:

The demethaniser has a reboiler and a full reflux condenser. The specifications on the column are the methane content in the bottom and the condenser temperature.
With the initial feed HYSYS converged the column correctly. It was observed that when the top temperature specification was too low, the column wouldn’t converge anymore. But, the required temperature specification was high enough not to cause problems.

In a later phase of the project, the feed containedslightly more methane and the column refused to converge. As the specs seemed reasonable, it was first thought that the HYSYS column algorithm was having a problem. However, analyzing and reflecting about what the column is actually doing revealed the true cause of non convergence.

The top product of the column is a vapour stream with about 65 mole % of hydrogen. The hydrogen can be considered an inert gas at the condenser conditions. This effectively means that at a given pressure, the amount of methane that can leave in the top product is constrained by the vapour pressure of methane at the imposed condenser temperature and the flow of hydrogen. On the other hand, the specification on the bottom methane fraction really also defines how much methane will have to go to the overhead product (essentially all the methane minus the little amount allowed in the bottom). The increased amount of methane in the feed to the column simply doesn’t have anywhere to go. The top temperature prohibits the extra methane from leaving through the top and the bottom methane spec prohibits it from leaving through the bottom. The demands placed on the column are simply infeasible and that is really what the non-convergence of the column means. The same phenomenon also explains why the column wouldn’t converge at lower top temperatures, this reduced the vapour pressure of methane and hence the amount of methane that could leave the top was below the amount that was fed to the column.